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,
8 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.
Bi 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 MM33 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, 99, 8127-8134 and
subsequent versions, e.g. MM2-87, MM2-89, MM2-91.
(3) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. SOC. 1989,ll 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.
0002-7863/95/1517-5179$09.00/0 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 (E = 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, 6661-6666.
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.22
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.
Am. Chem. SOC. 1992, 114, 6798-6801. (b) Sun, Y. X.; Kollman, P. A.
Hydrophobic Solvation of Methane and Nonbond Parameters of the TIP3P
Water Model. J. Cornput. Chem., in press. Pang, Y. P.; Kollman, P. A.,
unpublished.
(22) Williams, D. E. Biopolymers 1990, 29, 1367-1386.
(23) Bayly, C.; Cieplak, P.; Comell, W.; Kollman, P. A. J. Phys. Chem.
1993, 97, 10269-10280.