fajer's encyclopedia

8/8/2019 Fajer's Encyclopedia

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Electron Spin Resonance Spectroscopy Labeling in Peptide andProtein Analysis

Peter G. Fajer

in

Encyclopedia of Analytical Chemistry

R.A. Meyers (Ed.)

pp. 57255761

John Wiley & Sons Ltd, Chichester, 2000


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ESR LABELING IN PEPTIDE AND PROTEIN ANALYSIS 1

Electron Spin Resonance

Spectroscopy Labeling inPeptide and Protein Analysis

Peter G. Fajer

Florida State University, Tallahassee, USA

1 Introduction 2

2 Historical Perspective 2

3 Sample Preparation 3

3.1 Nitroxide Spin Labels 33.2 Labeled Sites 33.3 Attachment Rigidity 43.4 Impairment of Function/Structure of

Labeled Proteins 4

4 Techniques and Instrumentation 44.1 Continuous Wave Electron Spin

Resonance 44.2 Saturation Transfer Electron Spin

Resonance 84.3 Time Domain Methods 8

5 Applications of Spin Labeling 10

5.1 Protein Orientation 105.2 Protein Dynamics 135.3 Kinetic Experiments 205.4 Protein Folding 215.5 Ligand Binding 225.6 Distance Measurements 225.7 Structural Biology 26

6 Conclusion 30

Acknowledgments 30

List of Symbols 30

Abbreviations and Acronyms 31

Related Articles 32References 32

Electron spin resonance (ESR) is a powerful analytical

tool used in protein and peptide biochemistry. It is used

in the determination of secondary, tertiary and quaternary

protein structure and associated conformational changes.

Protein dynamics and the relative orientation of protein

components in ordered systems can also be measured. The

majority of proteins do not contain unpaired electrons

whose spin transitions give rise to an ESR signal, hencenecessitating the use of extrinsic probes called spin labels.

Spin labels are nitroxide derivatives with a stable unpaired

electron and a functional group for specific attachment to

the protein (covalent or as a ligand). The most popular

covalent sites are cysteine residues, which, if necessary, canbe introduced into the protein structure using molecular

biology techniques.

The physical basis for nearly all ESR applications is

the anisotropy of the nitroxide signal and the sensitivity

of the ESR spectra to various relaxation pathways. The

interaction between an electron of a spin label and

an external magnetic field depends on their relative

orientations. The splitting and the center of ESR spectra of

an oriented sample are used to determine the orientation

of labeled domains. For samples with little disorder the

orientational sensitivity is better than 1. The width of

the signal is proportional to the orientational disorder,which is used to measure conformational heterogeneity of

proteins.

If the spin label reorientates itself on the ESR timescale

(nanoseconds) then the spectral anisotropy is averaged.

The extent of averaging defines the ESR line shape which

is used to determine the rotational rate and anisotropy

of motion. The dynamic range of ESR is very broad,

rotational correlation times range from 1012 to 107s forconventional ESR and the sensitivity can be extended to

slower motions (103s) with nonlinear saturation transferelectron spin resonance (STESR). Protein (spin label)

mobility is used to follow conformational changes, steric

restrictions on the spin label and the formation of large

complexes.

Spin labels are also sensitive to the presence of other

paramagnetic species. Collisions with water and lipid-

soluble relaxing agents provide additional relaxation

pathways measured by changes in relaxation times. The

probability of these collisions reflects the accessibility of a

spin label to the relaxant. The periodic patterns along the

polypeptide chain of this accessibility are used to deter-

mine the secondary and tertiary structure of proteins. In

the presence of another bound spin label or a param-

agnetic metal complexed by histidine residues, spectra

become broadened by dipolar or exchange interactions.Both mechanisms depend on the distance between the

paramagnetic centers. Thus ESR can be used to determine

intra- and intermolecular distances. The range of sensi-

tivity is 525 A and there are intensive efforts to increasethe upper range to >50 A. ESR as a spectroscopic ruleris used in protein structure determination and the investi-

gation of macromolecular assembly processes and protein

folding.

The foremost limitation of spin labeling ESR is the

necessity to modify a protein with a spin probe. In some

cases, the spin labels may perturb protein function and

therefore cannot be used for spectroscopy. However, evenan unsuccessful modification that results in functional

Encyclopedia of Analytical Chemistry

R.A. Meyers (Ed.) Copyright John Wiley & Sons Ltd


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2 PEPTIDES AND PROTEINS

loss identifies functional regions of proteins and as such

represents successful mutational analysis experiments.

1 INTRODUCTION

A spinning electron orbiting around a nucleus is amagnetic dipole. When placed in an external magneticfield, the dipole aligns parallel or antiparallel with theexternal field. These two orientations of the magnetrepresent two energy levels, with the difference in energylevels of the electron spin proportional to the strengthof the magnetic field. The electron can be excited fromone level (i.e. parallel dipole orientation) to another(antiparallel orientation) by an oscillating magnetic field.

The energy of the oscillating field has to match the energydifference between the two levels. For a free electronin a magnetic field with a strength of a few hundredgauss, the frequency range of the exciting field is in themicrowave region of the electromagnetic wave spectrum.The resonance between the orbiting electron and themicrowave field forms the basis of ESR, also known aselectron paramagnetic resonance or electron magneticresonance.

ESR is commonly used to investigate protein andpeptide structure, particularly studies of molecular orien-tation, protein dynamics and ligand binding. Observationof a resonance requires samples containing an unpairedelectron, e.g. transition metals or organic radicals. Pro-teins and peptides are generally not paramagnetic andtherefore require the use of extrinsic probes called spinlabels. Spin labels are derivatives of nitroxides, smallstable organic radicals, which are covalently attached toprotein side chains or to metabolic substrates. In the lastdecade, the development of site-directed spin labeling(SDSL), which utilizes molecular biology to introducenew labeling sites, has established ESR as a proteinstructural determination technique. Patterns of side-chainmobility, accessibility to quenchers and the measurementof distances between spinlabels have allowed the determi-

nation of the secondary, tertiary and quaternary structureof proteins.

This article is focused exclusively on spin labelingapplications in protein and peptide biochemistry. Thevast literature on metalloproteins, photosynthesis andreactive radicals in biology is not discussed here, andinterested readers are directed to the many excellentreviews on these topics.1 6

2 HISTORICAL PERSPECTIVE

The first ESR experiments were performed by Zavoiskyat the University of Kazan (Russia) during the Second

World War.7 Inspired by the experiments of Gorter8

and Rabbi et al.9 on paramagnetic relaxation and atomicbeams, Zavoisky demonstrated resonance betweenmicrowaves and the precession of Cu2C ions in a mag-netic field. Resonance was observed as an absorptionof microwaves whenever the frequency of the oscil-lating microwave field was equal to the ion precessionfrequency.

In the decade following the Second World War, ESRwas the domain of physical chemists and physicists,with the first biological applications appearing in themid-1950s. This early work included structural studiesof metalloproteins,10 measurement of free radicals inbiological tissues,11 carbonized carbohydrates,12 andX-ray irradiated silk and hair.13 Assenheim provides an

excellent review of this early work with intrinsic ESRsignals.14

In 1965, McConnell introduced extrinsic spin labelsdesigned to label proteins. Using nitroxide derivativesfirst synthesized in Russia,15,16 McConnell et al. demon-strated a helixcoil transition of a polylysine peptide. 17

Since then, ESR spin labeling has been used to study con-formational changes in a number of proteins modified bymaleimide nitroxides, which specifically target cysteineresidues. However, reliance on the naturally occurringcysteine residue was a severe limitation. The SDSL strat-egy developed by Hubbell in 1989 employs molecular

biology to introduce new cysteines for spin label attach-ment. The use of SDSL to scan the protein sequencewith cysteines has stimulated the resurgence of ESR as astructural biology method.

The methodology of ESR was also undergoing an evo-lution. In 1957, Feher invented electron nuclear doubleresonance (ENDOR) spectroscopy, a combination ofboth ESR and nuclear magnetic resonance (NMR), 18

in which nuclear spin transitions are observed indirectlyby monitoring electron spin transitions. A few years later,electron electron double resonance (ELDOR) spec-troscopy was developed by Hyde et al.19 and Benderskiiet al.20 which allowed the measurement of spectral diffu-

sion between distinct spin populations. The developmentof spin-echo instruments by Mims et al.21 introducedtime-domain ESR in the 1960s. This was followed byFourier transform electron spin resonance (FTESR),developed independently in the 1980s by Eliav andFreed,22 Dinse et al.23 and Bowman.24 The first spinlabel applications appeared in 1986 when Gorester andFreed performed two-dimensional (2-D) FTESR experi-ments to measure spin dynamics.25

ESR moved towards high field (high frequency) withLebedev et al.s construction of a 150-GHz spectro-meter,26 followed by Freed et al.s 250-GHz spec-

trometer, which was based on quasi-optics. The latterinstrument was used extensively to investigate spin labels


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in biological systems.27 Ultra-high-field spectrometersoperating at 550 GHz now exist and their application tonitroxide labels is only a question of time.28

Readers interested in the history of ESR are directedto a series of historic recollections of the ESR pioneersassembled by Eaton et al.29

3 SAMPLE PREPARATION

3.1 Nitroxide Spin Labels

Proteins are ESR silent, with the exception of metallopro-teins, and must therefore be labeled with paramagnetic

probes. These probes, or spin labels, are nitroxide deriva-tives containing an unpaired electron in the pp orbitalof the NO bond (Figure 1ac). The nitroxide radicalis stable owing to the presence of methyl groups onneighboring carbon atoms. To limit flexibility, the NOgroup is enclosed in either a six-membered piperidineor a five-membered pyrrole ring. Pyrrole rings with anunsaturated bond are the least flexible.

