J . A m . Chem. SOC.1986, 108, 7163-7172
7163
An Empirical Examination of Potential Energy Minimization Using the Well-Determined Structure of the Protein Crambin Marc Whitlow and M. M. Teeter* Contribution f r o m the Department of Biochemistry, Boston University, Boston, Massachusetts 021 18, and Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02167. Received February 18, 1986
Abstract: Empirical potential energy functions for proteins may be used to study protein stability and motion. However, it is difficult to evaluate these functions because most protein crystal structures are not accurate enough to act as test cases. We have empirically examined how well potential energy minimization can model the high resolution crystal structure (0.945 A) of the hydrophobic protein Crambin (Hendrickson, W. A.; Teeter, M. M. Nature (London) 1981, 290, 107-1 13). Over 70 minimizations have been performed by using the program AMBER (Assisted Model Building with Energy Refinement) written by Kollman and Weiner ( J . Comp. Chem. 1981,2,287-303) and the parameters from Weiner et al. ( J . Am. Chem. SOC.1984, 106, 765-784). We have examined the effects of (1) the form of the electrostatic potential energy, Le., constant vs. distance-dependent, (2) the value of the dielectric constant, (3) the size of the "united atom" van der Waals radii, (4) the nonbonding cutoff, ( 5 ) the inclusion of the HC,, and (6) the addition of crystal environment and of explicit water. Empirically, the best overall conditions for minimization are employing Jorgensen's van der Waals radii ( J . Am. Chem. SOC.1981, 103, 335-340), a distance-dependent dielectric constant of 4.0r and a 6.0-A residue-based or 9.0-A atom-based nonbonding cutoff.
Potential energy functions for proteins have proven useful in investigations of protein stability and motion. Minimization of the calculated potential energy has provided descriptions of protein-ligand interactions,' refinement of an initial structure after model b ~ i l d i n g , and ~ , ~ constraints for crystallographic refinement of protein^.^ The parameterization of potential energy functions has been based on small molecule X-ray crystallography, infrared and Raman spectroscopy, quantum mechanical calculations, and a large number of other types of i n f o r m a t i ~ n . ~ - ~ One problem encountered in the use of potential energy functions with proteins is the lack of published data needed to empirically evaluate the agreement between these functions and observed structures of proteins. A comparison of different potential energy functions has been made for several small, crystalline cyclic peptides9 However, small peptides are not the best test cases for potential energy functions applied to proteins because of the following: (1) their crystalline conformations are often different from their solution conformations; (2) they are too small to have extensive secondary structure; and (3) their potential energy surface is less complicated than those of proteins. Nuclear magnetic resonance ( N M R ) studies of small peptides have shown that their solution conformations can be different from their conformations in the crystalline state.'" Simulations of peptides in both their crystalline environment and in vacuo also may result in different conformations.i'~'2 Crystal structures of small peptides have a large number of intermolecular interactions, which may play a major role in determining their crystalline conformations. The smaller proportion of these interactions in proteins suggests that they have a minor role in determining the conformation of a protein in its crystal structure. Arguments that support the idea that proteins have similar crystalline and solution conformations ( I ) Blaney, J.; Weiner, P.; Dearing, A.; Kollman, P.; Jorgensen, E.; Oatley, S.; Burnridge, J.; Blake, C. J . Am. Chem. SOC.1982, 104, 6424-6434. (2) Whitlow, M.; Teeter, M. M. J . Biomol. Struct. Dynam. 1985, 2, 83 1-848. (3) Levitt, M. J . Mol. Biol. 1983, 170, 723-764. (4) Jack, A.; Levitt, M: Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gem. Crystallogr. 1978, A34, 93 1-935. (5) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.;States, D. J.; Swaminathan, S.; Karplus, M. M. J . Comp. Chem. 1983, 4 , 65-86. (6) Weiner, S. P.; Kollman, P. A.; Case, D. A.; Singh, U. C.; Ghio, C.; Alagona, G.; Profeta, S., Jr.; Weiner, P. J . A m . Chem. SOC.1984, 106, 765-784. (7) Hermans, J.; Ferro, D. Biopolymers 1971, IO, 1121-1 138. (8) Monany, F.; McGuire, R.; Burgess, A,; Scheraga, H. J . Phys. Chem. 1975, 79, 2361-2381. (9) Hall, D.;Pavitt, N. J . Comp. Chem. 1984, 5, 441-450. (IO) Tonelli, A . E.; Brewster, A . I. J . Am. Chem. Soc. 1972, 94, 2851-2854. ( 1 1 ) Go, N.; Scheraga, H . A. Macromolecules 1973, 6, 525-535. (12) Go, N.; Scheraga, H. A. Macromolecules 1978, 1 1 , 552-559.
