Overview of EPR Methods to Measure Interspin Distances

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Overview of EPR Methods to Measure Interspin
Distances
Sandra S. Eaton, University of Denver
ACERT Workshop, August 7, 2004
Funding EB002807
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Outline

• Dipolar Interaction
• Two slowly relaxing spins
• Half-field transition
• Lineshape changes
• Fourier deconvolution
• Pulse methods
• Rapidly relaxing spin slowly relaxing
• T1e
• T2
• Fluid Solution

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Dipolar Interaction
The energy of interaction of a magnetic dipole ?1
with magnetic dipole ?2 at distance r is
More generally, considering the vector properties
of the magnetic dipoles
Which is proportional to (1-3 cos2q) where q is
the angle between the interspin vector and the
external magnetic field.
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Dipolar Splittings
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Weak and Strong Exchange Cases
Figure prepared by Gunnar Jeschke
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Interaction between two slowly relaxing spins
Typically two spin labels. Could apply to metal
radical distance if measurement is done at
sufficiently low temperature that the metal is
relaxing slowly relative to the dipolar coupling.
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Human Carbonic Anhydrase II
Selected distances in HCA II 67-206 121-206 67-12
1 59-174
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Half-Field Transitions
Dipolar interaction between two spins shifts the
triplet state ms ? 1 energy levels relative to
the ms 0 level, and causes the normally
forbidden transition probability between the ms
-1 and ms 1 levels to become non-zero. This
transition occurs at half the magnetic field
required for the allowed transitions (at constant
microwave frequency), and hence is called the
half-field transition.
r is the interspin distance in Å and ? is the
microwave frequency, in GHz, at which the
experiment was performed.
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Resolved Splittings of CW Spectra

• Analysis by computer simulation of lineshapes
• For shorter distances may need to include
  exchange as well as dipolar interaction
• In favorable cases may be able to define the
  relative orientations of the interspin vector and
  hyperfine axes for two labels.
• Usually assumes that relative orientations of
  magnetic axes for two centers are well defined
• Analysis of data at two microwave frequencies may
  be required to obtain definitive results.

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Half-field Transitions and CW Simulations
Interspin distance is 7 8 Å The relative
intensity of the half-field transition is 1.7x10-4
Doubly-labeled
Sum of spectra of Singly-labeled
After subtraction of singly-labeled, with
simulation
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Fourier Convolution/Deconvolution

• Assume random distribution of relative
  orientations or interspin vector and hyperfine
  axes.
• Fourier convolve spectrum of singly-labeled
  sample with broadening function to match spectrum
  of doubly-labeled samples
• OR
• Divide Fourier transform of doubly-labeled
  spectrum by Fourier transform of singly-labeled
  spectrum to obtain broadening function
• Calculate the interspin distance from the
  "average" broadening.

M. D. Rabenstein and Y.-K. Shin, Proc. Natl.
Acad. Sci (US) 92, 8329 (1995). H.-J. Steinhoff
et al., Biophys J. 73, 3287 (1997).
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Fourier Deconvolution
Doubly-labeled
Sum of singly-labeled
After subtraction
Note that the baseline for the deconvoluted
function is close to zero for the subtracted
spectrum.
r 8 9 Å
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Simulation and Fourier Deconvolution
First integral
r 16 18 Å
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The echo intensity is recorded as a function of
t. In the absence of dipolar interaction, a pulse
at frequency 2 has no impact on echo intensity at
frequency 1. Dipolar interaction causes
oscillation in echo intensity with a period that
is characteristic of the interspin distance.
M. Pannier, S. Veit, G. Jeschke, and H. W.
Speiss, J. Magn. Reson. 142, 331 (2000).
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DEER measurement of distance between spin labels
in carbonic anhydrase
r 18 Å (70) 24 Å 30)
r 20 1.8 Å
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Distances (Å) Between Spin Labels on Carbonic
Anhydrase Determined from EPR Spectra
aDistance between b-carbons of native amino acids
at the sites where substitution with cysteine
was performed, calculated from the X-ray crystal
structure, b Including unconstrained contribution
from singly-labeled protein, cAssuming 100
doubly-labeled protein.
Persson et al., Biophys. J. 80, 2886 (2001).
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Other pulsed techniques for measuring distances
between two slowly relaxing spins
Double-Quantum Coherence will be covered in
subsequent lectures. Out-of-phase echo
Specific to spin-correlated radical pairs.
Very powerful in photosynthesis.
Hoff et al., Spectrochim. Acta 54, 2283 (1998).
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Measuring Distance Between a Rapidly Relaxing
Metal Ion and a Slowly Relaxing Spin
Types of systems

