*National Biomedical Electron Spin Resonance Center, Department of Radiology, Medical ..... Hyde, J. S. (1979) in Time Domain Electron Spin Resonance, eds.
Proc. Nati. Acad. Sci. USA Vol. 84, pp. 964-968, February 1987 Biophysics
Lateral diffusion of lipids in membranes by pulse saturation recovery electron spin resonance (bimolecular collision rates/spin labels/Monte Carlo method/Heisenberg exchange)
JUN-JIE YIN*, M. PASENKIEWICZ-GIERULAt, AND JAMES S. HYDE*: *National Biomedical Electron Spin Resonance Center, Department of Radiology, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226; and tDepartment of Biophysics, Institute of Molecular Biology, Jagiellonian University, Krakow, Poland
Communicated by George Feher, September 22, 1986 (received for review July 28, 1986)
ABSTRACT Short-pulse saturation recovery electron spin resonance methods have been used to measure lateral diffusion of nitroxide-labeled lipids in multilamellar liposomal dispersions. Nitroxides with 14N and 15N isotopes introduced both separately and together were used. Differential equations have been written and solved for complex saturation recovery signals involving several superimposed exponentials. The time constants contain various combinations of the spin-lattice relaxation time (Tie) for both isotopes, Heisenberg exchange rates, and nuclear spin-lattice relaxation times (Tln). Signals of high quality were fitted by Monte Carlo variation of the amplitudes and time constants. The reliability of the approach was tested extensively by verifying that (i) the predicted number of exponentials agreed with the experimental number, (ii) relaxation parameters that were determined were independent of the observed hyperfine transition, (iii) the time constants were independent of saturating pulse length, (iv) Tie and TMn do not change when Heisenberg exchange is changed by varying the concentration, and (v) Heisenberg exchange is indeed proportional to the concentration. It has been established that bimolecular collision rates over a wide range of conditions can be reliably measured using the methodology described here. The methods depend on the favorable match of bimolecular collision rates at micromolar concentrations to nitroxide spinlattice relaxation probabilities. For several years we have been developing and applying methodology to measure short-range translational diffusive motions in synthetic and cellular membranes. These methods depend on Heisenberg exchange (HE) between nitroxide radical spin labels; bimolecular collisions between spin labels produce the observed effects. HE results in transfer of saturation between different portions of the spin-label electron spin resonance (ESR) spectrum, and the observed signals arise from this effect. There are two other competing saturation-transfer mechanisms-the nitrogen nuclear spinlattice relaxation characterized by rate Wn, which under certain conditions can be more rapid than the electron spinlattice relaxation rate We, and slow rotational diffusion that causes spectral diffusion of saturation. [Relaxation times T," and Tle are related to these rates by Tl, n = (2Wen)-".I The latter two are intramolecular, and HE is intermolecular§. One might think that HE could readily be distinguished by changing concentrations, but in practical situations the separation of these processes remains an important consideration. Popp and Hyde (1) used steady-state continuous wave electron-electron double resonance (ELDOR) to determine HE rates (Wx) for stearic acid spin labels substituted into dimyristoylphosphatidylcholine (Myr2-PtdCho) liposomal dispersions. The ELDOR experiment gives the ratio of the The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
HE rate to the electron spin-lattice relaxation rate. The latter was determined using the saturation-recovery method. Nuclear spin-lattice relaxation rates were separated by changing the concentration, but because these rates were much faster than HE rates under conditions of the experiment, the quality of the HE data was degraded. Using the theoretical model of Trauble and Sackmann (2) Popp and Hyde calculated values for the diffusion constants from their measurements of bimolecular-collision rates. Feix et al. (3) introduced two spin-labeled lipids, with the nitroxide moieties at different positions on the acyl chain. One of these contained the 14N isotope and one the '5N isotope. Nuclear relaxation cannot give rise to saturation transfer between the two species. When the isotopes were at the same position, they could obtain lateral diffusion data in good agreement with Popp and Hyde; with the isotopes at different positions, "vertical fluctuations" of the acyl chain could be measured. Hyde et al. (4) introduced the loop-gap resonator (5) into steady-state continuous wave ELDOR spectroscopy and demonstrated that 14N-'5N ELDOR sensitivity was then sufficient for experiments on cells. They