The unpaired electron in the pp orbital also interactswith the spin of the nitrogen nucleus, splitting the ESRsignal into resonances corresponding to different nitrogennuclear manifolds. Thus, the number of resonant peaks

depends on the nitrogen isotope, three for14

N and twofor 15N. 15N labels have the advantage of less spectraldispersion which increases the signal amplitude 1.5-foldin conventional ESR and allows for full spectral coveragein FTESR. Reduction of the nuclear manifolds alsosimplifies the interpretation of nuclear relaxation andaccelerates computer simulations of ESR line shapes.15N labels, however, are considerably more expensivethan 14N and only a handful of them are availablecommercially.

A weaker interaction occurs between the electron spinand the hydrogen nuclei of the ring and methyl groups.Each resonance peak is split by the nuclear spin, butthe splittings are unresolved, resulting in a broad peak.The broadening can be removed by the substitutionof hydrogen with deuterium which increases the peakheight 1.5-fold for Gaussian and 5-fold for Lorentzianlines.

(a)

N

O

N

O

N

O(b) (c)

Figure 1 Commonly used nitroxides: (a) six-membered piperi-

dine ring; (b) saturated five-membered pyrroline ring; (c) un-saturated pyrrolidine ring.

3.2 Labeled Sites

Nitroxide spin labels are used either covalently as modi-

fiers of selected amino acids or noncovalently as analogsof substrates or enzymatic cofactors. The specificity ofthe label is conferred by the functional group attachedto the nitroxide. For example, maleimide, iodoacetamide,indanedione and a-ketone groups attached to the nitrox-ide moiety target cysteine residues, while lysines aremodified by activated esters in Figure 2(ad). Attach-ment of the nitroxides by disulfide bonds allows forreversible modification. Reduction of the disulfide bondswith a mild reducing agent yields the unmodified pro-tein. Bifunctional spin labels with two linker groupsfacilitate attachment to two sites on a protein, reduc-

ing probe mobility with respect to the protein. The abilityto engineer neighboring attachment sites in a proteinusing molecular biology is likely to increase the use ofbifunctional labels.

The molecular biology revolution has had a profoundimpact on spin label ESR. The limitations of usingnaturally occurring binding sites are circumvented by thesite-directed spin-labeling method pioneered by Hubbellet al.30 In SDSL, native cysteines are mutated outand new cysteines are introduced at desired vantagepoints. The power of this method is best illustratedby cysteine scanning where each residue along thepolypeptide chain is changed to a cysteine and labeledwith nitroxide.

Noncovalent labels are used in the investigation ofactive sites, e.g. substrate or cofactor analogs, adenosinetriphosphate(ATP) or nicotinamide adenine dinucleotide(NAD) nitroxide adducts (Figure 3a c). The bindingand function of these substrates are often not compro-mised by the presence of the nitroxide. Both approaches

(a)

N

O

N

O(b)

NO OS

SH3C O

O

(c)

N

O

N

O(d)

CI

CH2C

NH

O

OO

NO

O

Figure 2 Various spin labels used in covalent modification ofproteins: (a) maleimide spin label; (b) methyl thiosulfonate spin

label; (c) iodoacetamide spin label; (d) hydroxysuccinamide(lysines).


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N

N

NH2

N

NO

HHH

HO

N

O

H

OPOPOPO

O

O

O

O

O

O

N

N

NH

N

N

OHH

HHOH

H

OPOPOPO

O

O

O

O

O

O

N

O

N

N

NH2

N

N

O HHH

HOHH

OPOPOPO

O

O

O

O

O

O

HN

N

O

OHH

HHOH

H

N CN

N

(a)

(b)

(c)

Figure 3 (a, b) ATP spin labels and (c) NAD spin label.

are combined in photoactivated labels with an addi-tional azido or nitrene groups. The label is guided

by a substrate analog moiety to an active site andphotoactivation attaches the label covalently to theprotein.

3.3 Attachment Rigidity

Spin labels are attached to a protein via one or more singlebonds about which the nitroxides can rotate on a sub-nanosecond timescale. In studies of protein orientationand dynamics, such an independent (librational) motionis a major hindrance since it averages the orientationaldependenceof magnetic tensors anisotropy. Anisotropy

of magnetic tensors is the basis for ESR orientational andmotional sensitivity as discussed in sections 5.1 and 5.2.

The extent of probe motion is estimated by immobilizingthe protein on either glass or ion-exchange beads andcomparing spectral parameters such as effective splitting

(in conventional ESR) or line-height ratios (in STESR) totheir rigid limit values. Alternatively, the protein mobilitycan be reduced by increasing the medium viscosity, h. Theobserved spectral parameters can then be plotted againsth (Perrin plots) and extrapolated to infinite viscosity. Ifthe extrapolated values are lower than the rigid limitof the nitroxide, or if discontinuities exist in the Perrinplots, then it can be concluded that the probe movesindependently of the protein.

3.4 Impairment of Function/Structure of LabeledProteins

Covalent modification of proteins with extrinsic probescarries the danger of damaging the function of themolecule. Certain labels are innocuous at certain siteswhile others are not. No generalizations can be made. Forexample, out of 32 spin-labeled cysteine mutants of T4lysozyme, 11 displayed intact activity and 11 had activity50%. Modification of buried residues and residues intertiary contacts decreased appreciably the enzymaticactivity.31 In KC channels, ion pumping was affectedby


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where H is the magnetic field strength. The magneticmoment of an electron is generated by its spin (S)(Equation 2):

D gbS 2

with b denoting the Bohr magneton (intrinsic unitof electron magnetic moment) and g denoting thespectroscopic splitting factor (relates contribution of spinand orbital motion of the electron to its total angularmomentum).

Unlike a compass needle, electron spin is quantized.For a single electron, the projection ofS on the magneticfield axis Sz can only take values of1/2. Thus the energylevels from Equations (1) and (2) are E D 1/2gbH,

resulting in an energy gap which increases linearly withthe magnetic field, E D gbH (Figure 4). An oscillatingmagnetic field can flip the electrons from one energy levelto the other if its own energy, defined by the oscillatingfrequency n, equals the energy gap. Hence, for resonancebetween the oscillating field (microwave) and the electronspin, the condition in Equation (3) has to be satisfied:

hn D gbH 3

The resonance condition can also be obtained byconsidering a spinning electron moving in an orbit arounda nucleus placed in a magnetic field. From classical

mechanics, the rate of change of the magnetic momentis proportional to the torque produced by the interactionof the moment and the magnetic field and given by theirvector product (Equation 4):

d

dtD gH 4

+

1

+10

+1

10

IS

H0

E h h h

Figure 4 Energy level diagram of Zeeman and hyperfineinteractions for a [14N]nitroxide (S

D1/2, I

D1). The vertical

arrows denote ESR transitions with the resulting first-derivativespectrum below.

where g is a magnetogyric ratio (ratio of magneticand inertia moments) characteristic of a given electron(Equation 5)

g D gbh

5

where h is Plancks constant. The torque will force themagnetic dipole () to precess around the static field ata defined frequency, the Larmor frequency, w, given byEquation (6):

w D gH 6

Substitution of g from Equation (5) into Equation (6)yields the resonant condition hn D gbH stated in Equa-tion (3). Applying an oscillating microwave field of thesame frequency as the Larmor frequency cancels theorienting effect of the static magnetic field. The spinthen rotates about an axis perpendicular to the staticfield direction, periodically aligning itself with or againstthe static field. This is equivalent to dipole () flippingbetween the two energy levels.

The extent of microwave absorption, which definesthe intensity of the ESR signal, is proportional to thedifference in spin populations, N, between the upper andlower energy states. The ratio of the two populations isdetermined by the Boltzmann distribution (Equation 7):

NC1/2

N1/2D expEkT 7

The difference in spin populations is increased by eitherincreasing the magnetic field H or reducing the temper-ature T. For example, at 0.35 T and room temperaturethe population difference is 0.1% but it can be increasedto 13% by reducing the temperature to 3 K. The differ-ence between the levels decreases with absorption andan efficient relaxation pathway has to exist to restore theBoltzmann equilibrium. Relaxation pathways include thedipolar spinspin relaxation sharing of energy betweenelectrons or nuclei and spinlattice relaxation sharing

vibrational modes with the lattice. They are characterizedby relaxation times T2 and T1, respectively. Relaxationtimes are defined as the time interval between initialperturbation and when the deviation from equilibriumdecays to 1/e of its initial value. The relaxation rates areadditive and their sum defines the width (at half-height)of the resonance, (Equation 8):

D 1g

1

T2C 1

T18

Faster relaxation (shorter T1 or T2) results in broaderline widths. For paramagnetic ions, the strong coupling of

spins to lattice (short T1) produces broad lines. Loweringthe temperature weakens lattice coupling (increases


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T1) and is commonly used to observe resonance oftransition metal ions. The coupling of free radicals(including spin labels) to the lattice is weak, therefore

spinspin relaxation is more efficient and the line widthis determined by T2.

