1931
References and Notes (1) Issued as N.R.C.C. No. 15221. (2) (a) National Research Council: (b) Dept. of Energy, Mines and Resources. (3) J. Ehrlich. 0. L. Coffev. M. W. Fisher, M. M. Galbraith. M. P. Knudsen. R. W. Sarber, A. S.Schlingman, R. M. Smith, and J. K. Weston, Antibiot. Annu., 790 (1954-1955). (4) D. Vazquez, "Antibiotics", Vol. Ill, J. W. Corcoran and F. E. Hahn. Ed., Springer-Verlag, New York. N.Y.. 1975. (5) 0.R. Bartz, J. Standiford, J. D. Mold, D. W. Johannessen, A. Ryder, A. Maretzki, and T. H. Haskell, Antibiot. Annu.. 777 (1954-1955). (6) D. E. Ames, R. E. Bowman, J. F. Cavalla, and D. D. Evans, J. Chem. Soc., 4260 (1955). (7) D. E. Ames and R. E. Bowman, J. Chem. SOC.,4264 (1955). (8) D. E. Ames and R. E. Bowman, J. Chem. SOC.,2925 (1956). (9) P. de Mayo and A. Stoessl, Can. J. Chem., 38, 950 (1960). (IO) M. C. Fallona, T. C. McMorris. P. de Mayo, T. Money, and A. Stmssl, J. Am. Chem. SOC.,84,4162 (1962). (1 1) M. C. Fallona, P. de Mayo, T. C. McMorris, T. Money, and A. Stoessl, Can. J. Chem., 42, 371 (1964). (12) M. C. Fallona, P. de Mayo, and A. Stoessl, Can. J. Chem., 42, 394 (1964). (13) J. M. Stewart, G. J. Kruger, H. L. Ammon, C. Dickinson, and S.R. Hall, The X-RAY System of Crystallographic Programs, University of Maryland, 1972. (14) J. Karle, "Crystallographic Computing", F. R. Ahmed, Ed., Munksgaard, Copenhagen, 1970, p 37. (15) These and all subsequent calculations were carried out with the help of the NRC programs written by Ahmed, Hall, Pippy, and Huber. The ORTEP-11program of C. K. Johnson was used for drawing Figure 2.
.,
(16) J. A. lbers and W. C. Hamilton, Ed., "International Tables for X-Ray Crystallography", Vol. IV, Kynoch Press, Birmingham, England, 1974. (17) M. J. S. Dewar and I. J. Turchi, Chem. Rev., 75, 389 (1975). (18) G. R. Delpierre, F. W. Eastwood, G. E. Gream, D. G. I. Kingston, P. S. Sarin, Lord Todd, and D. H. Williams, J. Chem. SOC.C, 1653 (1966). (19) D. G. I. Kingston, Lord Todd, and D. H. Williams, J. Chem. SOC.C, 1669 (1966). (20) F. Durant, G. Evrard, J. P. Declercq, and G. Germain, Cryst. Struct. Commun.,3, 503 (1974). (21) M. Barbacid. A. Contreras, and D. Vazquez, Biochim. Biophys. Acta, 305, 347 (1975). (22) G. I. Birnbaum, J. Am. Chem. SOC., 08, 6165 (1974). (23) V. Albano, P. L. Bellon, F. Pompa, and V. Scatturin, Ric. Sci., 33, 1143 (1963). (24) I. Ambats and R. E. Marsh, Acta Crystaliogr., 10, 942 (1965). (25) (a) L. Pauling, "The Nature of the Chemical Bond", 3rd ed. Cornell University Press, Ithaca, N.Y., 1960, p 237; (b) p 303. (26) K. Yakushl, I. Ikemoto, and H. Kuroda, Acta Crystallog., Sect. B, 27, 1710 (1971). (27) A. Lotthus, Mol. fhys.. 2,367 (1959). (28) M. J. S. Dewar and I. J. Turchi. J. Chem. SOC.,Perkin Trans. 2, submitted for publication. (29) K. Kuchitsu, T. Fukuyama, and Y. Morino, J. Mol. Struct., 1, 463 (1968). (30) 0. I. Birnbaum, Acta Crystallogr., Sect. 8, 28, 1248 (1972). (31) R. Kuhn and K. Kum, Chem. Ber., 05, 2009 (1962). (32) C. H. Kuo, D. Taub, R. D. Hoffsommer, N. L. Wendler, W. H. Urry. and G. Mullenbach, J. Chem. Soc.,Chem. Commun.,761 (1967). (33) J. MacMillan and T. J. Simpson. J. Chem. Soc., ferkin Trans. 1, 1487 I (1973). (34) G. I. Birnbaum, E. Darzynkiewicz, and D. Shugar, J. Am. Chem. Soc., 07, 5904 (1975).
