Spectroscopic Investigations of the Photophysics of Cryptophyte Light-Harvesting · 2012-11-21 · ii Spectroscopic Investigations of the Photophysics of Cryptophyte Light-Harvesting

Spectroscopic Investigations of the Photophysics of Cryptophyte

Light-Harvesting

by

Rayomond Dinshaw

A thesis submitted in conformity with the requirements

for the degree of Master of Science

Graduate Department of Chemistry & Institute for Optical Sciences

University of Toronto

© Copyright by Rayomond Dinshaw 2012

ii

Spectroscopic Investigations of the Photophysics of Cryptophyte

Light-Harvesting

Rayomond Dinshaw

Master of Science

Department of Chemistry & Institute for Optical Sciences

University of Toronto

2012

Abstract

The biological significance of photosynthesis is indisputable as it is necessary for nearly all life on earth.

Photosynthesis provides chemical energy for plants, algae, and bacteria, while heterotrophic organisms

rely on these species as their ultimate food source. The initial step in photosynthesis requires the

absorption of sunlight to create electronic excitations. Light-harvesting proteins play the functional role

of capturing solar radiation and transferring the resulting excitation to the reaction centers where it is used

to carry out the chemical reactions of photosynthesis. Despite the wide variety of light-harvesting protein

structures and arrangements, most light-harvesting proteins are able to utilize the captured solar energy

for charge separation with near perfect quantum efficiency.1 This thesis will focus on understanding the

energy transfer dynamics and photophysics of a specific subset of light-harvesting antennae known as

phycobiliproteins. These proteins are extracted from cryptophyte algae and are investigated using steady-

state and ultrafast spectroscopic techniques.

iii

Acknowledgements

Firstly I would like to thank my supervisor, Greg; it was his enthusiasm for research and science in

general that encouraged me to pursue graduate studies. His interest in the topics we researched and his

pursuit for the deepest understanding at a fundamental level provided inspiration to continue working

when faced with difficulties and disheartenment. Chatting with him always left me reassured of the

science we were studying and the pattern of reasoning we applied to understanding it.

My time in the Scholes group was enjoyable because of the people who comprised it. Although

the make-up of the group changed over the years I was there, it was always fun and was a positive

working environment. The days were always entertaining whether we were going out for group dinner,

playing Risk in the office, designing pranks, or just randomly chatting. But more than just fun, I learned a

lot from the other group members and I am grateful to all of you for that. Thanks to Cathy, Duffy, and

Kyung for imparting a small amount of their optics knowledge on me and to Yaser and Hoda for helping

me think through the theoretical aspects of problems. Thanks to all the other members: undergrads,

grads, and post-docs who always seemed to know a little more about something than I did and were

always willing to help out.

In addition to an amazing group it was the great people in the Department of Chemistry that made

my time here most enjoyable. The staff, faculty, and other students are what make the Department a

great place to work. Thanks to Zaheen for the wasted time, espressos, and constant cynicism along with

all the others who partook in the day-to-day adventures.

Lastly, I would like to thank my parents who supported my decisions no matter what they were

and for providing me with the resources and encouragement to follow my own path.

iv

“Love truth, and pardon error.” –Voltaire

v

Contents

Abbreviations and Acronyms .................................................................................................................... viii

List of Tables ................................................................................................................................................ x

List of Figures .............................................................................................................................................. xi

List of Appendices .................................................................................................................................... xvii

Chapter 1

Introduction ................................................................................................................................................... 1

1.1 Photosynthesis..................................................................................................................................... 1

1.2 Light-Harvesting Proteins ................................................................................................................... 4

1.2.1 Introduction .................................................................................................................................. 4

1.2.2 Photosynthetic Excitons ............................................................................................................... 5

1.3 Electronic Energy Transfer ............................................................................................................... 10

1.4 Spectroscopy ..................................................................................................................................... 13

Chapter 2

Spectroscopy ............................................................................................................................................... 17

2.1 Steady-State Spectroscopy ................................................................................................................ 17

2.1.1 Linear Absorption ...................................................................................................................... 17

2.1.2 Fluorescence .............................................................................................................................. 18

2.1.3 Fluorescence Anisotropy............................................................................................................ 19

2.1.4 Circular Dichroism ..................................................................................................................... 21

2.2 Two-Dimensional Electronic Spectroscopy ...................................................................................... 22

2.2.1 Introduction ............................................................................................................................... 22

2.2.2 Experimental Setup .................................................................................................................... 27

2.2.3 Spectral Interferometry .............................................................................................................. 32

2.2.4 Test Case: Cresyl Violet ............................................................................................................ 35

vi

Chapter 3

Phycoerythrin 545: Low Temperature Spectroscopic Measurements ......................................................... 44

3.1 Introduction ....................................................................................................................................... 44

3.2 Cyrogenic Sample Preparation.......................................................................................................... 45

3.3 Structure ............................................................................................................................................ 47

3.4 Steady-State Spectroscopy ................................................................................................................ 48

3.4.1 Absorption .................................................................................................................................. 48

3.4.2 Fluorescence .............................................................................................................................. 49

3.4.3 Excitation ................................................................................................................................... 51

3.4.4 Fluorescence Anisotropy............................................................................................................ 51

Chapter 4

Phycocyanin 645: Physiologically Relevant 2D ES Measurements (including pH Dependence) .............. 53

4.1 Introduction ........................................................................................................................................... 53

4.2 Sample Preparation ............................................................................................................................... 55

4.3 Structure ................................................................................................................................................ 55

4.4 Steady-State Spectroscopy .................................................................................................................... 57

4.4.1 Absorption .................................................................................................................................. 57

4.4.2 Fluorescence .............................................................................................................................. 58


4.5 Two-Dimensional Electronic Spectroscopy .......................................................................................... 61

4.5.1 Results & Discussion ................................................................................................................. 61

4.5.2 Distinguishing Electronic and Vibrational Coherences ............................................................. 70

4.5.3 Assignment of Coherences......................................................................................................... 81

Chapter 5

Phycocyanin 612 and Phycoerythrin 555: Open Structures ....................................................................... 87

5.1 Introduction ........................................................................................................................................... 87

5.2 Sample Preparation ............................................................................................................................... 88

5.3 Structure ................................................................................................................................................ 88

5.4 Steady-State Spectroscopy .................................................................................................................... 90

5.4.1 Absorption .................................................................................................................................. 90

5.4.2 Fluorescence .............................................................................................................................. 94

vii


5.5 Two-Dimensional Electronic Spectroscopy of PC612 ......................................................................... 96

5.6 Two-Dimensional Electronic Spectroscopy of PE555 ........................................................................ 103

Chapter 6

Conclusion ................................................................................................................................................ 111

Bibliography ............................................................................................................................................. 114

Appendix A: 2D ES Spectra Generation Code (MATLAB) ...................................................................... 119

viii

Abbreviations and Acronyms

2D two-dimensional

2D ES two-dimensional electronic spectroscopy

Abs absorption

ADP adenosine diphosphate

BBO barium borate

CCD charge coupled device

CD circular dichroism

chl chlorophyll

DBV dihydrobiliverdin

EET electronic energy transfer

FFT Fast Fourier Transform command in Matlab

FRET Förster resonance energy transfer

FMO Fenna-Matthews-Olsen

GFT generalized Förster theory

FWHM full width at half maximum

HT-CpcA [His]6-tagged phycocyanin alpha subunit

LHC-II light-harvesting complex II

LO local oscillator

MBV mesobiliverdins

NADP+ nicotenamide-adenine dinucleotide phosphate

NPQ non-photochemical quenching

NOPA noncollinear optical parametric amplifier

OD optical density

PC612 phycocyanin 612 isolated from Hemiselmis virescens M1635

ix

PC645 phycocyanin 645 isolated from Chroomonas CCMP 270

PCB phycocanobilin

PE545 phycoerythrin 545 isolated from Rhodomonas CS24

PE555 phycoerythrin 555 isolated from Hemiselmis andersenii CCMP644

PEB phycoerythrobilin

PEB’ doubly linked phycoerythrobilin

PSI phyotosystem I

PSII photosystem II

qE energy-dependent quenching

TDC transition density cube

UV ultraviolet

x

List of Tables

Table 1. Electronic coupling between chromophores in wavenumbers (above diagonal, blue), center-to-

center separation of chromophores in angstroms (below diagonal, red), and site energies of chromophores

(diagonal, green). ........................................................................................................................................ 83

Table 2. Site energies and exciton energies in various units. ..................................................................... 84

Table 3. Frequency difference between likely candidates for eigenstates involved in electronic coherence.

.................................................................................................................................................................... 84

Table 4. Parameters used in the fits in Figure 49. (c) and (d). ................................................................... 91

Table 5. Parameters used in the fits in Figure 50. (c) and (d). ................................................................... 93

xi

List of Figures

Figure 1. (a) Simplified evolutionary tree depicting selected relationships between photosynthetic

organisms. (b) Illustrations of primary endosymbiosis and (c) secondary endosymbiosis events. ............... 2

Figure 2. Illustration of the light-harvesting systems in (a) most high order plants and (b) in cryptophyte

algae. Whereas in higher order plants the light-harvesting antennae are strictly membrane bound, in

cryptophyte algae the peripheral light-harvesting antennae, phycobiliproteins, reside in the lumen. .......... 3

Figure 3. Normalized absorption spectrum of LHC-II (green); the main light-harvesting protein in high

order plants along with the normalized absorption spectra of four cryptophyte light-harvesting proteins:

PE545 (blue), PE555 (pink), PC612 (purple), and PC645 (red). The different region in which these

complexes absorb is clearly evident. Investigations of the four cryptophyte light-harvesting proteins is

the focus of this thesis. .................................................................................................................................. 5

Figure 4. Illustration of the energy spacing of a homodimer, which consists of two identical

chromophores, each modelled as a two-level system. Molecular excited states, en and em, are coupled by

an electronic potential, Vnm, resulting in delocalized excited states, e and e. Absorption resonance

frequencies of the dimer occur at the corresponding eigenenergies, E and E. ........................................... 7

Figure 5. (adapted from references 25,26

) (a) Absorption spectrum of LH2 extracted from R. Acidophila.

The B800 ring absorbs at 800 nm and is due to the 9 weakly coupled BChl chromophores, while the B850

ring absorbs at 850 nm and is due to the 18 tightly packed BChl molecules. (b) X-ray crystallography

structure of LH2 from R. Acidophila illustrating 27 bacteriochlorophyll-a chromophores. Blue coloured

chromophores indicate the B800 ring, while red coloured chromophores indicate the B850 ring. Energy

level diagrams for chromophores in (c) B800 ring and (d) B850 ring. ........................................................ 9

Figure 6. (adapted from references 25,26

) (a) Absorption spectrum of LH2 extracted from R. Acidophila.



structure of LH2 from R. Acidophila consists of 27 bacteriochlorophyll-a chromophores. Blue coloured

chromophores make up the B800 ring, while red coloured chromophores make up the B850 ring. ............ 9

Figure 7. (a) The real part (n) of the complex valued refractive index function ( ) shows dispersive

lineshapes at each resonance frequency. The overall trend follows such that at the largest

frequencies, beyond any resonances, the refractive index is purely real and equal to unity. (b) The

imaginary part ( ) of the refractive index displays Lorentzian lineshapes at each resonance frequency. In

between transitions drops to zero signifying that the material is transparent at that frequency. ............. 15

xii

Figure 8. Illustration of absorption and fluorescence (emission) processes, based on ground state (S0) and

single excited state (S1). λ denotes the reorganization energy. .................................................................. 19

Figure 9. Schematic drawing of L-format fluorescence spectrometer and polarizers used in fluorescence

anisotropy measurements. ........................................................................................................................... 20

Figure 10. (a) Sequence of laser pulses and time delays. (b) Boxcar geometry of pulses: ksignal=+k1-k2+k3

when τ <0 (nonrephasing) or ksignal=-k1+k2+k3 when τ >0 (rephrasing). ................................................... 24

Figure 11. Guide on how to interpret a 2D spectrum for a simple system with two strongly coupled

chromophores (a). The energy level diagram and corresponding linear absorption spectrum (b) and 2D

ES spectrum (c). .......................................................................................................................................... 26

Figure 12. Experimental setup for 2D ES experiments. G = grating, BP = Brewster prism, RR =

retroreflector, DO = diffractive optic, ND = neutral density filter, SM = spherical mirror, C = chopper,

W = wedges, S = sample. ............................................................................................................................ 31

Figure 13. Spectral interferometry process in sequential order. (a) Raw data collected by CCD camera

after chopped signal is subtracted. (b) Fourier transform of the detection axis from frequency-space to

time-space. (c) A horizontal slice through figure 5.(b) at τ = 0 fs, the heavyside function (red) is used to

select . (d) An inverse Fourier transform is performed on the horizontal

dimension of the selected signal. (e) Signal is multiplied by phase factor and divided

by√ . (f) A fourier transform is performed on the vertical dimension, thereby producing the final

2D ES spectrum. ......................................................................................................................................... 34

Figure 14. Absorption spectrum of cresyl violet (black) along with the laser pulse spectrum used in this

2D experiment (red) after it had passed through the sample. The chemical structure is inset. .................. 36

Figure 15. Representative 2D spectra of cresyl violet in methanol at indicated waiting times (top left-

hand corner). The spectra are the absolute magnitude of the total signal and are individually normalized

with 20 evenly spaced contours. At T=60 fs features of interest are indicated: the two diagonal peaks at

535 and 515 THz are marked by blue and red circles respectively; while the cross peak at (535,515 THz)

is indicated with green circle and the cross peak at (515,535 THz) is indicated with a yellow circle. ....... 37

Figure 16. The imaginary part of the total complex valued signal at indicated waiting times. As expected

the imaginary part of the total signal displays a clearly dispersive characteristic shape. ........................... 38

Figure 17. The real part of the rephasing signal. ........................................................................................ 39

Figure 18. The real part of the nonrephasing signal. .................................................................................. 40

Figure 19. (a) Trace of diagonal signal (magnitude) centered at 515 THz: total (black), rephasing (red),

nonrephasing (blue). (b) Fourier transform of (a) with same colour coding, flat baseline subtracted and

first 10 fs omitted due to nonresonant solvent response. ............................................................................ 41

Figure 20. Traces of above diagonal (black) and below diagonal (red) cross peaks. Oscillations are

perfectly in-phase. ....................................................................................................................................... 42

Figure 21. An approximate 90° phase shift between the diagonal peak oscillations (black) and the cross

peak oscillations (red) of the magnitude signal of the rephasing spectra in one isolated scan. This

suggests that the rationale used by Panitchayangkoon et al. to suggest that this phase shift was indicative

xiii

of quantum transport is not necessarily valid as no such mechanism exists in a solution of cresyl violet.66

.................................................................................................................................................................... 43

Figure 22. (a) Cracked solution of PE545 in 90% ethylene glycol and buffer (v/v) at 77 K. (b) Close-up

of the fractured sample in (a) which results from using quartz or sapphire windows instead of plastic

windows. ..................................................................................................................................................... 46

Figure 23. (from references 5,70

) (a) Structural model of phycoerthrin 545, determined to 0.97Ǻ resolution

using x-ray crystallography. (b) Position of chromophores without protein scaffolding. ......................... 47

Figure 24. Chemical structures of the three chromophores present in PE545: phycoerythrhobilin (PEB),

doubly liked phycoeythrhobilin (PEB’), and 15,16-dihydrobiliverdin (DBV). .......................................... 48

Figure 25. (a) Normalized room temperature emission (blue), absorption (red), and excitation (green)

spectra of phycoerythrin 545 (PE545) in buffer. (b) Normalized 77K absorption (pink) and fluorescence

(blue) spectran 90% solution of ethylene glycol and buffer (v/v)............................................................... 50

Figure 26. Fluorescence emission spectra at various excitation wavelengths at room temperature; no

excitation dependence is observed. ............................................................................................................. 50

Figure 27. 2D excitation and emission spectrum of PE545 in buffer at room temperature. No change is

observed based on excitation or emission energies..................................................................................... 51

Figure 28. Polarization anisotropy measured at room temperature in 90% glycerol to buffer (v/v)

solution. Emission was monitored at 615 nm. ........................................................................................... 52

Figure 29. (from reference 29

) Structural model of phycocyanin 645 from x-ray crystallography;

determined to 1.4 Å resolution. ................................................................................................................... 56

Figure 30. Structures of phycocyaninbilin (PCB), mesobilverdin (MBV), and doubly liked 15,16-

dihydrobiliverdin (DBV) the three types of chromophores found in PC645. ............................................. 57

Figure 31. (a) Absorption spectra at three pH levels show identical features, minimal differences can be

accounted for by concentration differences. (b) Comparison of room temperature (red) and 77 K (blue)

absorption spectra. ...................................................................................................................................... 58

Figure 32. (a) Individually normalized fluorescence spectra at three pH levels show identical features. (b)

Comparison of room temperature (red) and 77 K (blue) absorption spectra. Excitation conditions are

different in figure (a) and (b). ..................................................................................................................... 59

Figure 33. (a) Visible region CD at three pH levels, differences are within statistical error. (b) Minimal

change is observed between the three ultraviolet CD measurements; these discrepancies can be accounted

for by concentration differences. ................................................................................................................ 61

Figure 34. (adapted from reference 60

) (a) Laser pulse (dashed black) overlayed with PC645 absorption

spectra. (b) Frequency-resolved optical gating (FROG) characterization of pulse. .................................. 62

Figure 35. (a) Normalized cross peak amplitude of the total magnitude spectra. (b) Normalized cross

peak amplitude of the total real spectra. Each trace in (a) and (b) are the average of three scans and are

displayed with one standard deviation error bars, the traces are vertically offset for clarity. The first 15 fs

of dynamics are not included due to nonresonant solvent response and pulse overlap effects. .................. 64

xiv

Figure 36. Representative 2D spectra of PC645 in aqueous buffer (pH 6.5) at indicated waiting times (top

left-hand corner). The spectra are the real part of the total signal and are individually normalized with 33

evenly spaced contours. At T=60 fs the coordinates of a major feature of interest an above diagonal cross

peak are indicated. ...................................................................................................................................... 65

Figure 37. The absolute magnitude of the total complex valued signal at indicated waiting times.

Coordinates from which traces are extracted indicated by cross of dashed lines. ...................................... 66


the imaginary part of the total signal displays a clearly dispersive characteristic shape. ........................... 67

Figure 39. The real part of the rephasing signal. ........................................................................................ 68

Figure 40. The real part of the nonrephasing signal. .................................................................................. 69

Figure 41. (a) Normalized cross peak amplitude of the rephasing magnitude spectra. (b) Normalized

cross peak amplitude of the nonrephasing magnitude spectra. Each trace in (a) and (b) are the average of

nine scans and are displayed with one standard deviation error bars. The first 15 fs of dynamics are not

included due to nonresonant solvent response and pulse overlap effects. .................................................. 74

Figure 42. (a) Normalized cross peak amplitude of the real valued rephasing spectra. (b) Normalized

cross peak amplitude of the real valued nonrephasing spectra. Each trace in (a) and (b) are the average of


included due to nonresonant solvent response and pulse overlap effects. .................................................. 75

Figure 43. (a) Mean trace of nine normalized absolute valued rephasing spectra for the cross peak;

displayed with one standard deviation error bars. Exponential decay fit (red) of the mean trace using

least squares analysis. (b) Plot of residuals along with details of the fit (inset). (c) Fourier transform of

the mean trace after the exponential fit was removed; the maximum frequency displayed is 50 THz.

Peaks of interest are indicated by their frequency values and occur at 2.5 THz, 5.9 THz, 13.9 THz, 21.2

THz, 26.0 THz, and 34 THz. (d) Parameters of exponential damped sinusoidal fit used in reference 60

to

fit the absolute valued total trace. ............................................................................................................... 77

Figure 44. (a) Mean trace of nine normalized the real part of the rephasing spectra for the cross peak;





THz, and 26.4 THz. (d) Parameters of exponential damped sinusoidal fit used in reference 60

to fit the real

part of the total trace. .................................................................................................................................. 78

Figure 45. (a) Mean trace of nine normalized absolute valued nonrephasing spectra for the cross peak;

displayed with one standard deviation error bars. Linear fit (red) of the mean trace using least squares

analysis. (b) Plot of residuals along with details of the fit (inset). (c) Fourier transform of the mean trace

after the linear fit was removed; the maximum frequency displayed is 50 THz. Peaks of interest are

indicated by their frequency values and occur at 1.6 THz, 4.0 THz, 7.5 THz, 11.3 THz, 13.1 THz, 21.5


to fit the

absolute valued total trace. .......................................................................................................................... 79

xv

Figure 46. (a) Mean trace of nine normalized the real part of the nonrephasing spectra for the cross peak;






to fit the real

part of the total trace. .................................................................................................................................. 80

Figure 47. Representative two-dimensional electronic spectrum at population time T=55 fs at 295 K (note

the change in axes). The spectrum is the real part of the total signal, plotted with 33 evenly-spaced

contours. The estimated exciton energies of the chromophores are plotted on the 295 K absorption

spectrum which is superimposed onto the excitation and emission axes. While the exciton energies of the

PCB and MBV chromophores correspond closely to the respective site energies, the DBV chromophores

are strongly coupled creating two distinct DBV states, DBV+ and DBV–. The black circle indicates the

position of the cross-peak of the DBV+–MBV exciton states while the green and yellow circles refer to

the corresponding diagonal peaks. .............................................................................................................. 85

Figure 48. (a) Structural model of PC612, determined to 1.7 Ǻ resolution using x-ray crystallography.

(b) Position of chromophores without protein scaffolding. ........................................................................ 89

Figure 49. (a) Structural model of PC612, determined to 1.7 Ǻ resolution using x-ray crystallography.

(b) Position of chromophores without protein scaffolding. ........................................................................ 89

Figure 50. (a) Absorption spectra of PC612 at 295 K (red) and 77 K (blue). (b) 295 K absorption

spectrum with approximate absorption energies of chromophores. Fit of absorption spectrum using two

Gaussians at (c) 295 K and (d) 77 K. .......................................................................................................... 91

Figure 51. (a) Absorption spectra of PE555 at 295 K (red) and 77 K (blue). (b) 295 K absorption


Gaussians at (c) 295 K and (d) 77 K. .......................................................................................................... 93

Figure 52. (a) Fluorescence spectra of PC612 at 295 K (red) and 77 K (blue). (b) Fluorescence spectra of

PE555 at 295 K (red) and 77 K (blue). ....................................................................................................... 94

Figure 53. Visible CD spectra at 293 K of (a) PC612 and (b) PE555. Ultraviolet CD spectra at 293 K of

(c) PC612 and (d) PE555. ........................................................................................................................... 96

Figure 54. Absorption spectrum of PC612 (black) along with the laser pulse spectrum (red) used in the

2D experiments after it had passed through the sample. ............................................................................. 97

Figure 55. (a) Trace of diagonal peak (530, 530 THz) of the absolute valued rephasing spectra.

Oscillations caused by scatter from particle of dust are clearly evident from T=120 fs till T=300 fs. (b)

Trace of diagonal peak (530, 530 THz) of the absolute valued nonrephasing spectra. .............................. 98

Figure 56. Representative 2D spectra of PC612 in aqueous buffer at indicated waiting times (top left

hand corner). The spectra are the magnitude value of the total signal and are individually normalized

with 20 evenly spaced contours. Spectra at waiting times T=150, T=200, T=250, and T=300 clearly

display artifacts resulting from a speck of dust on one wedge. At T=60 fs the coordinates of a major

feature of interest an above diagonal cross peak are indicated. .................................................................. 99

xvi

Figure 57. Mean trace (black) of three absolute valued (a) rephasing and (b) nonrephasing spectra for the

cross peak; displayed with one standard deviation error bars. Linear fit (red) of the mean trace using

least squares analysis, details of the fit (inset). ......................................................................................... 100

Figure 58. (a) Representative two-dimensional electronic spectrum at waiting time T=100 fs at 295 K.

