ESR Perspective on Complex Liquids

(A Retrospective)

Jack H. FreedDept. of Chemistry & Chemical Biology

Cornell UniversityIthaca, New York 14853 USA

www.acert.cornell.edu

PHYSICAL CHEMISTRY AWARD SYMPOSIUM247th ACS National Meeting, Dallas, TX

Joel Hildebrand Award March 18, 2014

ESR Hyperfine Linewidths of Radicals in Solution

Alternating LW’s : Out-of-phase correlation between the HF splittings of the two nitroxides.

Necessitated New Paradigm for HF Linewidths in Organic Radicals: Freed – Fraenkel Theory: Used Redfield Relaxation Matrix Based on WBR (Wangsness-Bloch-Redfield Theory) includes Degenerate HF Transitions. (JCP, 39, 326-48, 1963)

Asymmetric

Linewidth Variation

Spectrum of para-

dinotrobenzene anion radical

-55C DMF

Alternating Linewidth - Spectrum of para-dinotrodurene anion radical in 20C DMF

Terms in the perturbation H1(t).a

Anistropic Rotational Diffusion & ESRSpectral densities jA

(BC) (ω)are Fourier Transforms of the time correlation fns of the Wigner Rotation Matrix Elements: Dm,m

(L) .

The dependence on nuclear spin quantum numbers MN & MH enable several independent quantities to determine this tensor.

For Anisotropic Brownian Motion: They depend on eigenvalues of Rotational Diffusion Tensor (e.g. Perrin, Favro) (Freed, JCP, 41, 2077, 1964).

An Analysis of the p-dinitrobenzene anion linewidth (plus some assumptions about internal dynamics) yields:

These were preliminary results, but showed ESR linewidths in principle provide enough information to extract aanistropic diffusion tensors.

Better assessment was made for the simpler spectrum of

peroxylamine disulfonate (PADS), with a simple 3 line 14N ESR

Spectrumin ice clathrate cage

in glycerol solventFreed, JCP, 56, 716 (1972)

[K+]2

Analysis based on Stokes-Einstein type behavior with

with ro = 3.2Å geometric effective spherical radius

re = effective rotational spherical radius

Rotational Asymmetry

Rotational “Slip”

Electron Spin Relaxation and Molecular

Dynamics in Liquids: Solvent Dependence

PD-Tempone

Non-secular spectral densities:  j(ω)≈ τR/[1+ε2τR

2]-1, ε >1τR vs. η/T over five orders of magnitude

Zager & Freed, JCP,77, 3344 (1982)

Electron-Spin Relaxation and Molecular Dynamics

in Liquids: Pressure Dependencevs vη/kBT for PD-Tempone in toluene-d8. Variable pressure and temperature

results.

Empirical Fit to 60 Data PointsτR/η/T) = a + bP+ cP2+dT+eT2+fPT6 parameter fit gives R2 = 0.90

Zager & Freed, JCP, 77, 3360 (1982)

Plot of average value of τRT /ηβ for each constant density group (CDG) vs density, ρ

60 Data Points: 52C >T> -40 C1 bar ≤ P< 5 kbarv = solute volumeη = solvent viscosityβ = isothemal compressibility Led to Empirical Fit to all data points to

τRT/ηβ=C(ρ- ) /ρWith C=32 10-8 K s kbar/cP = 0.845 g/cm2 → The “expanded volume” =

Yields factor of 2 scatter in τR

Removes scatter in τR

Electron-Spin Relaxation and Molecular Dynamics in Liquids: Pressure Dependence

(continued)Expanded Volume Model: • is a solvent reference volume such that as

the solvent volume ( where ), then . • This is an ideal reference state, not

realized in real systems because this model relates to purely viscous motion, and as the liquid is becoming more gas-like, so inertial effects would take over. These experiments on PDT exhibit purely viscous behavior.

• This expanded volume model takes into account in a “natural” way the concept of slip of the rotating molecule in the solvent.

When two molecules, each with an unpaired electron spin, collide in solution this yields an exchange interaction.The ESR spectral line broadening depends on the Heisenberg Exchange frequency: 

Where J is the exchange interactionτ1 is the lifetime of exchange pairτ2 is the time between the biomolecular collisions.

