Simulation of EPR Spectra and Modeling Dynamics Effects

1
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
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
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. (Im 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.
WhiteheadQuoted in W H Auden and L Kronenberger
The Viking Book of Aphorisms (New York 1966).
4
Three Reference Spectra
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
50 mer DNA 20º C in Buffer taux,y150ns tauz13
ns
Perdeuterated-CTPO 100 glycerol, _at_ -15º C
tauiso170ns isotropic motion simulation.
5
Spin-Spin Interactions and Dynamics
Dipolar Coupled Nitroxide Spins separated by 13Å
bound to GAPDH.
Use Multi-Frequency Data Improve accuracy (via
error surfaces)
Hustedt et al Biophys J, 74, 1997
6
Modulation Frequency Effects
STEPR spectra of msl-Band3, with a uniaxial
rotational model, rotational correlation time of
15 microseconds
Taking Advantage of modulation frequency to
obtain more accurate dynamics information
Hustedt Beth Biophys J. 65, 1995
7
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
Trajectory Simulations
Theory applied to isotropic rotational motion,
for a range of motional rates.
Comparison of spectra from MD generated
trajectories overlaid with Freeds Analytic
Theory at the same effective rotational
correlation time
Method Utilized also by Robinson Hustedt Levine
Steinhoff Hubbell, Biophys J. 71, 1996
9
Side Chain Motion from MD
Simulated EPR Spectra from three positions of
sl-tri-Lucine
Experimental sl-BR spectra in the D-helix
Steinhoff Hubbell, Biophys J. 71, 1996
10
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
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.
Semi-Analytic Method Only one adjustable
parameter for each fit.
Okonogi et al, Biophys J. 72, 98 77, 99 78, 00
PNAS 99, 02
12
DNA spin labeled with a different probe
Using the DUTA probe of Bobst. Freeds 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
EPR Spectra of Spin-Labeled TAR RNAs
14
EPR of TAR RNAs in the Presence of Cations
native Ca2 Na
Edwards, T. E., et. al. Chem. Biol. 2002, 9(6),
in press
15
Dynamic Signature from EPR Spectra
Obtain characteristic information but NO
spectral Simulations. Very difficult problem
Internal Dynamics, uniform modes, differential
structures, etc.
16
Structures of TAR RNA (High-Resolution Crystals)
17
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 R1e (but the rate is an ad hoc
parameter) Generally one does not simulate
(partially)-saturated spectra, but it would
provide more information.
18
TEMPOL first harmonic

• Center line of 14NH18 Tempol in water. Low power

Absorption
Abs-Quad
Dispersion
Disp-Quad
19
TEMPOL second harmonic

• Center line of 14NH18 Tempol in water. Low power

Abs-Quad
Absorption
Disp-Quad
Dispersion
20
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 (1st Harmon)
21
Super Hyperfine Pattern

• Pattern of 3075 shf lines from Tempol protons and
  carbons

22
Are CW and TD results equivalent?

• Now examine the connection between
• R1e and R2e obtained from
• CW spectra and the
• Time Domain FID and SR spectra

23
FID as a function of Carrier Offset
No Adjustable Parameters

• Experimental Full simulation
  Simple SHF Pattern

24
SR Signal and Simulation
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
FID of Perdeuterated TEMPOL

• FID for the center 14N line of 0.25 mM 14ND17
  TEMPOL in H2O at 20oC

With O2
Without O2
Best single exponential dashed lines
Solid lines are fits to the product of a Gaussian
and an exponential decay, no adjustable
parameters.
26
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
Reference Spectra and Spin Labeled sPLA2
Canaan et al. J. Biol. Chem. 2002
14ND13 CTPO in 85 Glycerol
14N MTSSL sl-hGIIA-sPLA2 on micelles
solvent accessibility
28
Spin Lattice Relaxatin Rates for sl-sPLA2
rates from pSR and pELDOR for CTPO
solvent accessibility
29
Spin Lattice Relaxation Rates
Nuclear Spin Lattice
Spin Rotation plus O2 Relaxant
Spin Rotation
Electron and Nuclear Spin Lattice Relaxation
Rates for 15N model nitroxides (CTPO) in glycerol
water mixtures. The 14N version gives nearly the
same rates.
END (A G) tensors
Electron Spin Lattice
Spin Diffusion (Methyl Groups)
30
NaCl reduces Crox Relaxivity
Increasing Salt at high Crox
Increasing Relaxant Crox no Salt
Same Spectra
31
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
Sl-DNA CW and TD Data
Saturation Recovery on low field line
33
O2 relaxant on sl-DNA
O2 increases relaxation as it does on proteins in
aqueous buffer
Robert In your fig 15, can those spectra be
simulated? What about Tamaras simulations??
15N spin labeled 50-mer duplex DNA in 0 sucrose
at 20oC Rotational Correlation time
(perp) Cannot simulate spectra accuratly
34
Conclusions for Discussion and the Future
Many Spectrometer Frequencies (Identify
anistropy and hindered motions) Dont 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
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
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
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
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. Marshs
comments about integrated Absorption signal being
modulation amplitude independent (app., depends
on Mod Freq). Show an example of this.
39
Over Modulation Effects (I)
Under STEPR conditions, h10.36 G, _at_ 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
Over Modulation Effects (II)
Under STEPR conditions, h10.36 G, _at_ 62kHz Zeeman
Modulation 50 mer-duplexDNA buffer.
Convolving first harmonic to second harmonic in
phase. No adjustments for convolution, no
rescaling to fit.
41
Over Modulation Effects (III)
Under STEPR conditions, h10.36 G, _at_ 62kHz Zeeman
Modulation 50 mer-duplexDNA buffer.
First Harmonic Out of Phase at 1 Gauss Zeeman,
under Saturation
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
42
Over Modulation (IV)
Msl-BSA 60 Glycerol, 2C STEPR signal (I.e. under
saturation)
Second Haromonic out of phase STEPR spectra and
0.5G convolution (Black) overlaid.
Convolve 0.5G to 4 G (black) and compare with
experimental spectra (red).
43
C2 Domain of cPLA2
Stereo View looking onto the Membrane. Notice
the 3 looped regions near Ca (green) ions.
44
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.
R0 is near the phosphate head groups of the
(artificial) anionic membrane (DTPM).