The spectrum is the real part of the total signal, plotted with 33 evenly-spaced contours. The estimated

absorption energies of the chromophores are plotted on the 295 K absorption spectrum which is

superimposed onto the excitation and emission axes. The absorption energies are also plotted on the

diagonal of the 2D ES spectrum. (b) Fourier transforms of the mean trace of the nonrephasing (black) and

rephasing (red) spectra after the linear fits were removed. Peaks of interest are indicated by their

frequency values and occur at 7.4 THz, 20.3 THz, 26.2 THz, 38.5 THz, 43.1 THz, and 50.3 THz. ........ 102

Figure 59. Absorption spectrum of PE555 (black) along with the laser pulse spectrum (red) used in the

2D experiments after it had passed through the sample. ........................................................................... 104


left hand corner). The spectra are the real part of the total signal and are individually normalized with 20

evenly spaced contours. ............................................................................................................................ 105

Figure 61. The imaginary part of the total signal at various waiting times. ............................................. 106

Figure 62. The real part of the rephasing signal at various waiting times. .............................................. 107

Figure 63. The real part of the nonrephasing signal at various waiting times. ........................................ 108



absorption bands of the chromophores are plotted on the 295 K absorption spectrum which is


diagonal of the 2D ES spectrum. (b) Magnitude of an off-diagonal position (black “x” in (a)) as a function

of waiting time taken as a trace from the absolute value 2D ES spectra (first 15 fs are omitted due to

nonresonant solvent response). Individual trials were normalized to overlap; error bars indicate one

standard deviation as determined from six trials....................................................................................... 110

xvii

List of Appendices

Appendix A: 2D ES Spectra Generation Code (MATLAB) ..................................................................... 119

1

Chapter 1

Introduction

1.1 Photosynthesis

Photosynthesis is the mechanism by which electromagnetic energy is converted into chemical energy by

photoautotrophs. The process of photosynthesis involves converting carbon dioxide along with water into

sugars and molecular oxygen using energy provided by the sun. The biological significance of

photosynthesis is indisputable as it is necessary for nearly all life on earth. Plants, algae, and bacteria rely

on photosynthesis for their direct source of energy while heterotroph organisms rely on these species as

their ultimate source of food. Photosynthesis not only provides energy for most organisms, but it is also

necessary for all aerobic life because it maintains necessary levels of oxygen in the atmosphere. In

addition to the life-sustaining significance of photosynthesis, the sheer scale of photosynthesis is

fascinating. In total, photosynthetic organisms capture 100 terawatts of sunlight, converting CO2 and

water into 105 billion tons of biomass annually.2,3

The first photosynthetic organisms evolved 3.4 billion years ago and began to harvest sunlight to

drive the biochemical reactions necessary to sustain life.4 One billion years later the ‘oxygen catastrophe’

occurred and cyanobacteria started to oxygenate the predominantly CO2 atmosphere. This event led to

the extinction of most anaerobic life on earth but allowed more complex organisms to evolve.4 The next

major event in the evolution of photosynthesis occurred when a heterotrophic eukaryote engulfed a

relative of present day cyanobacteria, which resulted in eukaryotic photosynthetic organisms. This event

known as a primary endosymbiosis – a process in which a unicellular organism engulfs another cell and

adopts its organelles into the host cell – occurred approximately 1.4 billion years ago, and led to the

2 Chapter 1. Introduction

ancestors of modern day higher order plants. Primary endosymbiosis is one of the most significant events

in the evolution of photosynthetic organisms as it marks the transition from photosynthetic prokaryotes to

eukaryotes. Prokaryotes are typically unicellular, self-sufficient organisms that do not have a nucleus.

Eukaryotes, on the other hand, have a DNA-containing nucleus and are often multi-cellular. complex

organisms. Following this first endosymbiosis a number of secondary endosymbiosis events occurred in

which one of the products of the primary endosymbiosis (red or green algae) was engulfed by another

eukaryote, a phagocytotic protozoan. One of the classes that eventually emerged from a secondary

endosymbiosis of red algae was cryptophyceae, broadly known as cryptophytes.

Unlike higher order plants where the light-harvesting proteins are strictly membrane bound,

cryptophyte algae contain additional light-harvesting complexes known as phycobiliproteins, which are

located in the thylakoid lumen. Although other types of algae contain additional light-harvesting proteins

such as phycobilisomes, these proteins reside on the stromal surface of the thylakoid membrane.

Cryptophytes are unicellular photosynthetic algae, which are typically 5-20 μm in size.5 They are found

in both marine and fresh water environments all over the world. Cryptophytes are typically found in

shallow water where the spectral window of available light is minimized by the absorption of water. As a

result, the algae have evolved to absorb light in a region in where available spectral window is not

compromised by water.6 Cryptophytes either contain phycoerthryin or phycocyanin biliproteins that are

densely packed in the lumen. These proteins absorb in the region between 500-700 nm where chlorophyll

and water have minimal absorption.5 This allows cryptophytes to harvest sunlight that would not

otherwise be used by high order plants.

cyanobacterium

red algae

phagocytotic

protozoan

hetertrophic

eukaryote (b)

(c)

(a)

Figure 1. (a) Simplified evolutionary tree depicting selected relationships between photosynthetic organisms.

(b) Illustrations of primary endosymbiosis and (c) secondary endosymbiosis events.


Not only is the location and absorption spectrum of the light-harvesting antennae in cryptophytes

unique, but they also evolved in a particular manner. Emerging after a secondary endosymbiosis event of

red algae, in which cyanobacterial red algae was engulfed by a eukaryotic organism, a new organism

containing remnants of the red algal nucleus and the nucleomorph emerged.5 However, further changes

resulted in the loss of allophycocyanin from the phycobilisomes of red algae and changed the quaternary

structure from a trimer to a heterodimer.5 Furthermore, the remaining phycobiliproteins were transported

into the thylakoid lumen, which lead to the emergence of cryptophyceae (see Figure 2).

Figure 2. Illustration of the light-harvesting systems in (a) most high order plants and (b) in cryptophyte

algae. Whereas in higher order plants the light-harvesting antennae are strictly membrane bound, in

cryptophyte algae the peripheral light-harvesting antennae, phycobiliproteins, reside in the lumen.

(a)

(b)


1.2 Light-Harvesting Proteins

1.2.1 Introduction

Light-harvesting proteins play the functional role of capturing solar radiation and transferring the

resulting excitation to the reaction centers where they are used to carry out photosynthetic chemical

reactions. In high order plants and many algae, the major light harvesting protein is Light-Harvesting

Complex II (LHC-II) which contains the green pigment chlorophyll. In addition to chlorophyll-

containing complexes, some plants, algae, and bacteria utilize other light-harvesting antennae including

phycobilisomes and phycobiliproteins to supplement the absorption of sunlight. These peripheral light-

harvesting proteins transfer the photoexcitation to chlorophyll-a molecules located in the membrane

which subsequently transfer the excitation to photosystem I (PSI) and photosystem II (PSII).7 At the

center of the PSII complex is the reaction center which is the site of water oxidation, which is catalyzed

by the Mn4OxCa complex.7 The oxidation of water by PSII along with processes carried out by other

protein complexes including PSI, mobile electron carriers, and the cytochrome bf complex complete the

photosynthetic cycle. These processes include the release of molecular oxygen, the reduction of both

nicotenamide-adenine dinucleotide phosphate (NADP+) and adenosine diphosphate (ADP), as well as

generating a proton gradient across the membrane.

Photosynthetic organisms achieve numerous advantages by employing different complexes to

harvest sunlight and to drive chemical reactions: (a) Light-harvesting proteins are able to increase the

spatial and spectral cross section for the absorption of sunlight without being costly to the organism; in

many photosynthetic species the reaction center may be serviced by tens of light-harvesting proteins. (b)

The wide variety of these complexes allows individual species the ability to survive in varying light

conditions. (c) Light-harvesting antennae have evolved photoprotection responses, such as

downregulation, to avoid damage in the case of excessive exposure to sunlight.8

The light-harvesting protein is a multi-chromophoric system. The chromophore, a light absorbing

molecule, is typically a linear or cyclic tetrapyrrole attached to the apoprotein via a covalent bond. These

chromophores determine the electronic and spectroscopic properties of the protein. However, their

location in the protein can specifically alter the electronic properties of the entire protein depending on

their position relative to other chromophores and the local environment.


400 500 600 700

LHCII PE545 PC645

PC612 PE555

Wavelength (nm)

Figure 3. Normalized absorption spectrum of LHC-II (green); the main light-harvesting protein in high

order plants along with the normalized absorption spectra of four cryptophyte light-harvesting proteins:

PE545 (blue), PE555 (pink), PC612 (purple), and PC645 (red). The different region in which these

complexes absorb is clearly evident. Investigations of the four cryptophyte light-harvesting proteins is

the focus of this thesis.

Photosynthesis starts with the absorption of light by a chromophore in a light-harvesting protein,

resulting in an electronic transition from the ground state to an excited state. The excited state is short

lived and relaxes to the ground state after a mere nanosecond.9 Before the molecule can relax the energy

is transported to a reaction center where it is used for charge separation. Within a light-harvesting

complex, strong electronic interactions between chromophores can result in new delocalized excited

states. Although not always present, these delocalized excited states known as excitons can extend over

multiple chromophores10–12

and can have a profound impact on the electronic structure and energy

transfer dynamics within a light-harvesting protein.

1.2.2 Photosynthetic Excitons

The exciton model was first used to describe a nonconductive electronic excitation in solid-state

physics.13,14

In this case, the exciton describes the bound state between an electron and a hole. The

exciton model has been extended to describe delocalized excited states in biological systems15

and

molecular aggregates16

that arise from the quantum superposition of localized molecular excited states.


The quantum mechanical interaction between chromophores in light-harvesting proteins can be quantified

according to the electrodynamical interaction between their respective transition dipole moments.17

When

a molecule interacts with an electric field it undergoes an electronic transition; the absorption of a photon

results in a transition from the ground state to a higher energy excited state while emission of a photon

leads to a transition from an excited state down to the ground state. The oscillating electric dipole

moment associated with this transition is referred to as the transition dipole moment and is related to the

probability of the transition occurring.

The electronic coupling parameter, V, is a measure of the interaction between transition dipole

moments; its value is directly relatable to the extent of delocalization of an exciton. Traditionally,

chromophores are interpreted as simple dipoles, in which case V can be approximated by the dipole-

dipole interaction between transition dipole moments of the interacting chromophores.5 However, this

approximation fails to capture the shape of the interacting molecular wavefunctions often leading to

inaccurate estimates of the electronic coupling.17

A more accurate estimate of V is achieved by using the

transition density cube (TDC) method, which determines the transition densities between the ground and

excited states by discretizing the transition densities into infinitesimal volume elements and then sums

over all Coulombic interactions.17,18

An accurate estimate of the electronic coupling is critical in

determining the extent of delocalization of an exciton. Unlike solid state physics where excitons can be

long range, photosynthetic excitons are fairly localized. The typical delocalization length only 2-4

chromophores at the most and in many cases the excited states can be approximated to be fully localized

on one molecule.10,12

The magnitude of the coupling also has significant impact on the method of energy

transfer as described in the next section.

Delocalization of the excited state increases the spatial extent of the excited state which results in

a significant change in the electronic structure. This delocalization can be understood by considering the

Frenkel exciton Hamiltonian of such a system with N interacting chromophores

∑ | ⟩⟨ |

∑ | ⟩⟨ | | ⟩⟨ |

where |n is the molecular excited state of chromophore n, En is the site energy of chromophore n, defined

as the energy associated with the transition from the ground state to the excited state in the absence of

electronic coupling, and Vnm is the electronic coupling between chromophores n and m described above.

Diagonalization of the Hamiltonian, such that | ⟩ |

⟩, gives the eigenstates (i.e. excitons), k,

and the corresponding eigenenergies, Ek, which determine the absorption resonance frequencies. The


strength of these transitions are given by the excitonic transition dipole moments ∑

. For an

illustration of exciton splitting see Figure 4.

.

The LH2 complex, isolated from purple bacteria, is one of the most widely studied light-

harvesting complexes that provides a clear example of how excitons can substantially change the

electronic structure of a protein as well as the energy transfer dynamics. The LH2 complex only contains

one type of chromophore, bacteriochlorophyll-a molecules, 27 of these molecules are arranged in two

rings. In the B850 ring, there are 18 closely packed bacteriochlorophyll-a molecules. Due to their close

proximity and their preferential orientations, the coupling between these chromophores is strong with

nearest neighbor coupling being approximately 300 cm-1

.19

In the B800 ring there are nine loosely packed

bacteriochlorophyll-a molecules where adjacent molecules have a 30 cm-1

electronic coupling. The

absorption of the B800 ring occurs at 800 nm, corresponding to the absorption of isolated chlorophyll-a

molecules, while the B850 ring is red-shifted to 850 nm. This shift is partly a response to interactions

between the chromophores and the protein however a significant portion is due to the strong coupling of

molecules that shifts the absorption resonance frequency to the new eigenenergy of the exciton.20

For an

illustration of the absorption spectrum and crystal structure of LH2 along with energy level diagrams, see

Figure 5. In addition to changing the electronic landscape of the system, excitons in LH2 also change the

energy transfer dynamics by setting up a gradient that allows excitation to flow downhill from the high-

energy B800 ring to the lower energy B850 ring.

Figure 4. Illustration of the energy spacing of a homodimer, which consists of two identical chromophores, each

modelled as a two-level system. Molecular excited states, en and em, are coupled by an electronic potential, Vnm,

resulting in delocalized excited states, e and e. Absorption resonance frequencies of the dimer occur at the

corresponding eigenenergies, E and E.


The example of LH2 is not an isolated illustration of strong electronic coupling between

chromophores that modifies the electronic structure of a light-harvesting complex; exciton states are in

fact common among light-harvesting proteins. Present in all higher-order plants, the PS I complex has

been shown to include sections of strongly coupled chlorophyll molecules.21

Although the majority of

dynamics in PSI do not rely on strongly coupled chromophores, it has been speculated that the presence

of excitons may affect some of the more subtle steps, including the step involving trapping the excitation

at the reaction center.21

Another example of strongly coupled chromophores is found in the light-

harvesting machinery of cryptophyte algae.5,9,10

The light-harvesting antennae of cryptophytes are known as phycobiliproteins. The location,

structure, and absorption features of phycobiliproteins are all unique. Typically 8 nm across in the largest

dimension, phycobiliproteins contain eight chromophores known as bilins. Unlike chlorophyll, bilins are

composed of four linearly attached pyyrole rings; the conjugation length along with their substituents

determines the absorption features of these chromophores. All phycobiliproteins include either a

phycocyanobilin or a phycoerythrobilin and other bilins that cause the overall absorption of the protein to

occur in the blue and green spectral regions. The arrangement of the bilins in a number of

phycobiliproteins has given rise to delocalized excitonic states.

Phycocyanin 645, the phycobiliprotein extracted from Chroomonas CCMP270 has been studied

extensively.9,22–24

The strongly coupled central dimer composed of two dihydrobilverdin (DBV)

chromophores are coupled through an electronic interaction of 320 cm-1

whereas the coupling strength

between other chromophores is an order of magnitude weaker.22

The coupling between the two dimer

chromophores leads to excitonic states that act as the primary receptors for sunlight in this complex.

Another phycobiliprotein, phycoerythrin 545, isolated from Rhodomonas CS24 also has strong coupling

between chromophores with the largest coupling being on the order of 100 cm-1

. Although not as large as

the coupling in PC645, this 100 cm-1

coupling is still on the order of the spectral line broadening, which

suggests excitonic states may be important.10


Figure 5 (adapted from references 25,26

). (a) Absorption spectrum of LH2 extracted from R. Acidophila.



structure of LH2 from R. Acidophila illustrating 27 bacteriochlorophyll-a chromophores. Blue coloured

chromophores indicate the B800 ring, while red coloured chromophores indicate the B850 ring. Energy

level diagrams for chromophores in (c) B800 ring and (d) B850 ring.

(a)

(c) (d)

(b)


1.3 Electronic Energy Transfer

Electronic energy transfer (EET) is a photophysical process whereby excitation is transferred from an

initially populated donor molecule(s) to an acceptor molecule(s) due to intermolecular interactions.27

Electronic excitation transfer from one chromophore to another is a ubiquitous photophysical process

found in a variety of systems including conjugated polymers27,28

, light-harvesting proteins29,30

, and various

other multi-chromophoric systems.31

Traditionally, energy transfer in light-harvesting proteins has been

understood according to Förster resonance energy transfer (FRET) theory. However, in recent years it

has been shown that Förster theory fails to capture some of the subtle dynamics observed in light-

harvesting proteins. Consequently, changes have been made to this model.

Attributing an appropriate EET theory to explain the dynamics of a particular system can be

challenging depending on how the magnitude of the interchromophoric interaction compares to the

system-bath interaction. The interchromophoric interaction is characterized by the electronic coupling

(V), while the system-bath interaction can be characterized by the system-bath coupling. The system-bath

coupling is quantified according to the reorganization energy

∫

where J(ω) is the spectral density. Förster theory is applicable in the weak coupling limit, where the

electronic coupling is small compared to the system-bath coupling. In this case the electronic coupling

acts as a small perturbation to promote energy transfer but is not sufficiently large to create delocalized

excited states. In the weak coupling regime, vibrational equilibrium is achieved much faster than the rate

at which EET occurs and thus the states are no longer coupled when EET takes place. In this case the

excitation is localized to one molecule at any time and the transfer of excitation from the donor to the

acceptor occurs incoherently in an irreversible hopping fashion. In this case the dynamics of EET can be

described according to classical rate laws given by Förster theory.

According to quantum electrodynamics the transfer of energy can be conceptualized as the

exchange of a virtual photon between the donor and acceptor molecules. According to Förster theory, the

rate of energy transfer, k, is dependent on the donor-acceptor separation, the orientation of the respective

transition dipole moments, and the spectral overlap of the relevant absorption and emission profiles. The

rate of energy transfer can be explicitly calculated according to the Fermi golden rule expression17

| | ∫


where s=1/n2 is the solvent screening factor, V

dip-dip is the electronic coupling determined by the dipole-

dipole approximation, and S(ε) is the normalized overlap between the donor emission spectrum and the

acceptor absorption spectrum with the integral having dimensions of inverse energy. Using the dipole-

dipole approximation the coupling can be expressed according to the transition dipole moments of the

donor (μD) and acceptor (μA) molecules and their separation (R):

where and is known as the orientation factor.

Since Förster theory explicitly relies on the dipole-dipole approximation, it breaks down when

this approximation is invalid. This problem occurs when an electronic transition can be dipole moment

forbidden but weakly allowed by a higher order multipole transition moment. This often occurs between

highly symmetric chromophores. Dexter32

aimed to overcome this limitation in his theory of energy

transfer and achieved it by extending Förster theory to include higher order multipoles.33

The higher

order multipoles are accounted for by taking the Taylor expansion of the Coloumbic interaction between

the transition densities. The first non-zero term is the dipole moment, while the following terms

contribute to higher order multipoles. In the same way that dipole coupling promotes energy transfer,

multipole coupling can also promote energy transfer in the same way but to a lesser extent. Higher order

terms of the Taylor expansion have very strong distance dependence. As a result they are only significant

at close separation between donor and acceptor molecules. Yet the expansion is only convergent when

the distance between the donor and acceptor is much greater than their dimensions; as a result, the

multipole correction has little significance for molecular systems.33

This problem can be overcome by

using the transition density cube (TDC) method in which the interaction between relevant transition

densities on the donor and acceptor are calculated explicitly.

Dexter was also able to make a significant correction to Förster theory when the acceptor and

donor separation is small (~4 Å) such that orbital overlap contributes significantly to the electronic

coupling.17,33

In this case, where the donor and acceptor wavefunctions overlap Dexter proposed that

another term, Vshort

, contributes to the total electronic coupling such that V=Vdip-dip

+ Vshort

. This additional

term tends to have a more significant impact for transitions that are weakly coupled. An important note is

that since the sign of the two components of V can be different the overall coupling can amount to zero

even if the magnitude of each component is large.

Lastly, the effect of the solvent on the transfer rate is included in the screening factor, s=1/n2, in

Förster theory. This assumes that the solvent has the same effect on any chromophoric system. However


it has been shown theoretically that the solvent screening effect depends on the specific orientation,

shape, and distance of the donor and acceptor molecules within the chromophoric system.34

Specifically,

the screening effect diminishes at small separation to the point of negligible or no screening at very close

separations and increases exponentially, reaching the Förster limit in large separation cases.17

The fundamental break down of Förster theory and the Fermi golden rule occurs in the

intermediate and strong coupling regimes. In this case the interchromophoric coupling between donor

and acceptor molecules is no longer small enough such that it acts as a perturbation promoting incoherent

energy transfer. In the strong coupling limit when the coupling between the donor and acceptor

molecules is large compared to the system bath coupling, new delocalized excitonic states are created. In

this case the excitation can be shared coherently between two or more molecules and is localized neither

on the donor nor the acceptor molecule(s). The applicable theory that describes the strong coupling

regime is known as Redfield theory. In Redfield theory it is the bath that promotes energy transfer and

relaxation through stochastic fluctuations.

In the intermediate coupling regime, where the electronic coupling is similar in magnitude to the

system-bath coupling, understanding energy transfer becomes far more difficult because it falls in

between the two extremes of strong and weak coupling. The intermediate coupling regime is the most

applicable to multichromophoric light-harvesting proteins. One potential solution is generalized Förster

theory (GFT) which attempts to partition the system into both strongly coupled chromophores and weakly

coupled chromophores.35–38

GFT is applicable when multiple, strongly coupled chromophores act as a

donor and are weakly coupled to another group of strongly coupled acceptors. Although this requirement

may seem rather limiting, GFT has been able to capture the essence of energy transfer in large light-

harvesting complexes where there are different coupling domains, such as in purple bacterium

Rhodobacter sphaeroides.36

However, when the electronic coupling between multiple donors and

acceptors is significant such that the excitation is largely delocalized then even generalized Förster theory

fails to capture the coherent nature of the energy transfer. Understanding energy transfer in this

intermediate regime is currently a topic of extensive studies. Experimental work done to elucidate the

details of energy transfer in this regime often use a multitude of spectroscopic techniques.


1.4 Spectroscopy

Spectroscopy broadly refers to the study of the interaction between electromagnetic radiation and matter.

Electromagnetic radiation refers to a type of energy that has wavelike properties as it permeates space and

is composed of both an electric field component and a magnetic field component . Both

components are perpendicular to each other and the direction of propagation . The

magnitudes of the two components are related by , where c is the speed of light, thus making the

electric field component much larger than the magnetic field component. Maxwell’s equations along

with the constitutive relations describe fundamental electrodynamic phenomena and are the foundation of

classical electromagnetic theory.

The above equations are Maxwell’s equations for radiation in differential form, where is the

permittivity of free space, is the permeability of free space, and

√ . The first equation is known

as Gauss’s Law and describes how a distribution of electric charge (ρ) produces an electric field. The

second equation is the Maxwell-Faraday equation, which states a changing magnetic field creates an

electric field. The third equation is Gauss’s law of Magnetism, which stipulates that there are no

magnetic charges analogous to electric charges such as electrons and that instead the source of magnetic

fields are dipoles. Lastly, the fourth equation is known as Ampère’s Law with Maxwell’s correction and

states that magnetic fields can be produced by electrical current (J, charge density) or changing electric

fields.

For many materials, namely non-magnetic materials, the optical properties can be fully

determined by solely considering the interaction between the electric field component of the radiation

with the material. In this case, the electric field induces an electron polarization response ( ) in the

medium; the law describing this phenomenon is known as a constitutive relation and takes the following

general form:


where is the electric susceptibility of the medium, a tensor (commonly rank 2) that describes the

medium’s ability to be polarized by an applied electric field. The electric susceptibility is related to the

electric permittivity (i.e. dielectric constant, ) of the medium via

. Therefore the electric

permittivity is a tensor of the same rank as the electric susceptibility. If the material is isotropic then the

electric susceptibility and dielectric constant of the medium become scalar quantities, this happens to be

an appropriate approximation for many materials such as glass, air, water, and metals. However, some

optically active media, such as crystalline solids are anisotropic, which means the dielectric constant and

electric susceptibility are tensors, suggesting that the polarizability of the medium depends on the

orientation of the electric field. Both the dielectric constant and the electric susceptibility tensors are

symmetric and can thus be reduced to a diagonal matrix, which at most has three independent non-zero

elements39

:

[

]

For dispersive media, where the frequency of the applied field is close to a resonance frequency of the

medium, the response is not instantaneous and the electric susceptibility function and thus the dielectric

constant function are complex and have frequency dependence (i.e and ).39 The

dielectric constant can then be related to the more familiar term known as the refractive index, which is

also a complex valued function which is frequency dependent ( ), through the following

formula: . The real and imaginary parts of these complex functions are related through the

Kramers-Kronig relations.

For an isotropic medium all the optical properties of the material are governed by the complex

refractive index. The real part of the complex refractive index determines the phase velocity of the

electric field propagating through the material and thus governs the dispersion characteristics of the

material. At an absorption or emission resonance of the material the real part of the refractive index

shows a typical dispersive lineshape. Phenomena that arise because of a response to the real part of the

refractive index are known as parametric processes. Such processes include refraction, diffraction,

Rayleigh scattering, and four-wave mixing (nonlinear process). Parametric processes describe processes

where the initial and final quantum states are the same, thus population can only reside outside the ground

state in a virtual state for a short period of time as governed by the Heisenberg Uncertainty Principle


(

).

40 Since parametric processes have identical initial and final states, conservation of momentum

and energy are required.

On the other hand, the imaginary component of the refractive index determines the absorption

characteristics of the material and has a Lorentzian lineshape at each absorption resonance frequency.

The imaginary component of the refractive index would display peaks at all rotational, vibrational, and

electronic transitions and in some cases, where the resonance frequencies are closely spaced, the peak

may appear as a continuum or band.39

Phenomena that arise due to a response to the imaginary

component of the refractive index are known as non-parametric processes and involve population transfer

between real states. Examples of non-parametric processes are absorption and fluorescence.

Nonlinear optics refers to the branch of optics where the polarization of the medium depends

nonlinearly on the electric field. In contrast to linear optics, in nonlinear optics the superposition

principle no longer holds and thus the response of the medium is no longer proportional to the sum of

inputs. High light intensities, such as those produced by lasers are required to modify the optical

Frequency,

Frequency,

n

1

Figure 7. (a) The real part (n) of the complex valued refractive index function ( ) shows dispersive lineshapes at

each resonance frequency. The overall trend follows

such that at the largest frequencies, beyond any

resonances, the refractive index is purely real and equal to unity. (b) The imaginary part ( ) of the refractive index

displays Lorentzian lineshapes at each resonance frequency. In between transitions drops to zero signifying that

the material is transparent at that frequency.

(a)

(b)


properties of the media to produce nonlinear effects. In nonlinear optics the polarization of the medium

can be expressed as a power series of the electric field.

