J . Phys. Chem. 1984, 88, 620-627
620
Vibrational Analysis of Peptides, Polypeptides, and Proteins. 19. Force Fields for a-Helix and @-SheetStructures in a Side-Chain Point-Mass Approximation Ani1 M. Dwivedi and S. Krimm* Biophysics Research Division, University of Michigan, Ann Arbor, Michigan 48109 (Received: March 2, 1983)
Force fields have been refined for a-and P-poly(L-alanine) in which the CH3 group is taken as a point mass. The detailed force fields for these molecules were used as a starting point, and the criteria for refinement were comparable frequency agreement with observed non-CH3 modes and good reproduction of the normal modes of the detailed calculation. Both of these goals were achieved without changes in a large number of starting force constants. The resulting "approximate" force field should provide for meaningful normal mode calculations on larger molecules, such as globular proteins.
TABLE I: Nonequal Force Constants for Detailed and
Introduction Recent advances in normal mode analysis of peptides and polypeptides' have clearly shown that vibrational spectroscopy is a powerful tool for studying the conformational structures of such molecules. It is desirable to be able to extend these analyses to larger nonregular structures such as globular proteins, but the calculational problem rapidly becomes prohibitive because of the large dimensions of the matrices involved. Part of this difficulty has been overcome by developing algorithms for routinely setting up and efficiently diagonalizing the necessary dynamical matrices for a polypeptide chain of arbitrary conformation; an initial application of these methods to the calculation of the normal modes of glucagon has been reported.* However, even in such a case it is still not feasible to include all of the atoms of the side chains, and to make the calculation manageable the side chain is taken as a point mass of 1 (for glycine) or 15 (for alanine), the latter meant to be representative of all non-glycine side chains. This assumption may not be too bad: the conformation-dependent frequencies are expected to be main-chain modes (peptide and skeletal), and these should, in general, be identifiable from the spectra if characteristic side-chain frequencies are known. In calculating the normal modes of such large polypeptides, it is therefore necessary to have a reliable force field that is applicable in a point-mass side-chain approximation. This is no problem for glycine, since we have refined force fields for such polypeptides both in the extended chain3 and 3,-helix4 conformations. In the case of an alanyl side chain, there have been calculations in which the CH3 group was initially taken as a point but this was done in order to simplify the calculation. The problem with this method is that the assignments used to refine the force field are subject to the uncertainty in knowledge of the true character of the normal modes. We have adopted a different approach. Since we have refined detailed force fields for a-poly(L-alanine)* and for P-poly(L-alanine),g it is possible to use such a force field, with appropriate deletions for the replacement of the CH3 group by a point mass, as a starting point for the refinement of what we call an "approximate" force field. More importantly, in refining the starting set of force constants we can require not only optimum frequency agreement but also minimum deviation from the form (1) (2)
S Krimm, Biopolymers, 22, 217 (1983). M. Tasumi, H. Takeuchi, S.Ataka, A. M. Dwivedi, and S.Krimm,
Biopolymers, 21, 71 1 (1982). (3) A. M. Dwivedi and S. Krimm, Macromolecules, 15, 177 (1982). (4) A. M. Dwivedi and S. Krimm, Biopolymers, 21, 2377 (1982). (5) T. Miyazawa, K. Fukushima, and S . Sugano in 'Conformation of Biopolymers", G . N. Ramachandran, Ed., Academic Press, London, 1967, p 557. (6) K. Itoh and T. Shimanouchi, Biopolymers, 9, 383 (1970). (7) B. Fanconi, E. W. Small, and W. L. Peticolas, Biopolymers, 10, 1277 (1971). (8) A. M. Dwivedi and S. Krimm, Biopolymers, in press. (9) A. M. Dwivedi and S. Krimm, Macromolecules, 15, 186 (1982); 16, 340 (1983).
