Vol. 14, No. 1-4 35

New Developments inPulsed Electron Paramagnetic Resonance:

Direct Measurement of RotationalCorrelation Times from

Decay CurvesDuncan A. Haas, Colin Mailer, Tetsukuni Sugano and Bruce H. Robinson

Department of ChemistryUniversity of Washington

Seattle WA 98195

Perdeuterated ^ N TEMPOL in glycerol-water mixtures and spin-labeled hemoglobin are studied using the timedomain technique of saturation recovery electron double resonance (SR-ELDOR), in the ultra-slow motional timeregime. The electron spin lattice relation rate (Tig"1) and the nitrogen spin-lattice relaxation rate (Tin*1) are de-termined. Moreover, the characteristic rotational correlation times (TR) are measured directly. It is not possi-ble, in general, to separate uniquely these rates from one another with Saturation Recovery Electron ParamagneticResonance (SR-EPR) experiments alone. The SR-ELDOR technique of pumping one spin manifold or orienta-tion and observing at another changes the sign of the amplitudes of selected components contributing to the over-all signal. Pooling the SR-EPR and various SR-ELDOR spectra enables all rates to be uniquely determined.

1 Review of Isotropic motionPerdeuterated 15N-Tanol [1] and spin-labeledhemoglobin (sl-Hb) [2] have been used as modelsystems undergoing Brownian isotropic rotationalmotion in the micro to millisecond time range asdescribed by the characteristic rotational correlationtime, (TR). The continuous wave technique ofSaturation Transfer EPR (ST-EPR), which is verysensitive to motion on this time scale [3], relies onthe competition among the different magnetizationtransfer mechanism of T i e , Ti n , TR and theZeeman modulation frequency, com. There aremany applications of ST-EPR to slow motion,primarily using 14N spin labels. However, therelaxation and rotational rates can only be indi-rectly inferred from ST-EPR [4]. We will showthat these rates may be directly obtained from SR-ELDOR experiments.

Hyde and co-workers invented the technique ofContinuous Wave Electron-Electron Double Reso-nance (CW-ELDOR) [5]. They demonstrated that,by pumping one point in a spectrum and observingat another point, energy transfer could be detected.However, CW-ELDOR is an extremely complextechnique and the results can be influenced by in-strumental artefacts [6]. The technique has beenapplied by Stetter et al. [7] to nitroxides movingwith sub-nanosecond times and by Smigel et al.[8] to nitroxides with microsecond correlationtimes. From CW-ELDOR, one cannot estimateeither Ti e or Tin independently, only their ratio.The Stetter [7] work used different isotopes of ni-trogen to separate exchange due to lateral diffusionfrom nitrogen relaxation. (There can be no nuclearspin lattice relaxation between different isotopes soany interaction between them must come fromcollisions.)

L.R. Dalton, B.H. Robinson, L.A. Dalton and P.Coffey, in Advances in Magnetic Resonance VIII,(J.S. Waugh, ed.) Academic Press, NY, 1976.D.D. Thomas, L.R. Dalton, J.S. Hyde, J. Chem.Phys., 65, 3006-3024, 1976.J.S. Hyde and L.R. Dalton, Chem. Phys. Lett., 16,568-572, 1972.A.H. Beth, and B.H. Robinson, in Biological Mag-netic Resonance VIII Spin Labeling: Theory andApplication (L J . Berliner and J. Reuben, eds.),Plenum Press, NY, 1989.

J.S. Hyde, J.C.W. Chien and J.H. Freed, J. Chem.Phys.,4S, 4211-4226, 1968.L.A. Dalton and L.R. Dalton, in Multiple ElectronResonance Spectroscopy eds. M.M. Dorio and J.H.Freed. Plenum Press 1979 Chapter 5.E. Stetter, H.-M. Vieth, and K.H. Hauser, J. Mag.Res., 23, 493-504, 1976.M.D. Smigel, L.R. Dalton, J.S. Hyde, and L.A. Dalton,Proc. Nat.Acad. Sci. USA, 71, 1925-1929, 1974.