In linear optics we are only concerned with the first term in this expansion. In nonlinear optics we are

interested in the higher order terms, which include the nonlinear electric susceptibilities, where

corresponds to the n

th-order nonlinear electric susceptibility, which is a (n+1)-rank tensor.

Convention denotes the first term in the expansion as the first-order polarization; the second term is the

second-order polarization and so on. Phenomena that occur as a result of second-order polarization are

uncommon and this thesis will only focus on phenomena that arise due to first- and third-order

polarizations. The next chapter will focus on the details of specific spectroscopies used to investigate the

photophysics of cryptophyte light-harvesting proteins.

17

Chapter 2

Spectroscopy

2.1 Steady-State Spectroscopy

2.1.1 Linear Absorption

Linear absorption spectroscopy measures the absorption of light by a medium as a function of frequency

at a specific concentration and path length. An intuitive picture for linear absorption can be achieved by

considering the semi-classical picture which is useful when the flux of photons is very high. In this case

the polarization induced in a medium by an electric field radiates a signal that is out of phase with the

transmitted radiation. This results in a decrease in the intensity of the overall output radiation. The out-

of-phase polarization in the medium is proportional to the imaginary component (κ) of the material’s

complex refractive index ( . In practice, the linear absorption can be described according to

the Lambert- Beer law:

( )

where I0 is the incident light and I is the transmitted light. The more useful form is defined according to

the molar absorptivity (ε) which is frequency dependent, the path length (l), and the molar concentration

(c). This indicates that absorption is proportional to both the concentration of a sample and the path

length (i.e. the distance of sample the light passes through).

18

Chapter 2. Spectroscopy

In the case of light-harvesting proteins the shape and position of the linear absorption spectrum

depends on the electronic transitions of the protein being measured and their respective absorption

lineshapes. The absorption lineshape of an electronic transition is centered at the eigenenergy of that

exciton, while the shape is broadened and possibly shifted due to homogeneous and inhomogeneous line

broadening. Inhomogenous broadening refers to the Gaussian distribution of eigenenergies for a

particular exciton that arises due the fact that an ensemble of proteins is being measured. In any

individual protein the chromophores can take on many, slightly different conformations altering their

eigenenergy. Homogeneous broadening refers to the Lorentzian lineshape that arises due to the

interaction between collective vibrational modes (phonons) and electronic transitions. The absorption

spectrum that is measured is the sum of each absorption lineshape associated with a particular exciton.

The linear absorption spectra were recorded using a Varian Cary 100 Bio UV-Visible Absorption

Spectrophotometer.

2.1.2 Fluorescence

A molecule in the excited state can decay to the ground state by emitting a photon; through a phenomenon

known as fluorescence. Although there are other means through which an excited state can relax to the

ground state, such as internal conversion or intersystem crossings, the most easily observable process in

proteins is fluorescence. In phycobiliproteins the quantum yield of photon resulting in an excitation is

usually very high (>95%) with the fluorescence occuring from the lowest energy eigenstate. As a result,

the lineshape of the fluorescence spectrum is narrow and does not mirror the absorption spectra which is

often the case among simple molecular systems. The fluorescence spectrum is red-shifted from the same

electronic transition in the absorption spectrum by an amount known as the Stokes shift. The Stokes shift

is twice the reorganization energy (λ) which defines the energy related to the solvent’s response to the

change in the molecule’s properties after excitation. The Stokes shift depends on a variety of parameters

including the temperature of the solvent and its dielectric constant. Steady-state fluorescence

spectroscopy of proteins is useful for determining quantum yield, Stokes shift, the lowest energy

eigenstate, and vibrational modes. Fluorescence emission spectra were recorded using a Varian Cary

Eclipse Fluorescence Spectrophotometer. Another related spectroscopy is time-resolved fluorescence,

which is extremely useful due to the fact that it can provide information on energy transfer rates and

excited state lifetimes; however it is beyond the scope of this thesis.

19


2.1.3 Fluorescence Anisotropy

Chromophores typically absorb light along a preferred direction depending on the electronic transition

involved. If the light is linearly polarized, then the probability that a chromophore will be excited is

proportional to cos2θ, where θ is the angle between the electric field vector of the incident light and the

absorption transition dipole moment of the chromophore. Photoselection occurs since those

chromophores with transition dipole moments oriented closely with the polarization of the electric field

are preferentially excited. As a result, the emission from these preferentially excited chromophores is

highly polarized. Transfer of excitation energy to another chromophore with different orientation will

result in a depolarization of the overall emission. By exciting at various wavelengths (and thus exciting

different chromophores) and monitoring the emission, the polarization anisotropy can be measured. A

local maximum/minimum may indicate the position of an eigenstate. Therefore electronic energy transfer

within a molecular system can be monitored through measurements of fluoresce anisotropy. Anisotropy

is defined as the following dimensionless quantity:

λ

λ

Reaction Coordinate

S0

S1

Absorption Emission

Figure 8. Illustration of absorption and fluorescence (emission) processes, based on ground state (S0)

and single excited state (S1). λ denotes the reorganization energy.

20


r = (I|| – I┴)/(I|| + 2I┴)

where I║ and I┴ are the observed intensities when the emission polarizer is oriented parallel or

perpendicular to the excitation polarizer respectively. The following equation provides a more useful

form of Equation 2.2 for anisotropy measurements done using a L-format fluorescence spectrometer:

r = (IVV – GIVH)/(IVV + 2GIVH)

where G = IHV/IHH corrects for the difference in sensitivities of the detection system to vertically and

horizontally polarized light (subscripts denote orientation of exciting and emitting polarizers). Figure 9

illustrates the experimental schematic used to measure fluorescence anisotropy in an L-format

fluorescence spectrometer.

By employing the correct environmental conditions extrinsic causes of depolarization can be

minimized. For example Brownian motion results in an increase in angular displacement between the

absorption and emission fluorophores and thus lowers the true anisotropy values. The effect of this

extrinsic depolarization can be minimized by using viscous solvents or by conducting measurements at 77

K. It is also preferential to use optically dilute samples as this will minimize depolarization due to

radiative energy transfer (i.e. where fluorescence from one chromophore is reabsorbed by another

chromophore).

V

V

H

H

Orientation of Excitation

Polarizer

Orientation of Emission

Polarizer

Figure 9. Schematic drawing of L-format fluorescence spectrometer and polarizers used in fluorescence

anisotropy measurements.

21


In the absence of other depolarizing processes the fundamental anisotropy value (rο) can be used to

calculate the angle between the absorption and emission transition dipole moments according to

Equations 2.2 and 2.3. One simply substitutes the maximum measured anisotropy value for r0 and solves

Equation 2.4 for β, the angle between the absorbing and emitting transition dipole moments.

Fluorescence anisotropy measurements were recorded using a Varian Cary Eclipse Fluorescence

Spectrophotometer, operating in the right angle geometry and equipped with plastic polarizers.

2.1.4 Circular Dichroism

Circular dichroism (CD) measures the difference in absorption ( ) by a medium of left- and right-

circularly polarized light:

For circularly polarized light is polarized light, the electric field vector rotates around the propagation

vector. It is composed of two linearly polarized waves, equal in magnitude but with a phase difference of

±π/2. CD measurements can be performed on any optically active medium as it measures how chiral

molecules interact differently with left- and right-circularly polarized light. CD is a particularly important

measurement for biological molecules because it can provide useful information on the secondary

structure of proteins. A protein’s secondary structure refers to the general three-dimensional shape of

local segments of the protein. By measuring the UV CD spectrum of a protein it can be determined to

what extent a protein’s secondary structure is composed of α-helices and β-sheets. In light-harvesting

proteins, CD measurements can also provide useful information on the electronic structure of the protein,

this is due to the chirality of the chromophores. By measuring the CD spectrum of a protein in the visible

region – where the chromophores absorb – it can be determined if exciton splitting is present. CD also

probes the magnetic dipole moments of these molecules, which is responsible for the rotational strength

of the chromophores. CD spectra were recorded using a Jasco J-810 CD Spectrometer equipped with a

Jasco PTC-423S/15 temperature controller.

22


2.2 Two-Dimensional Electronic Spectroscopy

2.2.1 Introduction

Elucidating the energy landscape and understanding excitation energy transfer dynamics in

multichromophoric systems are significant challenges. Even in simple molecular aggregates, determining

the electronic properties can be a difficult task. Molecular interactions along with system-bath

interactions can make it difficult to develop a detailed understanding of the system. Not only are

photosynthetic systems inherently complex, often consisting of tens of thousands of atoms, but the

requirement of maintaining physiologically relevant conditions during measurements makes their

investigation even more difficult.

Using a number of different steady-state and ultrafast spectroscopic techniques in unison can

provide a plethora of information on the energy transfer dynamics and electronic structure of

photosynthetic systems. Steady-state measurement such as linear absorption, fluorescence, excitation

anisotropy, and circular dichroism can provide useful information on the electronic structure of these

systems. Additional information can be obtained by conducting these measurements at cryogenic

temperatures which helps minimize the obscurity caused by homogeneous line broadening. Vibrational

states can be investigated using stimulated resonance raman spectroscopy,41

and excitation energy transfer

dynamics can be studied using transient absorption spectroscopy10

and time-resolved fluorescence.

However, these conventional techniques are not able to distinguish between coherent and incoherent

energy transfer dynamics, inhomogeneous and homogeneous broadening are often convolved, and direct

evidence of exciton splitting tends to be elusive.

Two-dimensional electronic spectroscopy (2D ES) has emerged as an optical technique that can

accomplish many of the objectives of conventional spectroscopies in a single measurement. In addition to

elucidating typical optical properties of molecular systems, 2D ES can distinguish homogenous and

inhomogeneous broadening and detect correlations between excitonic states. 2D ES is a nonlinear

technique in which three electric fields interact in the weak-field limit with a sample generating a third-

order macroscopic polarization, which in turn produces an optical response.42

The resulting spectrum

plots this optical response as a function of the excitation frequency and detection frequency. The majority

of experimental evidence suggesting quantum effects in light-harvesting proteins comes from 2D ES

experiments. However, distinguishing quantum signatures is still a difficult task; congested spectra

along with a limited knowledge of the excitonic and vibrational landscape of many light-harvesting

proteins provide significant challenges in deciphering signals. Consequently, an in-depth understanding

of the 2D spectroscopy is required and a technical account of the technique follows.

23


2D ES spectroscopy is a type of four-wave mixing spectroscopy; three femtosecond laser pulses

interact with the sample on two dynamical time scales and a fourth pulse is used to heterodyne detect the

signal through means of spectral interferometry43

. The first pulse (wavevector k1, where the subscript

describes the geometry and not necessarily the ordering) creates a coherent superposition between the

ground state and a first excited state of the system (e.g. |ge,|) which evolves over the coherence time (τ).

The second pulse (k2) can create population in the ground or an excited state (e.g. |ee,|) or when the

pulses interact with multiple excitonic states simultaneously, a coherent superposition of two excited

states can be created (e.g. |ee,|). Depending on the system under investigation, vibrational states may

also be populated and vibrational coherences can be excited. The system evolves over some time

typically denoted as the waiting or population time (T) and then a third pulse (k3) interacts with the

sample. Pulse k3 can either create a coherent superposition between the ground and the first excited state

in the case of stimulated emission and ground state bleaching or in the case of excited-state absorption it

can create a superposition between the first excited state and a higher-excited state. The sample generates

a signal after some time t, known as the echo time. The signal is heterodyne detected by overlapping it

with a fourth attenuated pulse known as the local oscillator (LO). The noncollinear beam geometry

typically used results in the signal being isolated in a phase-matched direction according to momentum

conservation. The pulse sequence and beam geometry used for the 2D measurements presented in this

thesis are illustrated in Figure 10.

The total 2D spectrum is composed of two parts, the rephasing contribution and the nonrephasing

contribution. The rephasing component corresponds to the scenario when k1 precedes k2, in which case τ

is positive and the signal is emitted in the ksignal=-k1+k2+k3 direction. When τ is negative, such that k2

precedes k1 then the signal is radiated in the ksignal=+k1-k2+k3 direction corresponding to the nonrephasing

component. Due to the inherit heterogeneity of the proteins under investigation, transition energies of the

chromophores in different proteins within the ensemble are slightly different. This inhomogeneous

broadening has a significant impact on the phase evolution of the system during the different time

periods. In rephasing spectra, the superpositions of ground-excited states during the coherence and echo

times have opposite phases of equal magnitude. In this case, the (photon echo) signal is emitted after a

time known as the echo time, which is equivalent to the coherence time, and results after all the

complexes have accumulated the same relative phase. On the other hand, in nonrephasing spectra the

ground-excited state superposition that occurs during the coherence time has the same phase as the

superposition that occurs during the echo time. In this case, the signal is emitted immediately after the k3

interaction, in which case all the complexes have different phases which do not constructively interfere.

As a result, in media where inhomogeneous effects are substantial, the rephasing signal is significantly

24


stronger than the nonrephasing signal. The total 2D spectrum is a sum of the individually measured

nonrephasing and rephasing components. It is often useful to look at the rephasing and nonrephasing

components independently as different pathways contribute to each of the signals; however, phase twist

can limit this type of analysis. Phase twist – the mixing of the dispersive and absorptive components in

rephasing and nonrephasing spectra – limits the ability to analyze their individual lineshapes.44

Under

proper conditions, once the rephasing and nonrephasing spectra are summed to form the total spectra,

phase twist no longer exists.

Figure 10. (a) Sequence of laser pulses and time delays. (b) Boxcar geometry of pulses: ksignal=+k1-k2+k3

when τ <0 (nonrephasing) or ksignal=-k1+k2+k3 when τ >0 (rephrasing).

The experimental procedure described above can be achieved using an experimental setup similar

to a pump-probe or transient absorption experiment45

, the difference being that the time delay between the

excitation pulses is nonzero. The typical 2D ES experiment uses a commercially available Ti:sapphire

regeneratively amplified laser system to pump a noncollinear optical parametric amplifier (NOPA), which

allows tuneability of the excitation frequency. The pulse can be compressed using a conventional prism

compressor but often requires an additional grating compressor or chirped mirrors if one desires

broadband Fourier transform limited pulses. Using a diffractive optic based setup46,47

four phase-locked

beams in a BOXCARS phase-matched geometry can be obtained. The time delays are achieved using

pairs of glass wedges48

oriented perpendicular to the beam direction which allows the pulses to be delayed

relative to each other without changing the beams path; alternatively passively stabilized retroreflectors

mounted on translation stages49

can be used. The sample is placed in the focal plane of the four beams

and in the case of biological samples, is often flowed to minimize photo-damage. Since it is desirable to

(a)

(b)

25


know the amplitude of the signal and not the intensity, the signal is heterodyne-detected by overlapping

the signal with the LO in the phase-matched direction. The signal and LO pass through a spectrometer

producing an interferogram which is detected by a charge coupled device (CCD). The LO interacts with

the sample hundreds of femtoseconds before the excitation pulses, thus limiting its use to a reference field

with no impact on the third-order response.

Heterodyne detection allows the complex electric field of the signal to be detected; however, only

the real part of the data is typically presented. This requires separation of the real (absorptive) and

imaginary (dispersive) parts of the complex signal, thus knowledge of the correct phase factor is required

and is typically achieved by fitting a projection of a 2D ES signal onto the emission axis to a pump-probe

spectrum50

although other methods have been developed51

. In some cases it is sufficient to present the

magnitude spectra, in which case knowledge of this phase factor is not needed. In either case, the 2D ES

spectrum is a plot of the emission frequency (ωt) as detected by a CCD camera as a function of optical

excitation frequency (ωτ), which is obtained through a Fourier transform of the coherence time, for a

given waiting time, T.

A complete understanding of a 2D spectrum requires a thorough knowledge of the energy

landscape of the system being measured and the ability to interpret different signals as various Liouville

space pathways.42,52–54

However, a basic understanding of a 2D spectrum can be achieved by treating one

axis as the emission axis and the other as the excitation axis. Both cases, one where the excitation axis is

in the horizontal dimension and the other where it is in the vertical dimension are often used to plot 2D

spectra, both provide distinct advantages. 2D spectra presented with the horizontal axes representing the

excitation axes and the vertical axes representing the emission axes intuitively suggest emission as a

function of optical excitation and are easier to understand for newcomers. However, during the

processing of the raw data and for those familiar with pump-probe spectroscopy it is customary to plot a

2D ES spectrum with the excitation axis oriented vertically and the emission axis orientated horizontally,

in which case integrating onto the horizontal axes provides the more familiar pump-probe spectrum. In

both cases signals along the diagonal represent transitions where the excitation and emission frequency

are the same, corresponding to absorption transition frequencies. Alternatively, off-diagonal signals

correspond to transitions where the excitation and emission frequencies are different and represent

correlations between states. At T=0, before the system has a chance to evolve, these correlations can

indicate which states are electronically coupled providing evidence for excitonic states. After the system

has a chance to evolve, such that T > 0 then cross peaks indicate energy transfer.55

The position of the

cross peak indicates which energy transfer pathway is involved; while changes in the amplitude of a cross

peak during the waiting time can indicate that the system is evolving in a non-stationary state. Broadband

26


pulses can generate the coherent superposition of excitonic states; in some incidences when dephasing is

not overbearing, the system can evolve in this non-stationary state for hundreds of femtoseconds.

Figure 11. Guide on how to interpret a 2D spectrum for a simple system with two strongly coupled

chromophores (a). The energy level diagram and corresponding linear absorption spectrum (b) and 2D

ES spectrum (c).

The changing amplitude of the cross peak that occurs because of a coherent superposition of

states evolves with a phase factor that takes the form of , where Eα and Eβ correspond

to the eigenenergies of the two states, α and β, in superposition. The coherent superposition of states

during the waiting time is not limited to electronic coherence, instead vibrational coherences are also

possible and in some cases extremely likely.56–58

Distinguishing between vibrational and electronic

coherences is currently a topic of intense investigation51,59

; a task that is made more difficult by

homogeneous and inhomogeneous broadening. Inhomogeneous broadening which is the result of 2D ES

being an ensemble measurement elongates the spectrum in the diagonal dimension. Homogeneous

broadening on the other hand depends on system-bath interactions and elongates the spectra in the anti-

diagonal direction. Thus changes in the lineshape of the 2D spectrum can indicate solvation dynamics

and spectral diffusion.

Following this same reasoning it has been incorrectly argued that the 2D spectrum can be

considered a map of the system density matrix. In this case most of the signals leading to features along

the diagonal would correspond to population in stationary (excitonic) states, while off-diagonal signals, or

(a)

(b)

(c)

27


cross peaks, are indicative of coherences. Using this method of analysis can prove to be useful as a

preliminary analysis of 2D spectra but is fundamentally incorrect. In many circumstances, specifically in

simple, ordered systems where the spectrum is not congested, excited states are well resolved, and

vibrational modes are negligible or nonexistent then this type of analysis can be sufficient. However in

complex systems such as light-harvesting proteins this analysis can give rise to misleading results. In this

case a more detailed treatment is necessary. One must explicitly takes into account all possible Liouville

pathways which is normally achieved using the double-sided Feynman diagram methodology – a pictorial

representation of the response function.42

Even this method has its limitations; determining all possible

Liouville pathways requires a detailed knowledge of the electronic and vibrational structure of the system,

which is often lacking. However, details of the electronic structure can be calculated through careful

simulations of conventional spectroscopies while the vibrational structure can be computed through

resonance Raman spectroscopy. If one wishes to use 2D ES to elucidate the electronic structure of the

system under investigation then problems can arise in multichromophoric systems where the transition

energies of different chromophores are closely spaced and the signals from different pathways can

overlap deconstructively leading to negligible signal in some cases. Often neglected, Feynman diagrams

also need to be weighted by the likelihood that the transition will occur. One of the most impressive finds

of 2D ES is that electronic coherence may exist for hundreds of femtoseconds in photosynthetic

organisms.

The 2D ES experiments presented in this thesis were conducted with guidance and assistance

from Dr. Daniel B. Turner and Dr. Kyung-Koo Lee, my introduction to 2D ES and experimental optics

was provided by Dr. Cathy Y. Wong.

2.2.2 Experimental Setup

The laser pulses used in the 2D ES experiments are produced by a Ti:sapphire (Spectra-Physics)

regenatively amplified laser system. The pulses exiting the amplifier are centered at 800 nm and

approximately 150 fs in duration (nearly transform limited), the repetition rate is 5 kHz and the pulse

energy is about 0.6 mJ. A 50:50 beam splitter reduces the intensity of the beam that enters a home-built

noncollinear optical parametric amplifier (NOPA). The NOPA allows the wavelength of the entering

800 nm beam to be tuned to anywhere in the visible through a nonlinear optical process. The 800 nm

beam passes through a 95:5 beam splitter; 95% of the beam is used to create the pump beam and the other

5% becomes the signal beam. The intensities of the 800 nm beams used for pump and signal beam

28


generation can then be attenuated independently using a combination of a polarizer and a half waveplate

in each arm of the setup. The pump beam is generated by second harmonic generation, colloquially

known as frequency doubling, whereby the 800 nm beam passes through a barium borate (β-BBO) crystal

that doubles the frequency of the incident photons. The exiting pump beam is centered at 400 nm with a

FWHM of 2-4 nm. The signal beam is generated by focusing the 5% 800 nm beam onto a sapphire

window to generate a white light continuum. Uncoated fused silica of varying thickness (0.5-3 mm) may

be inserted into the white light to reduce the amplified bandwidth. The spatial mode of the signal beam is

adjusted using a parabolic mirror. The signal beam and the pump beam are then overlapped in another

BBO mixing crystal in a noncollinear geometry thereby producing the desired beam through a difference

frequency generation process. Obtaining an exit beam with the desired profile is a tedious process which

requires exploring a large phase-space. Maximum amplification requires that the pump and signal

overlap both in space and time such that only the desired spectral component of the white light continuum

is amplified by the pump. Temporal overlap requires adjusting the delay between the signal and the

pump, which is achieved with a translation stage in the pump beam. Spatial overlap is achieved by

adjusting the angle between the two beams as well as the BBO angle and tilt. The output beam from the

NOPA contains approximately 15% of the energy of the pump beam and is nearly free from angular

dispersion; an average pulse has a bandwidth of 60 nm (spectral intensity FWHM).

The ~125 fs exit beam from the NOPA is compressed to 10-15 fs using a combination of a

grating compressor and a single prism compressor. The beam first passes through a 4-f configuration

grating compressor which uses a 600 lines/mm grating and then passes through the single prism

compressor which utilizes a Brewster angle UV-fused silica prism and a retroreflector for the second pass.

The pulse compression is determined by measuring the nonresonant third-order response from methanol.

After passing through the grating compressor the intensity of the beam can be attenuated using a half-

waveplate and a 0.7 mm thick wire-grid polarizer.

The compressed pulse then enters the four-wave-mixing setup. The beam is focused onto a two-

dimensional diffractive optic (2 mm thick UV fused silica substrate, 10 μm-wide features), a transparent

grating that is optimized for first-order diffraction of 500 nm incident wavelength. Higher (and the

zeroth) diffraction orders are blocked and the four first order diffraction beams are allowed to pass

through in the BOXCARS geometry. Each beam has approximately 12% of the total input power.51

Two

of these beams will be used as excitation pulses, a third beam will be used as the probe pulse, and the

fourth pulse will act as the reference field colloquially known as the local oscillator (LO) which allows

for heterodyne detection. The four beams are then collimated using two 50 cm focal length spherical

mirrors. The mirrors are aligned at exactly 0° with respect to each other, this is achieved by using a small

29


steering mirror that reflects the four beams 90° upon exit from the diffractive optic. The four beams then

bypass the steering mirror as they pass between the collimating spherical mirrors. Perpendicular to three

of the beams are pairs of 1° UV fused silica glass wedges. One glass wedge from each pair is mounted

onto a translation stage (Newport VP-25XL) which allows the timing between pulses to be controlled

with approximately 850 zeptosecond accuracy.51

Two pairs of glass wedges control the time delay

between the two excitation pulses (coherence time, τ). The second excitation pulse passes through a

chopper (Thorlabs MC200), which chops the beam at 25 Hz, which allows scatter to be subtracted from

the third-order signal. This is achieved by subtracting the chopped signal (scatter) from the unchopped

signal (third-order response). The chopper also serves to trigger the detection by the CCD camera, which

when prompted acquires signal for 20 ms. The probe pulse is delayed relative to the pump pulses

(population time, T) via a third pair of wedges. The fourth pulse, the LO, is attenuated by a factor of 104

using a neutral density filter. Although the additional glass in the LO pulse introduces a time delay of ,

this is less than the time delay introduced by the glass wedges. Thus the LO interacts with the sample

approximately 250 fs before the final excitation field, thus limiting its use to a reference field as it does

not impact the third-order response. The exact delay between the signal and the LO (i.e. tLO) is

determined via a third-order, nonresonant, interference measurement between the two excitation pulses,

which have zero time delay between them and the LO.49

The four pulses, each with an approximate

energy of 5-10 nJ, are then focused onto the sample plane where the beam waist diameter is 50 μm. After

the beams pass through the sample the two excitation beams and the probe beam are blocked and the

signal and LO are collimated using a curved mirror and directed into the CCD detector (Andor iDus

DU401A-FI) equipped with a spectrometer (Andor SR-163). The spectrometer has a 600 lines/mm

grating, which corresponds to a resolution of approximately 1 nm; the spectrometer is attached to the

CCD camera which is cooled to -60 °C for detection. The detection dimension of the CCD has 1024

pixels and is calibrated using a Hg/Ar lamp. Measurements of the homodyne signal and LO are also

measured by blocking the appropriate beams with shutters.