0022-3654/84/2088-0620$01.50/0
Side-Chain-Approximated a-Poly(L-alanine) force constantsa approximate f(NC"j ,f(C"C 1 f(C"CN) f(NCaC) f(NC"CP) f (CC" CP) f(H"C"CP) f(NC", CNC" f (NC",NC"C ) f(CN,CNC") f(C"CP,NC"CP) f(C0,C"CN)
2
4.823 5.080 0.833 0.819 1.093 0.981 0.6647 0.150 0.217 0.600 0.317 0.150
detailed
4.323 4.980 1.033 1.119 1.193 1.181 0.6147 0.300 0.417 0.300 0.517 0.000
'f(AB) = A B bond stretch,f(ABC) = ABC angle bend, ,f(X,Y) = X Y interaction. Units are mdyn/A for stretch and strctch,stretch force constants, nidyn for stretch,bend force constants, and nidyn. A for all others.
TABLE 11: Nonequal Force Constants for Detailed and
Side-Chain-Approximated@-Poly(L-alanine) force constantsa approximate 4.823 5.280 0.833 0.5759 1.0783 0.8687 0.5275 0.300 0.600 0.600 0.7 1 7 0.129 0.450 0.300 0.100 0.667 0.029 0.3 17 0.170 -0.141 0.150 0.096
detailed 4.523 4.980 0.933 0.5259 1.193 1.181 0.5175 0.101 0.300 0.300 0.4 1 7 0.079 0.300 0.200 0.205 0.367 0.079 0.617 0.050 -0.04 1 0.200 0.000
' f ( A B ) = A B bond strctch,J'(ABC) = A B C angle b e n d , j ' ( X , Y ) = X Y intcraction. Units are m d y n / A for stretch and stretch,strctch force constants. nidyn for rtrctch,bcnd force constonts, and n i d y n , A for all othcrs.
of the normal mode, as represented by the potential energy distribution (PED). If these requirements can be satisfactorily met, then the resulting approximate force field should have a meaningful applicability in calculations on, for example, globular proteins. 0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 621
a- and @-Poly(L-alanine)Force Fields
TABLE 111: Observed and Calculated Frequencies (in cm-' ) of a-Poly(L-alanine) ~~
obtd'
Rnman
culcdb
~IR
3279VSlld
A
E,
E,
3279 3279
3279 3279
3279 3279
potential cnergy distributionc
CH, 'is1 (99)
2984 2984 2988 S
2983 VS I1
(
I
2930 M, sh
2925 M I/
CH, ~ (98) F I
-
CH, as2 (96)
2984
CH, a52 (99)
2984 -
L
NH s (98) NH s (98) CH, dS1 (96)
2984
CH, as2 (98)
-
CH,
2930
SF
(100)
-
2942 VS
CH, ss (100)
2930
2939 M 1
-
2930
2880 M
1655 S
2883 W 11, 1
t
1658 VS II
2883 2884
2884 2883 2884 2883
1657 1656 1655 1653 1645 1643 1540 1549
1543 VW
1538 1546
1545 VS 1 1516 M, sh
CH, s\ (100)
-
1519 1523 1452
C"H" 9 (99) C"H" F (99) C"H" F (99) CaHa s (99) C"H" F (99) CaHa s (99) CO s (82), CN 5 (IO), C"CN d (10) CO s (81) CO s (82), CN s (1 I ) , C"CN d ( I O ) C O s (82) CO F (83), CN s (12), C"CN d (10) CO s (83) NH Ib (46), CN s (31), CO ib (12), C"C s (1 1) NH Ib (41), CN s (35), CO ib (12), C"C s (10) NH ib (46), CN s (33), CO Ib ( l l ) , C"C s (10) NH Ib (41), CN s (36), CO ib (12) NH Ib (45), CN s (34), CO ib (1 1) NH ib (42), CN s (37), CO ib (1 2) CH, ab1 (47), CH, nb2 (41), CH, I 1 (10) CH, db2 (54), CH, dbl (31)