reported data on erythrocytes. Similarly, Lai et al. (6) used the method to study lateral diffusion in platelets. Saturation-recovery pulse ESR methods have become increasingly important in our work. The loop-gap resonator has been introduced into our pulse saturation-recovery spectrometer, thereby improving the sensitivity and making time domain studies on both model and biological membranes feasible and straightforward. With long saturating pulses, the spin system approaches a steady state, and recovery tends to follow electron spin-lattice relaxation even in the presence of transverse relaxation mechanisms (7). With short saturating pulses, transverse and translational relaxation processes are convoluted. The short pulse saturation-recovery method is under active development. It was employed by Fajer et al. (8) to study rotational diffusion. It was important in the pulse ELDOR experiment of Hyde et al. (9) to measure nitrogen nuclear relaxation. It is the primary subject of the present paper, where it is employed to measure HE. Under conditions when Wn is negligible, a single 14N spin label can be used to measure HE, but dual labeling with 14N and 15N has been found to give important advantages not only in ELDOR, but also in saturation recovery. Solutions of Abbreviations: HE, Heisenberg exchange; ELDOR, electron-electron double resonance; Myr2-PtdCho, dimyristoylphosphatidylcholine; Ole2-PtdCho, dioleoylphosphatidylcholine; 5NC16 and 1NC16,
2-(14-carboxytetradecyl)-2-ethyl-4,4-dimethyl-3-oxazolidinoxyl (stearic acid) that contains 15N or 14N. tTo whom reprint requests should be addressed. §There exists a dipole-dipole pseudosecular (SS-jt5) term that is of uncertain magnitude and is indistinguishable from HE. Following the approach of Popp and Hyde (1), this term is ignored here, because inclusion would simply alter the magnitude of the interaction distance (itself an uncertain quantity) between spin labels.
Biophysics:
Yin
et
aL
Proc. Natl. Acad. Sci. USA 84 (1987)
the coupled differential equations describing relaxation for a number of restricted conditions of practical importance are given here. These theoretical models are compared with experimental saturation-recovery curves using the Monte Carlo approach for optimizing the fit. It is shown here that the short pulse saturation-recovery method can be used to measure HE rates with exceptional precision. The thrust of this paper is primarily methodological development.
THEORY Model I. If the hyperfine lines are strongly coupled by nitrogen nuclear relaxation and two isotopes are employed, the appropriate energy level diagram is shown in Fig. 1. This is the situation encountered by Popp and Hyde just above the main-phase transition temperature of Myr2-PtdCho. Fig. 1 also shows the spectrum with the ESR transitions labeled. Because of the strong coupling, it is sufficient in the energy level diagram to combine the hyperfine transitions for each isotope into single transitions for the purpose of calculating saturation-recovery signals. Spin-lattice relaxation couples both spin systems to the lattice, and HE couples them together. A variation on this model occurs when the concentration of spins in the observed spin system is sufficiently high to maintain equilibrium through HE within that spin system, even if the nuclear spin-lattice relaxation time is not sufficiently short. Using the usual rate equation notation (10), the rate equations for model I are d(n1- n2) = -2Wel[(nl - n2) - (N1 - N2)] dt +
drn-
2Kx(n2n3
-2We2[(n3
=
-
-
nin4)
n4)
-
(N3 -
Wei
NI Model
-1/2
Wn
+1/2
.,-
N
I
N "I
A
.1
We KxXKx We 1*'
PN
-
Wn 14N -1 0 +1
lodel 11
2 Wn 4 Wn 6
WeWe 1 Wn 3 Wn 5
[1]
Aodel III FIG. 1. The three relaxation models. Model I: '4NC16 (0.005 mol ratio) and "NC16 (0.0025 mol ratio) stearic acid spin labels in Myr2PtdCho at 37TC. Because of very fast nuclear relaxation, hyperfine lines of each isotope are assumed to be strongly coupled. Model II: 15NC16 (0.0025 mol ratio) stearic acid spin label in Myr2-PtdCho at 470C. Model III: 14NC16 (0.004 mol ratio) stearic acid spin label in Ole2-PtdCho at 54TC. All spectra were at pH 9.5, well above the pKa values of the carboxyl protons.
[2]
where
N4)]
- 2Kx(n2n3-
965
A = We1 + We2 + (1/2)Kx(NI + NII)
where n values represent the instantaneous populations per unit volume of the four levels and N values represent the equilibrium Boltzman populations per unit volume. The bimolecular collision rate Wx of species na with species nb is given by Kxnb. Because
[9]
B = [(Wei - We2)2 - Kx(NI- N2)(Wel - We2) +
(1/4)K2(N1
N2)2]1/2,
+
[10]
id I1, I2 are constants to be defined by initial conditions. n2n3 -
njn4
(NII/2)(n2
=
-
nj)
+
(NI/2)(n3
-
n4) [3]
where NI and NII are the concentrations of spin systems I and II, respectively (n, + n2 = N1; n3 + n4 = NII), Eqs. 1 and 2 are linear differential equations. The observable signals are i = (n1
-
n2)
-
(N1 - N2);
iI = (n3 - n4) - (N3 - N4).