The sample is placed at the focal plane of the four beams in a 1 mm pathlength cuvette. Dyes are

measured in a standard 1 mm glass cuvette (Starna Cells 21-G-1) at a peak optical density of <0.4, while

proteins are measured in a 1 mm pathlength flow cell (Starna Cells 48-Q-1) with an optical density <0.25.

Proteins are flowed at a rate of 0.06 mL/min using a peristaltic pump (Cole-Parmer Masterflex) to

minimize the probability of photobleaching. The typical 2D ES scan parameters are as follows: τ scans

from -45 to +45 fs in 0.15 fs or 0.2 fs steps and T scans from 0 to 400 fs in 5 fs or 10 fs steps. The

nonrephasing spectra corresponds to scanning τ for negative time (i.e. τ = -45 to 0 fs), while the

rephasing spectra corresponds to scanning τ for positive time (i.e. τ = 0 to +45 fs); if done in 0.15 fs

30


intervals this corresponds to 301 τ steps. The τ step size and bounds limit the excitation frequency

resolution, zero padding allows the frequency step size to increase but does not improve the fundamental

resolution. A detailed diagram of the 2D ES experimental setup, with a focus on the four-wave-mixing

setup and the compressors is presented in Figure 12.

As mentioned before, the time delay between the excitation pulses is controlled by inserting a pair

of glass wedges into each beam path such that the outer faces of the wedges are perpendicular to the beam

direction and the inner faces are parallel to each other. This allows the delay between the two pulses to be

controlled by inserting more or less glass without altering the beam direction. One wedge from each pair

is mounted on a translation stage. To control the delay accurately the wedge velocity (i.e. the time delay

achieved by moving the wedge a certain distance) must be known with high accuracy. This calibration

factor is determined through an interference measurement using a HeNe laser; the value is then refined

according to a frequency-resolved heterodyne-detected transient-grating measurement of a laser dye.

This allows the wedge velocities to be known with ±0.0001 fs/mm accuracy.60

In addition the frequency

dependence of these calibration values was determined to be minimal, only changing 0.2 fs/mm over the

wavelengths of 532 to 730 nm.60

31


Figure 12. Experimental setup for 2D ES experiments. G = grating, BP = Brewster prism, RR =

retroreflector, DO = diffractive optic, ND = neutral density filter, SM = spherical mirror, C = chopper,

W = wedges, S = sample.

32


2.2.3 Spectral Interferometry

To produce a 2D ES spectrum from which dynamical information can be extracted it is necessary to

isolate Esignal from the heterodyne detected signal measured by the CCD camera. This is achieved through

a process known as spectral interferometry. This process involves isolating the desired signal, Fourier

transforming the coherence time into a frequency axis, and phasing the data into its real and imaginary

components. This section will focus on explaining the theoretical foundation underlying this process as

well as details of the technical algorithm used to process the raw interferograms into the final 2D ES

spectrum presented in this thesis.

In the absence of scatter the heterodyne detected signal measured by the CCD camera can be

written as follows:

| | (2.5)

| | | | (2.6)

ES(ω) corresponds to the electric field of the signal, ELO(ω) corresponds to the electric field of the local

oscillator (LO), and tLO corresponds to the time delay between when the signal is emitted and when the

local oscillator passes through the sample. tLO is negative because the local oscillator passes through the

sample before the signal is emitted. A final 2D ES spectrum is proportional to ES(ω) and is obtained by

isolating and manipulating the second term in Equation 2.5. The additional terms in this equation can be

removed predominantly by time-ordering arguments. However the last term | | is

removed prior to plotting the raw interferograms; this is achieved by chopping E2, which effectively

removes scatter from E1, E3, ELO, and ILO. The raw interferogram is the result of the subtraction of the

chopped signal from the unchopped signal, since the unchopped signal contains ILO, this is already

removed when the interferogram is plotted. A detailed treatment of the effect of chopper on the measured

signal can be found in Dr. Cathy Y. Wong’s doctoral thesis and in reference 61

.

The raw data collected by the CCD camera after subtraction of the chopped signal is plotted

below in Figure 13 (a). Along the horizontal axis is the frequency resolved emission axis as detected by

the CCD camera, the vertical axis corresponds to the coherence time, ranging from negative values for

nonrephasing spectra to positive values for rephrasing spectra. A horizontal slice through the plot

provides a single interferogram, produced by the interference between the local oscillator and the signal at

a specific τ time. An inverse Fourier transform with respect to the horizontal axis provides a time-time

33


spectrum. As a result of the properties of Fourier transforms, a phase shift in the spatial domain

introduces a translation of the function in the frequency domain:

{ } (2.7)

As a result, the Fourier transform of the signal described by the second term in Equation 2.5 translates to

ts- tLO in the time domain (positive, because τ is negative), while the third term translates to ts+ tLO, while

Is occurs at ts. Figure 13 (b) shows the result of inverse Fourier transforming Figure 13 (a) with respect to

the horizontal axes. Since the local oscillator arrives prior to when the signal is emitted, causality

enforces that we only select the signal that occurs when ts- tLO is positive. This is achieved by using the

product of a heavyside function and a window function to select the signal occurring at positive ts- tLO,

which corresponds to ; the complex conjugate of this signal along with IS are

discarded. Figure 13 (c) corresponds to a horizontal slice of Figure 13 (b) at coherence time zero. The

signal at ts- tLO is isolated as described above for the entire spectrum and presented in Figure 12 (d). The

isolated spectrum is then Fourier transformed back to time-frequency space by performing a Fourier

transform on the horizontal axis. In order to isolate Es(ω) from the signal

must be multiplied by and divided by ELO(ω). ELO(ω) is obtained by measuring the local

oscillator spectrum for each T time and then taking the square root of it, i.e. √ . Performing these

two mathematical functions on the isolated spectrum gives the desired signal as displayed in

Figure 13 (e). Performing one last inverse Fourier transform with respect to the vertical axis produces the

final frequency-frequency spectrum, taking the absolute magnitude of this spectrum produces the

magnitude 2D ES spectrum.

If one wishes to separate this spectrum into its real and imaginary components further processing

is needed. This is because a phase difference develops between the signal field and the local oscillator

field, . The process to determine this arbitrary phase factor is known as phasing. This

phase difference was not implicitly included in the above description but can be easily included by

multiplying ES by a factor of . The complex spectrum can be separated into its real and

imaginary components with knowledge of this phase factor. This is normally achieved using the

projection-slice theorem50

, which states that a projection of the real component of a 2D ES spectrum onto

the emission axis should be equivalent to the frequency resolved pump-probe spectrum. Adjusting the

phase between 0 and 2π systematically until the projection matches the pump-probe spectrum can be used

to determine the phase. Some phasing procedures rely on monitoring spatial or spectral fringes, such as

the phasing method initially developed by Daniel B. Turner for the experimental setup described in this

thesis.51

However, it is often sufficient to look at the absolute 2D ES spectrum in which case phasing is

34


not an issue. Even when the 2D ES spectrum is separated into its real and imaginary components, only

the real component is often presented and the imaginary component is often discarded due to the current

inability to extract useful information from it.

Figure 13. Spectral interferometry process in sequential order. (a) Raw data collected by CCD camera

after chopped signal is subtracted. (b) Fourier transform of the detection axis from frequency-space to

time-space. (c) A horizontal slice through figure 5.(b) at τ = 0 fs, the heavyside function (red) is used to

select . (d) An inverse Fourier transform is performed on the horizontal

dimension of the selected signal. (e) Signal is multiplied by phase factor and divided by

√ . (f) A fourier transform is performed on the vertical dimension, thereby producing the final 2D

ES spectrum.

(d)

(e)

(f)

(a)

(b)

(c)

35


2.2.4 Test Case: Cresyl Violet

Cresyl violet (C16H11N3O·HClO4, MW=361.74) is a well-studied, commercially available, organic dye.

Often used for biological and medicinal purposes, cresyl violet is frequently used as a histological

dye.62,63

In addition to its biological applications, the electronic and optical properties of cresyl violet

have been studied extensively using spectroscopic techniques.51,64,65

The fact that previous spectroscopic

measurements of cresyl violet are available in literature along with its commercial availability and its

well-studied electronic structure make it ideally suited to test our two-dimensional electronic

spectroscopy apparatus. As a result, a 2D ES scan of cresyl violet was performed before any 2D ES

measurement on a protein using the same configuration that would be used for the protein (i.e. same pulse

spectrum and identical experimental setup). By comparing the resulting spectra to published 2D ES data

on cresyl violet it was possible to confirm that our apparatus was working adequately and that no

significant artifacts were being introduced into the data.

The cresyl violet perchlorate (CAS #: 41830-80-2) was purchased from Sigma Aldrich and used

as sent. A small amount was dissolved in methanol and stored at room temperature for later use in all

experiments. The peak optical density was approximately 0.2 in a 1 mm pathlength cuvette. The

absorption spectrum of cresyl violet in methanol falls between 500-625 nm, with the peak absorption

occurring at 593 nm. Although the details of each 2D scan on cresyl violet vary slightly, a typical scan is

presented below. In Figure 14 we show the absorption spectrum of cresyl violet in methanol along with

the chemical structure and laser pulse used to excite the sample. The laser pulse spectrum illustrates the

pulse spectrum after it has passed through the sample and is therefore weighted by the sample’s

absorption spectrum. The pulse used in this measurement had a temporal FWHM of 14 fs. To a

reasonable approximation the pulse was Gaussian before passing through the sample.

36


The following 2D scan parameters were used for the data presented below. The coherence time

was scanned in intervals of 0.2 fs from -45 to 45 fs, while the waiting time ranged from 0 to 400 fs in 10

fs steps. The measurement was conducted at 298 K and the sample was stationary. The spectra presented

below are individually normalized and have 20 equally spaced contour intervals (i.e. 5%). In most

spectra the noise level is approximately 5%.

The total spectra display a distinct rectangular feature which is characteristic of cresyl violet.51

The rectangular features arises from two diagonal peaks and two cross peaks; the lower energy diagonal

peak (515 THz) corresponds to the major electronic transition, while the high energy diagonal peak (535

THz) corresponds to the vibronic shoulder (see Figure 15). The diagonal peak at 515 THz is shifted

slightly off the diagonal to a lower emission frequency. The close spacing between these two transitions

prevents the peaks from being well resolved. The imaginary part of the total spectra, as well as the

rephasing and nonrephasing components of the total spectra show characteristic lineshapes typical for a

dye (see Figure 16). The imaginary part of the total spectrum displays a distinctly dispersive lineshape.

No rotation of the nodal line between the positive and negative features is noted, nor is any substantial

change in the shape of the imaginary spectra observed. The real part of the rephasing spectra display

features elongated in the diagonal direction, while the nonrephasing spectra exhibit elongated features in

the antidiagonal direction (see Figures 17 and 18). Underlying signatures of the total spectra can be seen

in both the rephasing and nonrephasing components. These characteristics are typical of 2D spectra of

dyes and indicate the apparatus is in good working form.

500 600 700

Cresyl Violet

Laser Pulse

650 600 550 500 450

Frequency (THz)

Wavelength (nm) Figure 14. Absorption spectrum of cresyl violet (black) along with the laser pulse spectrum used in this 2D

experiment (red) after it had passed through the sample. The chemical structure is inset.

37


Figure 15. Representative 2D spectra of cresyl violet in methanol at indicated waiting times (top left-

hand corner). The spectra are the absolute magnitude of the total signal and are individually normalized

with 20 evenly spaced contours. At T=60 fs features of interest are indicated: the two diagonal peaks at

535 and 515 THz are marked by blue and red circles respectively; while the cross peak at (535,515 THz)

is indicated with green circle and the cross peak at (515,535 THz) is indicated with a yellow circle.

0

+1

38



the imaginary part of the total signal displays a clearly dispersive characteristic shape.

-1

+1

39


Figure 17. The real part of the rephasing signal.

0

+1

40


Figure 18. The real part of the nonrephasing signal.

0

+1

41


An analysis of the time evolution of the peaks observed in the 2D spectra of cresyl violet is

conducted. The analysis is conducted by taking an amplitude trace of the desired feature and monitoring

how the amplitude changes with waiting time. In an effort to obtain an average signal the desired feature

is integrated over a 1.2 THz range in the excitation dimension and 0.14 THz range in the emission

dimension. The first trace conducted was on the absolute signal of the diagonal peak centered at 515 THz

(see Figure 19). Clear oscillations are observed in the total spectra as well as both the rephasing and

nonrephasing spectra. The dephasing time is expected to be significantly longer than the 400 fs

measurement as no obvious damping is observed over the waiting time period of 400 fs. The amplitude

of the nonrephasing trace is slightly less than that of the rephasing trace, as expected for an

inhomogeneously broadened sample. In the time domain, the traces appear to be of a similar nature in all

three spectra; all three traces oscillate with what appears to be one predominant frequency. A very low

frequency mode may also be present, evidence for this is provided by an increase in the overall amplitude

at waiting times between 0 and 100 fs as well as between 250 and 400 fs and a corresponding dip in

overall amplitude between 100-250 fs. This noticeable change in overall amplitude on long time scales is

fully reproducible; however it may still be an artifact introduced by the apparatus.

0 100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

Total

Rephasing

Nonrephasing

0 10 20 30 40

Sp

ectr

al A

mp

litu

de

(a

.u.)

Total

Rephasing

Nonrephasing

Figure 19. (a) Trace of diagonal signal (magnitude) centered at 515 THz: total (black), rephasing (red),

nonrephasing (blue). (b) Fourier transform of (a) with same colour coding, flat baseline subtracted and

first 10 fs omitted due to nonresonant solvent response.

The quality of oscillations allowed a Fourier analysis to be conducted. The Fast Fourier

Transform (FFT) function in Matlab was utilized to perform the Fourier transform on the traces, no

smoothing or fitting of the data was conducted. The first 10 fs of signal was omitted due to nonresonant

solvent response and a baseline was subtracted so that the long time average amplitude of each individual

trace was approximately zero before the FFT was performed. The only peak above the signal-to-noise

level in all three traces occurrs at 18 THz, residual peaks are present but within the signal-to-noise level

Waiting Time (fs) Frequency (THz)

(a) (b)

42


and are likely artifacts of the FFT. Typically a damped exponential should be subtracted from the trace

and the waiting time should be sufficiently long such that the oscillations damp out before the end of the

measurement. Otherwise, significant artifacts can be introduced into the frequency domain trace which

can be mistaken for real signal. In this case it was sufficient to simply subtract a flat baseline as a detailed

analysis of the oscillations was not being conducted; instead the sample was being used as a test case and

being compared to data already published in literature. The oscillating signal along the diagonal in both

the rephasing and nonrephasing spectra suggests that this is due to nuclear wavepacket motion. A trace of

the 535 THz diagonal peak shows similar oscillations albeit weaker in magnitude. An analysis of the

cross peaks of the 2D spectra also show clear oscillations. In this case both the above diagonal (515, 535

THz) and the below diagonal (535, 515 THz) cross peaks show in-phase oscillations which oscillate at the

same frequency as the oscillations observed in the diagonal peak (see Figure 20).

0 100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

515,535 THz

535, 515 THz

Figure 20. Traces of above diagonal (black) and below diagonal (red) cross peaks. Oscillations are

perfectly in-phase.

In agreement with literature it can be concluded that the observed oscillations are due to nuclear

wave packet motion and that the 2D ES apparatus is working adequately.51

This provides significant

evidence that the mere observation of oscillations in the cross peak of 2D spectra does not necessarily

indicate the presence of electronic coherence (i.e. the superposition of two electronic excited eigenstates

of the system). In the case of cresyl violet, it can be concluded without hesitation that the oscillations

must be indicative of vibrational coherence as electronic coherence is not possible in a single

chromophore system such as a dye. The long dephasing time observed is also typical of vibrational

Waiting Time (fs)

43


coherence as the vibrational wavepacket motion is a normal mode of the system that is decoupled from

other modes and thus dephasing is much slower than electronic coherence.

As a side note, an isolated 2D measurement of cresyl violet presented some interesting results

with implications for light-harvesting proteins. In a recent study by Panitchayangkoon et al. a 90° phase

shift between the diagonal peak oscillations and cross peak oscillations was presented as evidence of

coherence-to-population transfer.66

The justification for this observation is not fully clear and others have

noted difficulty in including in their models.67

In a particular 2D measurement of cresyl violet a similar

90° phase shift was observed between oscillations of corresponding peaks in the magnitude valued

rephasing spectra (see Figure 21). Although, this peculiar phase shift was only observed once, it perhaps

suggests that the nonsecular effects included in the Panitchayangkoon et al. model may not be necessary

and that their observation may simply be coincidence or an artifact of the apparatus. At the very least it

suggests that this signature is not conclusive or necessarily indicative of “direct evidence of quantum

transport” as they claim as no such possible mechanism exists in a solution of dye. It should be noted that

a Fourier transform of these oscillations provide a single peak at 18 THz in accordance with the other

cresyl violet data.

0 100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

Diagonal Peak (520, 520 THz)

Cross Peak (490, 520 THz)

Figure 21. An approximate 90° phase shift between the diagonal peak oscillations (black) and the cross

peak oscillations (red) of the magnitude signal of the rephasing spectra in one isolated scan. This

suggests that the rationale used by Panitchayangkoon et al. to suggest that this phase shift was indicative

of quantum transport is not necessarily valid as no such mechanism exists in a solution of cresyl violet.66

Waiting Time (fs)

44

Chapter 3

Phycoerythrin 545: Low Temperature

Spectroscopic Measurements

3.1 Introduction

Conducting spectroscopic studies at temperatures of 77 K and lower can reveal new information about the

electronic structure and bath properties of a protein. This is possible because performing these

measurements at low temperatures helps minimize homogeneous broadening, which often obscures subtle

spectral features. For example, conducting steady-state spectroscopic measurements at 77 K can help

resolve weak features, such as shoulders and overlapping peaks in the room temperature linear absorption

spectrum thereby providing a more accurate picture of the location of individual exciton peaks. Or in the

case of low temperature fluorescence, one may be able to better isolate vibronic peaks from a

corresponding electronic transition. However, there is an inherit limitation to how well spectral features

can be resolved by lowering the sample temperature; this is due to inhomogeneous broadening.

Consequently steady-state spectra of proteins at 77 K and those below 77 K often show minimal

spectroscopic differences.68

Although very useful, conducting low temperature spectroscopic measurements of proteins is

significantly challenging. Firstly, proteins are typically measured in an aqueous medium similar to that of

their native environment, this results in a notable challenge. When water freezes it does not form a

45

Chapter 3. Phycoerythrin 545: Low Temperature Spectroscopic Measurements

homogeneous glass but rather crystallizes. This is problematic for spectroscopic measurements due to the

increase in scattering and opacity. Another problem arises from the fact that water expands during the

phase transition from liquid to solid. This can put a nontrivial amount of strain on the sample if it is

tightly confined resulting in cracks and factures in the sample.

Although there have been previous spectroscopic measurements conducted at cryogenic

conditions on light-harvesting proteins23,68,69

and specifically on PE545 and PC645, the techniques used

have not been well documented. A method for conducting spectroscopic measurements on the light-

harvesting protein PE545 at 77 K in an aqueous medium is developed and detailed here. In the following

chapters this technique is used to conduct low temperature spectroscopic measurements on other proteins.

Only steady-state measurements were conducted at 77 K. However, the method developed here can be

extended to ultrafast measurements in future studies. Important problems to solve would include

compensating for the large amount of scatter caused by the frozen sample and to determine the effect of

additional glass from the cryostat chamber windows and the sample holder to the optical setup.

3.2 Cyrogenic Sample Preparation

For spectroscopic measurements conducted at 77 K a cold finger setup (Janis Research Supertran

System) with plastic windows and a path length of 0.5 mm (achieved using a Teflon spacer) was utilized.

In this setup, liquid N2 flows from a sealed Dewar, through a vacuum insulated hose into the cold finger

set up, which then cools the sample through conduction. In some instances a temperature controller

(Lakeshore 331 Temperature controller) equipped with a silicon diode was used to monitor the exact

temperature of the sample. Otherwise, if the sample had been cooled for a sufficient period of time the

temperature was assumed to be in the vicinity of 77 K. Final temperatures actually ranged from 77-79 K.

For spectroscopic measurements sensitive to scatter, it is necessary for the sample to form a homogenous

glass. If the sample crystallizes or has a significant amount of cracks in it, then getting high quality

absorption and fluorescence measurements becomes difficult due to the increase in opacity and scatter.

Absorption measurements are hindered by the decrease in overall transmittance as well as non-

homogeneity throughout the sample. Anisotropy measurements are affected because the cracks can cause

scattering which can cause the anisotropy values to be much greater than their true values. This is because

the scattered light that reaches the detector is highly polarized. Since the sample mainly consists of water

as it is cooled below 273 K it forms a crystal and expands. Employing a cryoprotectant such as glycerol

or ethylene glycol can help the sample form a glass, minimizing crystallization; however, getting the

46


sample not to crack can still be difficult. See Figure 22 for a picture depicting the sample fracturing due

to using sapphire windows. Using lower concentrations of the protein minimizes crack formation. The

large size of the protein disrupts lattice formation, thereby making the glass weaker and more susceptible

to cracks. As a result, using lower concentrations of the protein is less likely to disrupt lattice formation.

Sapphire or quartz windows which are typically used in cold finger setups because of their high thermal

conductivity put too much stress on these fragile samples because of their extreme rigidity. Plastic

windows on the other hand have lower thermal conductivity but are more flexible allowing for expansion

of the sample without cracking.

The PE545 sample was obtained from Krystyna E. Wilk who cultivated and extracted the protein

under the supervision of Paul M.G. Curmi at the School of Physics and Centre for Applied Medical

Research, St. Vincent’s Hospital, The University of New South Wales, Sydney, Australia. The sample

was used as sent with the exception of dilution. The isolated PE545 and the buffer were refrigerated in the

dark at 276 K until required for experimental use. The buffer solution consisted of 0.05 M potassium

phosphate and 0.15 M sodium chloride, had a pH of 6.8, and was 0.22 μm filtered. Before spectroscopic

measurements were conducted the PE545 sample was diluted in buffer (and a cryprotectant) to the

appropriate optical density (ODλ=545 < 0.4). It was observed that after dilution in buffer the sample

degraded fairly rapidly at room temperature, emission intensity decreased 60 percent after 24 hours.

Figure 22. (a) Cracked solution of PE545 in 90% ethylene glycol and buffer (v/v) at 77 K. (b) Close-up

of the fractured sample in (a) which results from using quartz or sapphire windows instead of plastic

windows.

(b) (a)

47


3.3 Structure

The PE545 investigated in this chapter is isolated from the cryptophyte algae species Rhodomonas CS24.

Like all phycobiliproteins, PE545 is a αβ heterodimer composed of two αβ monomers with a water pocket

separating the two monomers. The structural model of PE545 was determined via x-ray diffraction

analysis, with the crystal structure determined to 0.97 Ǻ resolution (see Figure 23).5 The dimensions of

the protein are estimated to be 75 Ǻ x 60 Ǻ x 45 Ǻ with an approximate mass of 60 kDa. Analysis of the

x-ray diffraction data has allowed the positions of the chromophores as well as their relative orientations

to be determined with accuracy. Each monomer contains three phycoerythrobilins (PEB) and one 15,16-

dihydrobiliverdin (DBV). The DBV chromophores are covalently bonded to the α19 cysteine residue of

each of the α subunits, while each of the β subunits contain three covalently linked PEB chromophores at

residue positions β82, β158, and β50/61. The PEB chromophore attached at residues β50/61 indicate that

the chromophores are doubly linked to the apoprotein via two cysteine bonds. The specific residue

number can be slightly different in any protein due to random amino acid mutations. Although the

orientation and spacing between these chromophores has been determined in the crystalline phase with

significant accuracy, this does not necessarily elucidate the protein conformation in solution, yet this

difference is usually expected to be minimal.

Figure 23 (from references 5,70

). (a) Structural model of phycoerthrin 545, determined to 0.97Ǻ resolution

using X-ray crystallography. (b) Position of chromophores without protein scaffolding.

Unlike chlorophyll which has a cyclic structure, the chromophores in phycobiliproteins consist of four

linearly attached pyrrole rings. Depending on the conjugation and substituents of the chromophores, each

(b) (a)

48


isolated bilin has a different absorption line shaft. For example the extra conjugation in the DBV

chromophores results in its absorption peak being red-shifted compared to the PEB chromophores. In

addition, the position of the cysteine bonds, the orientation of the chromophores in the protein

scaffolding, and the electronic interaction between chromophores can also significantly alter a

chromophore’s absorption energy. Therefore two chromophores which have identical absorption spectra

when isolated may have very different absorption spectra when embedded in a protein. The chemical

structures of the bilins in PE545 are displayed in Figure 24.

NHN

HN

O

HN

O

S

Cysteine

H

O

OH

O

HO

H

(PEB)

NHN

HN

O

HN

O

S

Cysteine

H

O

OH

O

HO

H

Cysteine (PEB’)

NHN

HN

O

HN

O

S

Cysteine

H

O

OH

O

HO (DBV)

Figure 24. Chemical structures of the three chromophores present in PE545: phycoerythrhobilin (PEB),

doubly liked phycoeythrhobilin (PEB’), and 15,16-dihydrobiliverdin (DBV).