1452 -
1452
CH, ab2 (59), CH, dbl (26)
-
1458 S
CH, db2 (45), CH, dbl (41), CH, r2 (10) CH, 'tbl (57), CH, 'ib2 (31)
145 1 -
1451
CH, dbl (62), CH, db2 (26)
-
1377 W
1381 S I
1379
1379
1379
-
-
1349 1354 1345 1343
1338 M. sh 1326 S
1328 M, sh I/
1334 1317 1314 1300 1308 1299
1308 M 1278 W
1287 1275
1271 W
1270 M 1
1261 W
1265 M,
1167 M
sli
1278 1267 1262
1I 6 7 1160 1162 1158
CH, sb (100) H" b l f34), NH Ib (17), C"C s (17), C"C0 s (10) N H Ib (27), Ha b l (27), C"C s (17), C"Cp s (12) H" b l (25), H" b 2 (20), C'C s (17), NH ib (12) Ha b l (26), NH ib (21), C"C s (17), C"Cp s (11) H" b 2 (58), C"C s (16) H" b 2 (52), C"C s (17), NH Ib ( I O ) , CN s (10) H" b 2 (81) H" b 2 (83), H" b l (10) H" b 2 (56), H" b l (23) H" b 2 (73), H" b l (18) H" b l (62) Ha b l (67), H" b 2 (16), C"Cp s (14) NH Ib (23), NC" Y (18), Ha b l (18) H" b l (42), NC" F (21), NH Ib (20), H" b 2 (12) NH Ib (28), Ha b 2 (15), NC" Y (14), Ha b l ( 1 1 ) H" b l (38), NH ib (25), NC" Y (19), Ha b 2 (14) NH ib (40). H" b 2 (28) NH ib (38), H" b2 (26), H" b l (19), NC" s (12) NC" F (32), CH, r l (20), C"Cp s (16) NC" s (53), CO'C s (17), C"Cp s (1 1) C"C0 F (32), NC" s (21), CH, r l (15), H" b l ( I O ) C"Cp F (35), NC" s (31), H" b l (16) C"Cp F (41), NC" s (16), H" b l (12), CH, rl (12) C"Cp 5 (41), NC" F (25), Ha b l (19)
Dwivedi and Krimm
622 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 TABLE I11 (Continued) obsda
Raman
calcdb
IR
A
El
E2
1115 1127 1105 S
1108 S I
1103 1094 1094 1075 1043
potential energy distributionC C a d s (64), CH, r2 (15) C"Cps (62), C"C s (11) C"Cp s (39), CH, 12 (18) C o l d s (34), NC" s (19) C"Cps (26), CH, r2 (21) C"Cp s (25), NC" s (22), CN s (13) CH, 11 (47), Ha b l (20)
-
1050 W
1051 VS 1
1017 W
1016 W II
970 W
968 M II
CH, 11 (39), Ha b l (22), CH, r2 (15)
1037 -
CH, 12 (28), Ha b l (25), CH, r l (24)
1026 962
CH, 11 (34), NC" s (29), CH, r2 (17), CQC s (15)
-
CH, 12 (32), NC" s (20), CH, r l (15)
955 95 1
940 VW
CH, r2 (41), NC" s (16)
-
908 VS
909 M II
910 904
893 S 1
901 900
882 W 773
vw
896 893 774 M
780 773 76 7 765
756 W 693 M
6 9 1 W, sh II
754 750 700 696 675 6 84
662 W
658 S 1
660 663 637 640
618 S 1
608 607 589 581
530 VS
375
s
522 517 492 490 375 S I -366 M , sh
3 74 369 367 367 366 360
328 W
324 S I
3 26 317
310 S
310 300
294 M
2 9 0 M I1
260 M
259 W, sh
307 3 05 264 24 9
240 W
24 5 244