36 Bulletin o[ Magnetic Resonance

Time Domain EPR: In a time domain EPR ex-periment, the spins are subjected to a short pulseof microwave power; the time dependence of thetransient relaxation after the pulsing is monitored.The rates of relaxation are functions of the mo-tional process. Two types of time domain experi-ments exist: one monitors spin echoes (a coherentdetection of the x- and y-components of the mag-netization) and the other monitors SaturationRecovery (as a polarization detection of the z-mag-netization).

Freed [9] has applied spin-echo methodology tostudy motion in liquids. A (90°-T-180°-i-Observe)sequence measures echo height as a function of thedelay time t to give the phase memory decay timeTM- Other workers have studied spin-labeledmembranes and vesicles - showing changes in TMwith temperature, but do not relate results to anytheory [10]. Freed [9] has also developed thetechnique of Fourier Transform EPR usingmultiple pulse techniques, originally developed forNMR. The variation of TM across the spectrumcan be directly obtained and related to motionalmodels. Cross-relaxation from one manifold toanother can also be measured. Rates are measuredfrom the volumes of the main and cross-peaks inthe 2-D display, and not from actual decay curves.

Huisjen and Hyde [11] pioneered the use of theSR-EPR technique in liquids and applied it to anumber of systems [12], [13]. The Hyde group[14] has used SR-EPR, in conjunction with CW-ELDOR, to measure lateral diffusion of 14N la-belled lipids in bilayers. These important papers ontranslational motion set the stage foT our work inrotational motion.

Measurement of rotational diffusion directly in thetime domain with SR-EPR alone has proved im-

9 J. Gorcester, G.L. Millhauser, and J.H. Freed, inModern Pulsed and Continuous-Wave Electron SpinResonance, L. Kevan and M.K. Bowman(eds.) JohnWiley 1990 Chapter 3.

10 K. Madden, L. Kevan, P.D. Morse and R.N. Schwartz,/ . Am. Chem. Soc, 104, 10, 1982.

11 M. Huisjen and J.S. Hyde, Rev. Set Inst., 45, 669-675, 1974.

12 P.W. Percival and J.S. Hyde, / . Mag. Res., 23, 249-257, 1976.

13 A. Kusumi,W.K. Subczynski and J.S. Hyde, Proc.Nat. Acad. Sci. USA, 79, 1854-1858, 1982.

14 J.-J. Yin, M. Pasenkiewicz-Gierula, and J.S. Hyde,Proc. Nat. Acad. Sci. USA, 84, 964-968, 1987.

possible. Typical of an SR-EPR experiment is thatof Fajer et al. on sl-Hb [15] which produced bi-exponential decays. The slower rate was(correctly) identified with Tie"1 and the faster de-cay rate was associated with the rotational motionof the hemoglobin. The faster decay rate remainedapproximately constant despite a two order ofmagnitude change of correlation time. These au-thors then used a qualitative theory of spin diffu-sion to extract an effective correlation time. Thedata agreed only approximately with the known 1Rvalues. The problem with this type of experimentis the strong influence of the nitrogen nuclear spin-lattice relaxation, on the decays. As explained be-low, the observed decays were a mixture of allthree relaxation processes. This makes the proto-col for data collection and for analysis of the vari-ous decays much more complex than originallyexpected. Attempts in our laboratory usingSaturation Recovery alone were similarly unsuc-cessful (unpublished experiments with Dr. P.Fajer). We believe we have now solved thesefundamental problems using pulsed SR-ELDORand SR-EPR together.

We will demonstrate that Pulsed EPR techniques,such as SR-EPR and SR-ELDOR, can be used toobtain both the nuclear and electronic spin-latticerelaxation rates directly and monitor changes in ex-change rates. Moreover, the correlation time con-necting two spectral positions can be directly mea-sured as well. Relaxation time measurements, es-pecially nuclear spin-lattice relaxation (Tin).c a n

also characterize the motion in the ultra-slow mo-tional time range.

