J . Chem. SOC., Faraday Trans. 1 , 1981, 77, 759-771

Influence of Rotational Diffusion on the Magnetic Relaxation of d 3 C Nuclei of Poly( 7-benzyl-L-glu tamate)

in the Helical Conformation

BY PETER M . BUDD, FRANK HEATLEY, TIMOTHY J. HOLTON A N D COLIN PRICE*

Chemistry Department, University of Manchester, Manchester M 13 9PL

Received 10th March, 1980

Spin-lattice relaxation times, T,, measured at two resonance frequencies, 25.1 and 75.5 MHz, for tl-'"C nuclei of poly(y-benzyl-L-glutamate) fractions in deuterated dimethyl formamide were found to increase with increase in molecular weight (Hw = 3 1000-81 000 g mol-I). The spin-spin relaxation times, &. for the aJ3C nuclei were found to decrease with increase in molecular weight. Within experimental error Ti was found to be independent of concentration over the dilute solution range covered (12.5-100 mg crnp3), whilst & was found to increase significantly with decrease in concentration. It is suggested that for the helical molecules is influenced by both the axial and end-over-end diffusion coefficients, while T, is governed mainly by the axial diffusion coefficient. The effect of internal librational motion on the a-C-H bond must be taken into account in order to explain the relaxation results quantitatively.

A number of studies have been made of the rotational diffusion of synthetic polypeptides in helical conformations. The experimental methods used have included Kerr-effect relaxation', dielectric relaxation2 and electric field light ~ca i t e r ing .~ .~ From the results a semi-quantitative understanding of the factors governing end-over-end rotational diffusion has been gained. The studies have provided no information, however, concerning rotational diffusion about the helix axis. Fluorescence- depolarization measurements6* ' offer a possible method for determining the axial diffusion coefficient but in practice this approach seems to have been avoided because of the difficulty of attaching fluorophores to the helical backbone rigidly.

In this contribution, we report the use of magnetic relaxation studies of the a - l T nucleus as a method of following the rotational diffusion of helical polypeptides. Measurements were made on a series of poly(y-benzyl-L-glutamate), (PBLG), fractions in deuterated dimethyl formamide [2H,]DMF as a function of concentration, temperature and resonance frequency. The chemical repeat unit of PBLG is

-(-NH-CHR-C0)- where R is -(CH,),C02CH,C,H5 and C is the a-carbon atom. A preliminary communication of results obtained at one frequency (25.1 MHz) and one concentration (50 mg ~ m - ~ ) has been presented elsewhere.8

* *

E X P E R I M E N T A L M A T E R I A L S

Two PBLG samples were synthesized by polymerization of y-benzyl-N-carboxy-L-glutamate anh~dr ide .~ Slightly different reaction conditions were used in the polymerizations in order to obtain materials with the required spread of molecular weights. The first sample was synthesized by polymerizing the anhydride in nitrobenzene for 60 h at 20 "C with n-hexylamine

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760 13C N. M. R. O F P O L Y ( ~ - B E N Z Y L - L - G L U T A M A T E )

added as initiator, The concentration of anhydride in the initial solution was 0.025 g ~ m - ~ and the molar ratio of anhydride to initiator was 76. The polymerization was stopped by pouring the reaction mixture into a large excess of methanol. The PBLG was collected by filtration and washed with methanol. After extraction with hot ethyl acetate, the polymer was reprecipitated from chloroform with methanol and then filtered and dried under vacuum. The second sample of PBLG was synthesized by polymerizing the anhydride (initial concentration = 0.01 5 g ~ r n - ~ ) in benzene. Otherwise the reaction conditions and recovery procedure were the same as described for the first sample.

Each of the samples was fractionated using dichloromethane/methanol as a solvent/non- solvent system. Details of this efficient fractionation method have been described previously.1° Five fractions were selected for use in the study, fractions designated (a) and (6) being isolated from the first sample of PBLG and fractions designated (c), (d) and (e) from the second.