CN s (23), CNC" d (16), CO ib (12), CH, r2 ( l l ) , CO s (10) CN s (39), (2°C s (14), CNC" d (13) CN s (18), C"C s (12), CO ib (12). C a d s (10) CN s (33), C"C s (21) C"C0 s (19), C"C s (14), CN s (14), CO ib (12), NC" s (11) CN s (30). C"C s (26) CO o b (42), Cp b l ( l o ) , CN t (10) CO ob (44), CN t (11) CO o b (52), Cp b l (10) CO o b (53) CO o b (38), CN t (30) CO o b (42), CN t (35) NC"C d (36), C"CN d (26) NC"C d (37), C"CN d (30), NH o b (10) CN t (32), CO ib (18), C"C s (14) CN t (25), CO ib (20), C"C s ( l l ) , NC"C d (10) CN t (37), NH o b (21), NCQC d (12) CN t (36), NH o b (21), NC"C d (14), CO ib (10) CN t (59), NH o b (43), NH-0 ib (13) CN t (66), NH ob (46), NH-0 ib (14) CN t (47), NH ob (23), CO ob (15), CO ib (12) CN t (47), NH ob (24), CO ob (1 9), CO ib (1 2) CN t (68), NH ob (36), CO o b (26), NH.-O ib (11 ) CN t (66), NH o b (36), CO ob (33), NH.-O ib (11) CO ib (29), C"CN d (21), CaC s (17), CO b 2 (17), NH o b (11) CO ib (32), C'CN d (21), Cp b 2 (19), (2°C s (18), NC" s (10) NC"C d (31), C"C s (14), C"CN d ( l l ) , CO ib (11) NC"C d (32), C"C s (14), C"CN d (13), CO ib (11) NC"C d (37), CO ib (17), C"C s (16) NC"C d (40), CO ib (16), C"C s (15) CO o b (16), NH o b (16), Cp b2 (15), C"CN d (15), CO ib (15), CNC" d (10) Cp b2 (20), CO ib (17), CaCN d (15), NH o b (14), CO ob (13), CNC" d (12) CO ob (21), Cp b l (17), NCaC d (14), NH o b (13), Cp b2 (11) CO o b (19), Cp b l (18), NC"C d (14), Cp b 2 (13), NH o b (12) Cp b2 (49), C"CN d (22), Cp b l (16) Cp b 2 (51), P C N d (26) Cp b 2 (42), Cp b l (19), CO ib (16) Cp b 2 (41), Cp b l (20), CO ib (15), CNC" d (12) CNC" d (3O), CO ib (20), Cp b l (20), CO o b (17) CNC" d (37), Cp b l (25), CO ib (18), CO ob (12) Cp b 2 (34), CO ib (29), CNC" d (15) Cp b 2 (39), CO ib (29), CNC" d (15) C"C0 t (35), C p b 2 (14) Cp b2 (17), C'CN d (13), NH ob (11) C"CP t (91) C"CP t (95)
-
223 W
C"Cp t (63)
23 0 -
209 VW
205 20 1
189 M
188 M 1
165 M
163 M I
159 S
197 200 155 155 151 154
C"CN d (27), Cp b 2 (25), Cp b l (12), CO ob (10) C"CN d (31), Cp b 2 (26), Cp b l (14), CO ob (10) C"CN d (15), Cp b 2 (12), CO ob (12) C"CN d (15), Cp b 2 (14), NH o b (12), CO o b (11) CNC" d (33), C"CN d (19), Cp b l (14), NH ob (14), NC"C d (12) CNC" d (30), C"CN d (25), Cp b l (14), NH ob (13), NC"C d (11) NH o b (43), CNCQ d (20), NC"C d (11) NH o b (48), CNC" d (17), NC"C d (lo), C"CN d (10)
a- and @-Poly(L-alanine) Force Fields
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 623
TABLE 111 (Coritiriircd) calcdb
obsd'
Ra inan
IR 120 s /I
A
1 1 3 M, ch 1
87 W
84 u'
E,
t,
136 138 96 96 94 95
87 85 49 48 40 39 38 38
potential cncrgy distributionc CNC" d (34), C"CN d (21). NC"C d (16), Cp b l ( 1 2 )