[4]
!uite generally a double exponential is observed. The coeffi-
cients are determined by initial conditions after the saturating pulse. If transition I is saturated, i4 is the saturation-recovery signal, and ill is the ELDOR signal. If the two spin labels are at the same position on the acyl chain, they have the same spin-lattice relaxation probability We to a good approximation. (This has been verified experimentally.) In this case, considerable simplification occurs. Eqs. 7 and 8 become
After some rearrangement, Eqs. 1 and 2 become
ditdl=
di1dt
-2Weji - N1Kxii + NIK~iII
= -2We2iI +
NIiKxil - NiKxiii.
iI = I1e2 Met +
[5] [6]
The solutions to Eqs. 5 and 6 are
ii ill
=
Ile
(A -B)t +
NIi
~
11
-(A +
12
-
B)
+
12e-(A+B)t
2We2
NIIKX
+
_(A + B) + 2We2
e
[7]
(-)
NiKx
e-(A+B)t
[8]
=
I1
-N e1 N1
2W't -
I2e-[2Wc+Kx(NI+NIj)]t
[11] [12]
For a short pulse, immediately after the pulse nj = n2, n3 = N3, and n4 = N4. Spin system I is fully saturated, and spin system II is not yet affected. Differentiating Eq. 11 and eval-
uating both it and Eq. 1 for these initial conditions yields 4,
NIKx +
iII
I2e-[2We+Kx(Ni+Nii)Jt
iI
=
=
ie- 2 Wet 1
+
N11 e-[2We+Kt(Ni+Nll)]t}
NI {e 2Wet N,
-
e-[2We+KX(NI+NiI)]}.
[13]
[14]
Biophysics:
966
Yin et aL
Proc. Natl. Acad. Sci. USA 84 (1987)
For a short pulse, the second terms in Eqs. 13 and 14 are the same in magnitude. Both saturation-recovery and ELDOR techniques are effective from the point of view of sensitivity in measuring HE. However the difference in sign in Eq. 14 is notable. It may be easier to separate double exponentials of opposite sign than of the same sign. Both techniques yield the spin-lattice relaxation probability We without contamination from HE at sufficiently long times; the fast initial decay contains HE information. For a long pulse, spin system II approaches steady state and d(n3 - n4)/dt approaches 0 during the pulse. Eq. 2 then yields as an initial condition
(n3 - n4)= =
2We(N3 2We +
-
N4)
KxN1
[15]
As with the short pulse, (nl/n2)t=O = 1. With these initial conditions, Eqs. 7 and 8 become
For a short pulse that pumps interval 1,2, one obtains
i1,2
= I1[e 2Wet + 3/2 + 1/2
+ 1/2
+
NII
2We
NI 2We + Kx(Nl + N11) iI
=
I
N11
e
[2We+KX(NI+NIj)]t}[16j
{et2Wt
N, 2We 2We + Kx(Ni +
NIl)
e-[2We+Kx(Ni+Nl)btj
[17]
Thus the effect of the long pulse is to diminish, both in ELDOR and in saturation recovery, the magnitude of the terms that contain HE information compared with short pulse techniques. The way in which the spin system is prepared, whether by short, long, or intermediate pulse, cannot alter the time constants of the superimposed exponentials but only the relative amplitudes. Use of long pulses tends to give single exponentials that yield We directly with reduced contamination by the second exponential. Model II. Fig. 1 shows an energy level diagram for a nitroxide that contains the 15N isotope where it is assumed that the concentration and rotational correlation times are such that HE, nitrogen nuclear spin-lattice relaxation, and electron spin-lattice relaxation are competitive and must be included in the calculation. This model differs from model I in its inclusion of nuclear relaxation and in the presumption from the beginning of the calculation that the two electron spin-lattice relaxation probabilities are the same. Fig. 1 illustrates a typical spectrum that corresponds to this energy level diagram. It was obtained using a stearic acid spin label with the nitroxide moiety at the 16 position (near the terminal methyl group) in Myr2-PtdCho. Following the same procedures as for model I, one can arrive in a straightforward manner at the solutions when the spin system is prepared by an initial short pulse, Eqs. 18 and 19.
