Report

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. Freed Dept. of Chemistry & Chemical Biology Cornell University Ithaca, New York 14853 USA www.acert.cornell.edu ESR Hyperfine Linewidths of Radicals in Solution Alternating Linewidth - Spectrum radical in 20C DMF Asymmetric Linewidth Variation Spectrum of paradinotrobenzene anion radical -55C DMF Alternating LW’s : Outof-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) of para-dinotrodurene anion Terms in the perturbation H1(t).a 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) . For Anisotropic Brownian Motion: They depend on eigenvalues of Rotational Diffusion Tensor (e.g. Perrin, Favro) (Freed, JCP, 41, 2077, 1964). The dependence on nuclear spin quantum numbers MN & MH enable several independent quantities to determine this tensor. An Analysis of the p-dinitrobenzene anion linewidth (plus some assumptions about internal dynamics) yields: [K+]2 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 Spectrum ∥ /⊥ = . ± in ice clathrate cage ∥ /⊥= . ± in glycerol solvent Freed, JCP, 56, 716 (1972) 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+ε2τR2]-1, ε >1 τR vs. η/T over five orders of magnitude Zager & Freed, JCP,77, 3344 (1982) Electron-Spin Relaxation and Molecular Dynamics in Liquids: Pressure Dependence vs vη/kBT for PD-Tempone in toluene-d8. Variable pressure and temperature results. Yields factor of 2 scatter in τR 60 Data Points: 52C >T> -40 C 1 bar ≤ P< 5 kbar v = solute volume η = solvent viscosity β = isothemal compressibility Zager & Freed, JCP, 77, 3360 (1982) Removes scatter in τR Empirical Fit to 60 Data Points τR/η/T) = a + bP+ cP2+dT+eT2+fPT 6 parameter fit gives R2 = 0.90 Plot of average value of τRT /ηβ for each constant density group (CDG) vs density, ρ Led to Empirical Fit to all data points to τRT/ηβ=C(ρ- ) /ρ With C=32 ×10-8 K × s × kbar/cP = 0.845 g/cm2 → The “expanded volume” = ≡ − 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. 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: Width vs. concentration for TCNE— samples in DME T = 15° C) Where J is the exchange interaction τ1 is the lifetime of exchange pair τ2 is the time between the biomolecular collisions. 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. Intermolecular Dipolar Interactions are not Important here. Can show [(T2)-1 dipole/ (T2-1) exchange] = K(η/kT)2 “for strong exchange” = J2τ12 >> 1 ∝ ℏ η = solvent viscosity Eastman, Kooser, Das & Freed,JCP, 51, 2690 (1969) ; 52, 2511 (1970) Translational Diffusion Coefficients by ESR Imaging of Concentration Profiles: DID-ESR 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. (− ) Concentration Profiles for Tempone diffusing in a nematic phase at 300K at increasing times. D ,PDT D ,PDT D D = 1.41± 0.1 Nematic D ,CSL D ,CSL ISOTROPIC/NEMATIC LIQUIDS: D to Nematic Director. D to Nematic Director Sample Preparation Smectic Liquid Crystal, S2 Small Probe: PDT D D > 1 Large Probe: CSL D D < 1 Lateral diffusion of CSL( & 16PC (- - ) in phospholipid POPC vs. cholesterol m.f. at different temperatures . CSL is Cholesterol Analogue Spin Probe Hornak, Moscicki, Schneider, Shin, Freed (JCP, 84, 1886 (1986); Biophys. J. 55, 537 (1989); JCP 99, 634 (1993)) ) Along Spatial Axis to Display The Spatial Distribution: Macroscopic Diffusion Microscopic vs. Macroscopic Diffusion Coefficients by ESR SpectralSpatial Imaging Aligned POPC Membrane/16PC • • Along Spectral Axis to Display Spectral Linewidth Dependence on Position: Heisenberg Exchange Spectral-Spatial Image in Perspective 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) 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: ∞ This is a Complex Expansion in powers of (t ) c † 1 () = = for t ≫ τc with R(n) of order † 1 (t ) n 3. n -1 c Here H1(t) is the fluctuating timedependent portion of the Spin Hamiltonian Operator and τc a correlation time. Also shows how to introduce “finite time” corrections when τc ≳ t . The Stochastic