2 TheoryFigure 1 shows an absorption CW-EPR signalwhen the correlation time is longer than 0.1 micro-seconds. The figure illustrates the dependence ofthe signal on molecular orientation. The reorienta-tion, characterized by a rotational correlation time,TR, moves the magnetization around within a givenmanifold. Nuclear spin flips, occurring at rateT^"1, move the magnetization from one manifoldto the other without causing molecular reorienta-tion. Regardless of orientation or manifold, themagnetization relaxes to the lattice at rate Tie'

15 P. Fajer, D.D. Thomas, J.B. Feix, and J.S. Hyde,Biophys. J., 50, 1195-1202, 1986.

Vol. 14, No. 1-4 37

Theory [4], [16] predicts for the SR-ELDOR ex-periment that the TR of a molecule should appear asan exponential decay with a rate (TR"1 + T^"1) andthat Tin should appear as a decay of rate (T\a'1 +T^"1). These two processes have very similarrates, which is why motional rates have been sodifficult to determine. However, suitable positionsof pump and observer can be chosen so that thesigns and the amplitudes of both Tin and the mo-tional decay curves can be individually changed,enabling analysis to disentangle the rates. The SR-ELDOR experiment measures the decay of thetransient component of the z magnetization,(Mz(t;v,8)), where v is the nuclear manifold(which is ±1/2 for 15N), and 6 is the orientation,as shown in Figure 1. The evolution of the mag-netization can be understood, qualitatively at least,by a simple population analysis treatment

Therefore the master equation is:

Lattice!

^Figure 1: Linear Absorption EPR spectrum of sl-Hbillustrating the positions where SR-ELDOR experi-ments are performed and the dependence of the resonance'positions of the magnetization on spin-label orienta-

°" T h e figure f u r t h e r illustrates how T R , and Tin! spectral diffusion, whereas T i e induces true spin-"J relation.

^•Sugano, C. Mailer, and B.H. Robinson, / . Chem.zfkys. 87, 2478-2488, 1987.

{(M2(t;v,e))-(Mz(t;-v,0))} (1)

-DV2 (Mz(t;v,e))

where D is the Einstein Rotational DiffusionCoefficient (D = 1/6 t R ) and V2, is the angularLaplacian operator. The system is pumped with aweak selective pulse so that the spin system isexcited in manifold vp and at orientation 8p. Thethe observer frequency is set to manifold v0 and atorientation 80. The recovery signal then has theapproximate form:

(Mz(t;vo,eo vp,ep)) =

* (l + P2(cos(9o)) • P2(cos(8p))e-t/xR)

where <Mz(t;vo,8o|vp,8n)> is the magnetization atthe observer position subject to the condition thatall of the magnetization was at the pump position attime zero; and (Mz(O;vp,0p)) is the initial magneti-zation at time zero (when the pumping is com-pleted). P2 (cos(8)) = (3 cos2(8) - l)/2 is the I =2 component of the Legendre polynomials P;(x),and f v y = +1 if v = v' and fvv- = -1 if v = -v '(which is the case of going from one manifold tothe other). This result assumes a short durationpump time, a low observer amplitude and that thehigher rotational functions are not significant [17].Equation 2 predicts that one will observe 4 expo-nentially decaying components, wherein the rate ofeach component is a linear combination of T^"1,Ti,,"1, and TR"1. The amplitude of the componentscontaining Tin"1, may be switched in sign by set-ting the pump and observer positions to differentspin manifolds. The amplitude of the componentscontaining TR"1 may be switched in sign by settingthe pump and the observer to different ends of thesame manifold.

17 T. Sugano, "A Study of Very Slow RotationalDiffusion by SR-EPR", Ph.D. Thesis, University ofWashington, 1987.

38 Bulletin of Magnetic Resonance

3 ExperimentThe details of the spectrometer and its performanceare discussed more fully in another paper in theseProceedings [18]. SR-EPR and SR-ELDOR ex-periments are both polarization experiments whichmeasure the recovery of the system to equilibrium.A selective pulse is applied to the spins which al-ters the polarization and burns a partial hole in theline. Under conditions of SR-EPR the frequencyof observation is the same as the pump and there-fore the signal is that of a pure recovery as the po-larization spreads throughout the spin system andout to the lattice. Under conditions of SR-ELDOR,the frequency of the observer is different from thatof the pump and the arrival of magnetization, aswell as relaxation to equilibrium, are both detected.It is neither necessary, nor desirable, for the pumpto be coherent with the observer. The experimentsobtain decay curves taken with various pump timesand pump-observer frequency differences; the ro-tational correlation time is determined by the sol-vent viscosity and temperature. The pump timecontrols the relative amplitudes of the various com-ponents which contribute to the overall relaxationof the magnetization; and the pump-observer fre-quency difference controls the signs of the ampli-tudes of the exponentially decaying components inways predicted by equation 2.

