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Proton magnetic relaxation of proteins in the solid state: molecular dynamics of ribonuclease
CHEMICAL
Volume 69. number 3
PHYSICS
LETTERS
1 February
1980
PROTON MAGNETIC RELAXATION OF PROTEINS IN THE SOLID STATE: MOLECULAR E.R.
DYNAMICS OF RIBONUCLEASE
ANDREW, DJ. BRYANT and E.M. CASHELL
Department Nottingham Received
of Physxs, Unnersity NG7 2RD. UK
1 November
of Nottingham.
1979
Measurements have been made of the proton NMR spin-lattice relaxation at 60,30 and 18 MHZ in solid ribonudwse A from IO to 300 K. and in a-chymotrypsin, lysozyme and deuterated lysozyme from 120 to 300 K. Reorientation of the methyl groups is the predominant moIecular motion causingrelaxation. A lognormaldistniution of correlation times best characterues the motions, with a spread of actwatron energies 14 t 6 kJ/mole.
1_ Introduction There is considerable current mterest in the dynamical behaviour of protein molecules. The somewhat ngid atomic architecture which emerges from the highly successful X-ray diffraction investigations in crystals contrasts with the very dynamic picture of protein molecules obtained from studies m the liquid state. Investigations of protem molecules by high-resolution NMR [l-3] , by thermodynamics and statistical mechanics [4], by ab irutio dynamics [5,6] and by other techmques give much informatlon on the liquid-state molecular dynamics. More re‘cently the analysis of temperature factors in protein crystallography [7,8] has cast much light on the conformatlonal flexibtity of protein molecules in crystals. The comparison and contrast provided by these descrlptions focus attention on the dynamical behavlour of macromoIecuIes in the solid state and on other methods of investigating these motions, one of which is solidstate NMR, through the temperature-dependence of the proton spm-Iattice relaxation time. Unlike the situation in fluids the more restrlcted motion of the protein molecules m the solid state does not sufficiently narrow the &polar-broadened spectra to resolve indivldual groups and study them separately. On the other hand, we can more easily vary the frequency of measurement and we can study processes over a very wide range of temperature.
We have therefore carried out a proton NMR spinlattice relaxation investigation of several well-characterized protems in powder form, and in particular nionrrclease A, which has been studied down to 10 K. Some preliminary results on solid lysozyme have been reported previously [9] _
2. Experimental The proteins investigated were ribonuclease A, orchymotrypsin and Iysozyme. The riionuclease A was supplied by Sigma from bovine pancreas, 5 X crystallized (type I-A), protease free and essentially salt-free. The or-chymotrypsin was supplied by Sigma from bovine pancreas, 3 X crystallized and lyophilised, dialysed saIt free (type 11). The lysozyme was obtained from BDH. described as crystalline from egg white, 3 X cryst&ized, approximately 25000 units per mg. A sample of “deuterated” lysozyme was also prepared by three recrystallizations from D,O, replacing all excha.ngeabIe protons with deuterons. Samples were pumped for 24 h at room temperature and sealed offMeasurements were made at 60.30 and 18 or 16 MHz using a Bruker B-KR 322s variable-frequency pulsed NMR spectrometer in conjunction with an AEI RS2 electromagnet. The range of temperatures extended from 300 K to 120 K and in the case of r&o-
CHEMICAL
Volume 69, number 3
1 February 1980
PHYSICS LETTERS
nuclease was continued down to 10 K using an Oxford Instruments gas flow cryostat_ A 90°-r-90” pulse sequence was used for measurement of the proton spinlattrce relaxation times T1, the signals being recorded from the free mduction decay about 10 /,B after the exciting pulse. All recoveries of nuclear magnetization were exponential within experimental error, and could therefore be characterized by a smgle relaxation time
@lMHz 0 SOMHZ
A
r
Tl-
3
Experimental values of Tl for sohd lysozyme between 120 K and 300 K are shown for three frequencies o. in fig. 1; rather similar results were obtained for cr-chymotrypsm and ribonuclease A. In contrast wrth the behaviour found earher for the monomeric ammo acids [lo-121, the results of fig. 1 exhrbrt many features typical of molecular matrons characterized by a distnbution of correlatron times ~c; the curves are broad and shallow, and T1 IS not independent of w at high temperatures nor proportronal to GJ* at low temperatures as the Kubo-Tomita [ 131 theory of relaxatron requires. That a distrrbution of correlation times is needed to characterize the complex motions of protein molecules is not surpnsing. Following Connor [ 141 we have fitted the data to an extended Kubo-Tomita relaxation equatron which includes a normahzed logarithmrc drstrrbutron F(S) of correlatron times:
+- F(S)[TC( 1 + w;+--1 s -_
f 47c( 1 + 4~;rz)-~]
Table 1 Rekuuon
parameters
Protem
riionuclease A lysozyme cz-chymotrypsm
552
16MHz
lleutsrokd
0otL
3. Results and analysis
T;&C
l
A
Fig. 1 The
5
5 6 IOx/1 (K-II
7
8
temperature dependenceof Tr in solid lysozyme
between 120 and 300 K. where s = Wc/Tcm)
(2)
and C is the relaxatron constant_ We suppose that the mean correlation time rrm follows a srmple activation law rem = romexp(EA/RT).
