Single Molecule Optics

Michel Orrit

Molecular Nano-Optics and Spins

Leiden University

Winterschool:

Spectroscopy and Theory15-18 December 2008, Han-sur-Lesse, Belgium

1. Introduction

• Optical detection of single molecules by fluorescence

• High signal/background ratio thanks to resonance

• Made possible by advances in sources, detectors, optics

Molecular Photophysics

• Electronic levels are split in a series of harmonic oscillator levels

• Transitions between levels are related to overlaps between oscillator wavefunctions

Mirror Image

Absorption and fluorescence spectra are related by a mirror symmetry around the 0-0 transition

Absorption & Emission of Cy3

300 400 500 600 7000

20

40

60

80

100

120

140

30000 150002000025000flu

orescen

ce

x 103

mo

lar

exti

nct

ion

(1/

cm M

)

wavelength (nm)

wavenumber (cm-1)

S2S0

S1S0 S1S0

vibronicvibronic

NN

NH2

O

SO3--O3S

Transition dipole moment

2112 re

characterizes the strength of the optical transition

212

Kasha’s Rule

• Radiative and non-radiative relaxation between electronic levels

• Fluorescence can only arise from the lowest excited singlet state S1;

• higher excited states relax to S1 faster than they can emit;

• triplet states emit weak phosphorescence.

Fluorescence quantum yield

knrkr

nrrfluo kk 1

1nrr

rfluo kk

k

S0

S1

Jablonski diagram: relaxation between electronic states

eGFP = 490 nm

N

C NH2

CNH2

NH

NH

DAPI = 355 nm

Typical fluorophores

NN

NH2

O

SO3--O3S

Cy5 = 630 nm

O

N

NO

O O

TDI = 630 nmO

O

O

N+

N

NH

S TMR = 514 nm

N

O

N

tryptophane = 280 nm

+

K. Brejc et.al., PNAS 94 (1997) 2306

1 nm

green-fluorescent protein (GFP)

R

2. Optical Microscopy

Working principle of an optical microscope

NAd

222.1min

Diffraction-limited resolution

sinnNA

object

objectivelens

intermediateimage

eye-piece

Both Collection Efficiency and Point Spread Function depend on the Numerical Aperture

NA

Immersion favors collection efficiency

Aberrations must be corrected

Spherical aberration, coma, pincushion/barrel deformation

Polarization structure in focal plane

Confocal Scanning Microscope

sample scanning

beam scanning

Total Internal Reflection

Other focusing and collecting elements used in single-molecule experiments

Near-Field Optics

3. Excitation and Detection of Fluorescence

• Sources: Lasers cw (ion), pulsed (Nd-YAG, Ti-sapphire, diodes)

• Photon Detectors: PhotoMultiplier Tube, Avalanche PhotoDiode, Charge Coupling Device

• Spectral Filters: colored glass, notch holographic, multidielectric

Photon Counting Analyses

• Field and Intensity Correlation Functions

)(

)()()(

2

*)1(

tE

tEtEg

2)2(

)(

)()()(

tI

tItIg

Field

Intensity

Thermal or Chaotic Light (Lamp)

Coherent Light (cw Laser)

nm

em

nmp

!)(

Poisson statistics:- independent photons,- correspondence with classical light wave for large numbers

nnnn 222

Correlation function versus Start-Stop

The two functions areidentical for short times,but differ for long times

Time-Correlated Single Photon Counting

• Histogram of delays between fluorescence photon and laser pulse

• Full time information: macroscopic arrival time of photon, and delay with respect to laser pulse

4. Single Molecules in Fluid Solutions

Molecules diffuse, bursts of fluorescence, photon-by-photon studies .

• Burst analysis (intensity)• Multiparameter analysis, statistical correlations• Fluorescence Correlation Spectroscopy

Translational Diffusion

2/1

2

1

2)2( 4

14

11

1)(

at

DD

Ng

D diffusion coefficient, t and a transverse and axial beam waistsN average number of molecules in the excitation volume.

Rotational Diffusion

For isotropic diffusion on a sphere, the correlation functiondecays exponentially, on some nanoseconds for small fluorophores in water, more slowly for bigger moleculesor more viscous fluids.

Blinking due to a Dark State (Triplet)

21

1

2)2( 1)( kkek

kg

Single-exponential decay of the correlation function with the sumof the two rates.

5. Immobilized Molecules

Signal/Background ratio must be large enough

tBS /3 SBt /10 2or

Sample preparation

Spin-coating

Langmuir-Blodgett films

Microscopy images

• Counting, stoichiometry, colocalization

• Orientation

Comparison of polarization modulation for epi-illuminationand total internal reflection.

Photophysics, Blinking

Triplet state

Electron transfer

Other photochemical reactions

Bleaching

I

t

I

tflickering blinking

6. Fluorescence Resonance Energy Transfer (FRET)

DAAD RRR

V

ˆˆ314

13

0

Dipole-dipole interaction(near-field)

Donor Acceptor

Förster transfer rate

• Decreases as (distance)

• Spectral Overlap between Donor Fluorescence and Acceptor Absorption

• Angular dependence 2

EEAEFWk ADDADA d)()(2 2

cossinsincoscos2 ADAD

isotropic:<2> = 2/3

-6

Transfer Efficiency

• Fraction of excitations transferred to acceptor

• R0 Förster radius, maximum 10 nm for large overlap

6

01

1

RRkk

kE

fDDA

DA

FRET Histograms and Dynamics