Internal Rotations of Side Chains and Backbone in Luteinizing Hormone-Releasing Hormone (LH-RH). Analysis of Carbon- 13 Spin-Lattice Relaxation Timeda Roxanne Deslauriers*lb and R. L. Somorjailc Contributionfrom the Division of Biological Sciences and the Division of Chemistry, National Research Council of Canada, Ottawa, Canada K I A OR6. Received July I O , 1975
Abstract: W e have analyzed the j3C spin-lattice relaxation times obtained for, L H - R H in aqueous solution in terms of contributions from both overall and internal motions of backbone and side chains. The method of analysis is based on a model of stochastic rotational diffusion about bonds. It assumes that these rotations about individual bonds are independent of and uncorrelated with rotations about all other bonds. W e have calculated minimum and maximum dimensions for the L H - R H monomer and computed the corresponding T I values for overall molecular tumbling. For this T I range, corresponding to 2 X IT ~ I2~ X I the internal motions of the backbone must be assumed slower than the overall molecular motion in order to simulate the observed near equality in N T I values for the cy-carbons in positions 3-8 of L H - R H . For the side chains, the observed N T I values are good qualitative monitors of internal rotations about bonds whose relaxing carbons are more than one bond removed from C,.
The purpose of this study is to gain qualitative insight into the types and rates of motion which can occur in linear peptides of intermediate molecular weight (=1000) and which can produce the spin-lattice relaxation times ( T I ) observed by carbon- 13 nuclear magnetic resonance spectroscopy. T I values have been measured and can be analyzed in terms of both overall molecular and internal motion in both cyclic and linear molecules.2-1 The carbon-13 ( I3C) spin-lattice relaxation times of luteinizing hormone-releasing hormone (LH-RH) (Figure 1) have been measured in aqueous solution and effective correlation times have been reported.12 W e now analyze the T I data in terms of rates of both overall and internal molecular motions. The latter comprise rotation about single bonds, both in the backbone and in side chains. The method of analysis is essentially that of Levine and c o - ~ o r k e r s . Because ~ ~ ~ ~ ~L' H ~ - R H is a linear and therefore potentially flexible peptide, it was necessary to explore the
effect of both isotropic and anisotropic overall molecular motion on the calculated T I values of the backbone and side chains. We have used various methods to estimate the maximum and minimum dimensions plausible in L H - R H for fully extended and compact conformations and examined the effect of varying these size parameters on the calculated rates of internal motion for the side chains of the various residues. Methods. Levine et al.3,'0311 have presented a method which extends previous treatmentsi3-I6 and permits the calculation of dipolar relaxation times when nuclei are reorienting in a magnetic field as a result of multiple internal motions in a molecule. The treatment applies to all values of rotational correlation times (7).The relaxation times of nuclei in chains attached to bodies undergoing overall isotropicIo and anisotropic3 motion have been considered. The formulation assumes that the motions about each individual bond are independent and uncorrelated with the motions
Deslauriers, Somorjai
/
Rotations of Side Chains and Backbone in LH-RH
1932 We have used a number of analytical approaches for correlating the observed N T I values with the diffusion coefficients for rotation about each bond in the peptide backbone and side chains. For the side chains of individual residues, we have estimated the overall rate of molecular reorientaI HzC-CH, CH2 tion and then determined the rates of diffusion about each I ,CH1 - C - N H - C H - C - N H - CCIHH 2- C - N H - CCH2 I I o+C, H -C -NH -CH bond by varying the values of D; separately until every obN II II II II I served T1 value was fitted. Rates of overall molecular moI 0 0 0 0 ?