A Second Generation Force Field for the Simulation of

A Second Generation Force Field for the Simulation of

(Parte 1 de 14)

J. Am. Chem. SOC. 1995, 117, 5179-5197 5 179

A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules

Wendy D. Cornell? Piotr Cieplak,’ Christopher I. Bayly,s Ian R. Gould,l Kenneth M. Merz, Jr.,” David M. Ferguson,& David C. Spellmeyer: Thomas Fox, James W. Caldwell, and Peter A. Kollman*

Contribution from the Department of Pharmaceutical Chemistry, University of California, San Francisco, California 94143

Received November IO, 1994@

Abstract: We present the derivation of a new molecular mechanical force field for simulating the structures, conformational energies, and interaction energies of proteins, nucleic acids, and many related organic molecules in condensed phases. This effective two-body force field is the successor to the Weiner et al. force field and was developed with some of the same philosophies, such as the use of a simple diagonal potential function and electrostatic potential fit atom centered charges. The need for a 10-12 function for representing hydrogen bonds is no longer necessary due to the improved performance of the new charge model and new van der Waals parameters. These new charges are determined using a 6-31G* basis set and restrained electrostatic potential (RESP) fitting and have been shown to reproduce interaction energies, free energies of solvation, and conformational energies of simple small molecules to a good degree of accuracy. Furthermore, the new RESP charges exhibit less variability as a function of the molecular conformation used in the charge determination. The new van der Waals parameters have been derived from liquid simulations and include hydrogen parameters which take into account the effects of any geminal electronegative atoms. The bonded parameters developed by Weiner et al. were modified as necessary to reproduce experimental vibrational frequencies and structures. Most of the simple dihedral parameters have been retained from Weiner et al., but a complex set of 4 and yj parameters which do a good job of reproducing the energies of the low-energy conformations of glycyl and alanyl dipeptides has been developed for the peptide backbone.

Introduction

The application of computer-based models using analytical potential energy functions within the framework of classical mechanics has proven to be an increasingly powerful tool for studying molecules of biochemical and organic chemical interest. These applications of molecular mechanics have employed energy minimization, molecular dynamics, and Monte Carlo methods to move on the analytical potential energy surfaces. Such methods have been used to study a wide variety of phenomena, including intrinsic strain of organic molecules, structure and dynamics of simple and complex liquids, ther- modynamics of ligand binding to proteins, and conformational transitions in nucleic acids. In principle, they are capable of giving insight into the entire spectrum of non-covalent interac- tions between molecules, and, when combined with quantum mechanical electronic structure calculations, modeling covalent bonding changes, essentially all molecular reactions and interac- tions. Given their importance, much effort has gone into consideration of both the functional form and the parameters that must be established in order to apply such analytical potential energy functions (or “force fields”).

t Graduate Group in Biophysics, University of California, San Francisco. * Permanent address: Department of Chemistry, University of Warsaw, Current address: Merck Frosst Canada, Inc., C.P. 1005 Pointe Claire- Current address: Deuartment of Chemism. Universitv of Manchester.

Pasteura 1, 02-093, Warsaw, Poland. Domal, Quebec H9R 4P8, Canada.

Lancs M13 9PL, U.K.

Current address: Department of Chemistry, The Pennsylvania State University, State College; PA 16802.

Minnesota, Minneapolis, MN 55455. Current address: Department of Medicinal Chemistry, University of # Current address: Chiron Corporation, Emeryville, CA 94608.

*Author to whom correspondence and reprint requests should be Abstract published in Advance ACS Abstracts, April 15, 1995. addressed.

In the area of organic molecules, the book by Allinger and

Burkert’ provides a thorough review pre-1982 and the subse- quent further development of the MM2* and M3 force fields by Allinger and co-workers has dominated the landscape in this area. The number of force fields developed for application to biologically interesting molecules is considerably greater, prob- ably because of the greater complexity of the interactions which involve ionic and polar groups in aqueous solution and the difficulty of finding an unequivocal test set to evaluate such force fields. Many of these force fields developed prior to 1987 are described briefly by McCammon and Harvey.4

Given the complexities and subjective decisions inherent in such biological force fields, we have attempted to put the development of the force field parameters on a more explicitly stated algorithmic basis than done previously, so that the force field could be extended by ourselves and others to molecules and functional groups not considered in the initial development. This is important, because, if the assumptions, approximations, and inevitable imperfections in a force field are at least known, one can strive for some cancellation of errors.