0002-7863/86/ 1508-7163$01.50/0
include the following: (1) the similarity of independently determined tertiary structures of the same or related proteins crystallized in different space groups and in the presence of different solvents and (2) the fact that a number of enzymes are catalytically active in the crystalline phase, albeit with reduced efficiency in some cases.I3 We present here an empirical evaluation of one potential energy function for a well-determined protein structure. We have completed over 70 minimizations, changing various parameters (Table I ) . Our goals were (1) to describe the effects of changing these factors in the minimization on the resulting structure, (2) to quantify these effects and stress which are most important for obtaining reliable conformations, and (3) to empirically determine which set of potential parameters resulted in the best agreement with the crystal structure a t a biologically relevant temperature (say 20 "C). The results will enable the users of potential energy functions to better understand the parameters which can be varied. They elucidate the current limitations of potential energy functions, which need to be addressed in the future. AMBER (Assisted Model Building with Energy Refinement)6J4Js has been employed for potential energy minimization on the high resolution structure of the protein crambin. Crambin was chosen for this study for four reasons: (1) it is a small hydrophobic protein with 46 residues and 327 non-hydrogen atoms. The larger protein bovine panceatic typsin inhibitor (BPTI, 58 residues and 454 non-hydrogen which has traditionally been used in molecular mechanics studies, would have taken more computational time for each calculation and is not as well-determined as crambin ( R = 20.0% for BPTIi8 vs. R = 11.3%for crambin). (2) Crambin has a variety of secondary structure types, i.e., two a-helices, a small anti-parallel @-sheet, an extended chain region, and five turns (Figure 1). (3) It has a high resolution X-ray structure. Crystals of crambin scatter to interplanar d spacings of at least 0.88 A.19 The published structureZoincluded diffraction data to 1.5 A and was refined with Konnert and Hendrickson's restrained least squares. In this study, we have used the structure refined against 0.945 A data (unpublished results of Hendrickson ~
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(13) Matthews, B. W. Ann. Rev. Phys. Chem. 1976, 27, 493-523. (14) Weiner, P.; Kollman, P. J . Comp. Chem. 1981, 2, 287-303. (15) Singh, U. C.; Kollman, P. A. J . Comp. Chem. 1984, 5 , 129-145. (16) Huber, R.; Kukla, D.; Ruhlmann, A,; Steigemann, W. Cold Spring Harbor Symp. Quant. Biol. 1971, 36, 141-150. (17) Deisenhofer, J.; Steigemann, W. W. Acta Crysrallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1975, 831, 238-250. (18) Wlodawer, A,; Walter, J.; Huber, R.; Sjolin, L. J . Mol. Biol. 1984, 180, 301-329. (19) Teeter, M. M.; Hendrickson, W. A. J . Mol. Biol. 1979, 127, 219-223. (20) Hendrickson, W. A,; Teeter, M. M. Nature (London) 1981, 290, 107-113.