The weight-average molecular weight of each fraction and the ratios of their weight-average to number-average molecular weights were determined by a combination of light scattering (in DMF) and gel-permeation chromatography (in N,N-dimethyl acetamide). The results are listed in table 1.

TABLE 1 .-MOLECULAR-WEIGHT CHARACTERISTICS OF THE PBLG FRACTIONS AND ROTATIONAL DIFFUSION COEFFICIENTS IN D M F AT 30 AND 60 "c CALCULATED FROM EQN (3) AND (4)

30 O C 60 O C

fraction MW Mw/@, 0,/105 s-I Ob/105 S-' 6,/105 s-1 Obj105 s-1

(4 31 000 1.06 305 13.0 463 19.7 35 000 1.08 274 9.38 41 5 14.2

(4 46 000 1.08 212 4.53 32 1 6.86 tb)

54 000 1.08 182 2.97 276 4.49 81 000 1.08 123 0.99 186 1 S O

(4 (4

N. M. R. R E L A X A T I O N M E A S U R E M E N T S

The a-13C n.m.r. relaxation measurements, 'H noise-decoupled,ll l3 were made using two Fourier-transform spectrometers manufactured by Varian Associates, an XL- 100 spectrometer operating at 25.1 MHz and an SC-300 spectrometer operating at 75.5 MHz. Studies were made on solutions of PBLG in [,H,]DMF at concentrations spanning the range 12.5-150 mg of polymer to 1 cm3 of the solvent. 13C chemical shifts are given in table 2. The assignments were made chiefly according to well-established basic correlations of chemical shift with chemical structure. Ambiguous cases were resolved by appeal to mobility arguments. Thus of the two carbonyl peaks at 182 and 178 ppm, the former was considerably broader than the latter, and was therefore assigned to the more restricted backbone group. Similarly the CH, peak at 31

TABLE 2.-13C CHEMICAL SHIFTS FOR PBLG IN [",]DMF AT 60 OC

chemical shift in ppm downfield from TMS peak assignment

182 178 142 134 71 63 36 31

backbone carbonyl side-chain carbonyl aromatic quaternary carbon aromatic protonated carbons benzyl carbon a-carbon y-carbon P-carbon

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P. M. B U D D , F. H E A T L E Y , T. J . H O L T O N A N D C. P R I C E 76 1

ppm was broader than that at 36 ppm and was therefore assigned to the P-CH, group. There was no significant variation in chemical shift with either temperature or concentration.

Spin-lattice relaxation times of the a - W nucleus were measured using the standard n - z - n/2 pulse sequence. Spin-spin relaxation times were obtained from the linewidths at half height, corrected for broadening arising from exponential weighting, field inhomogeneity and residual proton coupling. This correction amounted to ca. 10 Hz, and was estimated from the linewidths of the solvent and aromatic carbon peaks. Nuclear Overhauser enhancements were obtained by measuring the a-I3C resonance intensity with and without proton decoupling.

R E S U L T S at 25.1 MHz was determined for the a-13C nuclei of fractions (a)-(e) at 60 O C and

for fractions (b), (c) and (e) at 30 O C , whilst at 75.5 MHz was determined for two fractions [(b) and (e)] at 60 O C . Within the estimated errors of the measurements was independent of concentration over the range investigated (25- 100 mg ~ r n - ~ ) . Average values are listed in table 3 and a plot of & against concentration is shown in fig. 1 for fraction (e) at 75.5 MHz. The results show that 7; increases with increase in molecular weight and with decrease in temperature.

FIG. 1.-Variation of 7; (upper points) and (lower points) with concentration for the c P C nucleus in PBLG fraction (e ) in [*H,]DMF at 60 O C and 75.5 MHz.