Approximately a decade ago, Weiner et al.596 developed a force field for proteins and nucleic acids which has been widely

(1) Burke& U.; Allinger, N. J. Molecular Mechanics; American Chemical Society: Washington, DC, 1982.

(2)Allinger, N. L. J. Am. Chem. SOC. 1977, 9, 8127-8134 and subsequent versions, e.g. MM2-87, MM2-89, MM2-91. (3) Alinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. SOC. 1989,l I,

(4) McCammon, J. A.; Harvey, S. C. Dynamics of Proteins and Nucleic

Acids; Cambridge University Press: Cambridge, 1987. (5) Weiner, S. J.; Kollman, P. A,; Case, D. A,; Singh, U. C.; Ghio, C.;

Alagona, G.; Profeta, S., Jr.; Weiner, P. J. Am. Chem. SOC. 1984,106, 765- 784. (6) Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comp. Chem. 1986, 7, 230-252.

8551 -8566, 8566-8576, 8576-8582.

002-7863/95/1517-5179$09.0/0 0 1995 American Chemical Society

5180 J. Am. Chem. SOC., Vol. 117, No. 19, 1995 Comell et al.

used. Important independent tests of this force field were performed by Pavitt and Hall for peptides’ and Nilsson and Karplus8 for nucleic acids and it was found to be quite effective. Nonetheless, it was developed in the era before one could routinely study complex molecules in explicit solvent. Weiner et al. attempted to deal with this issue by showing that the same force field parameters could be effectively used both without explicit solvent (using a distance-dependent dielectric constant (E = Ru)) and with explicit solvent = 1) on model systems. Further support for this approach was provided by molecular dynamics simulations of proteins9-” and DNAl2.l3 which compared the implicit and explicit solvent representations.

As computer power has grown, it has become possible to carry out more realistic simulations which employ explicit solvent representations. It is therefore appropriate that any new force field for biomolecules focus on systems modeled in the presence of an explicit solvent representation. This approach has been pioneered by Jorgensen and co-workers in their OPLS (Optimized Potentials for Liquid Simulations) m0de1.I~ In particular, the development of parameters which reproduce the enthalpy and density of neat organic liquids as an essential element ensures the appropriate condensed phase behavior. The OPLS non-bonded parameters have been combined with the Weiner et al. bond, angle, and dihedral parameters to create the OPLS/Amber force field for peptides and proteins,I5 which has also been effectively used in many systems.I6

We have been influenced by the OPLS philosophy of balanced solvent-solvent and solute-solvent interactions in our thoughts about a second-generation force field to follow that of Weiner et aL5v6 The Weiner et al. force field used quantum mechanical calculations to derive electrostatic potential (ESP) fit atomic centered charges, whereas the OPLS charges were derived empirically, using mainly the liquid properties as a

guide. For computational expediency, Weiner et al. relied principally on the STO-3G basis set for their charge derivation. This basis set leads to dipole moments that are approximately equal to or smaller than the gas-phase moment but tends to underestimate quadrupole moments. Thus, it is not well balanced with the commonly used water models (SPC/E,” TIP3P,I8 TIP4PI8) which have dipole moments that are about 20% higher than the gas-phase value for water. These water models, which have empirically derived charges, include condensed-phase electronic polarization implicitly. Kuyper et aZ.l9 suggested that the logical choice of a basis set for deriving ESP-fit partial charges for use in condensed phases is the 6-3 lG* basis set, which uniformly overestimates molecular polarity. Standard ESP charges derived with that basis set were shown

(7) Pavitt, N.; Hall, D. J. Compur. Chem. 1984, 5, 441-450 (8) Nilsson, L.; Karplus, M. J. Comput. Chem. 1986, 7, 591-616. (9) Tilton, R. F.; Singh, U. C.; Weiner, S. J.; Connolly, M. L.; Kuntz, I.

D., Jr.; Kollman, P. A.; Max, N.; Case, D. J. Mol. Eiol. 1986, 192, 443- 456.

(10) Guenot, J. M.; Kollman, P. A. Prorein Sci. 1992, 1, 1185-1205. (1 1) York, D. M.; Wlodawer, A.; Redersen, L.; Darden, T. A. Proc. Narl.

