ESR Perspective on Complex Liquids (A Retrospective)

1. PHYSICAL CHEMISTRY AWARD SYMPOSIUM 247th ACS National Meeting, Dallas, TX Joel Hildebrand Award March 18, 2014 ESR Perspective on Complex Liquids(A Retrospective) Jack H. FreedDept. of Chemistry & Chemical BiologyCornell UniversityIthaca, New York 14853 USA www.acert.cornell.edu

2. ESR Hyperfine Linewidths of Radicals in Solution Asymmetric Linewidth Variation Spectrum of para-dinotrobenzene anion radical -55C DMF Alternating Linewidth - Spectrum of para-dinotrodurene anion radical in 20C DMF Alternating LW’s : Out-of-phase correlation between the HF splittings of the two nitroxides. Terms in the perturbation H1(t).a 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)

3. Anistropic Rotational Diffusion & ESR Spectral 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 peroxylaminedisulfonate(PADS), with a simple 3 line 14NESR Spectrum • in ice clathrate cage • in glycerol solvent [K+]2 Freed, JCP, 56, 716 (1972)

4. Electron Spin Relaxation and Molecular Dynamics in Liquids: Solvent Dependence PD-Tempone 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” Non-secular spectral densities: j(ω)≈ τR/[1+ε2τR2]-1, ε >1 Zager & Freed, JCP,77, 3344 (1982) τRvs. η/T over five orders of magnitude

5. Electron-Spin Relaxation and Molecular Dynamics in Liquids: Pressure Dependence vs vη/kBTfor PD-Tempone in toluene-d8. Variable pressure and temperature results. Empirical Fit to 60 Data Points τR/η/T) = a + bP+ cP2+dT+eT2+fPT 6 parameter fit gives R2 = 0.90 Removes scatter in τR Yields factor of 2 scatter in τR • Plot of average value of τRT/ηβfor each constant density group (CDG) vs density, ρ 60 Data Points: 52C >T> -40 C 1 bar ≤ P< 5 kbar v = solute volume η = solvent viscosity β = isothemalcompressibility Led to Empirical Fit to all data points to τRT/ηβ=C(ρ- ) /ρ With C=32 10-8K s kbar/cP = 0.845 g/cm2 → The “expanded volume” = Zager & Freed, JCP, 77, 3360 (1982)

6. 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.

7. Translational Diffusion: Heisenberg Spin Exchange &ESR Spectra • 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 interaction • τ1 is the lifetime of exchange pair • τ2 is the time between the biomolecular collisions. 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 = 4πdDfN τ1-1 = (6D/d2)feu Where N = radical density D = diffusion coefficient d = interaction distance for exchange f = (u/eu-1) and u = U(d)/kT are corrections for intermolecular potential energy at contact distance. • Width for aqueous solutions of PADS at 24°C as a function of electrolyte concentration. Eastman, Kooser, Das & Freed,JCP, 51, 2690 (1969) ; 52, 2511 (1970)

8. Translational Diffusion Coefficients by ESR Imaging of Concentration Profiles: DID-ESR Sample Preparation Using 1D field gradients & cw-ESR accurate translational diffusion coefficients ranging from 10-5to 10-9 cm2/s were measured in isotropic & anisotropic fluids. Smectic Liquid Crystal, S2 Small Probe: PDT D D> 1 Large Probe: CSL D D< 1 ) D,PDT Concentration Profiles for Tempone diffusing in a nematic phase at 300K at increasing times. D ,PDT D D= 1.41± 0.1 Nematic D ,CSL D ,CSL • Lateral diffusion of CSL( ) • & 16PC (-  - ) in phospholipid POPC vs. cholesterol m.f. at different temperatures . CSL is Cholesterol Analogue Spin Probe ISOTROPIC/NEMATIC LIQUIDS: Dto NematicDirector. D to NematicDirector Hornak, Moscicki, Schneider, Shin, Freed (JCP, 84, 1886 (1986); Biophys. J. 55, 537 (1989); JCP 99, 634 (1993))

9. Along Spatial Axis to Display The Spatial Distribution: Macroscopic Diffusion Microscopic vs. Macroscopic Diffusion Coefficients by ESR Spectral-Spatial Imaging Along Spectral Axis to Display Spectral Linewidth Dependence on Position: Heisenberg Exchange Spectral-Spatial Image in Perspective • Aligned POPC Membrane/16PC • DID-ESR: Macroscopic Diffusion • Heisenberg Exchange broadening vs. concentration gradient: Microscopic Diffusion • At 22°C : • Dmacro= (2.3 ± 0.4) X 10-8cm2/sec • Dmicro= (1.0 ± 0.4) X 10-7cm2/sec Shin, Ewert, Budil, Freed BJ 59, 950 (1991)

10. Generalized Cumulant Expansions (GCE) and Spin-Relation Theory (Freed, JCP 49 376 (1968)) • How to deal with break-down of Motional Narrowing (WBR) Theory Based on GCE method of Kubo. • Leads to Relaxation Matrix to all orders: for t ≫ τc 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 • Also shows how to introduce “finite time” corrections when τc ≳ t .