• Heme iron and a spin label
• Iron-sulfur cluster and a semiquinone radical

Approaches

• Changes in spin lattice relaxation times (T1e)
  measured by saturation recovery
• Changes in spin-spin relaxation times (T2)
  measured by two-pulse spin echo

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Spin-labeled metmyoglobin
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Saturation and Relaxation
After a brief exposure to the microwave field,
the populations of the spin energy levels would
become equal, if there were no way for the
electrons to relax back to the ground state. In
fact, there are many mechanisms for spins to
relax back to the ground state.
P.F. Knowles, D. Marsh, H.W. E. Rattle, Magnetic
Resonance of Biomolecules, Wiley, 1976.
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Relaxation Times

• Two relaxation times are fundamental to the
  narrowest EPR line, which we call spin packets.
• T1 characterizes the relaxation of the spin from
  the excited state to the ground state
  longitudinal relaxation spin-lattice
  relaxation.
• T2 is called the transverse relaxation time or
  the spin-spin relaxation time. In the simplest
  case, it is due to the variation in resonant
  fields that result from other spins in the
  vicinity.
• Usually, T1 is much longer than T2.
• If T1 is short enough, it may determine T2, and
  then the line width is characterized by T1 T2.

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Distance Determination by Saturation Recovery
Measurement of Changes in T1e

• Dipolar interaction between a rapidly relaxing
  center and a more slowly relaxing center enhances
  the spin lattice relaxation rate for the more
  slowly relaxing center.
• Measurements are made of the relaxation times for
  the two centers in the absence of interaction.
• The saturation recovery curve for the more slowly
  relaxing center is measured in the presence of
  the interaction.
• Studies have been done with spin-labeled
  hemoglobin and variants of myoglobin prepared by
  site-directed mutagenesis.

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Measure Metal Relaxation Rates Low Spin
Metmyoglobin
Temperature dependence of X-band spin-lattice
relaxation rates for 1 mM imidazole adducts of
metmyoglobin variants R-Mb-V66C-Im and
R-Mb-K98C-Im () and 1 mM cyanide adducts
R-Mb-V66C-CN, R-Mb-K98C-CN, and horse heart
myoglobin cyanide (?) in 11 waterglycerol. The
solid lines through the data are the fits to the
experimental data. The contributions from
individual processes to the relaxation for the
imidazole adducts are direct ( _ . . _ . . _),
Raman (- - - ), and thermal mode (_ . _ . _ ).
(Figure reproduced from Zhou et al., 1999).
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SR curves for Spin-Labeled Cyano-methemoglobin
Saturation recovery curves for the nitroxyl
signal in spin-labeled methemoglobin cyanide in
11 bufferglycerol at 9.2 GHz and 15, 59, and
120 K. The dashed lines were calculated for r
15.5 Å (Reproduced from Seiter et al., 1995).
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Bloembergen Equation

• where "f" and "s" denote the fast- and
  slow-relaxing spins, respectively,
• T1so is T1 for the slowly-relaxing spin in the
  absence of spin-spin interaction,
• T1s is T1 for the slowly-relaxing spin perturbed
  by the fast-relaxing spin,
• S is the electron spin on the faster-relaxing
  center,
• ?f and ?s are the resonant frequencies for the
  fast- and slow-relaxing spins,
• r is the interspin distance,
• J is the electron-electron exchange interaction
  for the Hamiltonian written as
• -JS1.S2, and
• is the angle between the interspin vector and
  the external magnetic field.
• For metals with S gt ½ and large ZFS additional
  terms including ZFS in the denominator are
  required.

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Characteristics of metal ion that maximize its
impact on spin label relaxation

• Rapid relaxation at lower temperature where probe
  relaxation is slower.
• Values of g near 2.00 maximize the B term.
• Contribution from C term is maximized when metal
  relaxation rate is comparable to the EPR
  frequency.

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Impact of Rapidly Relaxing Metal on Nitroxyl CW
Spectra and on Tm
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Two-pulse Spin Echo Decays for MbA15C-CN
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Spin-Labeled Low-Spin Methemoglobin
1/Tm at the center of the nitroxyl signal in
spin-labeled oxy-hemoglobin (?), two different
spin labels attached to methemoglobin cyanide
(, ?), and spin-labeled methemoglobin
imidazole (?). Although the ESE curves are not
single exponentials, a fit to a single
exponential was used to obtain a qualitative
description of the temperature dependence of
1/Tm. The lines connect the data points
(reproduced from Budker et al., 1995).
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Analysis of electron spin echo decay for nitroxyl
interacting with a rapidly relaxing metal ion.