T, at 25.1 MHz was determined for the a-13C nuclei of fractions (a)-(e) at 30 and 60 O C , whilst T, at a frequency of 75.5 MHz was determined for two fractions [(b) and (e)] at 60 O C . The results given in table 4 show that G increases with (i) decrease in concentration, (ii) increase in temperature and (iii) decrease in molecular weight. Extrapolation of T, values to infinite dilution was carried out by arbitrarily assuming that T, was linearly dependent on concentration below c = 5 0 mg cmP3. A plot of T, against concentration is given in fig. 1 for fraction (e) at 75.5 MHz. In order to obtain more reliable estimates of the limiting values of G it would have been desirable to determine T, for much lower concentrations. This was not feasible, however, because of the large experimental errors which are associated with measurements made on very dilute solutions using present techniques.

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762 13C N. M. R. O F P O L Y ( ~ - B E N Z Y L - L - G L U T A M A T E )

TABLE 3.-EXPERIMENTAL VALUES OF tC-l3c NUCLEAR MAGNETIC RELAXATION TIMES AND NUCLEAR OVERHAUSER ENHANCEMENTS FOR PBLG FRACTIONS IN [2H7]DMF

& (extrapo- fraction freq./MHz temp./OC K/ms n.0.e. lated)/ms

25.1 25.1 25.1 25.1 25.1 75.5 75.5 25.1 25.1 25.1

60 60 60 60 60 60 60 30 30 30

70+8 1.1 kO.1 26.0 75 f8 20.7 9 0 f 8 1.3 +O.l 17.4

120+ 10 1.1 kO.1 12.0 147f 10 1.1 fO.1 8.8 320f 16 1.2 f 0 . 1 19.0 505 25 1.5k0.1 8.2 9 0 f 8 - -

120f 10 -

160f 10 - -

-

-

TABLE 4.-EXPERIMENTAL VALUES OF T, FOR OI-'~C NUCLEI OF PBLG FRACTIONS IN [2H7]DMF

solution concentration/

fraction freq./MHz temp. /"C mg ~ r n - ~ G/ms

25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 25.1 75.5 75.5 75.5 75.5 75.5 75.5 75.5 25.1 25.1 25.1 25.1 25.1

60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 30 30 30 30 30

50 25 50 25 50 25 50 25

150 100 50 25 50 25 12.5

100 50 25 12.5 50 50 50 50 50

18.7 f 2.0 22.0 & 2.0 10.3 f 0.7 15.5k 1.1 8.6 k 0.6

13.0 f 0.9 8.0 f 0.6

10.0f0.7 2.1 k0.2 3.8 k 0.2 6.0 f 0.4 7.4 f 0.4

11 .Of 0.8 16.0 f 2.0 15.9 f 2.0 3.8 f 0.2 6.1 f0 .4 7.2 f 0.5 7.6f0.5

10.3 f 0.7 9.1 f0 .6 5.8 & 0.4 4.6 f 0.2 2.9 & 0.2

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P. M. B U D D , F. HEATLEY, T. J . H O L T O N A N D C. PRICE 763

DISCUSSION

SIMPLE H Y D R O D Y N A M I C MODEL FOR HELICAL C H A I N S

Investigations of Doty et aZ.14 showed that PBLG in DMF adopted an a-helical conformation.15 We have confirmed their results recently in our laboratory using a range of samples similar to those used in the present study. In treating the n.m.r. results it was logical to start therefore by considering that the chains behaved as rigid a-helices.

The diameter of a solvated helix was taken as 1.5 nm,16 the length per peptide residue as 0.15. nm, the a-C-H internuclear distance as 0.109 nm and the angle between the bond and the axis of a right-handed helix as 62'. The last was calculated from coordinates determined by Brown and Trotter1' using the X-ray data of Corey and Pauling.18 We assumed that a helical PBLG molecule could be considered as hydrodynamically equivalent to a highly prolate ellipsoid of the same length and volume.