11. The Stochastic Liouville Equation (SLE) and Slow Motional ESR (with Bruno and Polnaszek, JPC 75, 3385 (1971) ) ABSORPTION DERIVATIVE Incipient Slow Motion Incipient Slow Motion Slow Motion • 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 Matrix H(t): Random Hamiltonian Very Slow Motion Very Slow Motion Slow Motion P(, t) : Probability of finding  at t .  time independent MarkoffOperator. 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 Goldman Very Slow Motion --- Experimental Calculated for Brownian Diffusion Leads to SLE: ρ(,t): Joint Spin Density Matrix As Well As Classical Probability Density in . [K+]2

12. Electron Spin Relaxation of Nitroxide Probes in Solution: Fast & Slow Motions and Search for a Model (with Hwang, Mason & Hwang, JPC 79, 489 (1975)) Comparison of experiment and simulated spectra in the model-dependent slow-tumbling region for PD-Tempone in toluene-d8 Brownian vs. Jump Diffusion: Slow Motional Fits. Fluctuating Torques (Fast Bath Modes) vs. Slowly Relaxing Structures (Slow Bath Modes) PD-Tempone τRvs. η/T over five orders of magnitude Non-secular spectral densities: j(ω)≈ τR/[1+ε2τR2]-1, ε >1

13. 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: Distribution of the eigenvalues for calculation. Units are in G; x & y axis represent real & imaginary parts of the eigenvalues. from Lanczos algorithm;  exact. L - Liouvilleoperator associated with spin Hamiltonian  - Symmetrical diffusion operator ν> - 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-1where Pn projects out the “Relevant Sub-Space.” Derivative spectrum for nonaxialg tensor 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. Lanczos Steps rapidly converge to solution

14. ESR and Spin Relaxation in Liquid Crystals (with C.F. Polnaszek, JPC 79 2282, (1975)) Liquid Crystals Yield an Anisotropic Environment: Symmetrized Diffusion Operator: M: Vector Operator which generates an infinitesimal Rotation. T ≡ iMU() is the external torque derived from the potential U(). Yielding: U() : Anistropic Potential A challenge to diagonalization: Leads to non-symmetric matrices. Render symmetric by similarity transformation: Comparison of experimental (-----) and theoretical ( ) spectra for PD-Tempone in Phase V stresses the need for SRLS model.

15. 10kbar maximum High Pressure ESR(J.S. Hwang and K.V.S. Rao, JPC 80, 1490 (1976)) More evidence for SRLS from High Pressure Experiments Graph of τRvs. pressure for PD Tempone in phase V. 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. General Theoretical Analysis Led to Expressions for SRLS Spectral Density (JCP, 66, 483 (1977): Where τR’-1= τR-1+ τx-1and κ=1/5 for isotropic medium. Later referred to as “Model Free” expression. Slow-Wave Helix ESR High Pressure Vessel (Hydraulic)

16. Electron Spin Relaxation & Ordering In Smectic & Nematic Liquid Crystals ESR spectra of 10-3 M P probe in smectic A phase of S2 for various orientations θ between ňm& B. • The structures of some liquid crystals & some ESR spin probes. ESR spectra calculated based on model of cooperative chain distortions Meirovitch, Igner, Igner, Moro & Freed, 77, 3915 (1982)

17. MOMD ( Microscopic Order Macroscopic Disorder) Model The molecular motion is with respect to a local “static” ordering potential, which is disordered on a macroscopic scale. • 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. • 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. Meirovitch, Nayeem & Freed, JPC, 88, 3454 (1984)

18. SRLS (Slowly Relaxing Local Structure) Model The SRLS model allows for the (slow) motion of the local structure that is “frozen” in MOMD. • 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: • (D200) = -0.437, (D202) = -0.482, (D400) = 0.271, (D200) = 0.253. Polimeno & Freed, JPC, 99, 10995 (1995)

19. 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  (withEarle & Tipikin, RSI, 67, 2502 (1996) Fabry-Perot cavity M indicates mirror assembly Fabry Perot Resonator • ESR Spectra of • PD-Temponeat • 250 & 9.5 GHz in solvents of increasing • viscosity (a-e). Coupling Mesh ParaboloidalFocusing Mirror Corrugated Wave-Guide Polarization Transforming Reflector Detector *A motionally narrowed spectrum at 9 GHz looks slow motional at 250 GHz. Duplexing Grid Focusing Lens Gaussian Beam Two- Mirror Telescope Flat Mirror Source ParaboloidalFocusing Mirror Coupling Lens

