1. ROBINSONROBINSON Simulation of EPR Spectra and Modeling Dynamics Effects Focus on Nitroxides Spectra Include: G, A, and Dipolar tensors and Super Hyperfine (SHF) Effects Not commenting on Zero Field Splitting (ZFS) Tensors Dynamics effects on Lineshape Uniform Modes; Rapid Internal modes (of limited amplitude) Analytic Theories and Trajectories Approaches to Simulations Molecular-Collision Effects E.G. Oxygen Broadening, other Spin Relaxants Can we obtain structural information in the presence of dynamics? Redfield type Relaxation (first Principles) Can we use the dynamics theory to predict relaxation rates?

2. ROBINSONROBINSON Spectrometer Characteristics Can we take advantage of different data types to enhance dynamics information? Obtain/Simulate Spectra at Multiple Frequencies Saturation and Saturation Transfer Techniques CW-Progressive Saturation Technique Zeeman Modulation and Over-Modulation Different Fourier Components of Spectra Harmonics with respect to Zeeman Modulation Zeeman Frequency Effects (Simplicity of Spectra in low frequency limit). Simulation of Time Domain Spectra ESE, FID, SR, pELDOR, more-complex Pulsed Experiments Generalized Global Analysis Improved methods for fitting spectra and refining the simulations

3. ROBINSONROBINSON Simulation Strategies for Dynamics What sort of theoretical approaches are there for the simulation of EPR spectra? Analytic Methods such as MOMD (Microscopic Order; Macrosocopic Disorder) ie. Restoring Potential included in the diffusion operator. (I’m not distinguishing between transition rate method and eigenfunction expansion.) Trajectory Methods (Uses MM or BD methods) A combination of approximate methods with lots of uncontrolled (adjustable/floating) parameters. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much nearer the truth. -- Alfred N. Whitehead Quoted in W H Auden and L Kronenberger The Viking Book of Aphorisms (New York 1966).

4. ROBINSONROBINSON Three Reference Spectra 50 mer DNA 20º C in Buffer taux,y=150ns tauz=13 ns Perdeuterated-CTPO 100% glycerol, @ -15º C; tauiso=170ns isotropic motion simulation. Three spectra that should be fit very well. The DNA does not fit well under higher power. The BSA and CTPO do not fit well as they stand now. Tensors are floated. Deutero-Msl-BSA in 60% Glycerol at 2ºC “Best” isotropic Simulation overlaid

5. ROBINSONROBINSON Spin-Spin Interactions and Dynamics Hustedt et al Biophys J, 74, 1997 Dipolar Coupled Nitroxide Spins separated by 13Å bound to GAPDH. Use Multi-Frequency Data Improve accuracy (via error surfaces)

6. ROBINSONROBINSON Modulation Frequency Effects Taking Advantage of modulation frequency to obtain more accurate dynamics information Hustedt & Beth Biophys J. 65, 1995 STEPR spectra of msl- Band3, with a uniaxial rotational model, rotational correlation time of ~15 microseconds

7. ROBINSONROBINSON Side Chain Dynamics Using Analytic Theory with MOMD model to restrict side chain motion Sl-T4 lysozyme (at sites 44 and 69). 9 GHz 250 GHz Barnes et al Biophysical J. 76, 1999

8. ROBINSONROBINSON Trajectory Simulations Theory applied to isotropic rotational motion, for a range of motional rates. Comparison of spectra from MD generated trajectories overlaid with Freed’s Analytic Theory at the same effective rotational correlation time Steinhoff & Hubbell, Biophys J. 71, 1996 Method Utilized also by Robinson Hustedt Levine

9. ROBINSONROBINSON Side Chain Motion from MD Steinhoff & Hubbell, Biophys J. 71, 1996 Simulated EPR Spectra from three positions of sl-tri- Lucine Experimental sl-BR spectra in the D-helix

10. ROBINSONROBINSON Trajectories but no simulations Trajectory simulations were performed on protein side chains of myosin light chain containing nitroxide spin labels. The order parameters were calculated and compared with the experimentally determined order parameters. LaConte et al 83, 2002

11. ROBINSONROBINSON CWEPR Spectra for sl-DNAs: Pre-Averaging of Tensors Two different isotopes of spin labels. For duplex DNAs of different lengths, with the spin label uniquely in the middle of each DNA. Simulations overlaid. Okonogi et al, Biophys J. 72, 98; 77, 99; 78, 00; PNAS 99, 02 Semi-Analytic Method Only one adjustable parameter for each fit.