Electrons orbiting around a nucleus experience a smalllocal field produced by the nuclear magnetic moment.This field enhances or counteracts the external fielddepending on the orientation of the nuclear dipole.This interaction between the nucleus and the electronis known as hyperfine interaction. Similar to electron spin,nuclear spin (I) is also quantized to 2IC 1 levels. Sincethe selection rule for spin transitions dictates that the totalspin quantum number can only change by 1, the hyperfineinteractions lead to 2IC 1 transitions (Figure 4). In thecase of nitroxide labels, it is the nitrogen nucleus whichinteracts with the unpaired electron. For 15N the nuclearspin number mI is 1/2 so that two electron transitions areobserved; for 14N, ID 1 and therefore there are threeelectron transitions.

The resonance condition of Equation (3) is thus modi-fied to include hyperfine interactions, A (Equation 9):

hn D gbHCmIA 9

The hyperfine interaction between an electron and thenucleus has both an isotropic and dipolar component. Themagnitude of the isotropic splitting, a0, is proportional

to the electron spin density on the nucleus. Since theunpaired electron is located between the oxygen andnitrogen, increasing the polarity of the medium decreasesthe oxygens attraction and increases the electron densityon the nitrogen. Thus, a0 is a sensitive measure of the spinenvironment.

The pp orbital of an unpaired electron is asymmet-ric, making the dipolar interactions of the electron andnucleus orientation dependent. For example, hyperfineinteractions are stronger when the z-axis of the orbitalis aligned with the magnetic field and weaker whenthe field is aligned perpendicular. The hyperfine inter-

actions are best described by a second rank tensor,A (Equation 10):

A DAxx 0 0

0 Ayy 0

0 0 Azz

10Typical values for nitroxide spin labels areAxx Ayy

7 G and Azz 35 G. The difference between the x- andy-components is small and often the hyperfine tensor isassumed to be axially symmetric.

The Zeeman interaction of the electron spin with thestatic magnetic field (Equation 1), is also anisotropic.

Asymmetry of orbital motion in the pp orbital resultsin different contributions of spin and orbital momenta

and thus the g-value can also be described by a tensor(Equation 11):

g Dgxx 0 0

0 gyy 0

0 0 gzz

11In contrast to the hyperfine tensor, the g tensor is rhombicwith typical values gxx 2.0085, gyy 2.0065 and gzz 2.0027. The asymmetry of the Zeeman and hyperfineinteractions defines ESR sensitivity to orientation and torotational motion.

4.1.2 Electron Spin Resonance Spectrometer

A modern ESR instrument consists of three basic units:

(a) a microwave bridge and resonator, (b) a variable fieldmagnet and (c) signal amplification circuitry (Figure 5).

Microwaves of the desired frequency are generated byeither a klystron or Gunn diode. Their intensityis adjustedby an attenuator and transmitted via a waveguide to thesample chamber/resonator. During resonance, a smallamount of microwaves is reflected from the resonatorand detected by a Shottky diode. To separate thereflected and incident microwaves, a circulator is placedbetween the attenuator and resonator. The circulatorchannels the microwaves in a forward direction: incidentmicrowaves to the resonator and reflected microwaves

to the detector. The bridge often contains an additionalpathway a reference arm which taps off a small fractionof the microwaves from the source which bypasses theresonator and falls on to the detector to ensure its bias forthe optimal detection of small intensity changes duringresonance.

A static magnetic field is provided by an electromagnetstabilized by a Hall probe. The field is slowly sweptby varying the amount of current passing through theelectromagnet. In order to decrease microwave noise,

Lock-in amplifier

Reference arm

Circulator

Magnet

Modulation coils

Klystron

Attenuator Detector diode

Resonator

Field controller

,,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

Hall probe

Figure 5 Block diagram of a typical ESR spectrometer.


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(a)

(b)

C

LL

C

HH

(c)

Figure 6 Conventional ESR signals: (a) absorption, V0;(b) first derivative V1; (c) STESR spectrum, second derivative,90 out-of-phase display, V02.

the resonance signal is encoded by modulating the staticfield with a small magnetic field generated by modulation

coils. The modulation field sweeps periodically throughthe nitroxide resonance field. Therefore, the changesin microwave absorption due to resonance occur withthe modulation frequency. A lock-in amplifier selectsand amplifies only the signal which is in phase and infrequency with the modulation field and rejects all othermicrowave fluctuations as noise. The signal detected usingfield modulation is proportional to the changes in themicrowave intensity during one cycle of modulation,i.e. the signal is the first derivative of the absorption(Figure 6a b).

The microwave field produced by the klystron istoo weak to induce any detectable absorption by the

sample. Resonant cavities, loop gap resonators (LGRs)or, more recently, dielectric resonators (DRs) are usedto increase the microwave magnetic field at the sample.The cavities rely on the generation of a standing wavepattern of microwaves whose intensity builds up duringcavity resonance. The main drawback of cavities is thepresence of an electric component of the microwave.The electric component is absorbed by lossy, aqueoussamples (common in biology) causing sample heating andloss of cavity resonance. To avoid this problem, samplevolumeis restrictedto thenodal planesof theelectric field,limiting the usable volume of the cavity and thus resulting

in a low filling factor, h. Cavities are high-Q structures(Q D Estored/Edissipated ), storing thousands of times more

energy than is dissipated on the walls. High Q can only beachieved within a narrow frequency bandwidth of storedmicrowaves as Q

Dn/n. Small changes in the sample,

cavity geometry or temperature can all cause frequencyshifts and mismatching of the incident microwave withthe cavity. Automatic frequency control (AFC) circuitryis employed to track the frequency of the klystron tothat of the cavity. However, the AFC feedback responsetime limits the deadtime of signal changes in transientexperiments such as stop-flow. In pulse experiments it isnecessary to wait until the energy of the perturbing pulseis fully dissipated. This ring-downtime is proportional toQ; thusin the high-Q structures a longer time has to elapsebefore a relatively weak spin echo or free induction decay(FID) signal can be collected.

Most of these problems with cavities have beenovercome by low-Q resonators such as an LGR or DR.These resonators condense the magnetic component ofthe microwave, separating it from the electric component.Lossy samples are no longer heated by the electriccomponent. Small sample volumes and large fillingfactors offer an additional advantage especially whendealing with genetically engineered proteins which areoften purified in picomolar quantities. Furthermore, fastdissipation of energy and the large bandwidths of LGRsand DRs make them suitable for pulsed and transientexperiments.

4.1.3 Instrumental Variables Affecting the Electron Spin

Resonance Spectrum

Two instrumental parameters influence the line shapeof experimental spectra: modulation amplitude andmicrowave power. The amplitude of the ESR signalinitially increases with the modulation amplitude (Hm) asit approaches the intrinsic line width (Hpp). Maximumamplitude is attained at Hm D 3.5Hpp for Lorentzianand at Hm D 1.8Hpp for Gaussian line shapes. Anyfurther increases in Hm result in a decrease of the signal.The broadening of Hpp is observed well before the

maximum amplitude of the signal. When Hm D Hpp,theobserved Lorentzian and Gaussian widths are 25% and15% larger, respectively. As a rule of thumb, modulationshould be kept at one-fifth of the intrinsic line width whenresolution or line width is of importance. The errors inline width are then


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Equation (12):

y Dy0H1

1 CH21g2T1T2312

where y0 is a field-independent parameter. Hence itis important to keep power levels well below themaximum amplitude whenever spectra are used toquantify the number of spins. Line-width distortions areless pronounced than those due to the modulation field,but at powers giving maximum amplitude, the observedline width increases 1.2 times over the intrinsic line width.

4.2 Saturation Transfer Electron Spin Resonance

4.2.1 Qualitative Theory

STESR was developed to study slower molecular dynam-ics with rotational correlation times (tr) of >200 ns.

34

The timescale of conventional ESR is determined bythe spin spin relaxation time T2 (nanoseconds). TheESR timescale can be extended to a longer spinlatticerelaxation time T1 (microseconds) if a signal sensitive tospin saturation is observed. This can be done by saturatingthe signal with intense microwaves, creating a holein the absorption spectrum, and subsequently observingsignal recovery. When the saturating microwave is

switched off (or decreased to nonsaturating levels)the signal recovers with the rate determined by thespin lattice relaxation time, T1. The onset of motionprovides an additional relaxation mechanism: spectraldiffusion. The saturation is relieved as the resonating-saturated spins rotate away from the resonance field andthe unsaturated spins come into resonance. The holebroadens out across the spectrum and the intensity ofthe signal increases. The second harmonic, out-of-phaseESR signal (V02), collected at moderate saturation, isparticularly sensitive to spectral diffusion. The line shapeof V02, in the presence of saturation, bears a strong

resemblance to the absorption spectrum with the intensitylowered in the spectral regions most sensitive to thespectral diffusion (see Figure 6c).

4.2.2 Instrumental Parameters

The STESR signal is influenced by nitroxide relaxationtimes, spectral diffusion, spin saturation level and themodulation frequency with which the hole is observed.Hence the instrumental parameters which affect anyof these must be precisely controlled. The saturatingmicrowave field averaged over the sample volume is set

to 0.25 G. The microwave power is adjusted to this levelusing the microwave field conversion factor (c), corrected

for a filling factor (h) and dielectric losses, which lowerthe Q factor (Equation 13):

hH21is D chPQ 13where P is incident microwave power. The power-to-field conversion factor is determined experimentally bythe saturation of Fremy salt [peroxylamine disulfonate(PADS)] for which the half-saturation field is 0.1067 G.