Translational Diffusion: Heisenberg Spin

Exchange & ESR Spectra

Width vs. concentration for TCNE— samples in

DME T = 15° C)

Intermolecular Dipolar Interactions are not Important here. Can show  [(T2)-1 dipole/ (T2

-1) exchange] = K(η/kT)2

“for strong exchange” = J2τ12 >> 1   η = solvent

viscosity

For simple Brownian diffusion of the radicals in solution:τ2

-1 = 4πdDfNτ1

-1 = (6D/d2)feu

WhereN = radical densityD = diffusion coefficientd = interaction distance for exchangef = (u/eu-1) and u = U(d)/kT are corrections for intermolecular potential energy at contact distance.  Eastman, Kooser, Das & Freed,JCP, 51, 2690 (1969) ; 52,

2511 (1970)

Width for aqueous solutions of PADS at 24°C as a function of electrolyte concentration.

Lateral diffusion of CSL( )& 16PC (- - ) in phospholipid POPC vs. cholesterol m.f. at different temperatures .

Using 1D field gradients & cw-ESR

accurate translational diffusion coefficients ranging from 10-5 to

10-9 cm2/s were measured in isotropic & anisotropic fluids.

Translational Diffusion Coefficients by ESR Imaging of Concentration Profiles: DID-ESR

ISOTROPIC/NEMATIC LIQUIDS: D to Nematic Director. D to Nematic Director

D D = 1.41± 0.1Nematic

Smectic Liquid Crystal, S2Small Probe: PDT D D > 1 Large Probe: CSL D D < 1

Concentration Profiles for Tempone diffusing in a nematic phase at 300K at increasing times.

Sample Preparation

D ,PDT

D ,PDT

D ,CSL

D ,CSL

Hornak, Moscicki, Schneider, Shin, Freed (JCP, 84, 1886 (1986); Biophys. J. 55, 537 (1989); JCP 99, 634 (1993))

)

CSL is Cholesterol Analogue Spin Probe

Microscopic vs.

Macroscopic

Diffusion Coefficients by ESR Spectral-Spatial

Imaging

Aligned POPC Membrane/16PC• DID-ESR: Macroscopic Diffusion• Heisenberg Exchange broadening vs.

concentration gradient: Microscopic DiffusionAt 22°C :

Dmacro= (2.3 ± 0.4) X 10-8cm2/sec Dmicro= (1.0 ± 0.4) X 10-7cm2/sec

Along Spatial Axis to Display The

Spatial Distribution: Macroscopic

Diffusion

Along Spectral Axis to Display

Spectral Linewidth

Dependence on Position:

Heisenberg Exchange

Spectral-Spatial Image in Perspective

Shin, Ewert, Budil, Freed BJ 59, 950 (1991)

Generalized Cumulant Expansions (GCE) and Spin-Relation Theory (Freed, JCP 49 376 (1968))

1. How to deal with break-down of Motional Narrowing (WBR) Theory Based on GCE method of Kubo.

2. Leads to Relaxation Matrix to all orders:

for t τ≫ c with R(n)

of order

Here H1(t) is the fluctuating time-dependent portion of the Spin Hamiltonian Operator and τc a correlation time.

This is a Complex Expansion in powers of

3. Also shows how to introduce “finite time” corrections when τc t . ≳

† 11 ( ) n n

ct -

†1 ( ) ct

The Stochastic Liouville Equation (SLE) and Slow Motional ESR (with Bruno and Polnaszek, JPC

75, 3385 (1971) ) Kubo (1969)

showed this with heuristic argument.

Freed (1972) showed this with generalized moment expansion.

Hwang & Freed (1975) developed this by passing to semi-classical limit from quantum stat. mech. Leads to a “spin-force” and/or “spin-torque” back-reaction of spins on bath. Confirms high T limit.

Wassam & Freed (1982) developed this from even more general many-body quantum stat. mech.

ρ : Spin Density MatrixH(t): Random Hamiltonian

P(, t) : Probability of finding at t . time independent Markoff Operator.Leads to SLE:

ρ(,t): Joint Spin Density Matrix As Well As Classical Probability Density in .

Very Slow Motion

IncipientSlow Motion Slow Motion

ABSORPTION

DERIVATIVEIncipientSlow Motion

Very Slow Motion

Slow Motion

Line Shapes for S= ½, I= 1 (14N nucleus) with axially symmetric g tensor, hyperfine tensor, and small ωn.