12. ROBINSONROBINSON DNA spin labeled with a different probe Using the DUTA probe of Bobst. Freed’s group simulated the spectra as a function of DNA length. Freed found two components (~90/10%). The slower component times tracked the DNA length despite the small order parameter (~0.33); smaller than previous slide (~0.95). Analytic Method (MOMD/SRS) Liang et al J. Phys. Chem. 104, 2000

13. ROBINSONROBINSON G C G A G A G A C C G G G C U C U C U G G C C C 5' 3' 5' 3' C 40 U 23 U 25 38 EPR Spectra of Spin-Labeled TAR RNAs

14. ROBINSONROBINSON native Ca 2+ Na + G C G A G A G A C C G G G C U C U C U G G C C C 5' 3' 5' 3' C 40 U 23 U 25 38 Edwards, T. E., et. al. Chem. Biol. 2002, 9(6), in press EPR of TAR RNAs in the Presence of Cations

15. ROBINSONROBINSON “Dynamic Signature”: from EPR Spectra Obtain “characteristic information but NO spectral Simulations. Very difficult problem: Internal Dynamics, uniform modes, differential structures, etc.

16. ROBINSONROBINSON Structures of TAR RNA (High-Resolution Crystals)

17. ROBINSONROBINSON Proper Simulations should use/extract proper Rates: Can CW give correct relaxation rates? Yes if: Tensors are right Super Hyperfine Interactions are correct Dynamics are “Tractable” Now Compare CW and TD Techniques CW Technique is Progressive Saturation STEPR is a CW techniques that relies on R 1e (but the rate is an ad hoc parameter) Generally one does not simulate (partially)-saturated spectra, but it would provide more information.

18. ROBINSONROBINSON TEMPOL: first harmonic Center line of 14 NH 18 Tempol in water. Low power Absorption Dispersion Abs-Quad Disp-Quad

19. ROBINSONROBINSON TEMPOL: second harmonic Center line of 14 NH 18 Tempol in water. Low power Absorption Dispersion Abs-Quad Disp-Quad

20. ROBINSONROBINSON From CW Fits: Super Hyperfine Structure of TEMPOL Carbon 13 lines at 1.1% Obtained directly from the perdueterated spectra. Thee relaxation rates compare favorably to the theory Spin Rotation mechanism predicts ~ 70 to 80 mG (dominant term for spin lattice relaxation). The combined END and CSA mechanisms on the center line are also around ~60 mG. The sum of these two rates (130-140mG) dominates the spin-spin relaxation time. Essential: Absorption to Dispersion Ratio and Out of Phase dispersion (1 st Harmon)

21. ROBINSONROBINSON Super Hyperfine Pattern FID and theory with shf and no adjustable parameters Single exponential Pattern of 3075 shf lines from Tempol protons and carbons

22. ROBINSONROBINSON Are CW and TD results equivalent? Now examine the connection between R 1e and R 2e obtained from CW spectra and the Time Domain FID and SR spectra

23. ROBINSONROBINSON FID as a function of Carrier Offset Experimental Full simulation Simple SHF Pattern No Adjustable Parameters:

24. ROBINSONROBINSON SR Signal and Simulation Stimulated 0.5 Gauss off Resonance Stimulated on Resonance No adjustable Parameters in Fit, using exact (protonated TEMPOL) SHF pattern. Notice early time is not a “pure” recovery Best single exponential is 1.95 Mrads/sec, vs 1.64 in this simulation; no adjustable parameters

25. ROBINSONROBINSON FID of Perdeuterated TEMPOL FID for the center 14 N line of 0.25 mM 14 ND 17 TEMPOL in H 2 O at 20 o C Solid lines are fits to the product of a Gaussian and an exponential decay, no adjustable parameters. Best single exponential –dashed lines With O 2 Without O 2

26. ROBINSONROBINSON Human Secretory Phospholipase sPLA2 A highly charged (+20 residues) lipase And a highly charged (-70 mV) membrane All exposure data was determined by SR and pELDOR directly measuring spin-lattice relaxation rates.

27. ROBINSONROBINSON Reference Spectra and Spin Labeled sPLA2 14 ND 13 CTPO in 85% Glycerol 14 N MTSSL sl-hGIIA-sPLA 2 on micelles solvent accessibility Canaan et al. J. Biol. Chem. 2002

28. ROBINSONROBINSON Spin Lattice Relaxatin Rates for sl-sPLA2 rates from pSR and pELDOR for CTPO solvent accessibility

29. ROBINSONROBINSON Spin Lattice Relaxation Rates Electron and Nuclear Spin Lattice Relaxation Rates for 15N model nitroxides (CTPO) in glycerol water mixtures. The 14N version gives nearly the same rates. Spin Rotation END (A & G) tensors Spin Rotation plus O2 Relaxant Electron Spin Lattice Nuclear Spin Lattice Spin Diffusion (Methyl Groups)

30. ROBINSONROBINSON NaCl reduces Crox Relaxivity Increasing Salt at high [Crox]Increasing Relaxant [Crox]; no Salt Same Spectra

31. ROBINSONROBINSON Comparison of TD and CW measurement of Relaxivity Relaxivity of N70 sl-sPLA2 in 50 mM Tris/HCl buffer. Theory required +25 mV potential and is a double exponential dependence on [NaCl] CW values inherently off by 25%.