The modulation frequency and amplitude, which deter-mine the frequency of the stepping on- and off-resonance,i.e. the interval between burning and observing thehole, must also be calibrated. Modulation broaden-ing of a narrow line-width sample, e.g. Fremy salt, is usedfor this purpose. The observed line width (Hpp) is dom-inated by modulation broadening when the modulationamplitude is 10 times the intrinsic line width [Hpp0],i.e. Hpp D Hm Hpp0. Commonly used values forthe modulation field are 5 G and 50 kHz.

Finally, since the V02 STESR signal is 90 out of phase(phase quadrature) with modulation, the precise phasenil must be found. An error of 1 in setting the phasequadrature can result in significant line-shape changesdue to leakage of a more intense in-phase signal. Themost popular phase nulling method is by interpolationof the unsaturated in-phase signal: two or three readingsare taken within 15 on each side of the putative niland the phase at which the signal is zero is found

by linear interpolation. A general description of theexperimental procedures and calibration can be foundin Fajer and Marsh35 and Squier and Thomas.36 Digitalpost-acquisition methods have also been proposed butare not widely used.

As a footnote, protein mobilities measured by con-ventional ESR and STESR were independently verifiedby optical methods fluorescence and phosphorescenceanisotropy. Bovine serum albumin labeled with a dualprobe bearing a spin label moiety and the opticalprobe eosin was measured using optical methods andESR/STESR.37 The agreement between the fluores-cence/phosphorescence and ESR was excellent.

4.3 Time Domain Methods

Time domain ESR relies on the perturbation of the equi-librium magnetization by an intense microwave pulsewhich is then followed by one of the following: (a) con-ventional ESR to observe the return of magnetizationto equilibrium saturation recovery ESR; (b) refocusingof the magnetization in the xy-plane spin-echo ESR; or(c) free induction decay (FID) of the magnetization in thexy-plane which is then Fourier transformed (FTESR).

The development of time domain ESR posed a

formidable technical challenge. The microwave pulsemust be short (a few nanoseconds) and strong enough to


11/39


cover a 70-G wide spectrum of nitroxides. The resonatorsmust dissipate the pulse energy within tens of nanosec-onds before the loss of magnetization coherence and the

signal must be digitized with a subnanosecond dwell timeowing to the short nitroxide relaxation times. Fortunately,technological advances in microwave sources, resonatordesign and data acquisition electronics in the last decadehave facilitated development of commercial Fouriertransform spectrometers and the time domain method hasbecome increasingly popular. The various time domainESR techniques are illustrated in Figure 7(a c).

Saturation recovery electrospin resonance (SRESR) isa hybrid of continuous wave and pulse methods in whichthe pulse saturates a spin population at a desired fieldthereby creating a hole in the absorption spectrum

(Figure 7a). The kinetics of recovery are determinedby various relaxation pathways: spinlattice relaxation,nuclear relaxation, Heisenberg spin exchange (HSE) orspectral diffusion. These competing pathways can beresolved by varying the pulse duration. SRESR has beenused successfully in the determination of spin latticecorrelation times and spin exchange.

Spin-echo electron spin resonance (SEESR) uses asequence of pulses; in Hahn echo a 90 pulse is followedby a 180 pulse t1 seconds later (Figure 7b). The firstpulse tips the magnetization into the xy-plane whereindividual spins rotate with their respective Larmorfrequency, w. The difference in Larmor frequencies,

Pulse c.w. observation

Signal recovery

Saturation(a)

Microwave

Signalintensity

90 180 Echo t2(b)

t1

t190

FID

Tm90

t2

Preparation

90

Mixing

(c)

Figure 7 Time domain ESR methods: (a) saturation recovery;(b) spin echo; (c) 2-D FTESR (ELDOR).

which arises from different resonant fields, leads todephasing of the magnetization in the xy-plane whichis then refocused by the 180 pulse. Spins lagging bywt1 before the refocusing pulse are now wt1 ahead.At time 2t1, spins are brought into coherence and anecho is formed. In this way static differences in Larmorfrequency due to different resonant fields or differentlocal fields (inhomogeneous broadening) are annihilated.The dependence of the echo amplitude on time t1 revealsLarmor frequency fluctuations that cannot be refocusedby the 180 pulse. These fluctuations contain informationabout molecular dynamics, spin exchange and dipolarinteractions. Thedecrease of the spin echo as a function oft1 is a measure of the T2 relaxation time. The decay of theecho amplitude is often recorded as a function of spectral

position by stepping the magnetic field, resulting in a2-D spectrum: an inhomogeneously broadened spectrumalong the field axis and a homogeneous line shape onthe t1 axis. Since the inhomogeneous broadening oftenobscures a multitude of phenomena affecting ESR linewidth, then the ability to obtain a pure, homogeneouslybroadened spectrum is of considerable value.

2-D FTESR is the most versatile technique of timedomain ESR (Figure 7c). All the spins are excitedsimultaneously with a strong, short microwave pulsewhich tips the magnetization into thexy-plane. The lengthand strength of the signal determine the spectral rangecovered, e.g. for nitroxides with a 200-MHz spectral range,2-kW pulses 5 ns in duration are needed.

Coherently excited spins precess about a magneticfield at their Larmor frequency. This precession canbe detected as an oscillating signal in the xy-planewhich decays in time as the spins lose coherence. ThisFID signal is Fourier transformed into the frequencydomain to yield an absorption spectrum. Application oftwo or more pulses spaced by varying intervals allowssampling of spin coherences in multiple dimensions. Inthe simplest of these experiments, two-pulse spin-echocorrelation spectroscopy (SECSY), the first pulse tipsthe magnetization into the xy-plane where the spins

become frequency labeled during the evolution time t1.A second pulse reverses the magnetization during thecollection time t2, canceling inhomogeneous broadening.Fourier transformation with respect to t1 and t2 yields anabsorption spectrum along the f2 axis and a homogeneousline width along the f1 axis. Thus SECSY is an FTESRequivalent of field-stepped SEESR. The isolation of thehomogeneous line shapes out of an inhomogeneouslybroadened spectrum is used to study molecular dynamics.

Three pulse sequences are used in 2-D ELDORexperiments (e.g. Figure 7c). The first pulse creates atransverse magnetization in the xy-plane which evolves

for time t1. The second pulse stores this frequencyencoded magnetization along the z-axis allowing for


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Magnitude

1

22

1/2

(MHz)

45

68

30

4

22

2/2

(MH

z)48

7424

Figure 8 2-D ELDOR of PD-TEMPONE. In addition to auto-peaks occurring at f1 D f2, there are off-diagonal cross-peaksdue toHSE.25 (Reproduced with permission from J. Gorcester,J.H. Freed, J. Phys. Chem., 88, 46784693 (1986).)

magnetization transfer to take place during mixing timeTM. A third pulse transforms the magnetization backinto the xy-plane where it is observed during time t2.Magnetization transfer changes the resonant frequencyof a spin from fa to fb, creating an off-diagonal cross peak

at (fa, fb) (Figure 8). The time evolution of the amplitudeof the cross peak, measured by varying TM, is used todetermine the time course of magnetization transfer. Thebiophysically relevant phenomena causing magnetizationtransfer include HSE, modulation of dipolar interactions,nuclear flips and, most importantly, spectral diffusion dueto rotational motion.

5 APPLICATIONS OF SPIN LABELING

The orientational difference of magnetic interactions

(referred to anisotropy) forms the basis of spin label-ing techniques in biological research. In the absence ofmotion, each field position corresponds to a defined ori-entation of the label with respect to the field. Theintensityof the signal at a particular field position is directly pro-portional to the population of molecules with that givenorientation. Hence an ESR spectrum can be used todetermine the range of orientations present in a sample.Partially or fully averaging the g- and hyperfine tensoranisotropy results in spectral line shapes determined bythe frequency and amplitude of molecular motion. ESRcan also be used to measure intra- and intermolecular

distances. The presence of paramagnetic centers in thevicinity of spin labels modulates spin relaxation pathways

in a distance-dependent manner. In this section we shalldiscuss how ESR is used in the investigation of molecu-lar orientation, molecular dynamics, ligand binding, intra-

and intermolecular distance measurements and the deter-mination of various levels of proteins structure.

For each of these applications a qualitative descriptionof the physical principles allowing for these measurementswill be given, followed by examples. More extensivereviews of these topics can be found in a mono-graph by Lichtenstein,38 a series edited by Berlinerand Reuben39,40 and separate reviews by Hubbellet al.,4143 Marsh and Horvath,44 Millhauser et al.45,46

and, most recently, Hustedt and Beth.47

5.1 Protein Orientation

5.1.1 Orientation of a Single Molecule

The anisotropy of the Zeeman and hyperfine interactionsconfers orientational sensitivity to ESR spectra. Nitroxidespin labels with a z-axis parallel to the magnetic fieldgenerate a spectrum with a splitting of 70 G. Spinsoriented perpendicular to the field display a splittingof 14 G (Figure 9).