Liouville Equation (SLE) and Slow Motional ESR (with Bruno and Polnaszek, JPC 75, 3385 (1971) ) t - i H ( t ), ρ : Spin Density Matrix H(t): Random Hamiltonian t P ( , t) = - P ( , t ) 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 . Kubo (1969) showed this with heuristic argument. Freed (1972) showed this with generalized moment expansion. Hwang & Freed (1975) developed this by passing to semiclassical 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. ABSORPTION Incipient Slow Motion Very Slow Motion DERIVATIVE Incipient Slow Motion Slow 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 Goldman Very Slow Motion --- Experimental Calculated for Brownian Diffusion [K+]2 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 modeldependent slow-tumbling region for PDTempone in toluene-d8 PD-Tempone τR vs. η/T over five orders of magnitude Non-secular spectral densities: j(ω)≈ τR/[1+ε2τR2]-1, ε >1 Brownian vs. Jump Diffusion: Slow Motional Fits. Fluctuating Torques (Fast Bath Modes) vs. Slowly Relaxing Structures (Slow Bath Modes) Efficient Computation of ESR Spectra and Related FokkerPlanck Forms by the Use of the Lanczos Algorithm (LA) (with Moro, JCP 74 , 3757 (1981)) Spectrum from SLE: I( ) 1 R e{ [i ( 1 - L ] -1 } L - Liouville operator associated with spin Hamiltonian - Symmetrical diffusion operator ν> - Vector of allowed spectral components Distribution of the eigenvalues for calculation. Units are in G; x & y axis represent real & imaginary parts of the eigenvalues. △ from Lanczos algorithm; exact. 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 tridiagonal with An= PnAPn-1 where Pn projects out the “Relevant Sub-Space.” 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 Lanczos Steps rapidly converge to solution ESR and Spin Relaxation in Liquid Crystals (with C.F. Polnaszek, JPC 79 2282, (1975)) Liquid Crystals Yield an Anisotropic Environment: Po ( ) exp ( - U ( )/kT ) d exp ( - U ( )/kT ) U() : Anistropic Potential A challenge to diagonalization: Leads to nonsymmetric matrices. Render symmetric by similarity transformation: P ( ,t) P0 ( ) - 1/ 2 P ( ,t) Symmetrized Diffusion Operator: M R M + M R MU 2 κT TR T (2 κT ) 2 M: Vector Operator which generates an infinitesimal Rotation. T ≡ iMU() is the external torque derived from the potential U(). Yielding: P t - P ( ,t) Comparison of experimental (-----) and theoretical ( ) spectra for PDTempone in Phase V stresses the need for SRLS model. High Pressure ESR(J.S. Hwang and K.V.S. Rao, JPC 80, 1490 (1976)) More evidence for SRLS from High Pressure Experiments 10kbar maximum Graph of τR vs. 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. SlowWave Helix ESR High Pressure Vessel (Hydraulic) 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. 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. Meirovitch, Igner, Igner, Moro & Freed, 77, 3915 (1982) ESR spectra calculated based on model of cooperative chain distortions 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) SRLS (Slowly Relaxing Local Structure) Model 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. The SRLS model allows for the (slow) motion of the local structure that is “frozen” in MOMD. 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) ESR Spectroscopy at 1 MM Wavelengths: FIR-ESR (with Lynch & Earle, Rev. Sci. Instrum. 59, 1345, (1988)) First Quasi-Optical ESR Spectrometer – Transmission Mode Fabry-Perot cavity M indicates mirror assembly Newer: Quasi-Optical Reflection Bridge Significant Increase in S/N (with Earle & Tipikin, RSI, 67, 2502 (1996) Fabry Perot Resonator Coupling Mesh ESR Spectra of PD-Tempone at 250 & 9.5 GHz in solvents of increasing viscosity (a-e). Paraboloidal Focusing Mirror Detector Focusing Lens *A motionally narrowed spectrum at 9 GHz looks slow motional at 250 GHz. Corrugated Wave-Guide Polarization Transforming Reflector Duplexing Grid Gaussian Beam TwoMirror Telescope Flat Mirror Source Coupling Lens Paraboloidal Focusing Mirror 250 GHz Studies of Molecular Dynamics Dynamic Cage Effects Above the Glass Transition (with Earle, Moscicki, Polimeno, JCP, 106, 9996, (1997)) PDT MOTA CSL 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. 