32. ROBINSONROBINSON Sl-DNA: CW and TD Data Saturation Recovery on low field line

33. ROBINSONROBINSON O 2 relaxant on sl-DNA 15 N spin labeled 50-mer duplex DNA in 0% sucrose at 20 o C Rotational Correlation time (perp)= Cannot simulate spectra accuratly O 2 increases relaxation as it does on proteins in aqueous buffer Robert: In your fig 15, can those spectra be simulate d? What about Tamara’s simulatio ns??

34. ROBINSONROBINSON Conclusions for Discussion and the Future Many Spectrometer Frequencies (Identify anistropy and hindered motions) Don’t forget about low frequencies especially for Dynamics Using GGA with many different spectral components related by known ways (Zeeman Freq, Amplitude, Microwave Power, temperature, etc.) Use TD methods to obtain accurate relaxation parameters: A first principles Relaxation Matrix and relaxation rates. Use CW to obtain accurate SHF patterns (calibration spectra) Use Robust Dynamics Modeling methods to include the details of molecular motion.

35. ROBINSONROBINSON Relaxant Method: Nitroxide Spectra depend on concentration of relaxants Spin-Spin (T1 or R1 processes) Spin-Lattice (T2 or R2 processes) Rates are increased by the same amount due to additional relaxing agents (relaxants).

36. ROBINSONROBINSON Obtaining Relaxation Information Time Domain (Saturation Recovery or Pulsed ELDOR) depends on R1, directly. CW method (progressive saturation or rollover”) depends on P2. Signal Height is a function of incident microwave power:

37. ROBINSONROBINSON Errors of Fitting to TEMPOL data Chi Squared values for fits to TEMPOL spectra. The model completely accounts for the partially- saturating rf power

38. ROBINSONROBINSON Relations among various spectral components In Low Zeeman Modulation Frequency Limit: Spectra can be interconnected The Dispersion Absorption Ratio was critical to finding right SHF model So are other components rather simply related (at low Zeeman Frequency). Modulation amplitude (over modulation) highlights the simple relations Even for out of phase (STEPR) signals. Marsh’s comments about integrated Absorption signal being modulation amplitude independent (app., depends on Mod Freq). Show an example of this.

39. ROBINSONROBINSON Over Modulation Effects (I) Under STEPR conditions, h1=0.36 G, @ 62kHz Zeeman Modulation 50 mer-duplexDNA; buffer. Data: One Gauss Mod Amp; Convolution (black) of top spectrum (blue). No adjustable parameters. Data: 5 G (p/p) mod amp

40. ROBINSONROBINSON Over Modulation Effects (II) Under STEPR conditions, h1=0.36 G, @ 62kHz Zeeman Modulation 50 mer-duplexDNA; buffer. Convolving first harmonic to second harmonic in phase. No adjustments for convolution, no rescaling to fit.

41. ROBINSONROBINSON Over Modulation Effects (III) Under STEPR conditions, h1=0.36 G, @ 62kHz Zeeman Modulation 50 mer-duplexDNA; buffer. Convolving first harmonic to second harmonic OUT of phase (black line). No adjustments for convolution, no rescaling to fit. The STEPR spectrum: Second Harmonic Out of Phase under saturation First Harmonic Out of Phase at 1 Gauss Zeeman, under Saturation

42. ROBINSONROBINSON Over Modulation (IV) Convolve 0.5G to 4 G (black) and compare with experimental spectra (red). Second Haromonic out of phase STEPR spectra and 0.5G convolution (Black) overlaid. Msl-BSA 60% Glycerol, 2C STEPR signal (I.e. under saturation)

43. ROBINSONROBINSON C2 Domain of cPLA2 Stereo View looking onto the Membrane. Notice the 3 looped regions near Ca (green) ions.

44. ROBINSONROBINSON C2 Domain of cPLA2 Exposure Factor to aqueous Crox, a spin relaxant for nitroxide spin labels on C2 residues. Solid line is Poisson Boltzmann theory for the exposure factor. Negative r values are into the membrane. R=0 is near the phosphate head groups of the (artificial) anionic membrane (DTPM).