• E(2t) R-2exp(-2t/tC)tC-2sinh2(Rt)R2cosh2(Rt)
  
• RtC-1sinh(2Rt)D2sinh2(Rt)
  
• where
• E(2t) intensity of echo as a function of
  interpulse spacing, t
• tC correlation time for the dynamic process
  (T1fT2f)1/2
• ½ the angular frequency different between the
  two sites that are averaged by the dynamic
  process
• R2 tC-2 D2

Zhidomirov, G. M., Salikhov, K. M., Sov. Phys.
JETP 29, 1037 (1969).
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Echo Decay Curves with Simulations
Mb-A15C-CN r 28.3 Å Simulated based on
dynamic averaging of dipolar splitting due to
rapid Fe(III) relaxation.
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Relative Echo Intensity Calculated for Low-spin
Fe(III)
Relative echo intensity calculated for a nitroxyl
spin label interacting with low-spin met
myoglobin Fe(III)-imidazole at t 500 ns for a
range interspin distances.
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Relative Echo Intensities for Spin-Labeled
Metmyoglobin
The intensity of a two-pulse spin echo obtained
with 40 and 80 ns pulses and interpulse spacing
of 200 ns was measured as a function of
temperature. The minimum value correlates with
the interspin distance determined by saturation
recovery.
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Relative Echo Intensity for Spin-Labeled Mb
A19C-CN at ? 200 ns
Simulation includes a distribution in iron
relaxation rates.
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Relative Echo Intensities for Spin-Labeled
MbA57C-CN at ? 500 ns
Simulation includes a contribution from
hemichromes
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Comparison of Distances Obtained by ESE and SR
Data for 13 spin-labeled myoglobin variants. The
distances obtained by ESE are systematically
longer than from SR. This is the direction that
would be observed if there were a distribution of
distances. The impact of the dipolar interaction
on the ESE minimum intensity varies as r-3 but
the impact on T1e varies as r-6.
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Summary of Methods in Rigid Lattice
Approaches to Measuring Distances

• Two slowly relaxing spins
• Half-field transition
• Lineshape changes
• Fourier deconvolution
• Pulse methods
• Rapidly relaxing spin slowly relaxing
• Saturation Recovery Measurements of Changes in
  T1e
• Two-pulse spin echo measurements on echo decay
  shapes and relative echo intensities

These techniques all measure the
electron-electron dipolar interaction.
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Line Broadening in Fluid Solution
Berengian et al., J. Biol. Chem. 274, 6305-6314
(1999).
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Fourier Deconvolution in Fluid Solution

• Analysis of spectra of doubly-labeled T4 lysozyme
  in 40 sucrose solution at ambient temperature.
• Comparison of spectrum of double mutant (D) with
  sum of spectra of single mutants (S).
• Comparison of deconvolution of D with S and the
  sum of Pake patterns obtained by fitting
  procedure.
• Comparison of spectrum (D) with simulated
  spectrum (S convoluted with Pake functions)
• Distance distribution corresponding to sum of
  Pake functions.

Altenbach et al., Biochemistry 40, 15471 (2001)
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Pulse Methods in Fluid Solution

• Best for small dipolar couplings
• To avoid averaging small dipolar couplings
  molecular tumbling would have to be very slow.
• Long T2 is needed for pulse methods, which is
  difficult to achieve in fluid solution.

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Relaxation Enhancement in Fluid Solution

• T1
• Accessible distance range will be smaller than in
  a rigid lattice because T1 for organic radicals
  is shorter in fluid solution.
• Requires metal ion with relaxation times in the
  correct range, i.e. about 10-10 to 10-11. Two
  possibilities may be Cu2 and Gd3.
• T2
• T2 at ambient temperatures typically is quite
  short.
• Not likely to have a metal with relaxation rate
  comparable to dipolar couplings at ambient
  temperature.

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Further Information
Biological Magnetic Resonance , vol. 19, 2001
Distance Measurements by EPR Biological
Magnetic Resonance, vol. 23, 2004
Biomedical ESR - Part A Free Radicals, Metals,
Medicine, and Physiology Biological Magnetic
Resonance, vol. 24, 2004 Biomedical ESR -
Part B Methodology, Instrumentation and Dynamics