Treating the fluid medium surrounding an ellipsoid as a continuum and assuming the stick boundary condition (i.e. the relative tangential velocity of the solvent is zero at the surface of the particle), Perrin19 derived equations for the rotational diffusion coefficients. From these equations it follows to a good approximation that for a highly prolate ellipsoid the rotational diffusion coefficient, 8 b , about a minor axis (i.e. the end-over-end rotation) is given by 2o

and the rotational diffusion coefficient, O,, about the major axis (i.e. the 'axial' rotation) is given by

where b is the length of the semi-minor axis, a the length of the semi-major axis and q the viscosity of the solvent. For an equivalent helical molecule

and

where M is the molecular weight of the helical molecule, M , the molecular weight of the repeat unit, d the length of the repeat unit and R the radius of the helix. Values of 8, and 8, calculated from eqn ( 3 ) and (4) are given in table 1. In making these calculations we have set q equal to the viscosity of the pure solvent which was determined as 0.8561 CP at 30 O C and 0.6210 CP at 60 O C . Alternative hydrodynamic

22 for rods with stick boundary conditions were available for calculating 8,. They were not adopted, however, since they did not yield values of 8, significantly different from those given in table 1 and furthermore there were no alternative expressions from the same sources for 8,.

Since the correlation times for helix rotation are always >> lo-" s, it was assumed that the relaxation times of the protonated a-13C nuclei are determined entirely by dipolar interactions with the attached protons. The expressions for and T, when

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764 13C N. M. R. O F P O L Y ( Y - B E N Z Y L - L - G L U T A M A T E )

protons are decoupled are23

/q = (h) b0/4n)2 (YE r& h2/r6) [J(wU, - w C ) + 3J(wC) + 6 J ( a C + a,)] ( 5 ) 1 / = (&)@0/4n)2(~E & h2/ r6) x [ J ( m H - a c ) + 3J(mC) + 6J(w, + c+)

+ 440) + ~ J ( W H ) ] (6) where yc and yH are the magnetogyric ratios of 13C and lH nuclei, respectively, r is the C-H internuclear distance and oC and wH are the 13C and lH resonance frequencies. For a prolate ellipsoid,24

(7) where

J(w) = (a) (3 cos2 p- f(zA) +(a) sin2 2pf(z,) + (2) sin4 pf(z,)

= 60,, zgl= 8, + j ob , z, l= 48, + 28,, f(z) = r/(i + w 2 z 2 ) ,

and p is the angle between the bond-vector and the major axis of the ellipsoid. For the same conditions the nuclear Overhauser enhancement is given by

Values of T,, T, and n.O.e., calculated using eqn (5)-(8) together with the theoretical diffusion coefficients of table 1, are given in table 5 .

TABLE 5.--a-l3C NUCLEAR MAGNETIC RELAXATION TIMES AND NUCLEAR OVERHAUSER ENHANCEMENTS CALCULATED FOR THE SIMPLE HYDRODYNAMIC MODEL

fraction freq./MHz temp./OC Klms n.0.e.

25.1 25.1 25.1 25.1 25.1 75.5 75.5 25.1 25.1 25.1

60 60 60 60 60 60 60 30 30 30

52 55 63 69 90

332 719 67 81

127

1.27 1.25 1.22 1.20 1.18 1.17 1.16 1.20 1.18 1.16

14.0 12.2 8.6 6.9 3.53

13.7 3.60 8.5 5.9 2.35

In agreement with the observed behaviour the simple hydrodynamic model predicts that, for a given frequency and temperature, q for the a-13C nucleus increases approximately linearly with increase in molecular weight. The calculations showed that this dependence arises because q is governed predominantly by 8, whose molecular weight dependence is given by eqn (4). This behaviour contrasts strongly with that for other high molecular-weight polymers studied to date where chain segmental motion renders independent of molecular weight above a fairly low critical value.25

On diluting a solution of rod-like chains 8, is expected to approach its limiting dilute-solution value much sooner than 8,. Within experimental error, was found to be independent of concentration below c = 0.1 g ~ r n - ~ , consistent with the view that & is not significantly influenced by 8,.