20. PDT MOTA 250 GHz Studies of Molecular Dynamics CSL Dynamic Cage Effects Above the Glass Transition (with Earle, Moscicki, Polimeno, JCP, 106, 9996, (1997)) Experimental ESR spectra taken at 250GHz covering the entire temperature range of liquid to glassy behavior: (a)PDT; (b) MOTA; and (c) CSL. OTP Solvent PDT MOTA CSL OTP Cage 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.

21. Dynamics and Ordering in Mixed DMPC/DMPS Membranes (with Barnes, BJ 75, 2532 (1998)) 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. 10°C Gel Phase Excellent Orientational Resolution Enabled Key Qualitative Features of Model to be “read off” the spectra before detailed analysis. Model in DMPS: A cutting motion of CSL between domains of DMPS Shunt Fabry-Perot Resonator with Adjustable Interferometer

22. Multi-Frequency ESR & Molecular Dynamics in Biophysical Systems (with Zhang, Fleissner, Tipikin, Liang, Moscicki, Lou, Ge, & Hubbell, JPCB, 105, 11053 (2001); 114, 5503 (2010). 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 Membranes Complex Dynamics of Spin-Labeled T4 Lysozyme 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. 32°C 22° 12° 2° Spectra At 4 Frequencies Were Fit Simultaneously To SRLS. Yields 3 Distinct Components

23. 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. Two-Dimensional Fourier Transform ESR: 2D-ELDOR *(with Gorcester, JCP 85, 5375 (1986); 88, 4678 (1988)) Quadrature Mixer DC Block Isolator Modulator GaAsFET Pre-Amplifier Pin Diode Limiter TWT Amplifier 2D-ELDOR pulse sequence: 3 /2 pulses 2D-FT-ESR Spectrometer Block Diagram * Original CW-ELDOR: Hyde, Chien, Freed JCP, 48, 4211 (1968)

24. 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. Sc- Sc+ Time Domain in 2D-ELDOR Spectra 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 Frame DF – Director Frame MF – Molecular Frame CF – Cage Frame GF – g-tensor Frame AF – A tensor Frame

25. 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 Tm=110 ns Tm=250 ns 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 SRLS vs. Simple Fit of just Brownian Reorientation in a Macroscopic Aligning Potential

26. ESR Study of Heisenberg Spin Exchange in a Binary Liquid Solution near the Critical Point • Heisenberg spin‐exchange contribution ωHE to the ESR linewidthof 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 νnear 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. Short range biomolecular collisions are unaffected by long-range diverging hydrodynamic viscous modes. Lang & Freed, JCP, 56, 4103 (1972)

27. Divergence of OrientationalOrder Fluctuations about the Nematic-IsotropicWeakly First-Order Phase Transition (with Rao and Hwang PRL, 37, 515, (1976) & JCP 66, 4183, (1977)) Divergences are due to fluctuations in the nematic order parameter as seen by the spin probe. Divergence is symmetric about Isotropic-Nematic Phase Transition 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*)-1/2NematicPhase Diverges as (T†- T)-1/2

28. Critical Fluctuations & Molecular Dynamics at Liquid Crystalline Phase Transitions • 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. Zager, Freed, CPL, 109, 270(1984) Nayeem, Rananavare, Sastry & Freed, JCP 96, 3912 (1992)

29. Tricritical Points in the Nematic to Smectic Phase Transition • 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). • The nematic order parameter S is plotted versus McMillan ratio, M(n, m) = TAN/TNI for nO.mhomologues. The straight line fit yields a β2 = 0.94± 0.12 and MTCP = 0.959 ± 0.005. • The straight-line fit to curve 1 yields an exponent β2 = 1.00 ± 0.005, the expected mean-field prediction. Phase Diagram of He3-He4 Mixtures. C is Tricritical Point. Rananavare, Pisipati & Freed, CPL, 140, 255 (1987); Rananavare, Pisipati & Freed, Liq. Crys. 3, 957 (1988)

30. 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. Effects on PMV of Crosslinking of IgE Receptors Excellent discrimination of the three phases of mixed model membranes of DPPC/Cholesterol with 16 PC Yields this Phase Diagram % Population of Lo Phase: decreases when receptors are crosslinked. Pure Absorption Components 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)

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

32. 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 T4L Triangulation Accounting for Flexibility of Tether Left: Time evolution of DQC Signal from doubly labeled T4L; Right : their FT’s

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

34. The End