The experiment proceeds as follows: for one set ofexperimental conditions, a number of decay curvesover different time scales are obtained. These de-cays are linked by the fact that the exponentialswhich comprise them are all identical and only thetime range of data collection is altered. For a dif-ferent set of conditions e.g. in pulse length or inobserver field position, the relative amplitudesand/or signs of the individual decays are alteredand another set of linked spectra is collected Bothsets of linked data are then pooled with the con-straint that the rates of the exponentials whichmake up the spectra are common to all and theamplitudes of each component within a linked setare the same. This technique [19], as an

18 C. Mailer, B.H. Robinson and D.A. Haas, "NewDevelopments in Pulsed EPR: Relaxation Mechanismsof Nitroxide Spin Labels", [these proceedings] 1992.

19 J.M. Beecham, E. Gratton, M. Ameloot, J.R.Knutson, and L. Brand, in FluorescenceSpectroscopy: Principles J.R. Lakowicz (ed.) PlenumPress NY Volume 2 Chapter 5,1991.

application of Global Analysis, is well recognizedin optical spectroscopy as being extremely effec-tive in determining relaxation rates.

Once one has obtained a unique set of decay ratesthat minimizes the global x2 one must identify theprocesses which gives rise to each individual de-cay rate i.e.whether it is due to Tie"1, Tin"1 of ro-tation. Suitable choice of experimental conditionsfor acquisition of the decays enable the rates to bedistinguished. The strategies we have found usefulare:

(i) Pumping and observing at the magic anglewill reduce the amplitude of the motional rate,leaving just the Tie and Tin"1.

(ii) Pumping in one spin manifold and observ-ing in the other will always invert the amplitude ofa Tin containing term.

(iii) Pumping at one extreme turning point of aspin manifold and observing the other will invertthe amplitudes of the motionally dependent com-ponents.

(iv) Suppression of free induction decay (FID)is always important. In the nanosecond range ofmotion the FED has approximately the same time asTi e and Tin.

(v) A pump time that is long compared to therelaxation time of a particular component will tendto suppress the amplitude of that component.

(vi) Pooling the Saturation Recovery EPR andpulsed ELDOR decay curves for analysis is essen-tial for all rates to be found - no single experimentalone is sufficient.

4 ResultsWe have obtained correlation times from per-deuterated 15N TEMPOL in glycerol-water mix-tures over the TR range from 0.1 to 100 microsec- .onds: Bi-expOnential recovery curves were ob-1tained when using the SR-ELDOR protocol de- ̂scribed above, when the "magic angle" (8 = 54°);lwas chosen for the pumping and observing posi-Jjtions (as shown in Figure 1). In Figure 2 areplotted the Tie'1 and Tin"1 rates versus correlationtime in the slow motion range. The very weak;dependence of T ^ ' 1 on correlation time suggest|that the more traditional relaxation mechanisms"

Vol. 14, No. 1-4 39

such as spin rotation and Electron-Nuclear-Dipolarcoupling (END) are not the dominant ones. Thepower law dependence of Tie'1 is on the order of1/TR

1/8. The NMR literature suggests that a modelof spin diffusion in liquids will have the samepower law dependence as that experimentallyobserved [20]. This same power law dependencewas also observed in similar measurements usingSR-EPR [15]. The solid line superimposed on theTie"1 data is defined as:

(3)(coexR)

where fie is an adjustable parameter, and the sec-ond term (r.h.s.) is the END term and the third term

10

10' -uq>

<oco

OIToO

IUJ

10 -

10

10

- ' ' " ""I '

7"~ '

!

i • _

1

'1 ' ' ' ' ""1 ' '

V\ \- •

I ' ' ' ' " " 1 • ' ' ' • " »

• • • • • • • ~

. •

!