=O H tion have been estimated from molecular dimensions and NH I the rotational diffusion model. The minimum molecular diHzN-C-CH2-HN-CHC-NC - C H - H N - C- H C - H N - C - .CHI II II I I I1 I II I I1 mensions were estimated from van der Waals radii, maxi0 0 H&, ,C% 0 CHz CH2 I mum dimensions of a monomer from measuring space-fillO O ing (CPK) models in fully extended conformations. AlterYHz /CY YH2 CHI CH, natively, the cy-carbon of each side chain was assumed to be NH the “effective center of mass” for that side chain, and rates I of internal motion (0;) with respect to this point were calculated. The general behavior of the observed NT1 values was reproduced for the peptide backbone, using plausible values LUTEINIZING -HORMONE RELEASING-HORMONE Figure 1. Primary sequence of LH-RH. for the rate of overall molecular reorientation. This allowed us to simulate the effect of internal motions within the backbone itself. In one approach diffusion constants were about all other bonds. Furthermore, the calculations have evaluated for all the rotationally flexible bonds in a peptide been based on a model of stochastic rotational diffusion about the bonds. Threefold jump models of r ~ t a t i o n ~ ~ , ~ ~link. , ’ ’ Because of the partial double-bond nature of the peptide link it was assumed that rotation about the peptide have also been considered, yielding qualitatively similar results.3 Levine et al.3-1031I dealt with linear hydrocarbons for -c+which the angles between the bonds about which internal 11 rotations occurred were identical (109.8’). I n our study we O H found it necessary to include calculations of the matrix elebond was not possible. An arbitrary, large value of T = 1.0 ments d,,(2)(/3i) (Appendix) appropriate for peptides, X 1 O ’ O s was used to simulate the rigidity of the peptide where three different angles in the backbone must be conbond. Alternatively, diffusion was considered to occur about sidered. “pseudobonds” l 9which link adjacent a-carbons. The diffuThe T I values arising from dipole-dipole interactions sion constants so obtained are only “effective” values and were calculated from the standard expression,Isa which was comprise contributions from rotations about both bonds in derived for the extreme narrowing conditionlsb the peptide unit. Such an approach is justified since we 1/TI = l/T]DD = (NyH2yCZh2/lO)(r-6)[J(wH - w c ) measure only the T I values of the a-carbons and cannot 3J(wc) ~ J ( W H + w c ) ] (1 ) monitor the rates of rotation involving C=O. and NH groups. There is little difference between the true motion of where the spectral density function J ( w ) , the Fourier transthe C-H vector as $ and 4 of the peptide unit vary and its form of the angular autocorrelation function, is essentially effective motion due to an equivalent rotation of angle 0 that in Levine3 but generalized to arbitrary angles Pi about the pseudobond.20 The exact relation between 0 and ($,$) is known.21The experimental uncertainties (15%) in J ( o l )= armasm [T*/(I w j 2 ~ * ~ x) ] T I measurements mask any error introduced by the pseudom,r.s a1,a2,. . .ON bond approximation. On the other hand, this approximation d * r a , (PI )dsal(PI ) B o , w ~ ( P ~ ) B w w’( .P. ~ Ba*-,a&V) ) (2) reduces by a factor of 3 the number of bonds that have to be considered to calculate diffusion constants that correspond with to observable a-carbon T I ’ S This . leads to a ninefold deN crease in calculation time/pseudobond. An additional twoT* = [ E m 1 aj2Di (3) i= I fold overall time saving results from using the single effective angle, ( 1 4 6 O ) characteristic of the pseudobond geomeBaia,(Pi) = ldaia,(Pjl* try, instead of the three different angles of the peptide unit arm is the coefficient of the rth eigenfunction of the spheri(123, 114, 110’). Finally, the approximations of the model cal top rotor used in the expansion of the mth eigenfunction itself (independent and uncorrelated motion about bonds) of the symmetric top rotor. The latter has an energy of rotaare more likely to be valid for the pseudobonds than for the tion E,, with El21 = 2 0 , 4D,, El11 = 5D, + D,, Eo = more strongly coupled bonds of the peptide unit; it is also 60,. D, = Dy < D , are the rotational diffusion coefficients less difficult to estimate a single effective diffusion constant about the molecular x, y , and z axes, Di is the correspondfor a pseudobond than to guess the two Di needed in the ing coefficient about the ith bond. The time-independent peptide unit. matrix elements dmn(Pi) d,,(*)(Pi) depend on the angle Results and Discussion p i between adjacent bonds about which internal rotations occur (see Appendix). W H and w c are the resonance The T I values obtained a t 67.9 M H z (sample concentrafrequencies of ’H and I3C, respectively, h is Planck’s contion 200 mg/ml, temperature 308 K) are listed in Table I. stant divided by 2 ~N, is the number of protons directly atThe effective correlation time corresponding to each T I tached to the carbon under study, Y H and y c are the magvalue is also given. This effective correlation time (Teff) is netogyric ratios of proton and carbon, respectively, ( r-6) is calculated from eq 122,23with the vibrationally averaged inverse sixth power of the I3CIH internuclear distance.