0 1986 American Chemical Society
7164 J . A m . Chem. Soc.. Vol. 108, No. 23, 1986
Whitlow and Teeter
Table I. Summary of Minimizations on Crambin"
no. of nonbonding VDW HC, PE cycles FEG rms, A % CRG3 % CV energy -10.4 -1 592.2 0.095 1.096 -13.9 3960 A 99.0 1 .o -6.8 -850.9 0.099 0.986 -10.4 4735 A 99.0 2.0 -7.4 -4.3 -476.6 0.500 0.100 1186 A 99.0 4.0 -7.2 -4.4 -306.8 0.077 0.504 1522 A 99.0 8.0 -1 1.3 -6.1 -674.0 0.084 0.689 1957 A 99.0 1 .OR -4.5 -386.2 -8.3 0.523 0.091 1308 A 99.0 2.OR -265.9 0.8 16 -7.4 -5.0 0.097 2028 A 4.OR 99.0 -3.5 -5.3 -209.5 0.886 0.092 2668 A 8.OR 99.0 0.686 -1.8 -1366.3 -7.3 0.084 2181 J 99.0 1 .o -3.2 -0.3 -616.0 0.508 0.100 1642 J 99.0 2.0 -0.9 -290.1 -2.1 0.513 0.091 2160 J 99.0 4.0 -0.3 -118.4 -0.9 0.403 0.100 1462 J 99.0 8.0 -0.4 -462.4 0.599 -5.2 0.096 1919 J 99.0 1 .OR 0.2 0.464 -2.9 -174.8 0.092 1412 J 2.OR 99.0 0.4 -44.6 -1.1 0.349 0.088 J 887 4.OR 99.0 0.2 11.0 -0.4 0.331 0.096 J 808 99.0 8.OR -0.3 -1345.7 -3.8 0.420 0.097 2860 J 10.0 R 1 .o -621.9 0.2 0.352 -2.1 0.100 2386 J 10.0 R 2.0 -0.5 0.5 -275.1 0.269 0.096 1785 J 10.0 R 4.0 -0.2 0.9 -1 13.7 0.301 0.098 1848 8.0 J 10.0 R -3.7 -465.9 0.2 0.431 0.098 J 2932 1 .OR 10.0 R -176.5 -1 .o 0.1 0.261 0.099 J 1832 2.OR 10.0 R -59.0 -0.3 0.7 0.261 J 0.098 1582 4.OR 10.0 R 0.0 0.8 -5.2 0.285 J 0.098 2134 8.OR 10.0 R -7.9 -5.6 -3 16.7 0.652 0.098 3473 A 13.0 A 8.0 -4.5 -300.0 -3.6 0.562 0.096 1411 A 8.0 11.0 A 1776 -6.2 -3.5 -299.0 0.482 0.099 A 9.0 A 8.0 -3.7 -3.5 -295.6 0.431 1363 0.094 7.0 A A 8.0 -10.8 -5.2 -693.6 1665 0.653 0.097 13.0 A A 1.OR -9.4 -4.9 -689.5 1852 0.642 0.089 11.0 A A 1.OR -9.3 -4.8 -674.0 1091 0.559 0.1 10 9.0 A A 1.OR -7.1 -4.5 -635.2 1778 0.563 0.084 7.0 A A 1 .OR -5.1 -3.6 -202.6 0.383 0.094 A 916 8.OR 13.0 A -5.6 -4.0 -204.1 0.413 0.099 A 863 8.OR 11.0 A -6.3 -4.1 -194.7 0.447 A 962 0.090 8.OR 9.0 A -4.0 -0.087 -5.1 -203.5 0.405 7.0 A A 934 8.OR -0.2 0.5 1642 -59.6 0.276 J 0.090 4.OR 13.0 A -0.2 0.7 0.096 1934 -58.1 0.260 J 11.0 A 4.OR 0.6 0.0 0.096 1881 -56.6 0.252 J 4.OR 9.0 A 1.1 1.1 0.097 -55.0 0.255 J 7.0 A 1409 4.OR -0.2 0.6 -59.0 0.265 J 0.099 1684 4.OR 14.0 R -0.3 -58.8 J 0.7 0.090 1881 0.263 4.OR 12.0 R -0.3 0.7 0.098 1582 -59.0 0.261 J 4.OR 10.0 R 0.7 -0.3 0.093 -59.1 0.264 J 8.0 R 1336 4.OR -57.2 0.8 0.1 0.100 1934 0.245 J 4.OR 6.0 R A 2497 -5.6 -10.2 0.084 -1722.3 0.814 1 .o 99.0 A -5.8 -12.0 -1746.2 1.177 99.0 E 3597 A 0.095 1.o -3.8 A 1918+ -5.2 -336.1 0.885 99.0 A 0.099 8.0 -4.6 E 1493 -3.5 A 0.084 -321.6 0.495 8.0 99.0 -742.7 A A 3388 -5.8 -11.3 0.097 1.147 1.OR 99.0 E 3576 -5.7 -10.5 0.093 -760.4 0.848 A 1.OR 99.0 -3.2 -4.5 -197.6 0.469 A A 1366 99.0 0.093 8.OR -3.7 -4.7 -202.7 E 1548 A 99.0 0.087 0.498 8.OR -0.5 -1.2 -1600.3 0.112 A H 200 99.0 0.091 1 .o -0.6 -1 607.2 -1.8 A H 511 0.030 0.141 1 .o 99.0 -3098.0 C 77 1 -5.3 0.426 0.433 1.o A 99.0 E C 1382 -3647.0 -3.7 0.273 0.438 1 .o A 99.0 W 1751 -4.1 -3494.0 -9.3 0.469 0.552 1.o A 99.0 -2.3 W 7500 1.o J -0.5 -3740.5 10.0 R 0.337 0.298 W 7500 -0.7 J -3768.8 10.0 R -2.1 0.272 0.297 1 .o