(3)
The full lines in fig. 1 are theoretrcal curves least-
squares fitted by computer to the data for a gaussian or lognormal distnbution: F(S) = @r112)-1exp(-S2/p2),
(4)
in which the distnbution parameter P is temperaturedependent [ 1 S] , P* = P; + (P@-)*-
dS,
(1)
(5)
The same parameters C, ro, EA, PO, flQ are used for the three frequencies and the best values are tabulated m table 1; the rms devration of the points is 7.5%.
for sohd protems
c
EA
loiSTorn
(109 s-q
&J/mole)
(s)
2.14 2.1 2.8
13.9 15.5 11.7
-13.9 -13.5 -12.2
9
B0
@Q
n
(3/n) CCHB (109 s-q
66 5.8 5.4
16.7 15.6 11.7
1.44 154 2.05
Ckllmole)
2.9
Volume 69, number 3
CHEMICAL
PHYSICS
Other distnbution functions F(S) were considered and in particular the Fuoss-Kirkwood distriiution [ 161 and the gaussian with temperature-independent parameter fl; for these two distributions a closely similar quality of fit was obtained over this temperature range. It will be seen that above 250 K the experimental points for lysozyme fall away. This may be due to motion of the water molecules in the sample. Support for this view is obtained from the behaviour of *be deuterated lysozyme specimen in which this feature is seen to be absent. Experunental points above 250 K have therefore been omitted from the fitting process for normal lysozyme, though not for the deuterated specimen. We note that the curve for deuterated lysozyme is closely similar to that of normal lysozyme below 250 K, but lies about 10% lower. Assuming that below 250 K the water molecules are effectively at rest and are not contriiuting to the relaxation process, their protons being relaxed through the protein’s mot~ons, we conclude that about 10% of the protons present are exchangeable water protons. Support for this was obtamed by progressively heating a weighed sample to 100°C and reweighing. TEMPERATURE (K) 1000 lOtILL
100 , I , ,111,
,
I
10 I
1lll,
4 60MHz 0 30MHz 18 MHz
l
I February
LEl-l-ERS
L980
In order to di scriminate between-the three distributions F(s) which fitted the data satisfactorily down to 120 K, experiments were extended to 10 K OQriionuclease A, since ihe behaviour forecast by the three distributions diverges strongly from each other at lower temperatures_ The results are shown in fig. 2. The fe2tures characteristic of the distniution of cordation times are again observable. Over this much wider range of relaxation times only the lognormal distriiution with temperature-dependent fl gave a tolerable fit for all frequencies, with parameters given in table L, and shown as the full lines in fig. 2.
4. Diiussion
and conclusions
Our previous work on the amino acids IlO-121, peptides [9,17], and homopolypeptides [l&19] leads to the suggestion that one of the most important motions in polypeptides as a source of proton relaxation is the reorientation of the methyl groups in the sidechains of the six residues alanine, isoleucine, leucine, methionine, threonine and Mine. The relaxation minimum at 60 MHz occurs at about 180 K, which is approximately the expected temperature for MS rotor. The activation energy EA of the mean r,, of the distribution of correlation times is 139 kJ/mole (table I); the weighted mean of the activation energies of the methyl rotors in the pure amino acids is 14.6 kJ/moIe [ 121. While we should not expect the hindrances to reorientation to be the same in the protein as in the pure amino acid, nevertheless it is encouraging that they are not very different_ Next we examine the strength of the relaxation process, indicated by the relaxation constant C If the reorientation of the methyl groups provided the onEy source of relaxation in the solid protein, the whole assembly of protons being maintained at a cmmnon spin temperature by rapid spin diffusion, the relaxation constant would be given by [IO] c’ = (3/n) Cc&,
01' 10
I
w 1 I 1 ,?.I,, 100 lO'/T (K-'1
Fg. 2. The temperature dependence c&se A between 10 and 300 K.