In further agreement with the observed behaviour the simple hydrodynamic model

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P. M. BUDD, F. HEATLEY, T. J. H O L T O N A N D C. PRICE 765

predicts for a given temperature that T, decreases with increase in molecular weight but that it is virtually independent of frequency. The calculations showed that this behaviour arises because of the overriding influence of a large zero-frequency component, J(0). The model also predicts that both 8, and 8, contribute significantly to T,. The marked dependence of T, on concentration can be attributed to the influence of 8,. In further agreement with the observed behaviour the hydrodynamic model predicts that T, increases with increase in temperature, whilst q decreases.

Experimentally the n.0.e. could not be determined very accurately. However, the experimental values were all relatively low, as predicted, except for fraction (e) at 75.5 MHz.

Whilst the simple hydrodynamic model was able to account qualitatively for the relaxation behaviour, it was unsatisfactory quantitatively. For each fraction studied at 25.1 MHz, ( q)exp > (q)model whilst for fraction (e) at 75.5 MHz ( q)exp < (q)model ;

only for fraction (6) at 75.5 MHz was there satisfactory agreement between experiment and theory and for this case it was most likely fortuitous. For a meaningful quantitative comparison between experiment and theory could only be made for results which had been extrapolated to zero concentrations. In all these cases ( T,)exp > (&)model. Whilst the T, values obtained by our arbitrary extrapolation procedure must be viewed with some caution, it seems unlikely that the theoretical predictions in table 5 would show significantly better agreement with more accurately determined values, even at c = 0.0 125 g ( T,)exp > (&)model and there is no reason why (T,)exp should decrease on moving to lower concentrations.

C O N S I D E R A T I O N O F IMPROVEMENTS T O THE SIMPLE H Y D R O D Y N A M I C MODEL

Pecora and co-workers have shown that the use of stick hydrodynamic boundary conditions does not lead to a quantitative description of the rotational diffusion of small organic mo1ecules,26$27 It has been argued that when the solvent and solute molecules are of similar dimensions it is more appropriate to employ slip boundary conditions.26T 28- 29 The effect of this modification may be considered in terms of an additional parameter, the slip coefficient ps. The choice of any value of pS ( < 00) leads to a larger diffusion coefficient than would be obtained from stick boundary condition^.^^ We considered whether the values of 8, and 60 in table 1 were too low and whether a different choice of 8, and 8, values would lead to a better fit of the experimental results. These considerations were particularly relevant in the case of 8, since the diameter of the helix is not much larger than that of the solvent molecules. Alternatively, it could be argued that even if stick-boundary conditions are applicable in the case of axial diffusion, treatment of the helix as a solid rod (diameter 1.5 nm) might still lead to an under estimate in the value of 8,.

and T, were substituted into eqn (5) and (6) and then an iterative procedure was used to solve the equations for 8, and 8,. However, these calculations showed that physically sensible solutions to eqn ( 5 ) and (6) do not exist for the various sets of q and T, values determined in our study. Furthermore, choice of other values for the angle (e .g . p = 72O, which corresponds to the value for the often considered 3,,-helix) do not lead to any significant improvement in the situation. We therefore conclude that some additional motion must be involved in the relaxation processes.

Let us first consider the possibility of flexural bending of the helical molecules. Results in the literature on this matter are conflicting. End-over-end diffusion of PBLG in the helical conformation has been carefully studied by electric field light scattering.