PADS in Frozen D2O at -65°C. S. A GoldmanVery Slow Motion--- Experimental Calculated for Brownian Diffusion

N

O

SO3-

-

O3S

[K+]2

( ),i tt -

H

P( , t) = P( , )tt

-

Brownian vs. Jump Diffusion: Slow Motional Fits. Fluctuating Torques (Fast Bath Modes) vs. Slowly Relaxing Structures (Slow Bath Modes)

Electron Spin Relaxation of Nitroxide Probes in Solution: Fast & Slow Motions and Search for a

Model (with Hwang, Mason & Hwang, JPC 79, 489 (1975))

PD-Tempone

Non-secular spectral densities:  j(ω)≈ τR/[1+ε2τR

2]-1, ε >1

τR vs. η/T over five orders of magnitude

Comparison of experiment and simulated spectra in the model-dependent slow-tumbling region for PD-Tempone in toluene-d8

Efficient Computation of ESR Spectra and Related Fokker-Planck Forms by the Use of the

Lanczos Algorithm (LA) (with Moro, JCP 74 , 3757 (1981))

Spectrum from SLE:

This was the first significant application of the LA to Complex Symmetric (non-Hermitian) Matrices. Leads to Order(s) of Magnitude Reduction in Computer Space &Time.

Derivative spectrum for

nonaxial g tensor

L - Liouville operator associated with spin Hamiltonian - Symmetrical diffusion operatorν> - Vector of allowed spectral components

The Lanczos algorithm : Let L By operating with A n times on ν> & simple rearranging, an n-dimensional orthonormal sub-set of the N >> n total basis set is obtained such that An is tri-diagonal with An= PnAPn

-1 where Pn projects out the “Relevant Sub-Space.”

Lanczos Steps rapidly converge to solution

( 11I( ) Re{ [i 1 ] }

- - L

Distribution of the eigenvalues for calculation. Units are in G; x & y axis represent real & imaginary parts of the eigenvalues. from Lanczos algorithm; exact.

Liquid Crystals Yield an Anisotropic Environment:

U() : Anistropic PotentialA challenge to diagonalization: Leads to non-symmetric matrices. Render symmetric by similarity transformation:

Symmetrized Diffusion Operator:

M: Vector Operator which generates an infinitesimal Rotation.T ≡ iMU() is the external torque derived from the potential U().

Yielding:

ESR and Spin Relaxation in Liquid Crystals (with C.F. Polnaszek, JPC 79 2282, (1975))

Comparison of experimental (-----) and theoretical ( ) spectra for PD-Tempone in Phase V stresses the need for SRLS model.

1/20P( ,t) P ( ) P( ,t)-

2

M R MU T R TM R M +2κT (2κT)

P t P( ,t) -

P ( ) exp( U( )/kT) d exp ( U( )/kT)o - -

More evidence for SRLS from High Pressure Experiments

High Pressure ESR(J.S. Hwang and K.V.S. Rao, JPC 80, 1490 (1976))

General Theoretical Analysis Led to Expressions for SRLS Spectral Density (JCP, 66, 483 (1977):

Where τR’-1= τR

-

1+ τx-1 and

κ=1/5 for isotropic medium. Later referred to as “Model Free” expression.

Comparison of experimental and simulated spectra at 45°C for PD-Tempone in Phase V (a) 3450 bars (b)4031 bars ( - - - -) experimental results; (· - · - ·) and ( ) theoretical results for different models.

Graph of τR vs. pressure for PD Tempone in phase V.

ESR High Pressure Vessel (Hydraulic)

10kbarmaximum

Slow-Wave Helix

Electron Spin Relaxation & Ordering In Smectic & Nematic Liquid Crystals

Meirovitch, Igner, Igner, Moro & Freed, 77, 3915 (1982)

ESR spectra of 10-3 M P probe in smectic A phase of S2 for various orientations θ between ňm & B.

ESR spectra calculated based on model of cooperative chain distortions

The structures of some liquid crystals & some ESR spin probes.

MOMD ( Microscopic Order Macroscopic Disorder) Model

Meirovitch, Nayeem & Freed, JPC, 88, 3454 (1984)

Spectra simulated according to the MOMD model with decreasing ordering & increasing motional rates from top to bottom, illustrating typical temperature-induced spectral evolution of the ESR response from lipid dispersions doped with extended-chain doxy1 nitroxides.

A) ESR spectra of the doxylstearic acids I(m,n) in egg phosphatidylcholine randomly oriented on small glass beads (phospholipid: spin-label molar ratio 150:1). (B) ESR spectra from rabbit small intestinal brush border vesicle membranes doped with 12,3-DPPC.