I111111 1000
of Tl in solid riinu-
where CQI~ is the relaxation constant for isolated methyl groups and n is the number of protons which each methyl group must, on the average, relax. Taking = 0.8 X 1010 s-2 1121 we obtain values of C’ c-3 from (6) to compare with the measured values C, and these are given in table 1. For riionuclease thz calcu-
Volume
CHEMICAL
69, number 3 TEMi’ERLIllRE ml I
I
mi I
100 1
PHYSICS
1K 1 70 I
50 1
6L-
LETTERS
1 February
1980
this range. It corresponds to a distrrbution of actrvatron energies of 14 f 6 kJ/mole for the central 84.3% of the distnbution, and may be compared with the range of activation energies 14 f 8 kJ/mole found for methyl groups in the pure ammo acids [ 121.
2O-2 r” _&
-
References
tt1 I.D. Campbell, CM. Dobson and R.J.P. Wtllrams, Proc Roy
-6 -6 -10 -12 2 -1s :
[31 141 151 t61 t71 t81
Fig. 3. The distnbutron of correlatton trmes ~c and Its ranatron with temperature for sobd rtbonuclease A. t91
lated value C’ is 0.67 of the measured value C; for lysozyme and chymotrypsin, based on a more restricted range of measurements, the ratro IS0.73 For both. This resuh is consistent with the view that methyl group reorientation is the major source of proton relaxation, amounting to about 70%, leavmg some 30% to be attnbuted to sidechain reorientations, segmental motions, a small number of NH3 group reorrenratrons and whole body motions. Next we examme the drstrrbution of correlation times. In fig. 3 is shown the varration of the mean correlation time 7,, wrth temperature for sohd ribonuclease, using (3) and the parameters of table 1. A good measure of the spread of correlation tunes at each temperature is given by S = +p, from (2) and (4); this range encompasses 84.3% of the drstnbution, since-the error function I( 1) = 0.843. The shaded region in fig. 3 shows
554
Sot
B 189 (1975)
503.
121 DJ. Nelson, SJ. Opella and 0. Jardetzky,
I101 t111
[121 1131 114) 1151 [L6] [ 171
[18] 1191
Brochemtstry 15 (1976) 5552. K. Wuthrich. NMR in brologrcal research pepttdes and protems (North-Holland, Amsterdam, 1976). A. Cooper, Proc. Natl. Acad. Sn US 73 (1976) 2740. J A. McCammon, B-R. Gebn and M. Karplus. Nature 267 (1977) 585. J A. McCammon, B.R Gehn, M. Karplus and P-G. Wolyner, Nature 262 (1976) 325 H. Frauenfelder, GA Petsko and D. Tsernoglou. Nature 280 (1979) 5.58. P J. Artymurk, C C F. Blake, DE P. Grace, S J. Oatley, D C. Phrllips and MJ E. Stemberg. Nature 280 (1979) 563 E.R. Andrew,T.J. Green and MJ.R. Hoch, J. Magn Resort. 29 (1978) 331. E R. Andrew, W.S. Hmshaw, M G. Hutchms and R-0 I. SJobiom. Mol. Phys 31 (1976) 1479. E.R. Andrew, WS Hmshaw. M.G Hutchms. R-0 I Sjoblom and PC. Canepa. Mol Phys 32 (1976) 795. E R. Andrew, W.S. Hmshaw. M-G. Hutchms and R 0.1. SJoblom, Mel Phys 34 (1977) 1695. R. Kubo and K. Tomita. J. Phys Sot. Japan 9 (1954) 888. T-h%. Connor.Trans. Faraday Sot. 60 (1964) 1574. AS. Nowrck and B.S. Berry, IBM J. (1961) 297. R.M. Fuoss and J-G. Kirkwood. J. Am. Chem. Sot. 63 (1941) 385. E-R Andrew, R. Gaspar. T J. Green and W. Vennart, Proceedtngs of the 19th Congress Amp&e, Heidelberg (1976) p_ 131. E-R. Andrew, R. Gaspar and W. Vennart, Chem. Phys. Letters 38 (1976) 141. E-R. Andrew, R Gaspar and W. Vennart. Biopolymers 17 (1978) 1913.