Experimental values of

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766 Experimental values of 8, (determined in dichloroethane) were shown to be in close agreement with predictions for stiff rods provided polydispersity was taken into a c c o ~ n t ; ~ the latter point was considered important because many of the early studies were made on fractions which had relatively broad molecular-weight distributions. On the other hand dielectric studies on PBLG samples (in the mixed solvents benzene + E-caprolactam and transdichloroethylene + DMF), have given some indica- tion of chain curvature, but as pointed out by North31 the behaviour reported could also be due to sample polydispersity. On balance we feel the results in the literature suggest that chain curvature should not be important for helical PBLG molecules having M < lo5 g mol-l. Even in the absence of more positive evidence on 8b, flexural bending can still be ruled out as the main explanation for the n.m.r. discrepancy. Invoking the effect would merely lead to an increase in 8, and a decrease in 6, through an adjustment of the effective hydrodynamic dimensions of the ellipsoid; as explained above this adjustment cannot explain the discrepancy. The most likely explanation lies in the occurrence of internal librational motions of the macromolecules.

13C N. M. R . OF P O L Y ( Y - B E N Z Y L - L - G L U T A M A T E )

EFFECT OF I N T E R N A L L I B R A T I O N A L M O T I O N S

H o ~ a r t h ~ ~ has argued that many experimental anomalies concerning main-chain and side-chain carbon relaxation times in globular proteins were due to the influence of internal librational motions. The treatment used to account for this effect involved a simple adaptation of 'internal rotation' t h e ~ r y . ~ ~ - ~ ~ It assumed that in a globular molecule undergoing isotropic overall tumbling an a-C-H vector also rotates stochastically at a fixed orientation A to an axis which is itself fixed relative to the molecule. The a-C-H vector is free to take up any direction on the surface of a cone defined by the fixed value of A. The random jumps of the vector on this surface are assumed to be governed by a diffusion coefficient D. It was shown31 that the field dependence of & observed for a variety of proteins can be explained by assuming D = 1.7 x 1 O 1 O s-l and A = 20" for or-C-H internal rotation. It was argued that higher frequency vibrational motions had too small an amplitude to have an appreciable effect upon the relaxation.

By adapting equations developed by Woessner et ~ l . , ~ ' the internal rotational model may readily be extended to encompass molecules in the helical conformation. The treatment involves replacing the J(w) of eqn (5 ) , (6) and (8) by

S ( w ) = (A) sin2 28 sin2 2Af(zA2) + (g)( cos2 2p + cos2 p) sin2 2Af(zB2) + (g) (sin2 p+ a sin2 2p) sin2 2Af(tc2) + (A) sin4 p sin4 Af(zA3) +(#) (sin2p+a sin2 2p) sin4 Af(z,,) + (&) [( 1 + cos2 p)2 + 4 cos2 fl sin4 Af(zc3) + (i) ( 1 - 3 C O S ~ A)2 J(w)

where (9)

p is now the angle between the major axis of the ellipsoid and the axis of the cone of internal rotation of the a-C-H bond vector. J(w) is given by eqn (7) as before.

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768

4 P

13C N. M. R. O F P O L Y ( Y - B E N Z Y L - L - G L U T A M A T E )

FIG. 2.-Calculated dependence of the aJ3C T,, T, and n.0.e. on the internal rotational diffusion coefficient for M = 81 000, A = 20 O, and a temperature of 60 OC. The full curves are (a) at 75.5 MHz, (c) T2 at 75.5 MHz and (e) n.0.e. at 75.5 MHz, and the broken curves are (b) T, at 25.1 MHz, (d) & at 25.1 MHz

and (f) n.0.e. at 25.1 MHz.

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P. M. B U D D , F. HEATLEY, T. J. H O L T O N A N D C. P R I C E 769

30 40 50 60 70 80 90 EW/ 1 o3 g rno1-I

FIG. 3.Xalculated and experimental dependence of the aJ3C 7; and on molecular weight at 60 OC and 25.1 MHz. Curves are calculated for (a) no internal rotation, (b) internal rotation with D = 1.7 x 1Olo s-l and A = 20 O, and (c) internal rotation with D = 5.0 x 1 0 ' O s-' and A = 25 O. The

experimental values are indicated by: *, (T,) and a, (& extrapolated to c = 0).