Iie-2Wet + lie-[2We+2Wn+KNlt
[18]
i3,4= I1e-2 We- ie-[2We+2Wn+KXN]t
[19]
i1,2
=
Model III. Fig. 1 shows an energy level diagram for a single 14N nitroxide of concentration N with all possible relaxation paths included. This is an appropriate model at higher temperatures in membranes where all relaxation probabili ties are somewhat comparable. Also illustrated in this figure is a typical soectrum for these conditions.
e-(2We+3Wn+NKX)t]I
[21] [22]
[If interval 5,6 is pumped, the signs of the terms with (3/2) as coefficient change.] Here i1,2 is the saturation-recovery signal and is a triple exponential. A double exponential ELDOR signal is observed at the center line, i3,4, and a triple exponential ELDOR signal occurs at iS,6. For short pulse pumping of interval 3,4,
i3,4
ie-2Wet
[220]
i3,4 -= Ij[e 2Wet -e-(2Wc+3Wn+NK.)tI i5,6 = Ii[e 2Wet - 3/2 e-(2We+Wn+NKX)t
I[e2 Wet -e-(2We+3Wn+NKX)tI Ij[e 2Wet + 2e-(2We+3Wn+NKX)t].
il,2 = i5,6 4
e-(2Wc+Wn+NKx)t
e-(2We+3Wn+NKx)t]
=
=
[23] [24]
Double exponentials are observed for both saturation recovery, i3,4 and ELDOR, il,2, and i5,6. Model III is used in the experimental section of this paper for extensive verification of the theory. In particular, it will be shown that pumping and observing outside lines leads to triple exponentials, and that pumping and observing the central line leads to double exponentials. It will be shown that the values of We, Wn, and K, do not depend on which line is observed, nor on the length of the saturating pulse. And it will further be shown that if the concentration N is varied, the values obtained for We and Wn do not change and that the HE rate changes linearly with concentration.
METHODS Samples were prepared as described previously (1, 3). 15N stearic acid spin label [2-(14-carboxytetradecyl)-2-ethyl-4,4dimethyl-3-oxazolidinoxyl (stearic acid); designated here as '5NC16] was a gift from J. H. Park. 14NC16 was from Aldrich. Dimyristoylphosphatidylcholine (Myr2-PtdCho) and dioleoylphosphatidylcholine (Ole2-PtdCho) were from Sigma. Samples were in 1-mm-diameter capillaries made from methylpentene polymers (TPX) (11); a flow of temperature-regulated nitrogen gas over the capillary was used to remove oxygen (12). A loop-gap resonator was used for the pulse experiments (5). The actual sample volume was =2 ,ul. The microwave field for short pulse experiments was in the range of 2.0 to 3.5 G (1 G = 10-4 T), and the pulse length in the range of 0.1 to 0.5 ,sec. The saturation-recovery spectrometer is based on the design of Huisjen and Hyde (13). A multichannel signal acquisition system (14) greatly improves the signal/noise ratio over what could be achieved with the single channel boxcar of ref. 13. A field-effect transistor (FET) microwave amplifier has recently been introduced. The time response limit is about 0.1 ,usec. A high order-low pass filter at the input to the analog/digital converter cuts off at 25 MHz, which results in minimal distortion of the transient signal. Typically, 2 x 104 decays per sec are acquired with 512 data points on each decay. Total accumulation time is typically 5 min. Aperture intervals were 20 nsec. Data Processing. The number of unknowns in an n-tuple exponential is 2n, n time constants and n amplitudes. A normalization equation can be written that reduces the number of unknowns to (2n - 1): Z n
A,[1
-
exp(-At/T,)]
= 1.
[25]
Biophysics: Yin et aL
Proc. NatL Acad. Sci. USA 84 (1987)
Time t = 0 is arbitrarily assigned at some instant that is sufficiently delayed that instrumental artifacts can be neglected. Interval At is a delay such that substantial decay has occurred. In general it is not necessary to know the baseline, but it is a computational convenience if At is sufficiently long that one can write
I An
=
1.