Volume 69. number 3
PHYSICS
LETTERS
1 February
1980
PROTON MAGNETIC RELAXATION OF PROTEINS IN THE SOLID STATE: MOLECULAR E.R.
DYNAMICS OF RIBONUCLEASE
ANDREW, DJ. BRYANT and E.M. CASHELL
Department Nottingham Received
of Physxs, Unnersity NG7 2RD. UK
1 November
of Nottingham.
1979
Measurements have been made of the proton NMR spin-lattice relaxation at 60,30 and 18 MHZ in solid ribonudwse A from IO to 300 K. and in a-chymotrypsin, lysozyme and deuterated lysozyme from 120 to 300 K. Reorientation of the methyl groups is the predominant moIecular motion causingrelaxation. A lognormaldistniution of correlation times best characterues the motions, with a spread of actwatron energies 14 t 6 kJ/mole.
1_ Introduction There is considerable current mterest in the dynamical behaviour of protein molecules. The somewhat ngid atomic architecture which emerges from the highly successful X-ray diffraction investigations in crystals contrasts with the very dynamic picture of protein molecules obtained from studies m the liquid state. Investigations of protem molecules by high-resolution NMR [l-3] , by thermodynamics and statistical mechanics [4], by ab irutio dynamics [5,6] and by other techmques give much informatlon on the liquid-state molecular dynamics. More re‘cently the analysis of temperature factors in protein crystallography [7,8] has cast much light on the conformatlonal flexibtity of protein molecules in crystals. The comparison and contrast provided by these descrlptions focus attention on the dynamical behavlour of macromoIecuIes in the solid state and on other methods of investigating these motions, one of which is solidstate NMR, through the temperature-dependence of the proton spm-Iattice relaxation time. Unlike the situation in fluids the more restrlcted motion of the protein molecules m the solid state does not sufficiently narrow the &polar-broadened spectra to resolve indivldual groups and study them separately. On the other hand, we can more easily vary the frequency of measurement and we can study processes over a very wide range of temperature.
We have therefore carried out a proton NMR spinlattice relaxation investigation of several well-characterized protems in powder form, and in particular nionrrclease A, which has been studied down to 10 K. Some preliminary results on solid lysozyme have been reported previously [9] _
2. Experimental The proteins investigated were ribonuclease A, orchymotrypsin and Iysozyme. The riionuclease A was supplied by Sigma from bovine pancreas, 5 X crystallized (type I-A), protease free and essentially salt-free. The or-chymotrypsin was supplied by Sigma from bovine pancreas, 3 X crystallized and lyophilised, dialysed saIt free (type 11). The lysozyme was obtained from BDH. described as crystalline from egg white, 3 X cryst&ized, approximately 25000 units per mg. A sample of “deuterated” lysozyme was also prepared by three recrystallizations from D,O, replacing all excha.ngeabIe protons with deuterons. Samples were pumped for 24 h at room temperature and sealed offMeasurements were made at 60.30 and 18 or 16 MHz using a Bruker B-KR 322s variable-frequency pulsed NMR spectrometer in conjunction with an AEI RS2 electromagnet. The range of temperatures extended from 300 K to 120 K and in the case of r&o-
CHEMICAL
Volume 69, number 3
1 February 1980
PHYSICS LETTERS
nuclease was continued down to 10 K using an Oxford Instruments gas flow cryostat_ A 90°-r-90” pulse sequence was used for measurement of the proton spinlattrce relaxation times T1, the signals being recorded from the free mduction decay about 10 /,B after the exciting pulse. All recoveries of nuclear magnetization were exponential within experimental error, and could therefore be characterized by a smgle relaxation time
@lMHz 0 SOMHZ
A
r
Tl-
3
Experimental values of Tl for sohd lysozyme between 120 K and 300 K are shown for three frequencies o. in fig. 1; rather similar results were obtained for cr-chymotrypsm and ribonuclease A. In contrast wrth the behaviour found earher for the monomeric ammo acids [lo-121, the results of fig. 1 exhrbrt many features typical of molecular matrons characterized by a distnbution of correlatron times ~c; the curves are broad and shallow, and T1 IS not independent of w at high temperatures nor proportronal to GJ* at low temperatures as the Kubo-Tomita [ 131 theory of relaxatron requires. That a distrrbution of correlation times is needed to characterize the complex motions of protein molecules is not surpnsing. Following Connor [ 141 we have fitted the data to an extended Kubo-Tomita relaxation equatron which includes a normahzed logarithmrc drstrrbutron F(S) of correlatron times:
+- F(S)[TC( 1 + w;+--1 s -_
f 47c( 1 + 4~;rz)-~]
Table 1 Rekuuon
parameters
Protem
riionuclease A lysozyme cz-chymotrypsm
552
16MHz
lleutsrokd
0otL
3. Results and analysis
T;&C
l
A
Fig. 1 The
5
5 6 IOx/1 (K-II
7
8
temperature dependenceof Tr in solid lysozyme
between 120 and 300 K. where s = Wc/Tcm)
(2)
and C is the relaxatron constant_ We suppose that the mean correlation time rrm follows a srmple activation law rem = romexp(EA/RT).