3.4.1 Absorption

The room temperature (298 K) absorption spectrum shows a main peak centred at 545 nm and a red-

shifted shoulder at 567 nm. The absorption spectrum is fairly broad, spanning in excess of 100 nm. For

room temperature absorption spectra taken in buffer, see Figure 25 (a). At 77 K the constituent

49


absorption bands are distinct and the overall absorption spectrum is narrower. The optical density

increases as the sample is cooled to 77 K. There is no noticeable shift in the position of the peaks in the

77 K measurement; the main peak sill occurs at 545 nm, but now the red-shifted shoulder is better

resolved and appears as a distinct peak clearly visible at 567 nm. For an illustration of the 77 K

absorption spectrum in 90% solution of ethylene glycol and buffer (v/v) see Figure 25 (b).

3.4.2 Fluorescence

The room temperature emission spectrum peaks between 580 - 584 nm when excited at 545 nm; this

differs from literature which states that the emission peak occurs at 579 nm. There is no change in

lineshape of the emission spectra when excited at different wavelengths. Figure 25 (a) illustrates the

room temperature emission spectra; Figure 26 illustrates the emission spectra at various excitation

wavelengths. The emission bandwidth was set to 2.5 nm and the excitation bandwidth width was set to 5

nm.

Emission measurements were also taken in a 90% solution of ethylene glycol and buffer (v/v) at

room temperature. The Stokes shift was less for this solution than for the sample run in only buffer.

Ethylene glycol is a non-polar solvent, consequently it does not have dipoles which have to reorient

around the excited state of the chromophores. The buffer on the other hand is highly polarizable and thus

its dipoles do reorient around the excited chromophores. As a result, the solvent reorientation is much

greater in the buffer and is the cause of the larger Stokes shift. The emission spectrum peaks at 575 nm

for room temperature measurements in ethylene glycol. As the sample was cooled the emission spectra

narrowed, the Stokes shift decreased, and the peak intensity increased. At 77 K the emission spectrum

peaks at 570-573 nm and the intensity increases sixteen-fold (compared to the room temperature

intensity). For 77 K emission spectrum see Figure 25 (b). The additional decrease in the Stokes shift at

77 K is because the rate of solvation has decreased with increasing viscosity. The increase in

fluorescence quantum yield with decrease in temperature has been observed in other phcyobiliproteins.

50


400 450 500 550 600 650 700

Wavelength (nm)

Fluorescence (298 K)

Absorption (298 K)

Excitation (298 K)

400 450 500 550 600 650 700

Fluorescence (77 K)

Absorption (77 K)

Wavelength (nm)

Figure 25. (a) Normalized room temperature emission (blue), absorption (red), and excitation (green)

spectra of phycoerythrin 545 (PE545) in buffer. (b) Normalized 77K absorption (pink) and fluorescence

(blue) spectra 90% solution of ethylene glycol and buffer (v/v).

Figure 26. Fluorescence emission spectra at various excitation wavelengths at room temperature; no

excitation dependence is observed.

(b) (a)

560 580 600 620 640 660 680 700

Em

issio

n I

nte

nsity (

a.u

.)

Wavelength (nm)

400 nm

420 nm

440 nm

460 nm

480 nm

500 nm

520 nm

540 nm

51


3.4.3 Excitation

The line shape of the excitation spectrum closely resembles the absorption spectrum with the exception of

the red-shifted shoulder, which is more pronounced in the excitation spectrum. The spectrum peaks at

545 nm and displays a red shifted shoulder at 567 nm. The excitation bandwidth was set to 1.5 nm and

the emission bandwidth was set to 20 nm, with a scan rate of 1 nm/min. Emission was observed at 585

nm. Figure 25 (a) illustrates the room temperature excitation spectrum taken in buffer. Normalized cross

sections of the 2D excitation and emission spectrum illustrate that at all excitation wavelengths the

emission spectrum is nearly identical. The fact that the emission spectrum is independent of excitation

wavelength suggests that emission always occurs from the same chromophore.

Figure 27. 2D excitation and emission spectrum of PE545 in buffer at room temperature. No change is

observed based on excitation or emission energies.

3.4.4 Fluorescence Anisotropy

Figure 28 illustrates a room temperature fluorescence anisotropy scan, monitored at an emission of 615

nm. The scan was conducted with a 5 nm excitation bandwidth and a 20 nm emission bandwidth, the

scan rate was set to 5 nm/min. The G factor used in Equation 2.3 for the calculation of r was calculated at

each excitation wavelength and subsequently used for that individual calculation. Once the intensity of

52


one of the components of anisotropy (i.e. IVV, IVH, IHV, or IHH) reaches a minimum the anisotropy

calculations are stopped. At greater wavelengths the increase in intensity of the components is due to the

excitation wavelength approaching the monitored emission wavelength and the observed emission value

is no longer an indication of the sample but rather of the excitation light.

The increase in anisotropy from small wavelengths to large wavelengths is a trend that is

definitive of EET. Small values of r at lower wavelengths correspond to a large β value, which means the

angle between the absorbing transition dipole moment and the emitting transition dipole moment is large,

as expected. As wavelength increases, β decreases, which means the angle between the absorbing and

emitting transition dipole moment is becoming smaller. Eventually in the absence of extrinsic

depolarization factors, β would equal zero when the absorbing and emitting chromophores are the same.

This occurs at large wavelengths because emission occurs from the lowest energy state. The room

temperature anisotropy measurements (Figure 28) show a depolarization trend occurring at 525 nm,

suggesting a chromophore absorbs in this region. The fundamental anisotropy value at 590 nm was

measured to be 0.35 at room temperature; this corresponds to an angle of 16.8º between the absorption

and emission transition dipole moments. Since fluorescence typically takes place from the lowest singlet

state it is expected that monitoring at different emission wavelengths will not have a significant effect on

anisotropy values.

480 500 520 540 560 580 600

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

An

iso

tro

py,r

Wavelength (nm)

Figure 28. Polarization anisotropy measured at room temperature in 90% glycerol to buffer (v/v)

solution. Emission was monitored at 615 nm.

53

Chapter 4

Phycocyanin 645: Physiologically

Relevant 2D ES Measurements

(including pH Dependence)

4.1 Introduction

During photosynthesis a proton gradient is established between the lumen and the stroma. Under high

light conditions the pH difference between the lumen and stroma increases as the lumen acidifies. In

most photosynthetic organisms the light-harvesting machinery and reaction centers are located in the

thylakoid membrane. In cryptophyte algae, however, the light-harvesting proteins also reside in the

thylakoid lumen. As photosynthesis occurs, these light-harvesting proteins are bathed in an aqueous

environment that changes pH by about 2 units. It is well known that the change in thylakoid lumen pH

triggers a feedback mechanism allowing photosynthetic organisms the means to dissipate excess energy

as heat and prevents the formation of damaging reactive oxygen species. The effects of pH on the energy

transfer mechanism in light-harvesting protein phycocyanin 645 (PC645), isolated from the cryptophyte

algae Chroomonas CCMP270 is investigated by means of two-dimensional electronic spectroscopy and

steady-state spectroscopy.

The ability to regulate light harvesting processes is necessary for photosynthetic organisms to

work efficiently under varying light conditions as the intensity and spectral content of sunlight can

54

Chapter 4. Phycocyanin 645: Physiologically Relevant 2D ES Measurements

fluctuate significantly during the day. In conditions of excess sunlight, where the light-harvesting

proteins cannot utilize the excess energy for photochemistry, a process known as non-photochemical

quenching (NPQ) dissipates this excess energy as heat.71,72

NPQ refers to all fluorescence quenching that

is not directly related to charge separation and is composed of a de-excitation feedback mechanism

known as energy-dependent quenching (qE), a slow photoinhibitory quenching mechanism, and state-

transitions quenching.73

qE serves as the main component of NPQ and is the only mechanism that can

respond rapidly (in seconds to minutes) to changes in light intensity.74

This process is triggered by a

change in the thylakoid lumen pH; whereby under excess light conditions increased acidification of the

lumen result in the protonation of specific PSII proteins.71,73,75

Determining the exact mechanism by which fluorescence is quenched and excess energy is

dissipated safely as heat has been the subject of study for many years.74

It has been suggested that the

Psbs protein, a subunit of PSII, is indispensible for effective qE.73,75

Low thylakoid lumen pH results in

the protonation of two lumen-exposed glutamate residues on Psbs and induces zeaxanthin synthesis from

violaxanthin. It was proposed that zeaxanthin binds to PsbS resulting in de-excitation of the Chl

molecules and the dissipation of excess energy as heat.73,75

However, it was recently reported that qE-

type quenching has been observed in systems lacking the Psbs protein and that instead of being

indispensible the Psbs protein acts as a catalyst for qE formation.71

Regardless of the exact mechanism

through which qE occurs, in the absence of qE, excess sunlight can lead to an increased production of

damaging reactive oxygen species as byproducts of photosynthesis. This is due to the increased

probability that singlet chlorophyll will form triplet chlorophyll, which reacts with ground state oxygen to

form highly reactive oxygen species.73

qE prevents reactive oxygen species from forming by providing

an alternative nonradiative deactivation channel for singlet chlorophyll. In this manner, qE prevents

photooxidative oxygen from causing pigment bleaching and/or death.

The increased acidification of the thylakoid lumen which occurs in excess sunlight, directly

affects the local environment of the peripheral light-harvesting proteins in cryptophyte algae. We

investigate the effect of pH on the conformation as well as energy transfer mechanism of the light-

harvesting protein PC645. Two-dimensional electronic spectroscopy experiments as well as steady-state

spectroscopic measurements are conducted on PC645 ex vivo under predicted pH levels for normal and

excess light conditions.71

The presence of electronic and vibrational coherences is also commented on.

55


4.2 Sample Preparation

The PC645 sample was kept frozen at -20°C until required for spectroscopic measurements at which time

it was defrosted and diluted to the appropriate optical density (ODλ=645 ~ 0.2) in a suitable buffer. Three

100 mM potassium phosphate buffers were prepared with pH of 5.5±0.1, 6.5±0.1, and 7.5±0.1. The pH of

these buffers were based on the expected pH of the local environment of PC645 in vivo under normal

light conditions (approximately neutral) and excess light conditions (pH~5.5).71

After diluting the protein

in the appropriate buffer to the optical density required for spectroscopic measurements the pH of the

samples were 5.7±0.1, 6.5±0.1, and 7.4±0.1. The pH was determined using a calibrated microelectrode

from Metlertoledo. For 77 K measurements a mixture of 30% HEPES (4-(2-hydroxyethyl)-1-

piperazineethanesulfonic acid) at a pH of 7.5 and 70% glycerol (v/v) was used as the solvent. The PC645

sample was obtained from Krystyna E. Wilk who cultivated and extracted the protein under the

supervision of Paul M.G. Curmi at the School of Physics and Centre for Applied Medical Research, St.

Vincent’s Hospital, The University of New South Wales, Sydney, Australia. The sample was used as sent

with the exception of diluting.

4.3 Structure

The structure of PC645 determined by x-ray crystallography to 1.4 Å resolution is similar to the structure

of PE545 and is displayed in Figure 29.5 It is a αβ heterodimer containing 8 bilins, which consist of four

phycocyaninbilins (PCB), two mesobiliverdins (MBV), and two doubly liked 15,16-dihydrobiliverdin

(DBV); the α unit consists of one MBV on the α19 cystine residue, whilst the β unit consists of two PCBs

on residues β82 and β158 and one doubly linked DBV on residues β50/61. The specific residue number

in any individual protein can vary slightly due to random mutations.

56


Figure 29 (from reference 29

). Structural model of phycocyanin 645 from x-ray crystallography;

determined to 1.4 Å resolution.

Like the bilins in PE545, the bilins in PC645 consist of 4 linearly attached pyrrole rings, which connect to

the rest of the protein via a cysteine bond or in the case of the DBV through two cysteine bonds. The

chemical structures of PCB, MBV, and DBV chromophores are illustrated in Figure 30.

NHN

HN

O

HN

O

S

Cysteine

O

OH

O

HO (PCB)

NHN

HN

O

HN

O

S

Cysteine

O

OH

O

HO (MBV)

57


NHN

HN

O

HN

O

S

Cysteine

H

O

OH

O

HO

S

Cysteine (DBV)

Figure 30. Structures of phycocyaninbilin (PCB), mesobilverdin (MBV), and doubly liked 15,16-

dihydrobiliverdin (DBV) the three types of chromophores found in PC645.


4.4.1 Absorption

There is no significant difference between the room temperature absorption spectra at the three different

pH levels. Although the absorption spectrum at pH 5.7 is slightly more intense than the other two spectra,

we can attribute this minimal difference to concentration differences. The shape and relative peak

intensity in all three spectra are identical. The pH dependent absorption spectra at room temperature are

illustrated in Figure 31 (a). The room temperature (298 K) absorption spectra show a main peak centred

at 645 nm, a blue-shifted shoulder at 632 nm, and a second distinct but less intense peak at 586 nm. The

absorption spectrum is broad, spanning in excess of 150 nm. The absorption spectra were measured from

450-750 nm in 1 nm intervals, with 0.1 s averaging time and 600nm/min scanning rate. Each spectrum is

the average of two trials. The 77 K absorption spectrum was taken in a 70% solution of glycerol and

HEPES pH 7.5 buffer (v/v). At 77 K the constituent absorption bands are more distinct and the overall

absorption spectrum is narrower. The optical density increases as the sample is cooled to 77 K. There is

a noticeable shift in the position of the peaks in the 77 K measurements as well as a change in their

relative intensities. The 77 K absorption spectrum shows a main peak at 653 nm, the blue shifted

shoulder is now a distinct peak but located at the same position (586 nm), and the second peak is blue

shifted to 583 nm. While the room temperature spectrum shows peaks of relatively similar intensities, the

peaks in the 77 K spectra differ greatly. The main peak at 653 nm is significantly more intense than the

other two peaks, while the peak at 583 nm is the least intense. For an illustration of the 77 K absorption

spectrum in a 70% solution of glycerol and buffer (v/v) see Figure 31 (b). The absorption spectrum was

also taken in a 70% solution of glycerol and buffer (v/v) at room temperature (not shown) to determine

the effect of solvent. The line shape is nearly identical to the room temperature absorption spectrum

taken in buffer only, yet the shoulder at 632 nm and the peak at 586 nm are less intense.

58


500 600 700

pH 5.7

pH 6.5

pH 7.4

450 500 550 600 650 700

298 K

77 K

Figure 31. (a) Absorption spectra at three pH levels show identical features, minimal differences can be

accounted for by concentration differences. (b) Comparison of room temperature (red) and 77 K (blue)

absorption spectra.

4.4.2 Fluorescence

No noticeable difference between the lineshapes of the fluorescence spectra under the various pH

conditions was observed. Due to the incredible sensitivity of fluorescence spectroscopy on sample

concentration the three fluorescence spectra had slightly different intensities and they were therefore

normalized to their peak intensity before plotting. The room temperature emission spectra peak at 661

nm when excited at 640 nm; there is also a sub-band in the vicinity of 720 nm. Figure 32 (a) illustrates

the normalized room temperature emission spectra taken under all three pH conditions. The emission

bandwidth was set to 2.5 nm and the excitation bandwidth width was set to 5 nm. The excitation

wavelength was 630 nm and emission was monitored from 640-800 nm in 1 nm intervals, with 0.1 s

averaging time and 600nm/min scanning rate. Each spectrum is the average of three trials. The emission

spectra of the three samples are identical in lineshape; however, the sample at pH 6.5 is more stable than

the samples at pH 5.7 and 7.4 which decrease significantly in intensity on a short timescale; however this

change was not quantifiable.

Emission measurements were also taken in a 70% solution of glycerol and pH 7.5 HEPES buffer

(v/v) at 77 K. The main peak still occurs at 661 nm, however at 77 K this peak is narrower and the sub-

band at 620 nm is more distinct. The intensity of the peaks also increases as the sample is cooled. Since

glycerol is a polar solvent and since the buffer is highly polarizable, it was not expected that there would

be any change in the Stokes shift, since both solvents require their dipoles to reorient around the excited

chromophores. However, there is a change in the Stokes shift for the measurements done at room

Wavelength (nm) Wavelength (nm)

(a) (b)

59


temperature and those done at 77 K, even though the emission occurs at the same wavelength, the main

absorption peak is red shifted for measurements done at 77 K; therefore the Stokes shift is less for 77 K

measurements. The decrease in the Stokes shift at 77 K must be a result of the decrease in the rate of

solvation with increasing viscosity. For 77 K emission spectrum see Figure 32 (b).

640 680 720 760 800

pH 5.7

pH 6.5

pH 7.4

650 700 750 800

77 K

298 K

Figure 32. (a) Individually normalized fluorescence spectra at three pH levels show identical features. (b)

Comparison of room temperature (red) and 77 K (blue) absorption spectra. Excitation conditions are

different in figure (a) and (b).


Circular dichroism measurements were performed on PC645 in the ultraviolet and visible wavelength

regions. Near-ultraviolet measurements were conducted from 185 to 260 nm while the visible

measurements were conducted between 500 and 700 nm. The CD measurements were conducted in a

quartz sample cell with a path length of 1.0 mm, the spectral resolution was set to 0.5 nm, the scan rate

was 100 nm/min with a 2 s response time, and the sample was cooled to 20.0±0.2°C. Each measurement

performed at a specific pH was conducted 10 times and averaged. We observe no substantial change

between the CD spectra at the three pH levels in visible region which is outside the statistical error of the

measurement. This provides evidence which suggests that the electronic structure of the protein does not

change with changes in surrounding acidity levels. There are two distinct positive valued peaks in the

visible CD spectra. The most prominent, positive valued peak occurs in the vicinity of 580 nm while a

slightly less intense peak occurs at 608 nm. The stronger peak is roughly 20% more intense than the

weaker peak. The CD spectrum in the visible is positive-going from 500 nm, where the measurement

starts, until 627 nm at which point it becomes negative valued. There is one negative valued peak, which


(a) (b)

60


is most intense at 640 nm; by 655 nm the spectrum is positive valued again. The spectrum has an

apparent overall slop which increases in intensity with increasing wavelength. It is appropriate to note

that this slope may be an artifact of the measurement or a result of not subtracting the buffer signal and is

not necessarily indicative of the real response. There are noticeable changes in the three ultraviolet CD

spectra; the changes are in the relative intensity of features and not in the overall shape. The shape of the

all three spectra are typical of a protein composed of both α-helices and β-sheets. The changes in

intensity do not occur linearly with changes in pH; this suggests that the observed change is more likely

due to an unaccounted difference in concentration. CD measurements conducted on proteins in the

ultraviolet region tend to have very intense signals; thus additional dilutions are needed between CD

measurements in the visible and CD measurements in the ultraviolet region. To a first approximation it

can therefore be concluded that the ultraviolet spectra do not change with pH and that there is no change

to the secondary structure of the protein. Similar measurements, where corrections are made for the

changes in concentration are presented in reference 60

; in these spectra no overall slope is observed in

these spectra nor is there a difference in intensities. The lack of change in the visible and ultraviolet CD

spectra with increasing acidity levels suggests that no change occurred in the electronic or secondary

structure of the protein. This unique insensitivity to changes in physiologically relevant pH levels

suggests that these accessory light-harvesting proteins may not play a role in photoregulation. In fact this

insensitivity may be an evolutionary result which allows phycobiliproteins to function appropriately,

irrelevant of surrounding pH levels. This is in contrast to other proteins in this changing environment

which utilize this change to trigger feedback mechanisms. Extensive analysis of the CD spectra of PC645

under various conditions, including denaturing conditions by uric acid and heating have been conducted

by MacColl and coworkers.24,76,77

61


500 550 600 650 700

-10

-5

0

5

10

15 C

D In

ten

sity (

md

eg

) pH 5.7

pH 6.5

pH 7.4

200 220 240 260-15

-10

-5

0

5

10

15

20

CD

In

ten

sity (

md

eg

)

pH 5.7

pH 6.5

pH 7.4

Figure 33. (a) Visible region CD at three pH levels, differences are within statistical error. (b) Minimal

change is observed between the three ultraviolet CD measurements; these discrepancies can be accounted

for by concentration differences.

4.5 Two-Dimensional Electronic Spectroscopy

4.5.1 Results & Discussion

Numerous spectroscopic investigations of PC645 are present in literature5,9,23

, including ultrafast

measurements using two-dimensional electronic spectroscopy29

. This study adds an abundance of new

information to that already available in literature, some of the findings presented here are published in

reference 60

. This study presents the first study which focuses on understanding how a phycobiliprotein

adapts to physiologically relevant changes in the local environment. Understanding if these peripheral

light-harvesting proteins play a role in photoregulation provides vital insight into their functionality. In

addition, broadband pulses are used to excite the sample instead of the narrow pulses used in previous

studies; this allows more realistic dynamics to be elucidated. Furthermore the 2D apparatus used in these

experiments is far superior in terms of stability when compared to the apparatus used in previous studies,

thus allowing for more concrete conclusions to be drawn.

Ten 2D scans were conducted in total, three at each pH level, with one additional scan of the pH

5.7 sample using a power three-fold greater than the other measurements. Pulse energy was

approximately 5 nJ in the nine trials and approximately 15 nJ in the higher energy measurement. The

higher energy measurement was conducted to ensure that dynamics did not change with beam power.

The pulses had a spectral bandwidth of 61 THz and were compressed to 11 fs, with minimal evidence of

chirp or angular dispersion, see Figure 34. The ordering of trials was random as to ensure a proper


(b) (a)

62


statistical analysis could be conducted. In all trials the coherence time was scanned in intervals of 0.15 fs

from -45 to 45 fs, while the waiting time ranged from 0 to 400 fs in 5 fs steps. The measurements were

conducted at 298 K and the sample was flowed using a Cole-Parmer Masterflex peristaltic pump at a rate

of 0.06 mL/min. The portion of the sample not in the flow cell or tubing was submerged in an ice bath.

The spectra presented below are individually normalized and have 33 equally spaced contour intervals

(i.e. ~3%). In most spectra the noise level is under or on the order of 6%. Absorption spectra of each

sample were taken before and after all 2D measurements to ensure that no substantial degradation had

occurred. Additionally a 2D scan was performed on cresyl violet before and after the 10 scans to

determine the extent of laser drift, none was detected, these scans were also used in the phasing process.

Figure 34 (adapted from reference 60

). (a) Laser pulse (dashed black) overlayed with PC645 absorption

spectra. (b) Frequency-resolved optical gating (FROG) characterization of pulse.

Only the 2D spectra from one of the measurements on the pH 6.5 sample are presented below

since all spectra showed identical behaviour within the noise of the measurement. The higher energy

measurement also displayed identical behaviour albeit at higher signal intensities. Some spectra have

ripples throughout the entire spectrum indicating interference between the signal and unwanted scatter at

this waiting time, no filtering or smoothing process was conducted to eliminate this.

Broadband excitation of PC645 centered at 590 nm (508 THz) results in a peculiar anti-

symmetric 2D spectrum. In the real part of the total spectra a negative going above-diagonal cross peak is

clearly visible for the first 100 fs after photoexcitation. This cross peak is centered at approximately (499,

520 THz), after T=100 fs it is not nearly as distinct but remnants of it exist all the way till the end of the

measurement at T=400 fs. The cross peak oscillates with time and is most intense at T=20 fs and then

again at T= 60 fs at which times its amplitude is approximately 18% and 9% of the maximum signal

(b) (a)

63


amplitude respectively. The overall shape of the 2D spectrum can be characterized as rectangular with

the top left-hand quadrant being occupied by the cross peak, at later waiting times this quadrant is filled in

by the bleach signal. The peculiar, richly-featured shape of the 2D spectra suggests that complicated

dynamics are likely involved in the first few hundred femtoseconds after photoexcitation. Although any

number of these features could be investigated, we focus our study here to the very prominent cross peak

located at (499, 520 THz).

The absolute magnitude of the total, complex valued spectra display a rectangular feature, with a

sloping shoulder in the top left quadrant. Minimal change is observed in these spectra with changes in

waiting time. The imaginary part of the total signal displays a dispersive lineshape which is characteristic

of the imaginary component. The negative valued feature extends to lower excitation frequencies than the

positive feature at long waiting times; this may suggest that the actual phase value may have changed

with time. The real part of the rephasing spectra display characteristic lineshapes with nodal lines

oriented parallel to the diagonal and two negative valued lobes on either side of the positive signal

centered on the diagonal. The real part of the nonrephasing spectra are slightly different than typical

nonrephasing spectra. The nodal lines are oriented perpendicular to the diagonal as is common for

nonrephasing spectra. However, in addition to the negative lobes typically found surrounding the positive

anti-diagonally elongated feature, there is a second positive valued feature centered on the diagonal below

the negative lobe.

The dynamics of the cross peak of interest are investigated by taking a trace at the position

indicated by the dashed lines in Figures 36 and 37. The feature is integrated over a 1.2 THz range in the

excitation dimension and a 0.14 THz range in the emission dimension. Since the dynamics under all three

pH conditions are identical (see Figure 35), it is useful to look at the mean trace, in which case error bars

can be indicated for the 9 trials (higher-powered trial omitted). Complex oscillations are observed in both

the real and magnitude values of the total spectra as well as the rephasing and nonrephasing spectra. The

complex, but reproducible, beating pattern suggests that multiple pathways are contributing to the

observed signal. In reference 60

the beating pattern is fit to a sum of damped cosine functions for both the

real and magnitude valued traces of the total spectra. Eight such functions are needed to fit the mean

trace within one standard deviation error bars in both cases. The corresponding frequencies of the eight

oscillations in both fits are almost always within the standard deviation values of each other; thus

suggesting that both fits are reliable. Frequencies range from approximately 6 THz to over 50 THz, thus

suggesting a wide variety of contributing physical phenomena. Amplitudes between complementary

functions in the real and magnitude traces are not necessarily consistent as should be expected. However,

dephasing times which should be consistent between the two traces if the same physical phenomena are

64


giving rise to the same frequencies are often inconsistent with large error bars. The reason for this may be

the limited time frame used to monitor these dynamics. As a rule of thumb an accurate value of a

dephasing time can only be obtained if the dynamics are measured for a time three-fold greater than the

dephasing value. Since many of the dephasing times are on the order of hundreds of femtoseconds a

waiting time of 400 fs is insufficient to obtain an accurate measure.