The center position of the spectrum, determined by theg-tensor, is sensitive not only to the position of the z-axisbut also to the orientation of the x- and y-axes. At 9 GHzthe center is shifted 5 G downfield (left) for a spin with its

y-axis aligned with the magnetic field and another 4 G forspins with x-axis parallel to H0 (Figure 9).

The effectiveg- and hyperfine splitting tensors for a spinplaced at an arbitrary polar angle (q,f) with respect to thefield are given by Equations (14) and (15), respectively:

gq,f D gxx sin2q cos2fCgyy sin2q sin2fCgzz cos2q 14

NO,

,

,

,

,

,

,

,

,

,

,

z

x

y

H0||z

H0||y

H0||x

Figure 9 Orientational sensitivity of ESR spectra. Splitting ofthe spectrum changes when the z-axis of nitroxide rotates with

respect to themagnetic field. Thecenter of thespectrumchangeswhen nitroxide rotates about any axis.


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A2q,f D A2xx sin2q cos2fCA2yy sin2q sin2f

CA2zz cos

2q 15

It follows, then, that the resonance field for a givenorientation (q,f) is given by Equation (16):

Hresq,f, mI Dhn

bgq,fC mIAq,f 16

Equation (16) describes the orientational resolutionof ESR line shapes: a spin with a specific orientationcan be found at a defined position along the fieldaxis. The ESR intensity at any field position is directlyproportional to the number of spins at the orientationdefining Hres. An ESR spectrum can also be considered

as an orientational distribution function, Nq. Nqis approximated by an orthonormal set of sphericalharmonics and has been developed and applied tosamples with cylindrical and planar symmetry.48,49

Alternatively, the orientation can be modeled in termsof a Gaussian distribution with a width q and center q0(Equation 17):

rq D exp ln 2 qq02

q217

The ESR spectrum, YH, is created by calculatinga resonance field Hres for every q within the Gaussian

distribution of orientations and placing a Lorentzian firstderivative line width at Hres with the intensity weightedby rq (Equation 18):

YH D rq H HresHpp[H Hres2 C H2pp]2

18

where the peak-to-peak width of the Lorentzian (Hpp)is defined by the spinspin relaxation time, T2 (Equa-tion 19):

Hpp D2p

3gT219

ESR is one of the very few biophysical techniquesdirectly sensitive to orientational disorder. The spectra inFigure 10(ac) illustrate this sensitivity. As the width ofthe Gaussian distribution increases, the ESR resonancesbroaden to a powder pattern limit which is characteristicof isotropically disordered spins.

In summary, the parameters describing orientationaldistribution (axial, azimuthal angles and their disor-der) can be obtained from spectral parameters: spectralsplitting, center of the spectrum and the line widthrespectively. This can be achieved either by graphicalmethods or from the automated fitting of full spec-

tral line-shape parameters. Graphical methods comparethe effective splitting and width of the resonance to

(a)

(b)

(c)

Figure 10 Broadening of the spectra with increasing disorder:Gaussian disorder of (a)

1 and (b)

5 and (c) completely

disordered (isotropic) distribution.

graphs obtained from computer simulations. The auto-mated method allows modeling of more complex bimodaldistributions, in both q and f, and can be linked to stan-dard fitting routines such as Levenberg Marquardt50 orSimplex.51

5.1.2 Macromolecular Assemblies

Of considerable interest is the orientation of molecules

within macromolecular assemblies, e.g. proteins withinlipid membranes or contractile proteins in the muscle


14/39


Y

Z

z

y

x

x

x

y

X

Euler angles

(a)

Myosin headSpin label

NO

Fiber Magnet

H0(b)

Figure 11 Definition of (a) Eulerian angles a, b and g; (b) Eulerian transformations of the spin label orientation through theprotein (myosin head); sample (fiber) frame of reference into the laboratory frame (magnet).

fibers. If the assembly of proteins is ordered and ori-

ented at a specific angle with respect to the magneticfield, the orientational distribution of the labeled compo-nents of the assembly can be easily determined. Thespectra of such samples oriented with the symmetryaxis parallel to the field are the same as for a sin-gle spin (Equation 18). When the orientation of thespin label with respect to the protein is known, theESR spectra are interpreted in terms of the orienta-tion of the labeled domain with respect to the assemblywhich is of biological interest. This is achieved usingEulerian transformations between three frames:52,53

molecularframe (defining orientation of the label within

the protein), sample frame (orientation of proteinswithin the assembly) and laboratory frame (orienta-tion of the sample in the magnetic field) (Figure 11aand b).

The ESR spectra are simulated taking into accountthe orientational distribution in each of the frames. Themagnetic tensors are rotated frommolecular to laboratoryaxes using directional cosine matrices (L) according toEquation (20):

Alab D LtmolLtsamLtlabANOLlabLsamLmol 20

where Lmol, Lsam and Llab are cosine matrices defined inEquation (21) for each of the Eulerian transformations

and Lt is their transpose:

L D

cosb cosa cos g sin b sina cos g sin b cos g sina sin g C cosa sin g

cosb cosa sin g cosb sina sin g sinb sin g sina cos g C cosa cos g

sinb cosa sin b sina cosb

21

The resonant field for each spin packet is calculated asshown in Equation (22):

Hres Dhn

bgzzC mI

A2xz CA2yz CA2zz 22

Note that the subscripts of the g- and hyperfine tensors inEquation (22) denote elements in the laboratory frame.

5.1.2.1 Protein Orientation in Membranes The Eule-rian transformation approach was introduced by Griffithet al. to determine lipid orientation in membrane bilayers.The orientation of the spin label nitroxide with respectto the lipid molecule is well defined. A stack of lipidmembranes is tilted with respect to the magnetic fieldat a known angle, and the spectra can be defined solelyby the orientational distribution in the sample frame ofreference (sample).

52,54

Membrane-bound proteins are investigated in a similarmanner. The orientation of a spin-labeled ligand of the


15/39


erythrocyte anion transporter, Band 3, was determinedby flowing red blood cells into thin, flat, sample cells. Theflow shear oriented the red blood cells parallel to the

flow and the sample cell was rotated both parallel andperpendicular to the field in order to vary lab.

55 A globalanalysis of the tilt series resulted in a full descriptionof the label orientation with respect to the normalmembrane axis. The derived spin label orientation wasfound to be consistent with orientation results determinedindependently by analyzing the anisotropy of motion.

5.1.2.2 Muscle Proteins Similar approaches havebeen used to describe the orientation of various muscleproteins. Force generation in muscle is believed to bebrought about by the reorientation of the myosin cross

bridges. Since ESR is sensitive to the orientation of theproteins, muscle field proved to be a fertile ground forESR applications. Muscle fibers form a naturally orderedassembly with the fiber axis defining the cylindricalsymmetry required for ESR. Proteins can be labeleddirectly in muscle cells or labeled as isolated componentsand exchanged for corresponding unlabeled proteinsin the muscle sample. These include most of the thinfilament proteins actin, troponin C (TnC), troponinI (TnI) and tropomyosin and also the thick filamentcomponents myosin heavy chain, regulatory light chainand essential light chain. The orientation of many of thesecomponents has been extensively studied as a function

of the intermediate states of the acto-myosin cycle andalso during muscle activation. Thomas and Cooke haveestablished that in the absence of ATP, myosin headsattach themselves strongly and stereospecifically to actin.Muscle relaxation, in the presence of ATP, produceddisorder consistent with head detachment and Brownian

Acto

-myosin

Acto

-myo

sin.ADP

.Pi

Acto

-myo

sin.ATP

Myosin

Force

Figure 12 Orientation of catalytic domain of myosin headin the intermediate stages of the contractile cycle. As thehead progresses through the cycle, the dynamic disorder is

continually diminished, culminating in the disorder-to-ordertransition associated with force generation.

motion.56 Subsequent studies using various nucleotideanalogs to trap the intermediateadenosine triphosphatase(ATPase) states have revealed a sequence of orientationalchanges of the catalytic domain: a nonstereospecificattachment of transient, weakly bound heads followedby an equally large orientational disorder of the stronglyattached heads in the prepower stroke state.75,76 Forcegeneration was associated with the disorder-to-ordertransition. The postpower stroke state, with the hydrolysisproduct adenosine diphosphate (ADP) in the active site,showed a local domain heterogeneity, but overall thecatalytic domain was well oriented, q 8 (Figure 12).Release of ADP (rigor state) resulted in a slight changein the twist and the tilt angle of the heads.77 Duringisometric contraction, when most of the myosin heads

should be in the prepower stroke state (immediately priorto the rate-limiting step of the cycle), no species wereobserved at a different angle to that of the postpowerstroke heads.102 These findings excluded a simple modelin which the catalytic domain (accounting for most of themyosin head mass) generates a force while rotating by45 from one well-defined angle to another.

A different story emerged when the labels were placedin the regulatory domain of the myosin head. Twodistinct populations, centered 36 apart, were observedin contraction (predominantly prepower stroke heads),whereas in rigor, only one population was observed.57

Clearly, the rotation of the head is limited to theregulatory domain with the catalytic domain shifting froma disordered to ordered structure.

The disorder-to-order transition was also found forother muscle proteins. For example, spin-labeled TnC iswell ordered prior to Ca2C activation but becomes dis-ordered in the presence of Ca2C or activating myosinheads.58 The loss of stereospecific, protein proteininteractions is reflected by changes to the conformationalhomogeneity and is the basis of many molecular mech-anisms. ESR, with its capacity to see directly both theordered and the disordered populations, complementsmore popular methods such as X-ray crystallography or

electron microscopy image reconstructions which ignoredisorder.