(3)
The full lines in fig. 1 are theoretrcal curves least-
squares fitted by computer to the data for a gaussian or lognormal distnbution: F(S) = @r112)-1exp(-S2/p2),
(4)
in which the distnbution parameter P is temperaturedependent [ 1 S] , P* = P; + (P@-)*-
dS,
(1)
(5)
The same parameters C, ro, EA, PO, flQ are used for the three frequencies and the best values are tabulated m table 1; the rms devration of the points is 7.5%.
for sohd protems
c
EA
loiSTorn
(109 s-q
&J/mole)
(s)
2.14 2.1 2.8
13.9 15.5 11.7
-13.9 -13.5 -12.2
9
B0
@Q
n
(3/n) CCHB (109 s-q
66 5.8 5.4
16.7 15.6 11.7
1.44 154 2.05
Ckllmole)
2.9
Volume 69, number 3
CHEMICAL
PHYSICS
Other distnbution functions F(S) were considered and in particular the Fuoss-Kirkwood distriiution [ 161 and the gaussian with temperature-independent parameter fl; for these two distributions a closely similar quality of fit was obtained over this temperature range. It will be seen that above 250 K the experimental points for lysozyme fall away. This may be due to motion of the water molecules in the sample. Support for this view is obtained from the behaviour of *be deuterated lysozyme specimen in which this feature is seen to be absent. Experunental points above 250 K have therefore been omitted from the fitting process for normal lysozyme, though not for the deuterated specimen. We note that the curve for deuterated lysozyme is closely similar to that of normal lysozyme below 250 K, but lies about 10% lower. Assuming that below 250 K the water molecules are effectively at rest and are not contriiuting to the relaxation process, their protons being relaxed through the protein’s mot~ons, we conclude that about 10% of the protons present are exchangeable water protons. Support for this was obtamed by progressively heating a weighed sample to 100°C and reweighing. TEMPERATURE (K) 1000 lOtILL
100 , I , ,111,
,
I
10 I
1lll,
4 60MHz 0 30MHz 18 MHz
l
I February
LEl-l-ERS
L980
In order to di scriminate between-the three distributions F(s) which fitted the data satisfactorily down to 120 K, experiments were extended to 10 K OQriionuclease A, since ihe behaviour forecast by the three distributions diverges strongly from each other at lower temperatures_ The results are shown in fig. 2. The fe2tures characteristic of the distniution of cordation times are again observable. Over this much wider range of relaxation times only the lognormal distriiution with temperature-dependent fl gave a tolerable fit for all frequencies, with parameters given in table L, and shown as the full lines in fig. 2.
4. Diiussion
and conclusions
Our previous work on the amino acids IlO-121, peptides [9,17], and homopolypeptides [l&19] leads to the suggestion that one of the most important motions in polypeptides as a source of proton relaxation is the reorientation of the methyl groups in the sidechains of the six residues alanine, isoleucine, leucine, methionine, threonine and Mine. The relaxation minimum at 60 MHz occurs at about 180 K, which is approximately the expected temperature for MS rotor. The activation energy EA of the mean r,, of the distribution of correlation times is 139 kJ/mole (table I); the weighted mean of the activation energies of the methyl rotors in the pure amino acids is 14.6 kJ/moIe [ 121. While we should not expect the hindrances to reorientation to be the same in the protein as in the pure amino acid, nevertheless it is encouraging that they are not very different_ Next we examine the strength of the relaxation process, indicated by the relaxation constant C If the reorientation of the methyl groups provided the onEy source of relaxation in the solid protein, the whole assembly of protons being maintained at a cmmnon spin temperature by rapid spin diffusion, the relaxation constant would be given by [IO] c’ = (3/n) Cc&,
01' 10
I
w 1 I 1 ,?.I,, 100 lO'/T (K-'1
Fg. 2. The temperature dependence c&se A between 10 and 300 K.