100 200 300 400

Sig

na

l A

mplit

ud

e (

a.u

.)

pH 5.7

pH 6.5

pH 7.4

100 200 300 400

Sig

na

l A

mplit

ud

e (

a.u

.)

pH 5.7

pH 6.5

pH 7.4

Figure 35. (a) Normalized cross peak amplitude of the total magnitude spectra. (b) Normalized cross

peak amplitude of the total real spectra. Each trace in (a) and (b) are the average of three scans and are

displayed with one standard deviation error bars, the traces are vertically offset for clarity. The first 15 fs

of dynamics are not included due to nonresonant solvent response and pulse overlap effects.

The complex beating pattern observed in the rephasing and nonrephasing traces display multiple

frequencies with the two traces being distinctly different for the first 150 fs. According to references 51,60

the observation of oscillations in the rephasing trace along with the absence of oscillations in the

nonrephasing trace suggest electronic coherence at the frequency at which the oscillations are observed

and are absent, respectively. The difference in the two traces for the first 150 fs suggests that a more in-

depth analysis should be conducted to verify the presence or absence of electronic coherence in the

system. The next section discusses electronic and vibrational coherences in detail. A discussion of

previous results in literature is presented and an analysis of the beating pattern in PC645 is conducted.

Waiting Time (fs) Waiting Time (fs)

(b) (a)

65



left-hand corner). The spectra are the real part of the total signal and are individually normalized with 33

evenly spaced contours. At T=60 fs the coordinates of a major feature of interest an above diagonal cross

peak are indicated.

0

+1

66


Figure 37. The absolute magnitude of the total complex valued signal at indicated waiting times.

Coordinates from which traces are extracted indicated by cross of dashed lines.

0

+1

67



the imaginary part of the total signal displays a clearly dispersive characteristic shape.

0

-1

68


Figure 39. The real part of the rephasing signal.

0

+1

69


Figure 40. The real part of the nonrephasing signal.

0

+1

70


4.5.2 Distinguishing Electronic and Vibrational Coherences

Although the existence of excitons in photosynthetic light-harvesting proteins is common knowledge,

non-trivial quantum phenomena are not typically expected to be present in biological systems. Therefore,

the first results suggesting that the mechanism of energy transfer in some light-harvesting complexes

exploited quantum (electronic) coherence were surprising and regarded with skepticism. Since then a

plethora of experimental and theoretical research has supported this view and yet skepticism still

surrounds the field. Confirmation that electronic coherence does exist in a photosynthetic system at

physiologically relevant conditions, for a non-trivial period of time, could suggest that energy transfer

dynamics may be altered by the likes of a quantum walk or the ability to explore multiple pathways

simultaneously. However, any such conclusion would be largely speculative for biologically relevant

systems since these experiments are conducted using coherent, high-intensity light sources which are very

different than what these systems are exposed to in their native environment. Furthermore, all

experiments to date have been conducted on isolated proteins and do not indicate system dynamics in

vivo.

The first experiments suggesting quantum coherence in a photosynthetic protein were conducted

by Engel et al. on the Fenna-Matthews-Olson (FMO) bacteriochlorophyll complex using 2D ES.30

The

FMO complex is isolated from green sulphur bacteria; its function is to connect the peripheral light-

harvesting protein, the chlorosome, to the reaction center. The FMO complex used in these experiments

was isolated from Chlorobium tepidum; the readily available high-resolution atomic structure as well as

the absorption characteristics made it an appropriate system for investigation using 2D ES.

This first experiment, conducted at 77 K, provided evidence for electronic coherences that

persisted for more than 660 fs.30

The claim for electronic coherence was based on an analysis comparing

the amplitude of an exciton peak and the ratio of the diagonal to anti-diagonal widths of the peak. At the

time, the anticorrelation observed between the peak amplitude and width was thought to be indicative of

electronic coherence. These results suggested that the system could evolve in a nonstationary state–a

superposition of exciton states–for a substantial period of time; thus, it was suggested that the energy

transfer mechanism would be significantly altered by the presence of coherent energy transfer. It was

noted that these coherences were unlikely to survive as long at physiological temperatures, as dephasing

rates increase with increase in temperature. Yet it was hypothesized that the electronic coherence may

still be responsible for the remarkable quantum efficiency observed in light-harvesting proteins.

Future work was able to confirm that this observation was not isolated to the FMO complex and

that coherences persisted, albeit for a shorter time, at higher temperatures. In a two-colour 2D ES

71


experiment conducted by Lee et al., clear oscillations in the amplitude of the rephasing spectra were

observed in a measurement conducted on the reaction center of the purple bacteria Rhodobacter

sphaeroides.78

This experiment was performed at 77 K as well as 180 K; at 180 K the oscillations

survived for over 300 fs. Still well below ambient temperatures, these results provided additional

evidence that it may be possible for coherences to survive at room temperature. In this case the presence

of oscillations in the amplitude of the rephasing spectra was considered sufficent evidence of electronic

coherence.

Subsequently, evidence emerged that there were signatures of long-lived coherences at

physiologically relevant temperatures. The first experiments at room temperature were performed by

Collini et al. on light-harvesting proteins extracted from crytophyte algae.29

2D ES was used to

investigate phycoerythrin 545 isolated from Rhodomonas sp. CS24 and phycocyanin 645 isolated from

Chroomonas CCMP270 at ambient temperature. Both light-harvesting complexes had been investigated

extensively in the past and were known to contain strongly coupled chromophores, thus making them

likely candidates for the observation of long-lived coherences. In the case of PC645, evidence for

coherence came in the form of anticorrelated amplitude oscillations between the above and below

diagonal cross peaks of the rephasing spectra. In the measurements on PE545, anticorrelated oscillations

in the amplitude of the above and below diagonal cross peaks of the rephasing spectra as well as

anticorrelated oscillations in the diagonal amplitude of the nonrephasing spectra were observed. The

beating pattern was complicated and noisier than measurements conducted at cryogenic temperatures but

this was to be expected as thermal fluctuations and bath-induced dephasing would be stronger.

Nonetheless, the coherence lasted hundreds of femtoseconds providing evidence that the system could

evolve in a nonstationary state for a significant portion of time. This supported the idea that energy

transfer dynamics could be altered due to their coherent nature. Similar results were found in studies of

the FMO complex at near-room temperature conditions.79

2D ES measurements of the FMO complex

conducted by Panitchayagkoon et al. displayed oscillations in the cross peak of the rephasing spectra at

277 K which last for hundreds of femtoseconds.

The prevalence of coherences at room temperatures suggested to some that this might affect

biological function. At the same time it was shown that the method used to distinguish electronic

coherence from vibrational coherence was inadequate and that vibrational coherences could display

similar oscillations and anticorrelated features in 2D ES.56

This did not disprove the previous results,

instead it made it apparent that the signatures which had been believed to exclusively signify electronic

coherence could in fact be illustrations of vibrational modes of the chromophores. If what

experimentalists were observing in photosynthetic light-harvesting proteins was in fact vibrational

72


coherence, then this may have no effect on the energy transfer mechanism since these coherences would

be confined to single chromophores. It therefore became of utmost importance to be able to distinguish

between vibrational and electronic coherences.

Hayes et al. attempted to make the distinction between vibrational and electronic coherence by

making structural changes to the FMO complex (C. tepidum bchP) under investigation.59

Three structural

changes were made to the native FMO complex: (1) incorporation of 13

C, (2) deuteration, and (3) a

mutation. The 13

C incorporation was achieved with near-complete substitution, while the isotropic

abundance of deuterium was shown to be only 30% with random substitution. 2D ES measurements at 77

K were conducted on all variations of the complex and changes to the beating pattern were monitored.

No substantial changes in any of the variations were observed; frequencies and lifetimes of all four

complexes were identical within statistical error. Since deuteration, 13

C substitution, or a mutation would

likely change vibrational modes and since no change was observed in the beating pattern it was concluded

that these oscillations must be due to electronic coherence. Unfortunately, no experimental evidence was

provided to confirm that relevant vibrational modes had indeed changed.

Wong et al. conduct a similar investigation to confirm that oscillations observed in the 2D ES

spectra of PE545 were the result of electronic rather than vibrational coherences.70

The oscillations

observed in the rephasing and nonrephasing 2D ES spectra of PE545 were compared to similar

measurements of the structurally similar [His]6-tagged phycocyanin alpha subunit (HT-CpcA) with only

one chromophore. No beating with similar frequencies was observed in the HT-CpcA subunit at a cross

peak position similar to the one under investigation in the PE545 experiments. Since it is impossible to

observe electronic coherence in the HT-CpcA complex, as it only included one chromophore, it was

concluded that the oscillations seen in the PE545 measurements must have resulted from electronic

coherence.

Turner et al. took a more comprehensive approach to differentiate between electronic and

vibrational coherences in 2D ES.51,60

The method developed for distinguishing between the two types of

coherences utilizes the double-sided Feynman diagram methodology and attempts to differentiate a 3- and

4-level system. The 3-level system is modeled using a ground state, | ⟩, and two electronic excited

states, | ⟩ and | ⟩, assumed to be excitonic states of the system (e.g. model dimer). A coherent

superposition between these two electronic states, | ⟩⟨ |, is denoted electronic coherence. The 4-level

system is representative of a single chromophore (2-level system) with an additional vibrational level, ⟨ |,

in both the ground and excited states. In this case vibrational coherence is possible and either a ground-

state vibrational wave packet, | ⟩⟨ |, or an excited-state vibrational wave packet, | ⟩⟨ |, can be

73


created. In the 3-level system, the two excited states are unlikely to correspond to vibrational levels in a

single molecule as vibrational levels are usually identical in both the ground and excited states. Therefore

it is a valid assumption to associate the 3-level system with electronic coherence and the 4-level system

with vibrational coherence. Three distinct methods of distinguishing between vibrational and electronic

coherence in 2D ES are devised according to presence of the extra | ⟩ state.

The first distinguishing factor is based on a comparison between the rephasing and nonrephasing

contribution to the cross peaks. If the origin of the oscillations in the cross peak are purely electronic then

they will only occur in rephasing pathways. Contrarily, if the oscillations are due to vibrational

coherences then the beats will be observed in both rephasing and nonrephasing pathways. This tell-tale

sign requires high-quality data since the nonrephasing signal is often significantly weaker than the

rephasing signal. In light-harvesting complexes this may lead one to believe there are no oscillations in

the nonrephasing spectra when in fact there actually are oscillations. This would lead to the false

conclusion that the coherence is purely electronic. When using broadband pulses it is likely that multiple

transitions will be populated thereby increasing the likeliness that numerous vibrational modes and

electronic superpositions will contribute to the signal. It is therefore important that the quality of data is

sufficient that these modes can be distinguished in the beating pattern. Otherwise, one could mistakenly

assume that because there are oscillations in the nonrephasing contribution of a cross peak there is no

possibility that there can be electronic coherences. Distinguishing modes presents another difficult task.

Determining the frequency components in a complex beating pattern is usually carried out through a

Fourier analysis or a fitting procedure. Both cases are susceptible to errors which can easily lead one to

believe there is a nonexistent mode in the nonrephasing spectra while being present in the rephasing mode

if the signal-to-noise is not sufficiently high. It is therefore important to err on the side of caution when

investigating the absence of a mode before making any general conclusions. The second distinguishing

factor deals with the phase of the oscillations in the cross peaks. Oscillations in a cross peaks that arise

because of vibrational coherences will occur at both positive and negative frequencies, corresponding to a

phase-shift of the peak. Thus a Fourier transform of the waiting time for vibrational oscillations will

show peaks at both +υ and –υ. Lastly, in the 4-level system, if sufficiently broadband pulses are used,

additional cross peaks will be observed at an emission energy below the electronic transition frequencies.

In this section we focus on distinguishing between electronic and vibrational coherences using the

first method described above, which relies on investigating the rephasing and nonrephasing contributions

independently. Thus before summing the rephasing and nonrephasing contributions to obtain the total

spectra, they were analyzed separately. In reference 60

the authors also differentiate between electronic

74


and vibrational coherence using the second method which relies on examining the phase of the Fourier

transform of the oscillations.

Both the rephasing and nonrephasing components show clear signs of oscillations. Albeit similar

in general, these oscillations are distinctly different (see Figures 41 and 42). The nonrephasing traces are

much noisier than the rephasing traces with the signal-to-noise level being substantially higher in the

former case. This presents a significant challenge when attempting to decipher the beating pattern using a

Fourier analysis or fitting procedure. The amplitude of oscillations is also much greater in the rephasing

trace. This case illustrates one of the difficulties in using the absence of oscillations in the nonrephasing

spectra as proof of the presence of electronic coherence. Although noise in typical nonrephasing spectra

is substantial, the magnitude value is typically less noisy than the real part as shown below (Figures 41.(b)

and 42. (b)).

100 200 300 400

Rephasing

Sig

na

l A

mp

litu

de

(a

.u.)

100 200 300 400

Nonrephasing

Sig

na

l A

mp

litu

de

(a

.u.)

Figure 41. (a) Normalized cross peak amplitude of the rephasing magnitude spectra. (b) Normalized

cross peak amplitude of the nonrephasing magnitude spectra. Each trace in (a) and (b) are the average of


included due to nonresonant solvent response and pulse overlap effects.


(b) (a)

75


100 200 300 400

Sig

nal A

mplit

ud

e (

a.u

.)

Rephasing

100 200 300 400

Sig

nal A

mplit

ud

e (

a.u

.)

Nonrephasing

Figure 42. (a) Normalized cross peak amplitude of the real valued rephasing spectra. (b) Normalized

cross peak amplitude of the real valued nonrephasing spectra. Each trace in (a) and (b) are the average of


included due to nonresonant solvent response and pulse overlap effects.

The difference in the beating pattern between the real valued rephasing and nonrephasing traces is

most pronounced at early times, specifically the first 150 fs. Determining the exact frequencies of the

contributing components requires a Fourier analysis or a fit; here we chose to use a Fourier analysis. To

determine if there is a frequency component absent in the nonrephasing spectra when compared to those

of the rephasing spectra, Fourier analyses of the rephasing and nonrephasing traces are conducted

separately. The Fourier analyses were conducted in the following manner. The first 10 fs of each trace

was omitted due to pulse overlap effects and then the nine scans were individually normalized from 0 to 1

based on the minimum and maximum values, respectively. To ensure that the traces overlapped as well

as possible, individual traces were shifted vertically as necessary to acquire the best global mean trace.

The mean trace was fit to a damped exponential (or a linear function) using a least-squares method. The

damped exponential (or linear function) was removed from the trace and the Fourier transform was

conducted on this offset trace. Failure to remove a damped exponential can introduce substantial

artifacts into the resulting Fourier transform. The Fourier transforms were conducted using the Fast

Fourier Transform (FFT) function in Matlab and the data was zero-padded to minimize the frequency step

size of the resultant Fourier transform. Error bars are not included in the Fourier transform due to zero-

padding although they would be useful in determining the signal-to-noise level. Instead the signal-to-

noise level is approximated by comparing the peaks in the Fourier transform with the frequencies found in

the fitting procedure conducted by Turner et al.60

The frequencies of the modes found by Fourier analysis

should match those found by fitting the data to a sum of dampened sinusoidal functions; if modes appear

in the Fourier transform that do not appear in the fit then they are likely noise. The fits conducted in


(b) (a)

76


reference 60

were performed on the total spectra exclusively, individual fits of the rephasing and

nonrephasing components were not conducted. However all frequency components observed in the total

spectra should also be present in the rephasing spectra; while components can be absent in the

nonrephasing spectra while still present in the total spectra.

The Fourier transform of the absolute valued rephasing trace shows six distinct peaks centered at

2.5 THz, 5.9 THz, 13.9 THz, 21.2 THz, 26.0 THz, and 34 THz (see Figure 43). At frequencies higher

than 30 THz the signal-to-noise level makes it difficult to distinguish peaks from noise. In addition, the

bandwidth of the laser pulse limits the maximum determinable frequency to approximately 60 THz. The

lowest frequency mode does not match a frequency obtained by fitting; however the next four frequencies

are in excellent agreement with the frequency of modes obtained through fitting the trace. The two

highest frequency modes identified in the fit are not discernible in the Fourier transform nor is the 9.6

THz mode. However, this 9.6 THz mode can most likely be identified as the low-frequency shoulder on

the 13.9 THz peak. The Fourier transform of the real part of the rephasing trace shows five distinct peaks

at 5.8 THz, 9.6 THz, 15.4 THz, 20.3 THz, and 26.4 THz (see Figure 44). All five peaks are in excellent

agreement with those found by fitting the total trace. The three highest frequency modes are not

identifiable in the Fourier transform.

The fits of the absolute valued and real valued nonrephasing traces conducted here are of poorer

quality (lower R-squared value) than their corresponding rephasing traces. Therefore the resulting

Fourier transforms likely have lower signal-to-noise levels than those of the rephasing traces. The Fourier

transform of the absolute valued nonrephasing trace shows six peaks of interest centered at 1.6 THz, 4.0

THz, 7.5 THz, 13.1 THz, 21.5 THz, and 25.9 THz and one shoulder at 11.3 THz (see Figure 45). Again

at higher frequencies the signal-to-noise level makes it difficult to distinguish peaks from noise. The two

lowest frequency peaks are not identified in the fits conducted by Turner et al.60

The peaks at 7.5 THz,

11.3 THz, 16.4 THz, and 25.9 THz are in excellent agreement with the frequencies found by fitting the

absolute valued total trace. The peak at 21.5 THz is of particular interest. Although the fit conducted in

reference 60

of the absolute valued total trace indicates a 21.1±0.3 THz mode, the authors concluded that

only the rephasing pathways contributed to this mode. This conclusion was attributed to the fact that no

peak in the vicinity of 21 THz was observed in their Fourier transform of the real part of the nonrephasing

trace. The Fourier transforms conducted in reference 60

were performed without subtracting an

exponential or linear fit. However, due to the difficulty in determining the noise level in Fourier

transforms it is not clear whether the 21.5 THz mode observed in the nonrephasing Fourier transform

presented here is real. Support for this is provided by the peak at 16.4 THz which does not appear in the

fit of the absolute valued total trace conducted by Turner et al.60

therefore suggesting that it is noise. This

77


peak is of nearly the same spectral amplitude as the 21.5 THz mode and thus suggests that the 21.5 THz

mode may also be due to noise. The mode in the vicinity of 33 THz is also more predominant in the

rephasing Fourier transforms than in the nonrephasing Fourier transforms and therefore may also be a

candidate for electronic coherence, again though this may be just a result of the signal-to-noise level.

These examples outline the difficulties which arise when attempting to prove the presence of electronic

coherence by looking for the absence of a mode in the nonrephasing spectra when the signal-to-noise

level is low.

100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

Mean Rephasing

Exponential Decay Fit

0 10 20 30 40 50

26.0

21.2

13.95.9

Spe

ctr

al A

mplit

ud

e (

a.u

.)

Rephasing2.4

34.0

Figure 43. (a) Mean trace of nine normalized absolute valued rephasing spectra for the cross peak;





THz, 26.0 THz, and 34 THz. (d) Parameters of exponential damped sinusoidal fit used in reference 60

to

fit the absolute valued total trace.

0 100 200 300 400-1.0

-0.5

0.0

0.5

Equation y = A1*exp(-x/t1) + y0

Adj. R-Square 0.90544

Value Standard Error

Mean y0 0.07007 0.03609

Mean A1 1.12635 0.04191

Mean t1 115.9482 15.67971

Resid

ua

l o

f M

ea

n (

a.u

.)


Frequency (THz)

(b) (a)

(d) (c)

78


100 200 300 400

Sig

na

l A

mplit

ud

e (

a.u

.)

Mean Rephasing


0 10 20 30 40 50

9.6

Sp

ectr

al A

mp

litu

de

(a

.u.)

Rephasing

5.8

20.315.4

26.4

Figure 44. (a) Mean trace of nine normalized the real part of the rephasing spectra for the cross peak;






to fit the real

part of the total trace.

0 100 200 300 400

-0.2

0.0

0.2




Mean y0 0.8942 0.01383

Mean A1 -1.06769 0.06031

Mean t1 59.11872 5.29227

Resid

ua

l o

f M

ea

n (

a.u

.)


Frequency (THz)

(b) (a)

(d) (c)

79


100 200 300 400

Sig

na

l A

mplit

ud

e (

a.u

.) Mean Nonrephasing

Linear Fit

0 10 20 30 40 50

25.9

21.516.4

13.1

11.3

7.5

4.0

Spe

ctr

al A

mp

litud

e (

a.u

.)

Nonrephasing

1.6

Figure 45. (a) Mean trace of nine normalized absolute valued nonrephasing spectra for the cross peak;

displayed with one standard deviation error bars. Linear fit (red) of the mean trace using least squares

analysis. (b) Plot of residuals along with details of the fit (inset). (c) Fourier transform of the mean trace

after the linear fit was removed; the maximum frequency displayed is 50 THz. Peaks of interest are

indicated by their frequency values and occur at 1.6 THz, 4.0 THz, 7.5 THz, 11.3 THz, 13.1 THz, 21.5


to fit the

absolute valued total trace.

0 100 200 300 400

-0.2

0.0

0.2

Equation y = a + b*x



Mean Intercept 0.85161 0.00907

Mean Slope -0.00209 3.01195E-5

Re

sid

ua

l o

f M

ea

n (

a.u

.)


Frequency (THz)

(b) (a)

(d) (c)

80


100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

Mean Nonrephasing


0 10 20 30 40 50

26.3

19.3

15.4

9.7

Spe

ctr

al A

mplit

ud

e (

a.u

.)

Nonrephasing

5.7

Figure 46. (a) Mean trace of nine normalized the real part of the nonrephasing spectra for the cross peak;






to fit the real

part of the total trace.

The Fourier transform of the real part of the nonrephasing trace shows five peaks of interest

centered at 5.7 THz, 9.7 THz, 15.4 THz, 19.3 THz, and 26.3 THz (see Figure 46). As previously

discussed at larger frequencies it is impossible to distinguish real peaks from noise. The four modes at

5.7 THz, 9.7 THz, 15.4 THz, and 26.3 THz are in excellent agreement with the frequencies obtained by

fitting the total traces in reference 60

. In that study the Fourier transform of the real part of the

0 100 200 300 400-0.6

-0.3

0.0

0.3




Mean y0 0.78611 0.13747

Mean A1 -0.10589 0.09431

Mean t1 -209.21969 82.35032

Resid

ua

l o

f M

ea

n (

a.u

.)


Frequency (THz)

(b) (a)

(d) (c)

81


nonrephasing trace indicated no peak in the vicinity of 21 THz. Here too we note that there is no clear

peak above the signal-to-noise level in the vicinity of 21 THz. The 19.3 THz mode appears at the level of

noise. One reason for these slightly unconvincing results may be the fact that the first 100 fs of the

nonrephasing traces are particularly noisy, especially in the real part. We conclude that the quality of this

data makes it impossible to determine whether or not the 21 THz mode is absent in the nonrephasing

trace.

4.5.3 Assignment of Coherences

Whether the oscillations identified in the traces of the rephasing and nonrephasing components result

from vibrational coherence or electronic coherence assigning their origin can be difficult. Those modes

which were clearly present in the Fourier transforms of both the rephasing trace as well as the

nonrephasing trace can be identified as vibrational coherences arising from nuclear wavepacket motion.

However determining the specific vibrational mode that gives rise to this frequency is indeterminable

with the limited information provided by two-dimensional electronic spectroscopy. To identify their

origin further studies on the vibrational structure of the system would be needed. This could be achieved

through detailed simulations of the entire protein in the condensed phase to determine the vibrational

eigenstates. If electronic coherences are present in this system then identifying which eigenstates are in

superposition requires a detailed knowledge of the electronic Hamiltonian.

If the 21 THz mode is indeed absent in the nonrephasing traces and if this method for

differentiating between electronic and vibrational coherence is valid, then determining its origin is the

next logical question to address. With the understanding that the amplitude of a cross peak oscillates with

a phase factor, which takes the form of , where Eα and Eβ correspond to the

eigenenergies of the two states, α and β, in superposition, then using knowledge of the frequency one can

determine the energy difference between the states in superposition. If a detailed understanding of the

electronic structure is also available, such that the electronic eigenenergies of the system are known, then

this energy difference can be used to determine which eigenstates are in superposition. This knowledge

along with the position of the cross peak may help to identify its origin. This illustrates that even once

experimental confirmation of the existence of electronic coherence is achieved, determining which states

are in superposition is a difficult task because of the detailed system knowledge required.