J - L U I J 1 . i . . . . . . .

10

- 10'

- 10

- 10

1 0 " , - 8 , - 7 , - 6 ,-s10 ° 10"' 10"° 1O"3 10"

CORRELATION TIME seconds

1010

-3

_ 2: The spin lattice relaxation rates for Tanol|ffilled squares) and Hb (open squares); the nuclear spin-' -tice relaxation rates for Tanol (filled triangles) and sl-

* (open triangles), and x ^ 1 estimated from the recov-' rates (see Figure 3) for sl-Hb (open circles) as aaction of the rotational correlation time xR estimated""i the solvent viscosity and hydrodynamic volume,

""nposed on the curve are the theoretical fits from0 032? 3 a " d 4 ( a s s U m i n g P = 2 ' Pe = 0.0063, and p n

is the spin rotation term. The value of p in thesecond term is set to 2 when the motion is that of asimple isotropic Brownian diffusion. In this mo-tional region only the first term is significant [18].The values of Tin"1 were also determined from theSR-ELDOR experiments. The amplitudes of thecomponents with these relaxation rates clearlychanged sign when the experiments were per-formed in such a way that the pump and observepositions were in different spin manifolds. Thevalues are compared with the theory of the ENDmechanisms described previously [18] and a termadded for the spin diffusion from the nucleus

(4)( A t R / 2 ) F

where pn is an adjustable constant.

Within the motional range from 10'8 to 10"6 sec-onds the rates Tin'1 are a very strong function ofthe motion and uniquely determine the correlationtime. This nicely fills in the "hole" in CW-EPRand ST-EPR in the microsecond range where nei-ther technique is particularly sensitive to the corre-lation time alone. The fit using equation 4 as-sumed that p = 2. However, a closer examinationof the relation of the data to the theory suggest thatp = 1.8 may provide better agreement. There is alarge literature on stretched exponential, which aredescribed in the time domain by the Williams-Watts function and in the CW domain by the Cole-Davidson function [21]. The Cole-Davidson func-tion modifies the p = 2 spectral density function (inequation 4) and motivates a p < 2 for cases wherethere is not a single exponential but there are sev-eral exponentials clustered about an average rate.It may well be the case that p ~ 1.8 to 1.9 is moreappropriate than p = 2 because a detailed analysisof the relaxation parameters from SR-EPR andSR-ELDOR experiments shows [17] that thereshould be 6 exponentially decaying componentsaround the central rate and this may well be an ar-gument that p < 2 may occur. Other alternativeexplanations for the slight deviation of the experi-mental data from the theory may lie in the presenceof oxygen or additional paramagnetic interactions(such as concentration effects).

J G - P o w l e s 'P r o c- ., 88, 513, 21 C.P. Lindsey and G.D. Patterson, / . Chan. Phys., 73,3348, 1980.

40 Bulletin of Magnetic Resonance

SR-EPR: « B

Figure 3: Three different SR-ELDOR spectra, taken at different pump and observation positions (see Figure 1). The topcurve is the SR-EPR spectrum at position B (in Figure 1), the middle curve is the SR-ELDOR spectrum pumping at posi-tion A and observing at position B, and the bottom spectrum is the SR-ELDOR spectrum pumping at position B and observ-ing at position C. Superimposed on each spectra is the least-squares best fit consisting of an adjustable baseline and threecomponents each of which is a single exponential decay (see equation 2), the rates are given in Figure 2.