+1
Ta = 1.705 Tb = 0.694 Tc = 0.356
0
Ta= 1.616 Tb = 0.363
967
[26]
The experimental section of this paper focuses primarily on model III, where Eq. 20 predicts a triple exponential. Good baselines were always obtained, which for our instrument is an important control on adjustment. Eq. 25 would then be used, resulting in five unknowns. By using a long saturating pulse and by fitting the tail of the saturation-recovery signal to a single exponential, good preliminary estimates can be obtained of the amplitude and time constant characterizing spin-lattice relaxation. The other time constants involving W,, and NK& must be shorter, Eq. 20. We have used the Monte Carlo method for curve fitting. A grid is constructed in five-dimensional parameter space, with the range and step size of each parameter specified on the basis of physical insight. The intersections on this grid are tested randomly using a random number generator. The program can be stopped at any time; as the run time increases, the probability that each intersection is inspected approaches unity. A least-squares minimalization function was used as the criterion of excellence of the fit between model and experiment. The curve-fitting programs were written in the course of this work and run alternatively on a PDP 11/34 or an IBM 9000 computer.
C
.I, 'aC)
Tc = 0.359
0) 0
U1)
C._ C
0 cu
(I)
x5x
I I
I
\ -1
Ta = 1.822 Tb = 0.707
Tc = 0.354
RESULTS AND DISCUSSION Fig. 2 is illustrative of the data and curve fits. The concentration of spin-label for Fig. 2 was low (0.001 mol ratio) in order to give the reader a qualitative feeling for sensitivity of the experiment. The first row of Table 1 corresponds to this figure. Although the experimental and simulated data are superimposed, essentially no difference can be seen even in the residual, which is the difference between experiment and model at five times higher gain. Theoretically, it is likely that some dependence of We on nuclear quantum number ml of nitroxide radicals exists. However, the spin-rotational mechanism that is likely to be dominant exhibits no ml dependence. This is fortunate, because the problem could well be intractable if it were necessary to assign different values of We to each hyperfine transition. The theory predicts when observing the ml = 0 line that a double exponential should be observed. Nevertheless we fitted it to a triple exponential; the resulting two time constants were substantially identical. The theory predicts, Eqs. 20 and 24, that the shortest constant when observing ml = 0 should be the same as the shortest time constant when observing ml = + 1, and such is the case. The intermediate time constants for ml = ± 1 should be identical, and again agreement with the theoretical model is achieved. An extensive series of experiments were performed using Ole2-PtdCho at 540C as the membrane system. Some effort was taken to find experimental conditions where Ti, was as long as possible. The results are shown in Table 1. Errors are standard deviations for repeated experiments on the same sample. The first three rows of Table 1 permit the study of the effect of concentration. Increase in concentration changes Ta. A similar effect was observed previously for nitroxides in bulk fluids by Percival and Hyde (15). The average values
x
A
I
I
M
AA.\
4
1 & bA AAt
I
I
Time, 1-pts intervals
FIG. 2. Experimental test of model III. Data appear in the first row of Table 1. Simulations and experimental saturation-recovery signals are superimposed, and the difference multiplied by a factor of five is shown as the "residual." Each recovery signal obtained in 5 min at 20,000 accumulations per sec, 512 data points per accumulation.
for Tln for the three concentrations are 0.1 M%, 0.72 As; 0.4 M%, 0.78 Us; 0.8 M%, 0.75 ,s. Thus Tl, is independent of concentration as expected. The average values for (Wx/mol ratio) x 10-3 are 0.1 M%, 0.14 MHz; 0.4 M%, 0.17 MHz; 0.8 M%, 0.13 MHz. Bimolecular collision frequencies are linear in concentration, as expected. We report that the time constants in Table 1 (but not, of course, the amplitudes) are independent of the length of the saturating pulse (data not shown). The lipids Myr2-PtdCho and Ole2-PtdCho were selected in order to search for dependencies of the relaxation parameters on the presence of double bonds, but little effect of unsaturation is evident in the data of Table 1.
CONCLUSIONS The number of superimposed exponentials that can reliably be deconvoluted from an experimental transient signal de-
Biophysics:
%8
Proc. Natl. Acad. Sci. USA 84 (1987)
Yin et aL
Table 1. Experimental data for model III Mol ratio mI Ta* Tbt W Tin, ASS ± 0.02 0.74 0.36 1 1.70 0.70 0.001 0 1.62 0.36 0.72 ± 0.01 Ole2-PtdCho -1 1.81 0.70 0.35 0.70 ± 0.01 1 1.71 0.53 0.31 0.76 ± 0.10 0.004 0.31 0.78 ± 0.02 0 1.69 Ole2-PtdCho -1 1.71 0.53 0.32 0.80 ± 0.01 1 1.44 0.42 0.27 0.74 ± 0.04 0.008 0 1.43 0.27 0.75 ± 0.03 Ole2-PtdCho -1 1.43 0.42 0.27 0.75 ± 0.02 1 1.69 0.50 0.32 0.90 ± 0.02 0.005 0.32 0.90 ± 0.02 Myr2-PtdCho 0 1.69 -1 1.74 0.52 0.33 0.89 ± 0.04 *Ta = (2W,)-l ± 0.01 tTb (2W, + W, + W.)-1 t 0.01 /.Ls. tT, = (2Wc + 3Wn + W,)-' ± 0.01 us.