The molecular motion is with respect to a local

“static” ordering potential, which is disordered

on a macroscopic scale.

SRLS (Slowly Relaxing Local Structure) Model

Polimeno & Freed, JPC, 99, 10995 (1995)

Reference frames which define the structural and dynamic properties of the combined system of spin-bearing probe molecule and solvent cage: LF = lab frame, DF = director frame, MF = molecular frame, CF = cage frame, GF = g tensor frame, AF = A tensor frame.

SRLS potential vint(β,γ) obtained from the best fit to the PDT in toluene spectrum. This figure corresponds to the following order parameters for PDT in the solvent cage: (D2

00) = -0.437, (D202) = -0.482, (D4

00) = 0.271, (D200) = 0.253.

The SRLS model allows for the (slow) motion of the local structure that is

“frozen” in MOMD.

Fabry-Perot cavityM indicates mirror assembly

ESR Spectroscopy at 1 MM Wavelengths: FIR-ESR

(with Lynch & Earle, Rev. Sci. Instrum. 59, 1345, (1988))First Quasi-Optical ESR Spectrometer – Transmission Mode

Newer: Quasi-Optical Reflection Bridge Significant Increase in

S/N (with Earle & Tipikin, RSI, 67, 2502

(1996)

*A motionally narrowed

spectrum at 9 GHz looks

slow motional at 250 GHz.

Duplexing Grid

Paraboloidal Focusing

Mirror

Detector

Fabry Perot Resonator

Source

Coupling Lens

Paraboloidal Focusing Mirror

Gaussian Beam

Two- Mirror

Telescope

Flat Mirror

Polarization Transforming Reflector

Corrugated Wave-Guide

Focusing Lens

Coupling MeshESR Spectra of PD-Tempone at 250 & 9.5 GHz in solvents of

increasing viscosity (a-e).

250 GHz Studies of Molecular

DynamicsDynamic Cage Effects

Above the Glass Transition

(with Earle, Moscicki, Polimeno, JCP, 106, 9996, (1997))

Rotational Diffusion Rates for Probes dependent upon their

size.Relaxation of cage is the

same for all the probes.

Cage potential parameters below TM (nominal melting temperature) depend on

size & shape of probe; above TM they all are zero.

Experimental ESR spectra taken at 250GHz covering the entire temperature range of liquid to glassy behavior: (a)PDT; (b) MOTA; and (c) CSL.

OTPSolvent

CSL

MOTA

PDT

PDTMOTA

CSL

OTP Cage

Nitroxide labeled CSL was studied in oriented membranes. A special “shunt”

Fabry-Perot resonator enabled study of both 0°C and 90°C orientation.

In PC:PS 80:20 , CSL shows typical characteristics: long axis of CSL parallel to bilayer normal. As mole fraction of PS increases a second

component grows in. A detailed analysis shows that CSL senses a local, strongly biaxial environment.

Dynamics and Ordering in Mixed DMPC/DMPS Membranes

(with Barnes, BJ 75, 2532 (1998))

Excellent Orientational

Resolution Enabled Key Qualitative

Features of Model to be “read off”

the spectra before detailed analysis.

10°C Gel Phase

Model in DMPS: A cutting motion of CSL between domains of DMPS

Shunt Fabry-Perot Resonator with Adjustable Interferometer

Provides extensive experimental data to study microscopics of molecular dynamics.

The multi-frequency ESR studies to date cannot be adequately fit with simpler models,

but require the SRLS model, which provides adequate fit.

Complex Dynamics of Spin-Labeled T4 Lysozyme

Multi-Frequency ESR & Molecular Dynamics in Biophysical Systems

(with Zhang, Fleissner, Tipikin, Liang, Moscicki, Lou, Ge, & Hubbell, JPCB, 105, 11053 (2001); 114, 5503 (2010).

Complex Dynamics of Membranes

Standard MOMD fits are

in disagreement. Only by the SRLS

analysis could results at both frequencies be fit simultaneously &

with physically sound axial alignment of the

acyl chains.

Spectra At 4 Frequencies Were Fit Simultaneously To SRLS.

Yields 3 Distinct Components

32°C

22°

12°

2°

Two-Dimensional Fourier Transform ESR: 2D-ELDOR *

(with Gorcester, JCP 85, 5375 (1986); 88, 4678 (1988))

Absolute Value

2-D ELDOR of PD-

tempone in toluene-d8 at

21°C. Tmix= 3 10-7 s.Cross-peaks

due to Heisenberg

Spin Exchange.