YH2
I
+
+
+
I-’
+
Journal of the American Chemical Society
/ 98:7 / March 31, 1976
1933
Table I.
Spin-Lattice Relaxation Times' and Correlation Times of Carbons Bearing Protons in LH-RH Anisotropiqd = 0.9 X 10-9 S, T x Tmol = = rv = Tmol = 1.OX 1.9X 5.0X I 0-10 10-9 s,c I 0-9 s,
Isotropic rm0lchosen
Residue
NTi. ms
03OC
(r
W v)
0 0 0 0 0 0
20c 190 180
170
160 150 0 140 0 130 0 I20 0 110 0 100 0 090 0 080 0 07C 0 060 0
I
I
I
!
I
1
1
2
3
4
5
6
CARBON NUMBER FROM CENTER OF MASS
Figure 4. Simulation of backbone motion. Effect of varying ~i,, on observed T I of CH2 groups for a given value of T,,,~]. assuming isotropic overall molecular motion. Center of mass is located at carbon 0.
shape of L H - R H was assumed to be a n ellipsoid of rotation. W e set T = , the correlation time for rotation about the z , or long axis of the ellipsoid, equal to 0.9 X s. The correlation times for rotation about axes perpendicular to the long axis of the ellipsoid, T~ and T ~ were . set to 1.9 X s. These values were obtained from Table I1 and correspond to the values expected for L H - R H in a fully extended conformation. They can be compared with values obtained for the isotropic case (i.e., T~ = T~ = T , ) with ~~~l= 1.0 X s. The anisotropy of the motion has little effect beyond the fl-carbon, and even there the effect is less than 5%. Similar conclusions have been reached by Levine et aL3 In Table IV the calculated N T I values of leucyl carbons in the L H - R H are compared for the spherical and ellipsoidal
1 March 31, 1976
1937 Correlation Times for Internal Rotations in Leucine in LH-RH
Table IV.
Position
Obsd N T I , ms
CY-CH P-CH2 y-CH 6-CH3 6-CH3
175 240 260 1545 1440
s
2.1 1.8 4.3 0.04 0.05
Calcd N T I . ms
s
71nt,b
178 242 260 1540 1538
1.8 1.7 4.3 0.04 0.05
0 = 00
Calcd N T I . ms 0 = 40'
0 = 90°
177 240 258 1534 1434
176 240 260 1538 1438
176 242 260 1544 1444
s. Calculated for a sphere of 10-8, radius (vol = 37 699 A3). Anisotropic overIsotropic overall molecular motion: T~ = T~ = T~ = 1.0 X all molecular motion: T~ = 0.9X IOw9 s, T* = T~ = 1.9 X s. Calculation for an ellipsoid of revolution 18 X 8 8, (semiaxes) (vol = 43 429 A3). 0 = angle between first a-carbon and long axis of the ellipsoid of revolution. Table
V.
Simulation" of Backbone T I Values in LH-RH
Residue