(12) Sinsh. U. C.: Weiner. S. J.: Kollman. P. A. Proc. Natl. Acad. Sci. Acad. Sci. U.S.A. 1994, 91, 8715-8718.

U.S.A’l983, 82, 755-759. ’ (13) Seibel, G. L.; Singh, U. C.; Kollman, P. A. Proc. Natl. Acad. Sci.

U.S.A. 1985, 82, 6537-6340. (14) Jorgensen, W. L.; Pranata, J. J. Am. Chem. SOC. 1990, 112,2008-

2010. (15) Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. SOC. 1988, 110, 1657 - 1666. (16) (a) Tirado-Rives, J.; Jorgensen, W. L. J. Am. Chem. SOC. 1990,112,

2773-2781. (b) Orozco, M.; Tirado-Rives, J.; Jorgensen, W. L. Eiochem- istry 1993, 32, 12864-12874.

(17) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269-6271. (18) Jorgensen, W. L.; Chandreskhar, J.; Madura, J. D.; Impey, R. W.;

Klein, M. L. J. Chem. Phys. 1982, 79, 926-935. (19) Kuyper, L.; Ashton, D.; Men, K. M., Jr.; Kollman, P. A. J. Phys. Chem. 1991, 95, 6661-6.

to lead to excellent relative free energies of solvation for benzene, anisole, and trimethoxyani~ole.’~

A 6-3 1G* based ESP-fit charge model, like the OPLS model, is capable of giving an excellent reproduction of condensed- phase inter molecular properties such as liquid enthalpies and densities and free energies of solvation.20 A major difference between such a model and most others is the magnitude of the charges on hydrocarbons. For example, 6-3 lG* standard ESP charges derived from the trans conformation of butane have values of -0.344 for the methyl carbon and 0.078 for the methyl hydrogen. In both cases, however, the carbon and hydrogen charges offset each other, resulting in small net charges on the methyl groups of -0.1 10 and -0.059 for the trans and gauche charges, respectively. Furthermore, free energy perturbation calculations involving the perturbation of methane with standard

ESP charges (qc = -0.464 and qH = 0.116) to methane with charges of 0.0 in solution yield essentially no change in free energy.21 The standard ESP charges also result in conforma- tional energies for butane which are in reasonable agreement with experiment, when used with a 1-4 electrostatic scale factor of m.2.20

Nevertheless, the 6-3 lG* standard ESP charges are less than ideal for two reasons. First, when charges generated using different conformations of a molecule are compared, there is often considerable variation seen. This was demonstrated by Williams, who studied the conformational variation of ESP-fit charges in alanyl dipeptide for 12 different conformations.2

Butane is another example, where charges from the gauche conformation have values of -0,197 and 0.046 for the methyl carbon and hydrogen, respectively. Another example is pro- pylamine, which was studied at length by Comell et aL2O Five low-energy conformations can be identified for propylamine, and the 6-31G* standard ESP charges calculated for each conformation show significant variation. The average and standard deviation for the charge on a given atom over the five conformations are as follows: a-carbon qav = 0.339 and IJ =

0.059, /3-carbon qav = 0.033 and u = 0.060, and y-carbon qav = -0.205 and u = 0.146. This inconsistency is potentially problematic in terms of deriving other force field parameters which may be sensitive to the variation. Furthermore, it reduces the reproducibility of a particular calculation, which is not a problem in other force fields where the charges are assigned empirically.

The second reason that the 6-3 lG* standard ESP charges are less than ideal is that the charges on “buried” atoms (such as the sp3 carbons described above for butane and propylamine) are statistically underdetermined and often assume unexpectedly large values for nonpolar atoms. Bayly et aLZ3 found that the electrostatic potential of methanol could be fit almost equally well using either the standard ESP charges determined by the linear least-squares fit or an altemative set of charges derived with the methyl carbon constrained to have a much smaller value.

Considering the problems associated with the standard ESP charge model, it might seem tempting to adopt the OPLS approach of empirically derived charges. However, any empiri- cally derived charge model cannot easily describe transition states and excited states, as can an electrostatic potential fit

(20) Cornell, W.; Cieplak, P.; Bayly, C.; Kollman, P. A. J. Am. Chem.

SOC. 1993, 115, 9620-9631. (21) (a) Sun, Y. X.; Spellmeyer, D.; Pearlman, D. A.; Kollman, P. A. J.

(Parte 1 de 14)

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