5.2 Protein Dynamics

5.2.1 Sensitivity of Conventional Electron Spin

Resonance

Conventional ESR is used to study molecular dynamicson the nanosecond timescale. This timescale correspondsto motions of peptides and small proteins, or the mobilityof labels on the surface of large proteins. Sensitivity of

the ESR signal to motion arises from rotational modu-lation of the magnetic tensor anisotropy. The anisotropy


16/39


1/exAB

AB

av BA

Figure 13 Two-site exchange between environments givingrise to two resonances separated by w. Increased rate ofexchange initially broadens the resonances then averages theirresonant frequencies.

of Zeeman or hyperfine interactions results in differentresonant fields for different spin orientations. Therefore,rotational motions which change the spin label orientationwill modulate the ESR line shape. This can be explainedby using a two-site exchange example: two spins, A andB, resonate with frequencies wA and wB and exchange

their positions at a rate 1/tex. When the exchange rate issignificantly slower than the difference in resonant fre-quencies (1/tex w0AB D wA wB, slow exchange), thespectrum consists of resonances A and B centered at wAand wB, respectively, and the line widths are determinedby T2 (Figure 13). The effective relaxation rate1/T

eff2 isthe

sum of the intrinsic 1/T2 rate and the exchange rate 1/tex.When the exchange frequency increases, the line widthsstart to broaden. Further increase of the exchange ratecauses partial averaging of the resonance positions. Theobserved difference in resonant frequencies is reducedaccording to Equation (23):

wAB D w0AB 1 8

t2exw0AB

23

For exchange rates faster than the difference inresonant frequencies (1/tex wAB, fast exchange), thetwo resonant peaks coalesce into one peak at the averagefrequency (assuming equal populations of A and B)(Figure 13). The line width is determined by the effectiverelaxation time, Teff2 , with contributions from T2 of speciesA and B and the exchange broadening (Equation 24):

1Teff2

D 1T2A

C 1T2B

C w2ABt

ex8

24

In other words, at the fast exchange limit (1/tex wAB), the contribution of the exchange rate to linewidth disappears and the spectrum consists of a singlepeak at 1/2wA CwB with an average line width of1/T2A C 1/T2B (Figure 13).

The above considerations generally hold true for anyspins exchanging between different environments suchas different local magnetic fields, dipolar interactionsor association with different macromolecular assemblies.Spin label reorientation with respect to the magneticfield is also a form of exchange where the rotationalcorrelation time tr is the exchange rate and the anisotropyof the g- and hyperfine interactions defines the frequencydifference. At X-band, w D Azz Axx/h D 500 MHzor (gxx

gzzbH/h

D185 MHz.

As for the two-site exchange discussed above, variousmotional regimes of ESR can be defined: fast (tr 1011 109 s), slow (tr 109 2 107 s) and very slow(tr > 2 107 s). Fast and slow motion are of the orderof T2 (15 30 ns) for electron spin and have visibleeffects on conventional ESR spectra which measurethe transverse component of magnetization. The veryslow motions do not affect transverse magnetization, butthey do affect longitudinal magnetization which decayswith T1 (115 s). These slow motions can be detected(indirectly) using saturation transfer, pulsed ELDOR orsaturation recovery ESR.

5.2.1.1 Fast Motion (tr 1011 109s) In the fastmotional regime, the motion completely averages theanisotropy of the g- and hyperfine tensors. The rotationalrate is obtained from the line width broadening usingRedfields perturbation theory.59 The broadening itselfis a function of the nuclear quantum spin numberas different nuclear manifolds have varying anisotropyvalues (Equation 25):

HmI D AC BmI C Cm2I 25

The coefficient A is equal to homogeneous broadening

and coefficients B and C assure differential broadeningof lines belonging to different nuclear manifolds. Thesecoefficients are obtained from the line widths of theLorentzian lines according to Equations (26) and (27):

B Dp

3

4H0

V0

VC1 V0

V1

26

CDp

3

4H0

V0

VC1 CV0

V1 2

27

where VmI is the peak-to-peak height of a given nuclear

manifold resonance and H0 is the peak-to-peak linewidth of the central line.


17/39


Factors B and Care equal for isotropic motion and tisoris calculated directly from Equations (28) and (29):

tisoB D 1.22 109B 28tisoC D 1.19 109C 29

where B and Care expressed in gauss and t in seconds.61

In the case of anisotropic motion, B 6D C, and the ratesof rotation about the nitroxide z-, x- and y-axes aredifferent. The ratio of C and B can be used to definethe anisotropy as the coefficients are independent of therate of motion. Various models of anisotropic motion areconsidered in excellent reviews by Marsh61 and Beth andRobinson.67 If the molecule is diffusing in an isotropicmedium, then the rotational correlation times about the

nitroxide z-axis (tjj) and about an axis perpendicular tozt? are given by Equations (30) and (31):

tjj D2t20t22

3t20 t2230

t? D t20 31

where t20 and t22 describe spin relaxation and arerelated to the anisotropy of the magnetic interactions(Equations 32 and 33):

t20 D1.11 107

HA

5dAB 8dgHCgdA

dgA

32

t22 D3.69 108

HdA

8gHC 5ABgdA dgA 33

where A and dA are given by hyperfine anisotropy(Equations 34 and 35):

A D Azz 12 Axx CAyy 34dA D 12 Axx Ayy 35

with equivalent equations for g-anisotropy. The indicesin Equations (34) and (35) are permutated to calculatethe values oft

jjand t

?for the rotation about the x- and

y-axes of the nitroxide.The above equations hold for anisotropic motion about

a specific nitroxide axis in an isotropic medium. Anadditional complication arises when diffusion takes placewithin a strongly orientating potential such as in a lipidmembrane, or within the steric confines of a protein.The field position of resonances now depends on theamplitude of motion, which defines the time average ofavailable angular space; e.g. if the nitroxide can moveonly within an angular cone, then only the resonancescorresponding to the orientations within the cone areaveraged. Motionally averaged spectra are described in

terms of order parameters (S) time averages of thedirection cosines of the diffusion axis with respect to the

local director axis. For an isotropic diffusion within thecone angleqc, components of an ordering tensor are givenby Equations (36) and (37):

Szz D 12 cos2qc C cosqc 36Sxx D Syy D 12 Szz 37

Szz and Sxx are used to define the motionally averagedmagnetic g-tensors gjj and g? in terms of its average valueg0 and the anisotropy g and dg (Equations 38 and 39):

gjj D g0 C2

3gSzz C

2

3dgSxx Syy 38

g? D

g0

1

3

gSzz

1

3

dgSxx

Syy 39

with equivalent expressions for the effective hyperfinesplitting Ajj and A?. The latter two are resolved inthe experimental line shapes; see Figure 14. Thus Szzof the nitroxide z-axis can be easily obtained fromEquations (38) and (39) and the corresponding cone anglefrom Equation (36).

5.2.1.2 Slow Motion (tr 109 2 107s) For tr >2 ns, Redfields theory does not hold. The equation ofmotion for an electron spin is solved using a stochasticLiouville equation (SLE), developed by Schneider andFreed.60 Although the description of the SLE approachis beyond the scope of this article, one can rationalize theeffect of slow motion on ESR spectra in terms of the two-site exchange. The low- and high-field extremes of thepowder spectra correspond to nitroxides lying with the z-axis parallel to the magnetic field. Rotation (i.e. exchangewith any other orientation) results first in an exchangebroadening of the line width and then partial averagingof the anisotropy. Line width and effective splitting are

A

A||

Figure 14 Definition of the parallel and perpendicular hyper-fine splitting for calculation of order parameters.


18/39


used to determine tr (Equations 40 and 41):

tr D a0m HmHRm 1b0m

40

tr D a

1 A0zz

ARzz

b

41

where Hm and A0zz are the line widths at half-

height and hyperfine splitting, respectively, and thesuperscripts denote their rigid limit values. Coefficientsa0m, b

0m, a and b are calculated from SLE simulations.

Their precise values depend on the motional modelused for the simulations. For a Lorentzian line widthd D 3.0 G and isotropic Brownian diffusion, a0mD1 D11.5ns, b0m

D1

D 0.943, a0m

D1

D21.2ns, b0m

D1

D 0.778,

a D 0.54ns and b D 1.36. Values for different linewidths or motional models can be found in Marsh.61

It should be noted that the calculated tr values depend

r= 0.001ns

r= 10ns

r= 20ns

(a)

r= 23s

r= 4s

r= 200s

(b)

Figure 15 Sensitivities of (a) the conventional ESR spectraand (b) STESR spectra.

strongly on the chosen rigid limit values. A user-friendlysimulation and optimization program based on the SLEwas developed by Budil et al.50 Sensitivities of the

conventional ESR and STESR spectra are illustratedin Figure 15(a) and (b).