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. 10°C Gel Phase 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. 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 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 SpinLabeled 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 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. Quadrature Mixer DC Block Isolator Modulator TWT Amplifier Spectrum after LPSVD: Pure 2D- Absorption representation. GaAsFET Pre-Amplifier Pin Diode Limiter 2D-FT-ESR Spectrometer Block Diagram * Original CW-ELDOR: Hyde, Chien, Freed JCP, 48, 4211 (1968) 2D-ELDOR pulse sequence: 3 /2 pulses 2D-ELDOR & Slow Motions (with Lee, Patyal, Saxena, Crepeau CPL 221, 397 (1994)) with SRLS Analysis (with Polimeno, JPC, 99, 10995 (1995)) Sc- Sc+ 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. 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 nonMarkovian. 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 2D-ELDOR in Liquid Crystals: Multitude of Relaxation & Dynamic Data Optimum parameters obtained from fits to the SRLS Model (10 Tm=110 ns CSL in Macroscopically Aligned Smectic A phase of Liquid Crystal 4O, 8 (59°C). (Sastry, et al., JCP 105, 5753 (1996)) Tm=250 ns 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. Short range biomolecular collisions are unaffected by longrange diverging hydrodynamic viscous modes. Lang & Freed, JCP, 56, 4103 (1972) 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)) Divergences are due to fluctuations in the nematic order parameter as seen by the spin probe. Divergence is symmetric about Isotropic-Nematic Phase Transition ESR spectra of PD-Tempone in MBBA near Tc = 41.4°C Variation of B & C values with temperature. Linewidth = A+BMI + CM2I MI is 14N nuclear spin quantum number Obeys Landau-de Gennes Mean Field Theory : Isotropic Phase Diverges as (T – T*)-1/2 Nematic Phase Diverges as (T†- T)-1/2 Critical Fluctuations & Molecular Dynamics at Liquid Crystalline Phase Transitions Structures of some nitroxide spin probes. 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: Pretransitional 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. 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). Tricritical Points in the Nematic to Smectic Phase Transition The straightline fit to curve 1 yields an exponent β2 = 1.00 ± 0.005, the expected mean-field prediction. Rananavare, Pisipati & Freed, CPL, 140, 255 (1987); Rananavare, Pisipati & Freed, Liq. Crys. 3, 957 (1988) 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. Phase Diagram of He3He4 Mixtures. C is Tricritical Point. Dynamic Molecular Structure of Phase Domains in Model & Biological Membranes by 2D-ELDOR (with Chiang, Costa-Filho, JPCB, 111, 11260 (2007)) Excellent discrimination of the three phases of mixed model membranes of DPPC/Cholesterol with 16 PC Absoption Spectra in Normalized Contour Mode: Shows Homogeneous Linewidths. Yields this Phase Diagram Effects on PMV of Crosslinking of IgE Receptors % 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) 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).) Lipid-Gramicidin Interactions: Dynamic Structure of the Boundary Lipid by 2D-ELDOR (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, with its enhanced spectral resolution to dynamic structure provides a reliable & useful way of studying lipid-protein interactions. 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) 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. 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 Left: Time evolution of DQC Signal from doubly labeled T4L; Right : their FT’s Triangulation Accounting for Flexibility of Tether 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)) The End