Figure 3 shows an example of the SR-EPR andSR-ELDOR data for sl-Hb tumbling with xR in the1 to 5 microsecond time range. The top curve,(SR-EPR at B) is the SR-EPR data acquired atpoint B (defined in Figure 1). This curve is asimple recovery and all components have the samesign. The bottom curve (SR-ELDOR from B to C)is the data when the pump is set on B and the ob-server frequency is set to C. This represents ajump from one manifold to the other and the ampli-tude of the components, containing a Tin"1 in therate, change sign. The middle trace of Figure 3(SR-ELDOR from A to B) is the data for the pumpon A and the observer on B. This corresponds tothe pump-observe case within a manifold.According to equation 2, the amplitude of the

components containing TR in the rate will changesign. Clearly there is a peculiar dip in the shape ofthis SR-ELDOR curve. The dip is characteristic ofthe component that depends directly on the corre-lation time. Superimposed on each of the data setsis a least-squares best fit simulation composed ofthree exponentials and a baseline. The three ratesof the exponentials are the same in all three datasets. The rates arc interpreted, according to equa-tion 2, as Tie*1, Tin"1 and TR'1 as 0.0937, 1.983and 0.329 MRad/sec respectively with around a |10% error. Notice that the motional rate is in be-.|tween the spin-lattice relaxation rate and the nu-|clear relaxation rate. These data are also shown infFigure 2. The nominal correlation time, dctef1mined from solvent viscosity and hydrodynami

Vol. 14, No. 1-4 41

radius of sl-Hb, is 1.5 |j.sec. From the L"/L ratiocalibration curve of the ST-EPR [4] one may esti-mate the correlation time to be 4.0 p.sec and therotational correlation time measured by SR-ELDOR is 3.3 jisec, which is in excellent agree-ment with the ST-EPR calibration data. Thiswork, demonstrates that the different componentsof the experimental curve can be uniquely identi-fied and their rates quantitatively measure, andhence Tie, Ti n and TR may be directly measured.This is the first time that xR has been di-rectly measured in EPR and represents afundamental advance in time domainmethodology.

5 ConclusionsWe have measured the values of the electron andnuclear spin lattice relaxation times in the ultra-slow motion region using SR-ELDOR and SR-EPR and find that the measured values of Tie'1depend on 1/TR1/8, or a power law dependence,which is consistent with a model of spin diffusionin liquids. The measured values of Tin are welldescribed by the electron-nuclear dipolar relax-ation, (which has no adjustable parameters in it)and only the rates at motional times longer than100 fisec suggest the need for a spin diffusionmechanism for Tin as well as Tie. Notice that forthe case of spin labels the nuclear relaxation ismuch faster than the electron relaxation (an un-usual situation). This is primarily a result of theability of the electron, at this particular rotationalrate, to efficiently relax the nucleus and the factthat the electron has very few other spins to relaxit. By using SR-ELDOR and by pooling the dataat different orientations the rotational correlationtime can be measured directly, and is seen experi-mentally as a single exponential relaxation. Thisis, we believe, the first time rotational motion hasbeen quantitatively measured as a single exponen-tial decay in this type of experiment. These exper-

- imental results suggest that it may be possible to. directly measure rotational reorientation by SR-, ELDOR even for systems characterized by aniso-

> tropic motion.M -

|r. These type of time domain experiments are a nec-underpinning and improvement on tradi-

CW techniques. Quantitative simulation off-EPR spectra requires knowledge of the relax-

ation times of the spin system. When performingprogressive saturation studies using CW-EPR, theexperiments can only be used to detect relativechanges in relaxation times when motion is longerthan a nanosecond [22]. (Absolute values are diffi-cult to obtain accurately because the effective re-laxation time for the CW experiment is a complexmixture of competing relaxation processes.) Directmeasurement of Tie"1 a n d Tin w^h pulse tech-niques is clearly superior.

Prior to the time domain experiments it was foundin this laboratory that the Tin*1 value in calcula-tions of ST-EPR spectra in the microsecond mo-tional range had to be set artificially high for goodagreement between simulation and experiment[23]. The simulation assumes that the electron-nuclear dipolar (END) interaction is the sole mech-anism for nuclear spin-lattice relaxation. The datain Figure 2 clearly show that other mechanismsadd to the END rate (e.g. from proton spin diffu-sion) justifying the ad hoc addition of an extra rateinto the calculations.

22 B.H. Robinson, C. Mailer and D.A. Haas, Biophys. J.61, A167, Abstract # 960, 1992.

23 D. Haas, R. St Denis, C. Mailer, B.H. Robinson, 13thIntl. EPR Conf., Denver, CO, 1990.