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770 13C N. M. R. OF POLY(Y-BENZYL-L-GLUTAMATE)

For the special case of D % (Oa, 0,) and w2D-2 6 1, eqn (9) becomes

3 sin2 2 6 3 sin4 A ( 1 - 3 cos2 A)2 S(o) = -------+- + 4 J(4. D 160

Combining eqn (10) with eqn ( 5 ) and (6) we obtain

(T,)-l = 1 OaP + b( T)gl and

where (Q-l = 1 OaP+ b( G)g1

a = [(3 sin2 2A)/4D] +[(3 sin4 A/16D)] b = (i) (1 - 3 C O S ~ A)2 P = (h) olO/W2 (rEr"H2/r6).

(T& and ( T,)R are the relaxation times for the helix in the absence of internal rotation of the a-C-H vector [i.e. as predicted by eqn (5)-(7)]. Combining eqn (10) with eqn (8) gives

5a + b[ - J(o, - wc) + 6J(w, + o,)] n.0.e. = 1+- 1 Oa + b[ J(w, - wc) + 340,) + 6J(o, + w,)]

Values of T,, T , and n.0.e. were calculated for various combinations of D and A, using eqn (5 ) , (6) and (9) together with the data of table 1 . The results showed that inclusion of internal rotation in the hydrodynamic model gave significantly better agreement with the experimental values. Fairly reasonable fits of the data as a whole were obtained for various combinations of D and A in the range D = (1-5) x 1 O 1 O s-l, A = 18-25'. Four sets of calculated values are given in table 6. In fig. 2 we show the effect on T,, T , and n.0.e. of varying D whilst keeping A constant.

Some choices of D and A provided a slightly better fit for the T data than for the T, data, whilst other choices favoured the T, data; see for example fig. 3 where results for 25.1 MHz and 60 OC are compared graphically. Values calculated for the n.0.e. were all high. Nevertheless the model was able to predict the Occurrence of a relatively high n.0.e. for M = 81 000 at 75.5 MHz. The particular combination D = 1.7 x 1 O 1 O s-l and A = 20° corresponds to the choice made by Howarth for proteins. The applicability of this combination suggests that magnetic relaxation processes for a-13C nuclei in helical polypeptides are influenced by similar librational motions to those present in proteins.

The internal rotation model used to account for internal librations showed some measure of success, although it is extremely simple and was adopted because of its availability rather than its suitability. Further improvement in the agreement between calculated and experimental results cannot be expected until a more realistic model has been developed to account for the librational effect.

C O N C L U S I O N S

T, for the aJ3C nuclei of poly(y-benzyl-L-glutamate) fractions in deuterated DMF are strongly influenced by the diffusion coefficient for rotation about the helix axis, leading to an approximately linear increase in with increase in molecular weight. Because of the influence of a large zero frequency component, & for the a-13C nuclei decreases with increase in molecular weight, but is approximately independent of frequency. T, is dependent on both the axial and end-over-end diffusion coefficients.

In order to obtain a quantitative fit of the relaxation data it is necessary to take account of internal librational motion of the molecules.

The motion appears to be similar in nature to that which influences magnetic relaxation processes in globular proteins.

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P. M. B U D D , F. HEATLEY, T. J . H O L T O N A N D C. PRICE 77 1

We thank the S.R.C. for the provision of the n.m.r. spectrometer, for providing research studentships for P. M. B. and T. J. H., and for general support of our research programme on polymers.