Spectrum after LPSVD:

Pure 2D- Absorption

representation.

2D-FT-ESR Spectrometer Block Diagram

2D-ELDOR pulse sequence: 3 /2 pulses

Quadrature Mixer

DC Block

Isolator

Modulator GaAsFET

Pre-Amplifier

Pin Diode LimiterTWT Amplifier

* Original CW-ELDOR: Hyde, Chien, Freed JCP, 48, 4211 (1968)

2D-ELDOR & Slow Motions

(with Lee, Patyal, Saxena, Crepeau CPL 221, 397 (1994))

with SRLS Analysis (with Polimeno, JPC, 99, 10995 (1995))

The experimental technology for 2D-ELDOR had progressed substantially & the detailed theory based on the SLE was fully developed along with NLLS analysis.

By obtaining 2D-ELDOR spectra at 6-8 different mixing times → actually a 3rd dimension to the experiment.

We found the spin-relaxation and motional dynamics information is very extensive. Simple motional models could not fit data very well, so we applied the SRLS model with considerable success:

In a complex fluid, one expects the molecular reorientation to be non-Markovian. It is modeled in SRLS by both the Smoluchowski-type diffusive rotation of the probe in a mean potential, and the diffusive operator for the reorientation of the local structure (the cage) formed by the molecules in the immediate surroundings of the probe. Their collective motion constitutes a multi-dimensional Markov process.

Reference Frames for SRLS

LF – Lab FrameDF – Director FrameMF – Molecular FrameCF – Cage FrameGF – g-tensor FrameAF – A tensor Frame

Sc-

Sc+

Time Domain in 2D-ELDOR Spectra

CSL in Macroscopically

Aligned Smectic A phase of

Liquid Crystal 4O, 8 (59°C).

(Sastry, et al., JCP 105, 5753 (1996))

2D-ELDOR in Liquid Crystals: Multitude of Relaxation & Dynamic Data

Tm=110 ns Tm=250 ns

Optimum parameters obtained from fits to the SRLS Model (10 such Parameters). Shows that in lower temperature phases the dynamic cage freezes in to contribute to macro ordering

SRLS vs. Simple Fit of just Brownian Reorientation in a

Macroscopic Aligning Potential

ESR Study of Heisenberg Spin Exchange in a Binary Liquid Solution near the Critical Point

Heisenberg spin‐exchange contribution ωHE to the ESR linewidth of the di‐t‐butyl nitroxide (DTBN) radical dissolved in mixtures of 2,2,4‐trimethylpentane & n‐perfluoroheptane.

The critical composition χ(C8 H18) = 0.58.

Exhibits an anomaly in the macroscopic kinematic viscosity ν near Tc = 23.91°C (for 4.3 x 10-3M DTBN).

In the critical region, ωHE is not linear in T/ν. Instead, it is linear in T/ν′

Here ν′ is the macroscopically measured viscosity, but with the ``anomalous portion'' subtracted out.

The experiments near the critical region required temperature stability & control to within ±0.01°C at the ESR sample.

Lang & Freed, JCP, 56, 4103 (1972)

Short range biomolecular collisions are unaffected by

long-range diverging hydrodynamic viscous

modes.

Divergence of Orientational Order Fluctuations about the Nematic-Isotropic Weakly First-Order

Phase Transition (with Rao and Hwang PRL, 37, 515, (1976) & JCP 66, 4183, (1977))

Variation of B & C values with temperature.

Linewidth = A+BMI + CM2I 

MI is 14N nuclear spin quantum number

ESR spectra of PD-Tempone in MBBA near Tc = 41.4°C

Obeys Landau-de Gennes Mean Field Theory :Isotropic Phase  Diverges as (T – T*)-1/2 Nematic Phase Diverges as (T†-

T)-1/2

Divergences are due to fluctuations in thenematic order parameter as seen by the spin

probe.

Divergence is symmetric about

Isotropic-Nematic Phase Transition

Critical Fluctuations & Molecular Dynamics at Liquid Crystalline

Phase Transitions

Zager, Freed, CPL, 109, 270(1984)Nayeem, Rananavare, Sastry & Freed, JCP 96, 3912 (1992)

Nematic-Isotropic Transition: σ = ½ according to Mean Field Theory for Weak First Order Transitions: Pre-transitional nematic fluctuations affect probe rotational dynamics.