Examples. Side-chain and polypeptide backbonedynamics are determined using the above formalism.Spin labels attached to the surface of small a-helicalpeptides exhibit subnanosecond motions observed byESR which compare well with motions predicted bymolecular dynamics simulation programs.45,62 Scanningof the label position along a peptide length reveals aV-shaped gradient of the label mobility. The cone anglefor random motion in the middle of the peptide was

half the value found at either terminus. Interestingly,the C-terminus was found to be more flexible than theN-terminus, which explains the decreased stability ofthe C-terminus as compared with the N-terminus in a-helices.45,46 Backbone dynamics observed in isolatedpeptides are further modulated by tertiary interactions.A survey of 30 cysteine mutants of T4 lysozyme withspin labels at various structural sites (on the surface ofhelices, within the helix termini, interhelical loops, buriedsites and sites involved in tertiary contacts) revealed acharacteristic pattern of spin label mobility in relationto the secondary structure of the protein.31 When thesecond moment of the spectrum (defined as the reciprocal

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Figure 16 Reciprocal of the square of the splitting ver-sus reciprocal of the central resonance line width. Thespectral parameters cluster according to the labeled pro-tein structural elements.31 [Reprinted with permission fromH.S. McHaourab, M.A. Lietzow, K. Hideg, W.L. Hubbell, Bio-

chemistry, 35, 7692 7704 (1996). Copyright 1996 AmericanChemical Society.]


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of maximum splitting squared) is plotted against thereciprocal of the central field line width (H1mD0), sites insimilar environments are clustered together (Figure 16).

The clustering reflects the degree of motional restrictions,with the second moment related to the averaging of thehyperfine anisotropy and the central line width to theaveraging of the g-tensor. When motional restrictionsincrease, the averaging decreases and both the secondmoment and the line width of the resonances increase.Hence the second moment and line width can be used assemiempirical diagnostic tools to evaluate the secondaryand tertiary structure of a labeled site.

5.2.1.3 Very Slow Motion (tr > 109s) When tr >

100 ns, conventional ESR line shapes are no longer

sensitive to motion. The rate of angular exchange istoo small to affect the hyperfine or g-anisotropy and theline shapes become insensitive to very slow motions. Tostudy these biologically important motions, a related ESRtechnique was developed, STESR.

Isotropic Motion. In the presence of power satura-tion, the second harmonic out-of-phase (V02) line shaperesembles an absorption spectrum (Figure 6c), with theintensity reflecting the effective relaxation at that point.Since effective relaxation is related to spectral diffu-sion and spectral diffusion is a function of the rotationalcorrelation time, the V02 line shape reflects rotational

mobility. The rate of spectral diffusion (tsd) is a functionof the resonant field Hres. Some field positions are moresensitive to angular rotation than others and @Hres/@qvaries across the spectral line shape. For instance, therate of spectral diffusion is zero at the turning pointH D Hresq D 0), but increases in the intermediate fields(Equation 42):

tsdHres1 D

8

3p2

@Hres

@q

2

T22t1r 42

To the first approximation,63 the change of the signalintensity (I) at any field position is proportional to the

change of the spin lattice relaxation time due to spectraldiffusion (Equation 43):

IHres D I0HresTeff1 Hres

T143

where I0 is the rigid limit intensity in absence of motionand Teff1 is the intrinsic T1 modified by spectral diffusionaccording to Equation (44):

Teff1 Hres D T011 C I0Hres/T2T01tsdHres1

1 C T01tsdHres144

Since Teff

1 is a function of the field position (spin anglewith respect to field), it is customary to define the line

height at precise positions in the spectrum: L00, C0 or H00

at q D 35 (two-thirds of the way between resonant fieldcorresponding to q

D90 and q

D0) and normalize it

to the intensity at H (L, C and H positions) for whichspectral diffusion is zero.

By substituting Equation (44) for the effective relax-ation rate in Equation (43) a semiempirical expression forthe P0/Pratio dependence on tr is obtained (Equation 45):

P0

PHresD I0Hres

I0H1 C a/tr1C b/tr

45

The parameters a, b and I0Hres)/IH) can be esti-

mated from Equations (42) and (44) by numericallyevaluating sensitivity @Hres/@q at each spectral position.In practice, these values are obtained from fits to theexperimental curves of line-height ratios from spectra ofmolecules undergoing Brownian diffusion with a knowntr. Spin-labeled hemoglobin or bovine serum albumintumbling in media of a known viscosity (waterglycerolmixtures) is used for this purpose.63 The rotationalrate of hemoglobin (the abscissa in Figure 17) is calcu-lated from the StokesEinstein equation for a sphereof radius r, tumbling in a medium with viscosity h(Equation 46):

tr D4phr3

3kT46

0.00

0.50

1.00

1.50

2.00

2.50

1 10 100 1000 10 000

Correlation time (s)

P/P

C/C

L/L

H/H

Figure 17 Dependence ofV02 diagnosticratioson the rotationalcorrelation time. The curves are simulated with Equation (63)using the parameter values from Table 1.

Table 1 STESR parameters from maleimide spinlabel hemoglobin calibration curves63

Parameter I0Hres/IH) a (s) b (s)

L00/L 1.88 6.18 67.9C0/C 1.01 0 21.1

H00/H 2.17 21.7 210


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Table 2 Useful constants

Constant Symbol Value Units

Plancks constant h 6.63 1034 J sh 1.06 1034 J s

Bohr magneton b 9.27 1024 J T1Free electron g factor g 2.00232Electron magnetic moment 9.29 1021 J T1Magnetogyric ratio g 1.76 10C11 s1 T1Boltzmann constant k 1.38 1023 J K1

The parameter values listed in Table 1 were obtainedfor maleimide spin-labeled hemoglobin tumbling indifferent water glycerol mixtures. In principle, thesevalues should be transferable from one laboratory toanother. In practice, each cavity is sufficiently differentin its microwave distribution and modulation fieldsthat separate calibrations are often constructed. Newcalibrations are also necessary for different spin labels.Changes to the magnetic tensors and relaxation timesalter STESR line shapes. In rare cases, full numericalsimulation of the V02 line shape is used to determine thecorrelation time, but the computational time required isstill prohibitive.68

Anisotropic Motion. The effective rotational corre-lation times (teff) obtained from such calibration curves

reflect rates for isotropic rotation. However, isotropicmotion is not very common in biological systems.For example, the nonspherical shape of the diffus-ing molecules or the restoring potential of the mediaresults in anisotropic motion. Intuitively, rotation aboutthe long axis of a cylinder is faster than the tumblingmotion around its short axis. Assigning an isotropic tr toan anisotropic motion is obviously in error. For elon-gated molecules correlation times for rotation aboutthe major and minor axes are given by Equations (47)and (48):

tjj Dfjj

4kT1 Cfjj/2f? 47

t? Df?

6kT48

where T is absolute temperature and the frictionalcoefficients fjj and f? are a function of the shape ofthe molecule.64,65 For a cylinder of length 2a and radiusb the frictional coefficients are given by Equations (49)and (50):66

fjj D 8phab2[0.961 C djj] 49

f? D 8pha3

3[lna/b C d?] 50

where d? and djj are as given by Beth and Robinson(Equations 51 and 52):67

djj D 0.688

ba

0.202

ba

251

d? D 0.661C 0.891

b

a52

The anisotropic diffusion tensor (D) creates an addi-tional complication. The effect of the molecular rotationon the spectral line shape is a function of the label orien-tation with respect to the diffusion axis. If the principalaxis of diffusion is parallel to the z-axis of the spin label,the motion interconverts the x- and y-components only.If it is parallel to the x-axis, then the y- and z-components

will be mixed. To describe fully anisotropic diffusion ofthe anisotropic tensor, six parameters are needed: threediffusion coefficients about thex-,y- and z- axes and threeEulerian angles describing the orientation of the diffusiontensor with respect to the magnetic tensor.

The problem is simplified if either the diffusion tensor(D) and/or the magnetic tensors (g or A) are axiallysymmetric: the elements of the diffusion tensor arerelated to the correlation times by t? D 1/6D? witha corresponding expression for tjj. It has been shownthat the effective correlation time obtained from theL00/L and H00/H line-height ratios of STESR spectra(mI

D 1) can be described in terms of D

?, D

jjand

the angle q between the diffusion and magnetic tensoraxis (Equation 53):68

teffR 1 D1

3[Djj sin2qC D?1 C cos2q]

53

When q D 0 the outer manifolds reflect D? whichdefines the z- and x-(y-) element conversion (Djj leavesthe nitroxide z-direction unchanged). If q D 90 theintensity of L00 and H00 is determined by Djj, which nowinterconverts the z- and x-, y-axes.

In some cases, anisotropic rotation is about a singleaxis and the motion can be described by a uniaxial model.

The mobility of transmembrane peptides or proteins inlipid membranes is a good example. A uniaxial model,with a single diffusion tensor element Djj and an angleq defining the relative orientation of the magnetic anddiffusion axes, is sufficient to simulate STESR spectraof membrane-bound proteins.69 Ifq is not known, thenteff1 gives an upper estimate of 0.5tjj (q D 90). Itis important to realize that the changes of the q angle,brought about by conformational changes, might resultin STESR line-shape changes which can be mistakenlyinterpreted as changes in protein dynamics. A quickdiagnostic for the presence of anisotropic motion is the

comparison of the effective correlation times estimatedfrom the C0/Cratio and from L00/L (H00/H). If they agree,


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then the motion is likely to be isotropic. If they aredifferent, then either the overlap of the nuclear manifoldsis different in hemogiobin calibration spectra (unlikely) or

the motion is anisotropic.70 If the change in the STESRspectra is to be interpreted in terms of changed motionalrate and not changed anisotropy of motion, then at leastthe ratio of the correlation times teff1/teff0 shouldstay constant.