Wx, MHz 0.17 ± 0.03 0.11 ± 0.10 0.15 ± 0.02 0.67 ± 0.03 0.72 ± 0.01 0.70 ± 0.02 1.03 ± 0.04 1.00 ± 0.03 1.04 ± 0.02 0.83 ± 0.03 0.81 ± 0.02 0.80 ± 0.01
ALs.
=
pends ultimately on the quality of the data. The problem is greatly reduced in complexity if the number of exponentials is known. We have established a theoretical basis in the context of saturation-recovery experiments on nitroxide radical spin labels that predicts the number of exponentials and that permits the interpretation of the data in terms of relaxation probabilities between the various energy levels. The reader is also referred to the theoretical work on saturation recovery by Freed (16). We have demonstrated experimentally that high-quality data can be obtained that permits the determination of bimolecular collision rates over a wide range of conditions relevant to lipid transport in membranes. Our analysis and experiments suggest certain further improvements in the apparatus, but a benchmark has been established for triple exponentials. A number of other physical situations have been modeled by us in a parallel manner; these include introduction of chemical exchange, physical exchange between different environments, and HE involving three moieties. Bimolecular collision frequencies are typically 105 Hz at 10- M in fluids. These numbers match well with the spinlattice relaxation time of spin labels. Although collision frequencies in hard-sphere classical kinetic theory do not de-
pend on molecular dimensions, estimates of diffusion constants are dependent on the model and dimensions. We have in-hand methodology to investigate translational transport at a molecular level in a number of model and biological systems of great interest. This work was supported by Grants GM27665, GM22923, and RR01008 from the National Institutes of Health. J.-J.Y. was supported in part by the Biophysics Program of the Medical College of
Wisconsin. 1. Popp, C. A. & Hyde, J. S. (1982) Proc. Natl. Acad. Sci. USA
79, 2559-2563. 2. Trauble, H. & Sackmann, E. (1972) J. Am. Chem. Soc. 94, 4499-4510. 3. Feix, J. B., Popp, C. A., Venkataramu, S. D., Beth, A. H., Park, J. H. & Hyde, J. S. (1984) Biochemistry 23, 2293-2299. 4. Hyde, J. S., Yin, J.-J., Froncisz, W. & Feix, J. B. (1985) J. Magn. Reson. 63, 142-150. 5. Froncisz, W. & Hyde, J. S. (1982) J. Magn. Reson. 47, 515521. 6. Lai, C.-S., Wirt, M. D., Yin, J.-J., Froncisz, W., Feix, J. B., Kunicki, T. J. & Hyde, J. S. (1986) Biophys. J. 50, 503-506. 7. Hyde, J. S. (1979) in Time Domain Electron Spin Resonance, eds. Kevan, L. & Schwartz, R. N. (Wiley, New York), pp. 130. 8. Fajer, P., Thomas, D. D., Feix, J. B. & Hyde, J. S. (1986) Biophys. J. 50, 1195-1202. 9. Hyde, J. S., Froncisz, W. & Mottley, C. (1984) Chem. Phys. Lett. 110, 621-625. 10. Carrington, A. & McLachlan, A. D. (1967) Introduction to Magnetic Resonance (Harper & Row, New York), pp. 4-8. 11. Popp, C. A. & Hyde, J. S. (1980) J. Magn. Reson. 43, 249258. 12. Kusumi, A., Subczynski, W. K. & Hyde, J. S. (1982) Proc. Natl. Acad. Sci. USA 79, 1854-1858. 13. Huisjen, M. & Hyde, J. S. (1974) Rev. Sci. Instrum. 45, 669675. 14. Forrer, J. E., Wubben, R. C. & Hyde, J. S. (1980) Bull. Magn. Reson. 2, 441. 15. Percival, P. W. & Hyde, J. S. (1976) J. Magn. Reson. 23, 249257. 16. Freed, J. H. (1979) in Time Domain Electron Spin Resonance, eds. Kevan, L. & Schwartz, R. N. (Wiley, New York), pp. 3166.