To determine the electronic eigenenergies of a protein the site energies of chromophores must be

known as well as the coupling between chromophores. As discussed previously the coupling between

82


chromophores can be determined via quantum chemical calculations of the transition densities once a

detailed crystal structure is available. More complicated is determining the site energies for which there

is no direct method. The most common approach is to use theoretical calculations to get a rough idea of

the energy landscape (i.e. ordering of site energies) and then refining this picture by varying the site

energies while simulating different types of spectra (e.g. absorption, fluorescence, circular dichroism,

etc.) until simulations and experiments converge. Simulating steady-state spectra alone is insufficient to

determine accurate site energies. As shown in reference 10

simulating steady-state spectra will provide a

number of working models with widely different site energies; additional simulations of ultrafast

spectroscopies, such as transient absorption are needed to identify the best model. Even when time-

dependent spectroscopies are simulated there are limitations to this type of analysis. Determining the

appropriate form of the spectral density for a protein can be a difficult challenge. Obtaining the values for

parameters such as the reorganization energy, bath timescale, discrete high-frequency modes and Hyung-

Rhys factors are difficult to obtain directly from experiment and are often changed at will to obtain better

simulations.

An analysis similar to the one carried out by Novoderezhkin et al.10

on PE545 is in the process of

being carried out for PC645. The current electronic Hamiltonian (Table 1) is based on a slightly less

refined process but provides a starting point for identifying the origin of electronic coherence in PC645.

Site energies were computed using quantum chemical calculations and then shifted to lower energies to

agree with the experimental absorption spectrum (293 K).23

Separation distance between chromophores

was based on structural data and was used to compute the electronic couplings through electronic

structure calculations. The electronic Hamiltonian (site energies and couplings) presented here is similar

to the one used by Huo and Coker with slight modifications to the site energies based on further

refinement.22

In this refined Hamiltonian, complimentary chromophores (i.e. those with the same cystine

bonds but on different subunits) have identical or nearly identical site energies. Although this is a valid

approximation since chromophores bonded to the same residues experience very similar environments,

these environments are not identical and therefore future studies are likely to prove them to have slightly

different values. The most important feature of the system Hamiltonian is the strong 319 cm-1

coupling

between the central DBV dimer states, which results in delocalized excited states. Other chromophores

with non-negligible coupling include the MBV and DBV chromophores which are coupled through an

electronic interaction of approximately 40 cm-1

and the PCB β158 chromophores which are coupled to the

MBV chromophores through an electronic interaction of approximately 85 cm-1

. Most of the other

chromophores are negligibly coupled and can be assumed to be fairly localized for most purposes. Since

83


in this study excitation occurred on the blue side of the absorption spectrum the majority of population

resides in the MBV and DBV states.

electronic coupling (cm-1

)

DBVC

β50/61C

DBVD

β50/61D

MBVA

α19A

MBVB

α19B

PCBC

β158C

PCBD

β158D

PCBC

β82C

PCBD

β82D

DBVC

β50/61C 17316 319 -10 -44 20 25 -47 -20

DBVD

β50/61D 15.2 17316 44 8 30 29 22 48

MBVA

α19A 31.4 23.5 16534 4 -87 -3 -16 49

MBVB

α19B 23.2 31.1 46.3 16615 3 86 55 -15

PCBC

β158C 24.6 21.2 19.3 46.4 15889 8 11 10

PCBD

β158D 20.6 24 46.3 19.2 41.9 15889 29 -11

PCBC

β82C 22.5 31.6 33.9 24.9 35.4 36.9 15405 48

PCBD

β82D 31.7 22.2 25.3 33.8 37.2 35 34.8 15405

center-to-center separation (Å)

Table 1. Electronic coupling between chromophores in wavenumbers (above diagonal, blue), center-to-

center separation of chromophores in angstroms (below diagonal, red), and site energies of chromophores

(diagonal, green).

Solving the secular equations which describe Frenkel excitons

∑

where Vij is the electronic coupling between chromophores i and j and Eα is the transition energy of

eigenstates α gives the eigenvalues of the system. Knowledge of the exciton energies is of absolute

importance as these values determine the optical-electronic properties of the entire system. The exciton

energies (along with site energies) are presented in Table 2 in various units.

84


Chromophore

Site

Energy

(cm-1

)

Site

Energy

(eV)

Site

Energy

(THz)

Site

Energy

(nm)

Exciton

Energy

(cm-1

)

Exciton

Energy

(eV)

Exciton

Energy

(THz)

Exciton

Energy

(nm)

DBVC β50/61C 17316.0 2.1 519.1 577.6 17638.0 2.2 528.7 567.0

DBVD 50/61D 17316.0 2.1 519.1 577.6 17007.0 2.1 509.8 588.1

MBVA α19A 16534.0 2.0 495.6 604.9 16624.0 2.1 498.3 601.6

MBVB α19B 16615.0 2.1 498.0 601.9 16544.0 2.1 495.9 604.5

PCBC β158C 15889.0 2.0 476.3 629.4 15884.0 2.0 476.1 629.6

PCBD β158D 15889.0 2.0 476.3 629.4 15872.0 2.0 475.8 630.1

PCBC β82C 15405.0 1.9 461.8 649.2 15448.0 1.9 463.1 647.4

PCBD β82D 15405.0 1.9 461.8 649.2 15352.0 1.9 460.2 651.5

Table 2. Site energies and exciton energies in various units.

In Figure 47 the estimated position of the exciton energies are plotted on the room temperature

absorption spectrum which is superimposed onto the excitation and emission axes of a representative 2D

plot of PC645 (note the change in axis orientation). While the exciton energies of the PCB and MBV

chromophores correspond closely to their respective site energies the DBV chromophores are strongly

coupled creating two distinct DBV states, DBV+ and DBV–. The black circle indicates the position of the

cross-peak of the DBV+–MBV exciton states while the green and yellow circles refer to the corresponding

diagonal peaks. The position of the cross-peak suggests that the oscillations are due to the superposition

between the DBV+–MBV exciton states as indicated by the black circle in Figure 48. However, due to

the strong bleach signal on the diagonal, the position of the cross-peak may be shifted, thereby making it

inappropriate to assign the origin of the coherence based on the position of the cross peak alone. Since

the frequency at which the electronic coherence occurs corresponds more closely to the estimated energy

gap between the DBV–DBV pair than the DBV+–MBV (see Table 3), this procedure suggests a

superposition between the strongly coupled DBV dimer states. If the 33 THz mode is indeed absent from

the nonrephasing traces then it may arise from a superposition of the DBV+–MBV states.

Exciton Site Energy (cm-1

) Coupling (cm-1

) Exciton Energy

(THz) Difference (THz)

DBV+ 17316 ~320

528.71 19

DBV- 17316 509.79

DBV+ 17316 ~40

528.71 30

MBVA α19A 16534 498.31

Table 3. Frequency difference between likely candidates for eigenstates involved in electronic coherence.

85


Figure 47. Representative two-dimensional electronic spectrum at population time T=55 fs at 295 K (note

the change in axes). The spectrum is the real part of the total signal, plotted with 33 evenly-spaced

contours. The estimated exciton energies of the chromophores are plotted on the 295 K absorption

spectrum which is superimposed onto the excitation and emission axes. While the exciton energies of the

PCB and MBV chromophores correspond closely to the respective site energies, the DBV chromophores

are strongly coupled creating two distinct DBV states, DBV+ and DBV–. The black circle indicates the

position of the cross-peak of the DBV+–MBV exciton states while the green and yellow circles refer to

the corresponding diagonal peaks.

Using the frequency difference is likely to be the more reliable method in determining what states are in

superposition as the cross peak may not even originate because of electronic coherence. Therefore if the

21 THz mode can be attributed to electronic coherence then it is likely a superposition between the two

strongly coupled dihydrobiliverdin (DBV) eigenstates. In this case the data would represent significant

evidence for the confirmation of electronic coherence in biological systems at physiologically relevant

conditions. The dephasing time for this coherence is approximated to be on the order of 100 to 200 fs;

corresponding to a shorter dephasing time than previous experimental and theoretical studies had

predicted.22,29

Consequently it would mark a huge stride forward in understanding the energy transfer

mechanism in this light-harvesting protein, yet it would not necessarily imply that electronic coherence is

86


relevant to biological function nor that it is ubiquitous. Two more questions need to be answered before

substantiated claims can be made that electronic coherence plays a biological function in photosynthesis.

Firstly it must be shown that these results persist in vivo when the protein is in its native environment.

Conducting experiments on intact organisms presents an extraordinary challenge due to unwanted scatter

and the difficulty in isolating the desired signal. Secondly, in the experiments described above a coherent

laser source is used; this is very different than the solar radiation the proteins are exposed to in their

native environment. Therefore to extrapolate that these coherences would exist when irradiated with

sunlight requires further experiments using a thermal light source or theoretical backing.

87

Chapter 5

Phycocyanin 612 and Phycoerythrin 555:

Open Structures

5.1 Introduction

Unlike PC645 and PE545 little is known about the photophysics of the phycobiliproteins phycocyanin

612 (PC612) and phycoerythrin 555 (PE555), thus providing novel systems for spectroscopic

investigation. PC612 is isolated from the cryptophyte algae Hemiselmis virescens M1635 while PE555 is

isolated from Hemiselmis andersenii CCMP644. Previous steady-state and ultrafast measurements on

PC612 were conducted in the 1980s and 1990s but since then, new developments have been lacking.80–82

PE555 on the other hand, has negligible mention in literature and therefore presents a completely new

system for investigation. The insight provided by two-dimensional electronic spectroscopy suggests that

these systems be revisited.

In contrast to the closed structures of PC645 and PE545 where the chromophores in the central

dimer pair are closely spaced, PC612 and PE555 are open structures and thus the separation between the

dimer chromophores is large. Although the chromophores in phycobiliproteins are always bonded to the

same residue, the different secondary structures of these proteins may result in significant changes in the

photophysics and electronic-optical properties of these systems. Thus comparing spectroscopic results of

closed and open structured proteins will help determine the effect of the apoprotein and secondary

structure on the photophysics. PC612 and PE555 are therefore investigated using steady-state and

ultrafast spectroscopies, the results are compared to those of PC645 and PE545.

88

Chapter 5. Phycocyanin 612 and Phycoerythrin 555: Open Structures

5.2 Sample Preparation

The PC612 and PE555 samples, as with all other protein samples used in this thesis, were obtained from

Krystyna E. Wilk working under the supervision of Paul M.G. Curmi at the School of Physics and Centre

for Applied Medical Research, St. Vincent’s Hospital, The University of New South Wales, Sydney,

Australia. The proteins were cultivated, isolated, and harvested using methods described in reference 69

.

The PC612 sample was stored as sent at -75°C in an ultra-cold freezer. The PE555 sample was initially

stored in a residential freezer at -20°C and then moved to the ultra-cold freezer and stored at -75°C. After

defrosting a sample for a measurement, the remaining unused sample would be quick frozen by

submerging the protein-containing vial into liquid nitrogen and then transferred as quickly as possible to

its storage location. The protein sample was diluted to the appropriate optical density (ODλ max < 0.4) in

0.05 M potassium phosphate buffer, 0.25 μm filtered, pH 6.8.

5.3 Structure

The crystal structures of PC612 and PE555 were not published at the time of publication of this thesis.

However X-ray crystallography data has been taken and reveals structures similar to those of other

phycobiliproteins; the x-ray crystal structures were checked via gene sequencing. The structure of PC612

was determined up to 1.7 Å resolution and is illustrated in Figure 48. PC612 was determined to be a

homodimer containing 8 bilins, six PCB chromophores and two DBV chromophores. One doubly linked

DBV chromophore is located on each β subunit at cysteine residues β50, β61. Each β subunit also

contains two PCB chromophores at cysteine residues β82 and β158. The α subunit only contains one

PCB chromophore which is located at cysteine residue α18.

The PE555 structure was determined to 1.8 Å resolution. PE555 has two DBV chromophores

and six PEB chromophores (see Figure 49). The DBV locations are the same as those in PC612 and the

PEB chromophores replace the PCB chromophores in identical locations. In contrast to closed structures,

PE555 and PC612 have a large water pocket in between the two monomer units. In closed structures, like

PE545 and PC645, the central dimer would occupy this space. Again, the specific cysteine residue to

which a chromophore is bonded may vary from protein to protein due to random mutations.

89


Figure 48. (a) Structural model of PC612, determined to 1.7 Ǻ resolution using X-ray crystallography.

(b) Position of chromophores without protein scaffolding.

Figure 49. (a) Structural model of PE555, determined to 1.7 Ǻ resolution using X-ray crystallography.

(b) Position of chromophores without protein scaffolding.

90



5.4.1 Absorption

PC612 is similar to PC645 in that its absorption spectrum is broad with multiple distinct peaks and

absorbs in the same spectral region, yet it does not contain MBV chromophores. At room temperature the

absorption spectrum of PC612 spans in excess of 100 nm and has two distinct peaks . The less intense

peak is centered at 577 nm while the more intense peak (8% more intense) is centered at 613 nm. Similar

to the absorption spectrum of PC645 there is a slight shoulder at lower frequencies that becomes more

pronounced at lower temperatures. The absorption spectrum was measured for the range of 500-700 nm

in 1 nm intervals, with 0.1 s averaging time and a 600nm/min scan rate. The 77 K absorption spectrum

was measured in a solution of 50% glycerol and buffer (v/v). At 77 K the overall absorption spectrum is

narrower and the individual peaks along with the low frequency shoulder are more distinct. Both peaks

are shifted slightly to the red, the higher energy peak occurs at 579.5 nm and the lower energy peak is

centered at 621 nm. In the 77 K spectrum the ratio between the two peaks also becomes greater with the

more intense peak becoming 20% more intense than the weaker peak. The scan conditions for the 77 K

absorption spectrum were as follows, the scan range was 400-750 nm in intervals of 0.167 nm, with 0.1 s

averaging time and a 100nm/min scan rate. For the room temperature and 77 K absorption spectra of

PC612 see Figure 50 (a). An absorption measurement was also conducted at room temperature of PC612

in a 50:50 (v/v) mixture of glycerol and buffer to determine the effect of the cryoprotectant (not shown).

Minimal differences were observed between this spectrum and the room temperature spectrum taken

exclusively in buffer; however the absorption spectrum of the protein in the glycerol mixture displays a

slightly more intense peak at 577 nm and a slightly broader spectrum.

Based on the relative absorption energies of the individual bilins – PCB and DBV chromophores

– and based on the assignment of chromophores absorption energies in PC645 we expect that the higher

energy peak is dominated by DBV chromophores while the lower energy peak is dominated by PCB

chromophores.83

The 298 K and 77 K absorption spectra are fitted to two Gaussians using a least-squares

method to obtain a rough estimate of the absorption location of the DBV and PCB chromophores. For

fits of the absorption spectra see Figure 50 (c) and (d); parameters of these fits can be found in Table 4.

However, like in PC645 the absorption energies of individual chromophores are likely to be significantly

shifted from these positions. Based on this analysis we predict that the DBV chromophores dominate the

higher energy peak in the 579 nm vicinity and the PCB chromophores dominate the lower energy, more

intense peak (see Figure 50 (b)).

91


Figure 50. (a) Absorption spectra of PC612 at 295 K (red) and 77 K (blue). (b) 295 K absorption


Gaussians at (c) 295 K and (d) 77 K.

Fit Equation f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)

Coefficients (with 95% confidence bounds)

295 K 77 K

a1 = 0.5237 (0.4971, 0.5503) 0.7368 (0.7183, 0.7553)

b1 = 619.9 (619.5, 620.2) 622.6 (622.4, 622.8)

c1 = 17.79 (16.95, 18.63) 13.63 (13.26, 14)

a2 = 0.8895 (0.8794, 0.8996) 0.7033 (0.6967, 0.7099)

b2 = 581 (580.1, 582) 582.7 (582, 583.3)

c2 = 46.75 (45.91, 47.6) 41.15 (40.35, 41.94)

R-square: 0.9961 0.975

Table 4. Parameters used in the fits in Figure 49. (c) and (d).

450 500 550 600 650 700

295 K 77 K


Wavelength (nm)

(b) (a)

Wavelength (nm)

PCBs DBVs

500 550 600 650

500 800 600 700 500 400 600 700

(d) (c)

92


In contrast to the absorption spectra of PE545, PC645 and PC612, the PE555 absorption spectrum

is narrow and nearly featureless, showing minimal change between the room temperature and 77 K

spectra. The PE555 room temperature absorption spectrum is narrow compared to the other proteins and

only spans 75 nm. The main peak occurs at 551.5 nm and has a distinct high-energy shoulder. The

following scan parameters were used for the 295 K absorption scan. The scan range occurred from 350 to

650 nm in intervals of 0.167 nm and at a scan rate of 50.1 nm/min with an averaging time of 0.2 s. At 77

K the high-energy shoulder becomes much more distinct and there is a slight overall lineshape change.

There is practically no change in the peak position as it occurs at 552 nm. The scan parameters for the 77

K measurement are identical to those at 295 K with the exception of the minimum wavelength, which is

400 nm in this case. The 77 K measurement of PE555 was run in 50% glycerol (v/v). For the room

temperature and 77 K absorption spectra of PE555 see Figure 51 (a).

The nearly featureless absorption spectra suggest that all the chromophore absorption bands are

significantly overlapping. However, the presence of two distinct types of chromophores in PE555 – the

singly bonded PEBs and the doubly bonded DBVs – suggests that there could be at least two distinct

absorption energies. In a procedure identical to the one carried out on PC612, the room temperature and

77 K absorption spectra are fit using two Gaussians to give an estimate of the absorption energies of the

two types of chromophores. Fits of the absorption spectra are presented in Figure 51 (c) and (d);

parameters of these fits can be found in Table 5. Based on the relative site energies of the PEBs and

DBVs in PE545, the higher-energy shoulder is attributed to the PEBs and the lower-energy, main

absorption band is attributed to DBVs, this ordering agrees with previous assignment.10,83

Electronic

coupling has not been computed between the chromophores in PE555 so it is impossible to determine the

exact position of individual chromophore absorption bands or the extent of exciton splitting. Yet the

narrow, congested absorption spectrum suggests that the absorption bands of individual chromophores

significantly overlap possibly indicating that exciton splitting is minimal.

93


Figure 51. (a) Absorption spectra of PE555 at 295 K (red) and 77 K (blue). (b) 295 K absorption


Gaussians at (c) 295 K and (d) 77 K.

Fit Equation f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)

Coefficients (with 95% confidence bounds)

295 K 77 K

a1 = 0.6586 (0.6385, 0.6787) 0.721 (0.7039, 0.7381)

b1 = 553.9 (553.8, 554.1) 554.8 (554.6, 554.9)

c1 = 18.53 (18.18, 18.88) 16.2 (15.83, 16.56)

a2 = 0.5389 (0.5276, 0.5502) 0.4581 (0.4484, 0.4678)

b2 = 528.9 (528, 529.7) 527.3 (526.3, 528.3)

c2 = 36.54 (36.02, 37.05) 41.39 (40.64, 42.15)

R-square: 0.9965 0.9865

Table 5. Parameters used in the fits in Figure 50. (c) and (d).

450 500 550 600 650 400

295 K 77 K

Wavelength (nm)

PEBs DBVs

500 550 600 Wavelength (nm)

(b) (a)

(d) (c)

500 550 600 650 450 500 550 600 650 450 Wavelength (nm) Wavelength (nm)

94


5.4.2 Fluorescence

The fluorescence spectra for PC612 and PE555 are very typical of phycobiliproteins and show little

difference between their spectra and those of PE545 and PC645 with the exception of their position.

Spectra of both proteins show one main electronic transition with a red-shifted sub-band, most likely

resulting from vibronic transitions. This extended shoulder can span up to 100 nm. The 295 K

fluorescence spectrum of PC612 peaks at 641.6 nm as does the 77 K spectrum. The 77 K fluorescence

spectra displays two peaks in the vibronic shoulder, one in the vicinity of 675 nm and one around 705 nm,

thus suggesting multiple vibronic modes. The 295 K fluorescence spectrum was measured from 600 to

800 nm in 0.5 nm, with excitation occurring at 590 nm. The scan rate was 30 nm/min, with 1 s averaging

time, the excitation slit width was 2.5 nm and the emission slit width was set to 5 nm. The 77 K spectrum

had identical scan parameters except the excitation slit width was 5 nm and the solution consisted of 50%

glycerol (v/v). A room temperature spectrum for PC612 in 50% glycerol showed no lineshape difference

with the spectrum taken in buffer only.

The room temperature fluorescence spectrum of PE555 displays a very similar lineshape to that

of PC612 except it is shifted to the blue. The room temperature maximum occurs at 574.5 nm as does the

77 K maximum. The vibronic shoulder of PE555 is much narrower than that of PC612 and the 77 K

spectrum only shows one vibronic peak in the vicinity of 620 nm. In both the 295 K and 77 K

measurements the scan range was 550-750 nm and occurred in 0.2 nm intervals with an averaging time of

1 s; excitation occurred at 540 nm. The scan rate in the 295 K measurement was 30 nm/min while 12

nm/min in the 77 K measurement; emission and excitation slit widths were 5 nm and 2.5 nm in the 295 K

and 77 K measurements respectively. The low temperature measurement was conducted in 70% glycerol

(v/v).

Figure 52. (a) Fluorescence spectra of PC612 at 295 K (red) and 77 K (blue). (b) Fluorescence spectra of

PE555 at 295 K (red) and 77 K (blue).

550 600 750 700 650

295 K 77 K

650 700 750 800

295 K 77 K

600 Wavelength (nm) Wavelength (nm)

(b) (a)

95



Like the fluorescence spectra, the circular dichroism spectra of open phycobiliproteins are similar to those

of closed proteins. The visible CD spectra of PC612 and PE555 have positive going features at low

frequencies and negative going features at higher frequencies, indicative of exciton splitting and similar to

the CD spectra of PC645. The visible CD spectrum of PC612 was monitored from 450 nm to 700 nm

with 0.5 nm spectral resolution at a scan rate of 100 nm/min and a 2 s response time. The spectrum is

positive valued from 450 nm to 612 nm, then negative until 640 nm after which it becomes positive again.

The positive peak is centered at 570 nm with a broad shoulder in the vicinity of 590 nm. The negative

feature is a sharp Gaussian feature centered at 624 nm. The positive feature is roughly twice the intensity

of the negative feature.

The visible CD spectrum of PE555 has a positive feature that resembles its absorption spectrum,

with the exception that it peaks at 537 nm. To the red of this positive feature is a narrow, negative going

feature which is roughly the same intensity as the positive feature. The scanning conditions are identical

for the PE555 and PC612 measurements, with the exception of the scan range. Although both proteins

display features indicative of exciton splitting, namely both positive and negative going features, the

intensity of these features do not indicate the extent of the splitting. It would be therefore incorrect to

conclude that significant delocalization is present in open structures, strictly based on their CD spectra.

Contrarily, it may be expected that exciton splitting is minimal due to the large distance between

chromophores in open structures. Detailed calculations need to be conducted before concrete claims can

be made about the electronic coupling and exciton delocalization in these proteins. The ultraviolet CD

spectra show features characteristic of a protein composed of α-helices and β-sheets, with little to no

difference between the two proteins.

96


450 500 550 600 650 700

-10

0

10

20

CD

In

ten

sity (

md

eg

)

400 450 500 550 600 650-10

-5

0

5

10

CD

Inte

nsity (

mde

g)

200 220 240 260

-40

0

40

80

CD

In

ten

sity (

md

eg

)

200 220 240 260

-30

0

30

60

CD

In

ten

sity (

md

eg

)B

Figure 53. Visible CD spectra at 293 K of (a) PC612 and (b) PE555. Ultraviolet CD spectra at 293 K of

(c) PC612 and (d) PE555.

5.5 Two-Dimensional Electronic Spectroscopy of PC612

A number of ultrafast spectroscopic measurements have been conducted on PC612 in the past, namely

time-resolved fluorescence measurements conducted in the 1980s.80–82

In addition the steady-state

spectra of open structured phycobiliproteins have been detailed in literature; however 2D ES provides a

powerful new tool to analyze this system and offers the means to compare dynamical differences between

open and closed structured proteins.

The laser pulse used to excite the PC612 sample was centered at 525 THz corresponding to the

blue side of the absorption spectrum and thus mainly populating DBV chromophores. The pulse was

Gaussian in shape with a bandwidth of approximately 55 THz and the pulse duration was 14.3 fs. The

coherence time was scanned in intervals of 0.2 fs from -45 to 45 fs and the waiting time ranged from 0 to

400 fs in 5 fs steps. The measurements were conducted at 298 K and the sample was flowed using a

293 K 293 K


(b) (a)

293 K 293 K (d) (c)

97


Cole-Parmer Masterflex peristaltic pump at a rate of 0.06 mL/min. The portion of the sample not in the

flow cell or tubing was submerged in an ice bath. Three scans under identical conditions were measured

and will be discussed in this section. Illustrated below (Figure 54) is the absorption spectrum overlaid

with laser pulse spectrum after it has passed through the sample.

450 500 550 600 650 700

Laser Pulse

PC612

650 600 550 500 450

Figure 54. Absorption spectrum of PC612 (black) along with the laser pulse spectrum (red) used in the

2D experiments after it had passed through the sample.