Another motional model commonly encountered inbiology is restricted diffusion. In such a model, the motionis isotropic but constrained in amplitude. The smaller theamplitude of motion, the slower is the apparent mobilityderived from isotropic calibration. When the amplitudeis 60,

teff approaches tr.71 For small amplitudes, there is noisotropic line shape which will match the STESR spectrumof restricted motion. The amplitude effect is not justreflected in one or two places in the spectrum, but ratherit is distributed across the whole line width.

An extensive review by Beth and Robinson67 dealswith the effects of anisotropic motion on STESR spectraand the theoretical simulations of line shapes. Numericalsimulations are based on the transition rate matrix whichcouples neighboring angular zones with the rate of angularreorientation. The SLE approach and spin density matrixmethod have also been used. Both approaches have been

applied successfully to isotropic and anisotropic motionalmodels. The continuous increase in computational speedbodes well for the routine application of STESR simula-tions to analyze experimental data.

5.2.1.4 Examples in Muscle Proteins Microsecondmotions are common for large macromolecular com-plexes (1MDa) such as are present in muscle. Thetimescales of force generation, the actomyosin ATPasecycle and muscle activation coincide with the micro-tomillisecond timescale of STESR, thereby making it themethod of choice. The first application of the methodestablished the dynamics of myosin, its subfragments and

actin.72 Thomas et al. showed that the myosin head iscapable of moving independently of the large myosinfilament. Such motion was a prerequisite for force pro-duction. When bound to actin, in the rigor state (no ATP)the myosin heads were immobilized but when ATP wasadded the heads detached and were free to move. 73,74

Subsequent studies in muscle fibers at various inter-mediate states of the acto-myosin ATPase cycle haveestablished a progressive decrease of catalytic domainmobility during the contractile cycle: the 10-s motionof relaxed and weakly attached heads75 became 80 s

just before force was generated76 and was completely

frozen out in the postpower stroke states of ADP andrigor. In the ADP state the head, although globally rigid,

retained breathing motions, which were suppressedon the release of nucleotide.77 It is believed that thisgradient in protein mobility reflects tighter and more

stereospecific binding as myosin progresses through thecontractile cycle (Figure 12).

The dynamics of the myosin head are complicated bythe fact that this elongated protein does not behave like arigid body. A comparison of the dynamics of the catalyticandregulatory domains revealed a three-fold difference inthe rate of motion for the two domains.78 Moreover, thetwo domains were found to have dramatically differentorientational distributions.57 These results highlightthe complexity of the conformational changes in theactomyosin system: force generation is not synonymouswith force transmission and both events involve changes

of dynamics and orientation.This complex behavior of myosin is in contrast to thatof actin. Neither the orientation nor the dynamics of actinmonomers, as probed by labels attached near the myosinbinding site, were affected by head attachment.7982

The absence of any orientational changes in contractingmuscle fibers was also observed using spin-labeled toxinphalloidin bound rigidly to the interface between theactin monomers.83 This agrees with the current modelof actins passive role in force production in providingtracks for myosin motor protein to walk on.

Force activation involves a complex pathway withsubtle changes in protein protein interactions. It is

mediated by the conformations and dynamics of theparticipating molecules. Smooth muscle is activated viaphosphorylation of myosin light chain 2, whereas skeletalmuscle is regulated by a thin filament based systeminvolving Ca2C binding to TnC. STESR spectra ofphosphorylated myosin with a probe bound to myosinlight chain 1 have implied increased motional freedom ofthe head. This finding supports a model86 in whichunphosphorylated heads are tied to the surface ofmyosin filaments and inhibited from binding to actin.87

Phosphorylation abolishes the electrostatic attraction tothe filament surface allowing the heads to interact with

actin.In skeletal muscle, binding of Ca2C to TnC initiates asignaling pathway from the thin to thick filament whichultimately activates muscle contraction. Biochemicalchanges in the affinity of myosin for actin and of TnCfor Ca2C have a structural basis that is readily observedby both STESR and conventional ESR. The mobilityand orientation of TnC (and TnI) has been found tobe similarly affected by the binding of myosin heads toactin or by Ca2C binding to TnC.84 Interestingly, TnCwas capable of sensing not only the binding of the myosinheads to actin but also the intermediate ATPase states.85

5.2.1.5 Examples in Membranes Rotational diffusionof membrane-bound proteins is often the best way of


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determining the oligomerization state in their nativeenvironment without the possible dissociative effectof detergents. STESR of various integral proteins has

revealed monomers such as rhodopsin,88 dimers suchas cytochrome oxidase89 and ADPATP carrier90 oreven higher oligomers such as Na, K-ATPase.91

The biological significance of dynamic structuralchanges is best illustrated by the Ca-ATPase,92 whosemolecular dynamics correlate with transport activity.93,94

As shown by ST-EPR, allosteric interactions betweenCa-ATPase polypeptide chains and catalytically impor-tant domain interactions involved in the transportcycle are regulated by both alterations in membranelipid composition, anesthetics, and the regulatory pro-tein phospholamban.9597 Thus, physiological regulators

of calcium transport modulate catalytically importantmotions and provide a structural basis for b-adrenergicstimulation in the heart.

Protein dynamics measured by STESR and conven-tional ESR have differentiated between two modelsof steroid biosynthesis in mitochondria: the shuttlemechanism and the ternary complex of adrenodoxin,P450 and adrenodoxin reductase. Adrenoxin was foundto form binary complexes (but not ternary complexes)with either P450 or adrenodoxin reductase, supporting ashuttle mechanism.98

An excellent example of the potential of STESR in

describing complex anisotropic motions is in the studyof the transmembrane anion transporter Band 3 byHustedt and Beth.69 The STESR spectra were simulatedusing a uniaxial model for protein rotation. The diffusionrate and the angle between the magnetic and diffusiontensor were freely floated in the least-squares fits toexperimental spectra. The uniqueness of the solution wascorroborated by the orientational study of Band 3 inoriented erythrocytes.55

5.2.2 Mobility and Time Domain Methods

The measurement of the molecular dynamics by time-

resolved ESR methods is still in its infancy. Specializedhardware is necessary to perform such experiments.Spectral diffusion due to the reorientation of spinscan be observed either by recovery from saturationat the resonant field (saturation recovery ESR) or byarrival of saturation originally induced at some othernonresonant field (pulsed ELDOR). The initial promiseof these methods was not fulfilled when it was shown thatthe nuclear relaxation, which couples different nuclearmanifolds, contributed significantly to spectral diffusion.Combining pulsed ELDOR and saturation recoverydifferentiates between nuclear relaxation and rotational

spectral diffusion and can be used to measure the truerotational correlation time.99

2-D FTESR methods appear to be more promising.Nuclear relaxation is seen as cross peaks between themanifolds and can easily be distinguished from homoge-

neous broadening and spectral diffusion broadening.100

In the limits of fast motion, tr is obtained directly fromthe homogeneous line width and is defined by the pureT2 (similar information is obtained from the spin-echoexperiments). For slower motions, mixing time betweenthe pulses is varied (2-D ELDOR) and the dependenceof spectral broadening on mixing time is used to deter-mine tr. Correlation times in the range 130 s havebeen measured for small peptides tumbling in viscousmedia.101

5.3 Kinetic Experiments

Elucidation of molecular mechanisms involves primarilytwo approaches: (a) entrapment of reaction intermediateswith a subsequent reconstruction of the sequence ofevents and (b) transient kinetics in which the reactionsare synchronized with the observed spectral changes.Each of these approaches have potential problems. Inthe trapping approach, the states have to be relatedto the kinetic intermediates. There are cases in whichstates trapped with substrate or product analogs are notlying on the kinetic pathway. On the other hand, transientexperiments are easier to interpret, but technically morechallenging owing to lower signal levels, fast acquisitiontimes and difficulties in spectral assignment. The twoapproaches should be considered complementary. Inan ideal world, trapping approaches should be usedto identify and assign signals collected during transientexperiments.

Historically, optical spectroscopy was used for tran-sient kinetics owing to inherently higher sensitivity, butESR is making substantial inroads.102 Recent advancesin resonator design allow for millisecond resolution onmicroliter samples in the submillimolar concentrationrange.103 The DR developed for this purpose is capa-ble of measuring millisecond kinetics in a single shot on

100L of a 40 M sample with an 8-ms deadtime.104The further development of this DR/stop-flow config-uration allows the recording of a full spectrum within100 ms.105

Transient ESR was used to resolve the stages ofchannel formation in lipid membranes. Phospholipidvesicles and membrane channel collicin were mixedrapidly and the time course of the protein absorptionto the membrane surface was clearly resolved from theinsertion of the channel into the membrane.106 Forcollicin the process was fairly slow, with a timescaleof seconds, but the formation of another channel

annexin was followed on the millisecond timescale.107

The millisecond time resolution makes ESR a viable


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alternative to optical methods in investigations of kineticprocesses.

The photolysis of caged compounds, cATP and

cCa2C, to study conformational transients has beenused primarily in the muscle field and in the study ofCa2C-ATPase. A single ultraviolet (UV) pulse (10 ns induration with an energy flux of 150 mJ cm2 at 351 nm)from an excimer laser is capable of libera

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