I. Tinoco, J. Am. Chem. Soc., 1957,79, 4336. H. Block, E. F. Hayes and A. M. North, Trans. Faraday SOC., 1970, 66, 1095. M. L. Wallach and H. Benoit, J. Polym. Sci., 1962, 57, 41. B. R. Jennings and H. G. Jerrard, J. Phys. Chem., 1965, 69, 2817. B. R. Jennings, Light Scattering from Polymer Solutions, ed. M. B. Huglin (Academic Press, London, 1972), chap. 13, pp. 543-544. Fluorescence Techniques in Cell Biology, ed. A. A. Thaer and M. Sernetz (Springer-Verlag, Berlin, 1971). B. Valeur and L. Monnerie, J. Polym. Sci., Polym. Phys. Ed., 1976, 14, 1 1 . C. Price, F. Heatley, T. J. Holton and P. A. Harris, Chem. Phys. Lett., 1977, 49, 504. E. Katchalski, Advances in Protein Chemistry (Academic Press, New York, 1951), vol. 6, pp. 123-185.

A. Allerhand and R. K. Hailstone, J. Chem. Phys., 1972, 56, 3718.

1974), vol. 1 .

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l 2 J. Schaefer, Topics in C-13 N.M.R. Spectroscopy, ed. G. C . Levy (Wiley-Interscience, New York,

l 3 G. C. Levy, J. Am. Chem. Soc., 1973,95, 61 17. l4 P. Doty, J. H. Bradbury and A. M. Holtzer, J. Am. Chem. SOC., 1956, 78, 947. l5 L. Pauling, R. B. Corey and H. R. Branson. Proc. Natl. Acad. Sci. USA, 1951, 37, 205. l6 U. W. Arndt and D. P. Rdey, Philos. Trans. R. Soc. London, Ser. A, 1955, 247, 409. l7 C. H. Bamford, A. Elliott and W. E. Hanby, Synthetic Polypeptides (Academic Press, New York,

1956), chap. 4, p. 124. R. B. Corey and L. B. Pauling, Proc. R. SOC. London, Ser. B, 1953, 141, 10.

l9 F. Perrin, J. Phys. Radium, 1934, 5, 497. 2o J. T. Edsall, The Proteins, ed. H. Neurath and K. Bailey (Academic Press, New York, 1953), vol. 1 ,

21 J. G. Kirkwood and P. L. Auer, J. Chem. Phys., 1951, 19, 281. 22 S. Broersma, J. Chem. Phys., 1960, 32, 1626. 23 J. R. Lyerla and G. C. Levy, Topics in C-13 N.M.R. Spectroscopy, ed. G. C . Levy (Wiley-Interscience,

24 D. E. Woessner, J. Chem. Phys., 1962, 37, 647. 25 F. Heatley, Prog. Nucl. Magn. Reson. Spectrosc. 1979, 13, 47. 26 G. R. Alms, D. R. Bauer, J. I. Brauman and R. Pecora, J. Chem. Phys., 1973, 58, 5570. 27 D. R. Bauer, G. R. Alms, J. I. Brauman and R. Pecora, J. Chem. Phys., 1974,61, 2255. 28 C. Hu and R. Zwanzig J. Chem. Phys., 1974, 60, 4353. 29 G. K. Youngren and A. Acrivos, J . Chem. Phys., 1975, 63, 3846. 30 J. T. Hynes, R. Kapral and M. Weinberg, Chem. Phys. Lett., 1977, 46, 463. 31 A. M. North, Chem. Soc. Rev., 1972, 1, 49. 32 0. W. Howarth, J. Chem. Soc., Faraday Trans. 2, 1978, 74, 1031. 33 D. E. Woessner, J. Chem. Phys., 1962, 36, 1 . 34 D. Doddrell, V. Glushko and A. Allerhand. J. Chem. Phys., 1972, 56, 3683. 35 R. B. Visscher and F. R. N. Gurd, J. Biol. Chem., 1975, 250, 2238. 36 D. J. Nelson, S. J. Opella and 0. Jardetzky, Biochem., 1976, 15, 5552. 37 D. E. Woessner, B. S. Snowdon Jr and G. H. Meyer, J. Chem. Phys., 1969, 50, 719.

part B, chap. 2, p. 668.

New York, 1974), vol. 1 .

(PAPER 0/389)

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