Nematic-Smectic Transitions σ = 1/3 according to scaling laws analogous to the λ transition in He for 2nd order transition: Pretransitional fluctuation in smectic order affect position of probe in smectic layer: Expulsion of probe to lower-density regions of transitory smectic layer.

Structures of some nitroxide spin probes.

Tricritical Points in the Nematic to Smectic Phase Transition

The straight-line fit to curve 1 yields an exponent β2 = 1.00 ± 0.005, the expected mean-field prediction.

Phase diagram for mixtures of 4O, 6 & 6O,4 shown as a plot of nematic order parameter S versus the NA phase transition temperature, TNA (x).

Rananavare, Pisipati & Freed, CPL, 140, 255 (1987); Rananavare, Pisipati & Freed, Liq. Crys. 3, 957 (1988)

Phase Diagram of He3-He4 Mixtures.

C is Tricritical Point.

The nematic order parameter S is plotted versus McMillan ratio, M(n, m) = TAN/TNI for nO.m homologues. The straight line fit yields a β2 = 0.94± 0.12 and MTCP = 0.959 ± 0.005.

Excellent discrimination of the three phases of mixed model membranes of DPPC/Cholesterol with 16 PC

Dynamic Molecular Structure of Phase Domains in Model & Biological Membranes by 2D-ELDOR

(with Chiang, Costa-Filho, JPCB, 111, 11260 (2007))

The excellent resolution allowed the analysis of the effects of a complex biological process upon plasma membrane vesicles (PMV) (with Chiang, Costa-Filho & Baird, JPCB, 115, 10462 (2011).)

Absoption Spectra in

Normalized Contour Mode: Shows

Homogeneous

Linewidths.

Yields this

Phase Diagram

Effects onPMV of

Crosslinking of IgE

Receptors

Pure Absorptio

n Compone

nts for coexisting Lo & Ld phases

The tie-line fields for co-existing lipid phases could also be determined by ESR . (Smith & Freed, JPCB, 113, 3957 (2009)

% Population of Lo Phase: decreases when

receptors are crosslinked.

Lipid-Gramicidin Interactions: Dynamic Structure of the Boundary Lipid by 2D-ELDOR

2D-ELDOR, with its enhanced spectral resolution to dynamic structure provides a reliable & useful way of studying lipid-protein interactions. The 2D-ELDOR spectra of the end-chain spin label 16-PC in DPPC/GA vesicles is composed of two components, which are assigned to the bulk lipids (with sharp auto peaks & crosspeaks) & to the boundary lipids (with broad auto peaks). These spectra shows relatively faster motions & very low ordering for the end chain of the bulk lipids, whereas the boundary lipids show very high “y-ordering” & slower motions. The y-ordering represents a dynamic bending at the end of the boundary lipid acyl chain, which can then coat the GA molecules.

Costa-Filho, Crepeau, Borbat, Ge & Freed, Biophys. J., 84, 3364 (2003)

(A)Sketch of the effects of the presence of GA molecules in lipid biolayer at concentrations lower & higher than DPPC/GA = 15. (B) Molecular structure of the spin label 16-PC in its all-trans conformation (z-ordering).

2D-ELDOR contours for 16-PC at 35, 53, & 71°C, & mixing time Tm = 1600 ns. (A) 1:1 DPPC:GA; (B) 3:1 DPPC:GA; (C) 5:1 DPPC:GA; (D) pure DPPC.

Protein Structure Determination Using Long-Distance Constraints from Double-Quantum Coherence (DQC) ESR:

T4–Lysozyme (with Borbat & Mchaourab , JACS 124, 5304 (2002))

DQC-ESR Pulse Sequence /2 pulses = 3.2 ns pulses = 6.4 ns

Triangulation

T4L

Left: Time evolution of DQC Signal from doubly labeled T4L; Right : their FT’s

Accounting for Flexibility of Tether

Structureless Protein Which Binds to Membranes: α – Synuclein (with Georgieva, Ramlall, Borbat, Eliezer, JBC, 285 , 28261 (2010))

Protein Superstructure: Bridging the Gap Between X-ray Crystallography and Cyro-EM by Pulse-Dipolar ESR

(with Bhatnagar, Borbat, Pollard, Bilwes, Crane, Biochem. 49, 3824 (2010))

The End