Unfortunately after analyzing the PC612 data it was determined that a dust particle was present

on one of the glass wedges. Evidence for this was provided by the observation of fast oscillations (~65

THz frequency) in the rephasing and total spectra from T=120 fs till T=300 fs (see Figure 55). The

oscillations are not present throughout the spectra nor for the full waiting time. The oscillations are most

easily observed along the diagonal and in the rephasing spectra. The nonrephasing spectra show no such

oscillations. If the oscillations were induced by some other artifact, such as fluctuations in the laser

stability or outside noise, then oscillations would be expected in both the rephasing and nonrephasing

components. The fact that the oscillations only arise in the rephasing spectra suggest that the particle of

dust was on one of the wedges which control the delay of pulses k1 or k2. In past measurements similar

oscillations have been observed and when the apparatus was checked, a speck of dust was found on the

appropriate wedge. Since the analysis of data was conducted months after the data was collected it was

impossible to verify that a piece of dust was actually on one of the wedges; however this provides the

most plausible explanation for the observed phenomenon. With the exception of the speck of dust which

Frequency (THz)

Wavelength (nm)

98


ruins the spectra’s appearance for spectra from T=120 until T=300 fs, the rest of the spectra are of high

quality. It was therefore determined that further analysis should be conducted on these measurements.

The magnitude valued total spectra are presented below in Figure 56 with 20 evenly spaced

contour levels. It is obvious during which waiting times the speck of dust is present in the beam path.

Ignoring these spectra, the quality of data is immaculate. The total, magnitude spectra display a

rectangular feature with above and below diagonal cross peaks that oscillate with waiting time. The level

of noise in these spectra is below the 5% contour level. The imaginary valued total spectra as well as the

rephasing and nonrephasing components show lineshapes characteristic of those spectra; however they

are not displayed due to the artifacts introduced by the speck of dust at the discussed waiting times.

Traces taken at off diagonal positions show less evidence of the oscillations due to the dust. This

is because scattered light does not incur a change in energy instead only a change in wave vector direction

occurs and thus the scattered signal must appear on the diagonal. Also, since the periodicity of the

oscillations is fairly well defined (~15 fs) the frequency at which they occur can be determined (~66 THz)

and then removed from any trace by Fourier filtering if necessary (not conducted in this study).

0 100 200 300 400

Rephasing

0 100 200 300 400

Nonrephasing

Figure 55. (a) Trace of diagonal peak (530, 530 THz) of the absolute valued rephasing spectra.

Oscillations caused by scatter from particle of dust are clearly evident from T=120 fs till T=300 fs. (b)

Trace of diagonal peak (530, 530 THz) of the absolute valued nonrephasing spectra.


(b) (a)

99


Figure 56. Representative 2D spectra of PC612 in aqueous buffer at indicated waiting times (top left

hand corner). The spectra are the magnitude value of the total signal and are individually normalized

with 20 evenly spaced contours. Spectra at waiting times T=150, T=200, T=250, and T=300 clearly

display artifacts resulting from a speck of dust on one wedge. At T=60 fs the coordinates of a major

feature of interest an above diagonal cross peak are indicated.

100


Following the dynamics of the above diagonal cross peak (500 THz, 540 THz) in the absolute

valued rephasing and nonrephasing spectra provide insight into the initial dynamics after photoexcitation

(see Figure 57). The trace is taken at a position far enough away from the diagonal that scatter from the

particle of dust is not a significant issue. Both the traces of the rephasing and nonrephasing spectra show

clear oscillations that persist for the entire length of the experiment. The traces presented below are the

average of three scans and are presented with one standard deviation error bars. The complex beating

patterns present in both the rephasing and nonrephasing traces are of high quality, suggesting a Fourier

analysis be conducted to determine the frequencies of the oscillating components. In a procedure similar

to the analysis performed on PC645, a Fourier analysis was conducted on these traces. The first 15 fs of

each trace was omitted due to pulse overlap effects. Unlike the analysis done on PC645, no normalization

of individual scans was required as all three scans were conducted at identical pulse powers. The three

traces were then averaged to obtain the global mean. After which the mean valued trace was fit to a linear

function using a least-squares method. A linear fit was more appropriate than an exponentially damped

fit due to the long dephasing time of the oscillations observed in PC612. The linear function was

subtracted from the mean trace and the Fourier transform was conducted on this offset trace. Identical to

the Fourier transforms conducted on the traces of PC645, these Fourier transforms were conducted using

the Fast Fourier Transform (FFT) function in Matlab and the data was zero-padded to reduce the

frequency step size of the resultant spectra.

100 200 300 400

Sig

na

l A

mp

litu

de

(a.u

.)

Mean Rephasing

Linear Fit




Mean Slope -0.1566 0.00287

100 200 300 400

Sig

na

l A

mp

litu

de

(a

.u.)

Mean Nonrephasing

Linear Fit


Value Standard


Mean Slope -0.245 0.00191

Figure 57. Mean trace (black) of three absolute valued (a) rephasing and (b) nonrephasing spectra for the

cross peak; displayed with one standard deviation error bars. Linear fit (red) of the mean trace using

least squares analysis, details of the fit (inset).

The Fourier analysis identified that a number of different frequency modes contributed to the

complex beating patterns observed in the rephasing and nonrephasing traces. Six modes above the signal-

(b) (a)


101


to-noise level are clearly present in both the rephasing and nonrephasing Fourier transforms (see Figure

58 (b)). According to the procedure outlined in references 51,60

and used for the analysis conducted on

PC645, the presence of oscillations at the same frequency in the rephasing and nonrephasing spectra

would suggest that these modes arise due to vibrational coherences. The six modes occur at 7.4 THz,

20.3 THz, 26.2 THz, 38.5 THz, 43.1 THz, and 50.3 THz. Five of these modes: 7.4 THz, 20.3 THz, 26.2

THz, 43.1 THz, and 50.3 THz are nearly identical to the modes found in PC645. This would be expected

since DBV and PCB chromophores are present in both systems and are likely contributing to the observed

vibrational coherences. A few modes present in PC645 do not appear in PC612, these modes include

those occurring at 9.6 THz, 13.9 THz, and 33.3 THz (identified according to Figure 43 (d)). One

explanation for this is that these modes are due to vibrational modes of the MBV chromophores which are

not present in PC612. Contrarily, these peaks may be too weak in the Fourier analysis of PC612 to be

identified. This is plausible considering there are modes in the vicinity of 12 THz, 16 THz, and 34 THz

in the PC612 traces which have amplitudes similar to the noise level. On the other hand there is only one

mode present in PC612 that is not present in PC645, this occurs at a frequency of 38.5 THz.

Most intriguing is the mode at 20.3 THz, which clearly appears in both the rephasing and

nonrephasing traces of PC612. This mode closely identifies with the mode occurring at 21.1 THz in

PC645 which most prominently appears in the rephasing spectra. Since the systems are similar and since

many of the other modes are present in both systems it is tempting to claim that these too arise from the

same physical phenomenon and therefore the 21.1 THz mode in PC645 should be attributed to vibrational

coherence. At this time it would be imprudent to draw such a conclusion as no quantitative analysis has

been conducted to determine how related the two proteins actually are. Once electronic couplings have

been computed and a working electronic Hamiltonian is produced for PC612 a more complete

comparison between the two proteins can be made.

102


0 10 20 30 40 50 60

50.3

43.138.5

26.2

20.3

Sp

ectr

al A

mp

litu

de

(a

.u.)

Nonrephasing

Rephasing7.4



absorption energies of the chromophores are plotted on the 295 K absorption spectrum which is


diagonal of the 2D ES spectrum. (b) Fourier transforms of the mean trace of the nonrephasing (black) and

rephasing (red) spectra after the linear fits were removed. Peaks of interest are indicated by their

frequency values and occur at 7.4 THz, 20.3 THz, 26.2 THz, 38.5 THz, 43.1 THz, and 50.3 THz.

(a)

(b)

Frequency (THz)

103


5.6 Two-Dimensional Electronic Spectroscopy of PE555

The 2D ES experiments performed on PE555 represent the first published ultrafast measurements on

PE555. In addition these measurements were conducted at physiologically relevant temperatures which

suggests that the elucidated dynamics may be biologically relevant. Furthermore, these results provide

more evidence to compare the differences between open and closed systems and expand our knowledge

of EET in cryptophyte algae and photosynthetic systems in general.

The narrow absorption spectrum of PE555 along with the broadband laser pulses achievable in

the 2D ES experimental setup allowed a majority of the absorption spectrum to be excited. Although this

provides a more complete picture of the energy transfer dynamics elucidated, it presents a problem due to

the congested spectrum. Populating eight different chromophores with overlapping electronic features

means the emitted signal is likely to be the result of many different energy transfer pathways. Therefore

determining any specific pathway may be difficult due to interference between individual signals. The

following scan parameters were used for six measurements of PE555. The coherence time was scanned

in intervals of 0.2 fs from -45 to 45 fs and the waiting time ranged from 0 to 400 fs in 10 fs steps. The

measurements were conducted at 298 K and the sample was flowed using a Cole-Parmer Masterflex

peristaltic pump at a rate of 0.06 mL/min. The portion of the sample not in the flow cell or tubing was

submerged in an ice bath. The spectra presented below are individually normalized and have 20 equally

spaced contour intervals (i.e. 5%). In most spectra the noise level is under 5%. The pulse spectrum after

it has passed through the sample is illustrated below in Figure 59. The pulse spectrum before passing

through the sample has an approximately Gaussian profile with 55 THz bandwidth.

104


450 500 550 600 650

PE555

Laser Pulse

650 600 550 500

Figure 59. Absorption spectrum of PE555 (black) along with the laser pulse spectrum (red) used in the

2D experiments after it had passed through the sample.

The spectra presented below indicate a representative scan. The real part of the total spectra

(Figure 60) display a fairly round shape that does not change significantly with waiting time, thus

suggesting minimal electronic coupling. The other spectra, including the imaginary component of the

total signal (Figure 61) and the rephasing (Figure 62) and nonrephasing (Figure 63) components of the

total, real spectra display characteristic features with few signatures worth commenting on. However, the

fairly round, featureless shape of the real, total spectra is very different than the 2D spectra of PC645 and

PC612 which display more square-like lineshapes. This suggests that there is minimal coupling between

chromophores in PE555 and thus nominal exciton splitting. This conclusion is also corroborated by the

narrow linear absorption spectra. It is important to note that although the line shape of the visible CD

spectrum indicates exciton splitting, the intensity of the CD spectrum is not related to the extent of

exciton splitting in the protein. Therefore it is obvious that there is some exciton splitting but it is likely

to be small; this is also supported by the not totally round shape of the total spectra.

Frequency (THz)

Wavelength (nm)

105



left hand corner). The spectra are the real part of the total signal and are individually normalized with 20

evenly spaced contours.

106


Figure 61. The imaginary part of the total signal at various waiting times.

107


Figure 62. The real part of the rephasing signal at various waiting times.

108


Figure 63. The real part of the nonrephasing signal at various waiting times.

109


Since the individual absorption bands of the chromophores are overlapping in PE555, isolating

specific features in the 2D ES spectra proves to be very difficult. Oscillations are observed throughout

the spectra but are noisy with complicated beating patterns. Also the waiting step interval of 10 fs

severely under samples the dynamics and makes a meaningful analysis of the beating pattern complicated.

However, a trace at (530, 550 THz equivalent to 566, 545 nm) is conducted on six scans to obtain an

average trace after individual normalization. The trace is averaged over a 1.2 THz range in the excitation

dimension and 0.14 THz range in the emission dimension. Oscillations are clearly evident in the trace of

the magnitude value of the total spectra for the first 180 fs. After such time the standard deviation

becomes too large to determine the existence of oscillations. Oscillations are present in both the

rephasing and nonrephasing components (not shown). Based on the criteria outlined in references 51

and

60 for distinguishing between electronic and vibrational coherences, we can confirm the presence of

vibrational coherences due to the observation of oscillations in both the rephasing and nonrephasing

components of the trace. However, due to the large waiting time step size a Fourier analysis is impossible

and we are not able to confirm the presence or absence of electronic coherence. If the coupling between

chromophores in PE555 is small, as expected, then we can likely attribute these oscillations to vibrational

coherences exclusively; however, further experiments are required to verify these expectations.

110




absorption bands of the chromophores are plotted on the 295 K absorption spectrum which is


diagonal of the 2D ES spectrum. (b) Magnitude of an off-diagonal position (black “x” in (a)) as a function

of waiting time taken as a trace from the absolute value 2D ES spectra (first 15 fs are omitted due to

nonresonant solvent response). Individual trials were normalized to overlap; error bars indicate one

standard deviation as determined from six trials.

(a)

(b)

111

Chapter 6

Conclusion This thesis focused on the study of photophysical phenomena occurring in the light-harvesting machinery

of cryptophyte algae. Four different phycobiliproteins were discussed in this thesis: Phycoerythrin 545

from Rhodomonas CS24 (PE545), Phycocyanin 645 from Chroomonas CCMP 270 (PC645), Phycocyanin

612 from Hemiselmis virescens M1635 (PC612), and Phycoerythrin 555 from Hemiselmis andersenii

CCMP644 (PE555). These proteins were investigated using a number of different steady-state and

ultrafast spectroscopic techniques. Spectroscopic techniques such as linear absorption, fluorescence,

circular dichroism, fluorescence excitation anisotropy, and two-dimensional electronic spectroscopy were

employed to study the photophysics of these systems. Importantly, the presence of quantum phenomena

in light-harvesting systems was discussed.

Chapter 1 introduced various topics and concepts that would be discussed throughout the thesis.

This chapter was meant to familiarize the reader with the ideas, language, and method of analysis that

would be presented in the following chapters. Topics which were introduced included such principles as

electronic energy transfer, photosynthetic excitons, and spectroscopy. This provided the necessary

foundation to discuss the theory behind the specific spectroscopies which would discussed in Chapter 2.

Chapter 2 focused on detailing the various spectroscopic techniques that would be used to

investigate the photosynthetic proteins discussed in later chapters. A detailed introduction of two-

dimensional electronic spectroscopy (2D ES) was presented along with a technical account of the

experimental setup used. 2D ES experimental data was presented for a test case to verify the system was

working appropriately. The data presented for the test case Cresyl Violet agreed with results in literature.

Chapter 3 detailed a method developed to conduct spectroscopic measurements on proteins at

cryogenic temperatures as low as 77 K. The method was designed to conduct linear absorption and

112

Chapter 6. Conclusion

fluorescence measurements on PE545 but the method was then extended for spectroscopic investigations

of PC645, PC612, and PE555. Important discoveries included changing the sapphire sample holder to

plastic to minimize fracturing caused from rigid sample windows and using a cryoprotectant to prevent

crystallization.

Chapter 4 discussed two-dimensional electronic spectroscopy experiments conducted on PC645

at room temperature. Measurements were conducted under various pH levels to simulate the conditions

the phycobiliproteins would experience under excess light conditions. No changes in the electronic

structure, secondary structure, or initial dynamics were observed for physiologically relevant conditions.

The quality of 2D data surpassed previous experiments which allowed for a quantitative analysis of the

beating pattern observed in traces of the cross peak. By conducting a Fourier analysis the different

frequency components contributing to the oscillations were discovered. Following the method for

distinguishing between electronic and vibrational coherence detailed in references 51,60

most modes could

be assigned to vibrational coherences. One mode, oscillating at a frequency of 21 THz possibly arose due

to electronic coherence. If such a claim was verified, the electronic coherence was likely due to a

superposition of the two DBV eigenstates. However the signal-to-noise level in this experiment

prevented any concrete conclusion about the presence of electronic coherence from being drawn. The

difficulty in distinguishing vibrational and electronic coherences as well as its usefulness was noted.

Chapter 5 focused on discussing the difference between closed structured protein (PE545 and

PC645) and open structured proteins (PC612 and PE555). Spectroscopic differences and similarities were

commented on. Spectroscopic results suggest that the strongest couplings between chromophores in the

open structured proteins are smaller than those in closed structures due to the large separation between the

dimer pair in the former case. A comparison between the vibrational modes found in PC612 and PC645

was conducted. A number of modes were found to have similar frequencies suggesting that structural

differences have a limited influence on the vibrational modes of the chromophores.

In summary this thesis investigated the photophysics of four different phycobiliproteins: PE545,

PC645, PC612, and PE555. A variety of spectroscopic techniques, most notably 2D ES were used to

study these systems. New techniques were developed resulting in novel findings with broad implications.

One of the most important features of this thesis was detailing quantum phenomena in light-harvesting

proteins. A significant result of this work was the conclusion that distinguishing between electronic and

vibrational coherences may not be wholly meaningful or even possible in light-harvesting systems.

Current methods for distinguishing between the two types of coherence have proven to be difficult and

inconclusive at the current signal-to-noise level. More importantly though is the fact that high frequency

113

Chapter 6. Conclusion

vibrational modes are often strongly coupled to electronic transitions. Furthermore the frequencies of

these vibrational modes are often of similar magnitude as the frequency difference between excitonic

states. Therefore separating vibrational coherence and electronic coherence may only be possible in a

select number of limiting cases. The results presented here will hopefully direct future studies to

experimentally ascertain the validity of this prediction and also enable future studies to result in more

definitive conclusions on the observation of quantum phenomena in light-harvesting systems.

114

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119

Appendix A:

2D ES Spectra Generation Code

(MATLAB) clear all; clc; %% Input Parameters %% date='20110820'; summaryfile='043106';

LO_delay=275.17; %in fs phase=0.25; %if real and imag are switched phase=-1/2 fltr=2240:2350; %pixels included in filter n=81; %# of T points cn=33; %# of contour lines

tau=-45:0.15:45; %excitation axis (needs to match scanned parameters); middle

#= delta t1 t1=tau';

w1=(-3333:1.6276:3333); %scanned axis in THz (middle #=delta

nu=1000/(4096*delta t1); first/last #=+/-(4096*middle #)/2

%% Load Data %% c=299792.458; %c in nm/ps h=0.00413566733; %h in eV*ps sum=load(['C:\Users\user\Desktop\2DES Experimental Data\' date '\'

summaryfile '_summary_file.dat']); Tpts=sum(1,:); timestamps=sum(2,:);

for j=1:n; time=num2str(timestamps(j)); time=(['000000' time]); a=length(time); time=time(a-5:a);

t2=num2str(Tpts(j));

120

Appendix A: 2D ES Spectra Generation Code (MATLAB)

raw=load(['C:\Users\user\Desktop\2DES Experimental Data\' date '\' time

'.dat']); % retrieve raw data aux=load(['C:\Users\user\Desktop\2DES Experimental Data\' date '\' time

'.aux']); wavelength=aux(2,:); %retrieve wavelength axis LO=aux(3,:); % retrieve local oscillator spectrum

raw=fliplr(raw); wavelength=fliplr(wavelength); LO=fliplr(LO);

%% Plot Raw Data %% figure(1), set(gcf, 'WindowStyle', 'docked'); clf imagesc(wavelength,tau,raw); %plots interferogram (t vs wavelength) xlabel('Wavelength (nm)'), ylabel('tau (fs)')

%% 1st FFT from t vs. f %% data2=fftshift(fft(raw,4096,2),2); %zeropad emission axis for better

resolution

% figure(2), set(gcf, 'WindowStyle', 'docked'); clf % imagesc(real(data2)); %plots t vs t

%% Filter %% figure(3), set(gcf, 'WindowStyle', 'docked'); clf % plots a slice at tau=0 plot(real(data2(301,:)));

filter=zeros(1,4096); % creates filter filter(fltr)=1; filter=repmat(filter,601,1);

data3=data2.*filter; % applies heavy step function - enforces causality

%% 2nd FFT back to t vs f %% data4=ifft(ifftshift(data3,2),4096,2); data4=data4(:,1:1024);

figure(4), set(gcf, 'WindowStyle', 'docked'); clf imagesc(real(data4)) %plots t vs f.

%% Spectral Interferometry %% omega=(2*pi*(c/1000))./wavelength; % omega in exp(-iwt), c=299.792458 nm/fs D=exp(-1i.*omega*LO_delay); D=D*exp(1i*pi*phase); E=repmat(D,601,1); data5=(E.*data4)./(repmat(sqrt(LO),601,1));

figure(5), set(gcf, 'WindowStyle', 'docked'); clf imagesc(real(data5))

%% 3rd FFT to f vs f%% Q=data5(1:301,:); %splitting total spectra into R and NR components P=flipud(Q);

121


W=data5(301:601,:); nonrephasing=flipud(fftshift(fft(P,4096,1),1)); %nonrephasing rephasing=fftshift(fft(W,4096,1),1); %rephasing total=nonrephasing+rephasing; %total

w3=c./wavelength; % emission axis in THz,

%% Saves reduced files %% reducednr=nonrephasing(2318:2540,1:1024); reducedr=rephasing(2318:2540,1:1024); reducedt=total(2318:2540,1:1024); reducedw1=w1(2318:2540); reducedw3=w3(1:1024);

save(['C:\Users\user\Desktop\2DES Experimental Data\' date '\processed\T=' t2

'fs'], 'reducedw1', 'reducedw3', 'reducedt', 'reducedr', 'reducednr');

%% 2D Spectra in THz%% % figure(6), set(gcf, 'WindowStyle', 'docked'); clf %nonrephasing % contour(w3,w1,real(nonrephasing),cn); % xlabel('Emission Frequency (THz)', 'fontsize', 18),ylabel('Excitation

Frequency (THz)', 'fontsize', 18) % title('Real, Nonrephasing', 'fontsize', 18); xlim([425 575]); ylim([425

575]); % line(w3,w3); % % print('-djpeg',['C:\Users\Rayomond\Desktop\2DPE Experimental Data\' date

'\nonrephasing\T=' t2 'fs ']) % % figure(7), set(gcf, 'WindowStyle', 'docked'); clf %rephasing % contour(w3,w1,real(rephasing),cn); % xlabel('Emission Frequency (THz)', 'fontsize', 18), ylabel('Excitation

Frequency (THz)', 'fontsize', 18) % title('Real, Rephasing', 'fontsize', 18); xlim([425 575]); ylim([425 575]); % line(w3,w3); % % print('-djpeg',['C:\Users\Rayomond\Desktop\2DPE Experimental Data\' date

'\rephasing\T=' t2 'fs ']) % % figure(8), set(gcf, 'WindowStyle', 'docked'); clf %total % contour(w3,w1,real(total),cn); % xlabel('Emission frequency (THz)', 'fontsize', 18),ylabel('Excitation

frequency (THz)', 'fontsize', 18) % title('Real, Total', 'fontsize', 18); xlim([425 575]); ylim([425 575]); % line(w3,w3); % % print('-djpeg',['C:\Users\Rayomond\Desktop\2DPE Experimental Data\' date

'\total\T=' t2 'fs']) % % figure(9), set(gcf, 'WindowStyle', 'docked'); clf %total % contour(w3,w1,imag(total),33); % xlabel('Emission frequencyv(THz)'),ylabel('Excitation frequency (THz)') % title('Imaginary, Total'); xlim([450 575]); ylim([450 575]); % line(w3,w3); % print('-djpeg',['C:\Users\Rayomond\Desktop\2DPE Experimental Data\' date

'\imaginary\T=' t2 'fs'])

%% Plots reduced files - takes less time, but cant adjust axes %%

122


figure(9), set(gcf, 'WindowStyle', 'docked'); clf %nonrephasing contour(reducedw3,reducedw1,real(reducednr),cn); xlabel('Emission Frequency (THz)', 'fontsize', 18),ylabel('Excitation

Frequency (THz)', 'fontsize', 18) title('Real, Nonrephasing', 'fontsize', 18); xlim([440 580]); ylim([440

580]); line(reducedw3,reducedw3); print('-djpeg',['C:\Users\user\Desktop\2DES Experimental Data\' date

'\nonrephasing\T=' t2 'fs '])

figure(10), set(gcf, 'WindowStyle', 'docked'); clf %rephasing contour(reducedw3,reducedw1,real(reducedr),cn); xlabel('Emission Frequency (THz)', 'fontsize', 18), ylabel('Excitation

Frequency (THz)', 'fontsize', 18) title('Real, Rephasing', 'fontsize', 18); xlim([440 580]); ylim([440 580]); line(reducedw3,reducedw3); print('-djpeg',['C:\Users\user\Desktop\2DES Experimental Data\' date

'\rephasing\T=' t2 'fs '])

figure(11), set(gcf, 'WindowStyle', 'docked'); clf %total contour(reducedw3,reducedw1,real(reducedt),cn); xlabel('Emission frequency (THz)', 'fontsize', 18),ylabel('Excitation

frequency (THz)', 'fontsize', 18) title('Real, Total', 'fontsize', 18); xlim([440 580]); ylim([440 580]); line(reducedw3,reducedw3); print('-djpeg',['C:\Users\user\Desktop\2DES Experimental Data\' date

'\total\T=' t2 'fs'])

figure(12), set(gcf, 'WindowStyle', 'docked'); clf %imag contour(reducedw3,reducedw1,imag(reducedt),cn); xlabel('Emission frequency (THz)', 'fontsize', 18),ylabel('Excitation

frequency (THz)', 'fontsize', 18) title('Imaginary, Total', 'fontsize', 18); xlim([440 580]); ylim([440 580]); line(reducedw3,reducedw3); print('-djpeg',['C:\Users\user\Desktop\2DES Experimental Data\' date

'\imag\T=' t2 'fs'])

figure(13), set(gcf, 'WindowStyle', 'docked'); clf %abs contour(reducedw3,reducedw1,abs(reducedt),cn); xlabel('Emission frequency (THz)', 'fontsize', 18),ylabel('Excitation

frequency (THz)', 'fontsize', 18) title('Magnitude, Total', 'fontsize', 18); xlim([440 580]); ylim([440 580]); line(reducedw3,reducedw3); print('-djpeg',['C:\Users\user\Desktop\2DES Experimental Data\' date

'\mag\T=' t2 'fs'])

end

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