I111111 1000
of Tl in solid riinu-
where CQI~ is the relaxation constant for isolated methyl groups and n is the number of protons which each methyl group must, on the average, relax. Taking = 0.8 X 1010 s-2 1121 we obtain values of C’ c-3 from (6) to compare with the measured values C, and these are given in table 1. For riionuclease thz calcu-
Volume
CHEMICAL
69, number 3 TEMi’ERLIllRE ml I
I
mi I
100 1
PHYSICS
1K 1 70 I
50 1
6L-
LETTERS
1 February
1980
this range. It corresponds to a distrrbution of actrvatron energies of 14 f 6 kJ/mole for the central 84.3% of the distnbution, and may be compared with the range of activation energies 14 f 8 kJ/mole found for methyl groups in the pure ammo acids [ 121.
2O-2 r” _&
-
References
tt1 I.D. Campbell, CM. Dobson and R.J.P. Wtllrams, Proc Roy
-6 -6 -10 -12 2 -1s :
[31 141 151 t61 t71 t81
Fig. 3. The distnbutron of correlatton trmes ~c and Its ranatron with temperature for sobd rtbonuclease A. t91
lated value C’ is 0.67 of the measured value C; for lysozyme and chymotrypsin, based on a more restricted range of measurements, the ratro IS0.73 For both. This resuh is consistent with the view that methyl group reorientation is the major source of proton relaxation, amounting to about 70%, leavmg some 30% to be attnbuted to sidechain reorientations, segmental motions, a small number of NH3 group reorrenratrons and whole body motions. Next we examme the drstrrbution of correlation times. In fig. 3 is shown the varration of the mean correlation time 7,, wrth temperature for sohd ribonuclease, using (3) and the parameters of table 1. A good measure of the spread of correlation tunes at each temperature is given by S = +p, from (2) and (4); this range encompasses 84.3% of the drstnbution, since-the error function I( 1) = 0.843. The shaded region in fig. 3 shows
554
Sot
B 189 (1975)
503.
121 DJ. Nelson, SJ. Opella and 0. Jardetzky,
I101 t111
[121 1131 114) 1151 [L6] [ 171
[18] 1191
Brochemtstry 15 (1976) 5552. K. Wuthrich. NMR in brologrcal research pepttdes and protems (North-Holland, Amsterdam, 1976). A. Cooper, Proc. Natl. Acad. Sn US 73 (1976) 2740. J A. McCammon, B-R. Gebn and M. Karplus. Nature 267 (1977) 585. J A. McCammon, B.R Gehn, M. Karplus and P-G. Wolyner, Nature 262 (1976) 325 H. Frauenfelder, GA Petsko and D. Tsernoglou. Nature 280 (1979) 5.58. P J. Artymurk, C C F. Blake, DE P. Grace, S J. Oatley, D C. Phrllips and MJ E. Stemberg. Nature 280 (1979) 563 E.R. Andrew,T.J. Green and MJ.R. Hoch, J. Magn Resort. 29 (1978) 331. E R. Andrew, W.S. Hmshaw, M G. Hutchms and R-0 I. SJobiom. Mol. Phys 31 (1976) 1479. E.R. Andrew, WS Hmshaw. M.G Hutchms. R-0 I Sjoblom and PC. Canepa. Mol Phys 32 (1976) 795. E R. Andrew, W.S. Hmshaw. M-G. Hutchms and R 0.1. SJoblom, Mel Phys 34 (1977) 1695. R. Kubo and K. Tomita. J. Phys Sot. Japan 9 (1954) 888. T-h%. Connor.Trans. Faraday Sot. 60 (1964) 1574. AS. Nowrck and B.S. Berry, IBM J. (1961) 297. R.M. Fuoss and J-G. Kirkwood. J. Am. Chem. Sot. 63 (1941) 385. E-R Andrew, R. Gaspar. T J. Green and W. Vennart, Proceedtngs of the 19th Congress Amp&e, Heidelberg (1976) p_ 131. E-R. Andrew, R. Gaspar and W. Vennart, Chem. Phys. Letters 38 (1976) 141. E-R. Andrew, R Gaspar and W. Vennart. Biopolymers 17 (1978) 1913.