The molecular mechanics (mm) force field described in the paper provides a complete parameter set for the simulation of proteins and nucleic acids. It is widely used and cited due to its strong performance and its availability in the AMBER suite of software. Since the force field is widely used, there is a large user community and published body of results which encourages additional use and helps others to evaluate their results within a broader context.

The parameters were derived in a highly algorithmic manner, described in the paper, and users have the possibility to derive additional parameters as needed that are consistent with this force field. When combined with the particle mesh Ewald (PME) method for simulating long range electrostatic interactions, the force field performs well at modeling proteins and nucleic acids in solution, maintaining an equilibrium structure close to the x-ray crystal structure when known. This was a breakthrough for the nucleic acids in particular, which tended to fall apart in earlier molecular mechanical parameterizations. The force field successfully reproduces binding and solvation-free energies for many systems. The paper and parameterization were first in class for the new generation of force fields that emerged during this period.

One of us (PC) was working as a visiting scientist in the laboratory of the late Peter Kollman during the period when it became clear that a substantial upgrading of the lab’s first generation force field (Weiner et al.) was in order. The other (WC) joined the lab around this time as a first year graduate student in the Biophysics program. The Weiner et al. force field was published in united-atom form in 1984 and all-atom form in 1986. It was optimized for use in the gas phase, with a distance-dependent dielectric employed to mimic solvent charge screening. This force field was also very popular, but by the early 1990s advances in computer technology had made it possible to run larger simulations using explicit water models such as TIP3P. Such water models employed "enhanced" pre-polarized atom-centered charges that reproduce the correct condensed phase dipole moment. The larger pre-polarized charges in the water model were unbalanced with respect to the lower gas phase charges in the Weiner et al. force field, so it was necessary to derive a new force field for proteins and nucleic acids that was optimized for use in condensed phase.

It was really a privilege to work with Peter on this project, since his earlier quantum chemistry training on hydrogen bonding systems had given him deep insight into the key forces driving intermolecular interactions in biomolecular systems. Peter emphasized that the reproduction of the electrostatics is very important for modelling binding geometries and energetics. For the Weiner et al. force field, he adopted the use of electrostatic potential fit (ESP) charges derived from low-level STO-3G ab initio Hartree Fock calculations. With the new force field, the advances in computing power permitted us to run higher-level 6-31G* Hartree Fock calculations on larger model systems and this was useful both for charge derivation as well as the conformational energy calculations used to generate the reference values for dihedral parameter optimization.

We had the advantage of being able to keep the parameters and approaches that were known to work based on the previous five years of experience. The geometrical parameters were largely retained from the Weiner, et al. force field. The van der Waals parameters were primarily adopted from Bill Jorgensen’s OPLS force field, which had been optimized for condensed-phase simulations.

The main challenge was to find a charge model that retained the advantages of standard ESP fitting, but resulted in a better-behaved set of atomic charges that exhibited less conformational dependence. Don Williams had recently introduced the concept of multiple conformation fitting and we found this to be a useful tool. Chris Bayly was a postdoc in the group during this time and he proposed a method for fitting charges that incorporated hyperbolic restraints. We tested the resulting charges to evaluate their performance in conformational and interaction energy calculations. Chris initially investigated the use of harmonic restraints, but those were found to reduce the charges by too much.

Ian Gould carried out MP2 level calculations on the DNA base pairs and these results were employed in the evaluation of different charge models. Due to substantial computing advances we were also able to perform some limited conformational exploration for whole nucleotides. This allowed us to propose a new set of dihedral parameters for nucleic acids.

Another area of difficulty was in the optimization of phi and psi parameters for the protein backbone. Ian also generated MP2 level quantum chemical data for low-energy conformations of glycine and alanine dipeptides, but it was not possible to fit all of the conformations with our molecular mechanical model using a simple four-term Fourier expansion. We made the decision to absorb any error in the conformations that would not be highly populated in an actual protein, e.g., the alpha-helical conformation of glycine and the C7ax conformation of alanine. The resulting parameters were used to generate a full phi-psi map, which was then compared against lower-level quantum chemical results. This evaluation showed that the stationary points of the phi-psi map were reasonably well reproduced and there were no spurious minima created by the relatively large phi and psi parameters. Nevertheless, the energetic balance between extended alpha-helical and ß-sheet structures was not well reproduced and may require a more complicated model, such as one that includes polarization or charges that were derived in the condensed phase.

This force field has been applied with the AMBER simulation software in many exciting applications:

• 1-microsecond protein folding simulation on villin headpiece
• Evaluation of protein models for protein structure prediction
• Virtual alanine scanning studies
• MM-(GB/PB)/SA ligand binding energy calculations
• QM/MM studies on enzyme reaction mechanisms
• A to B form DNA transition in aqueous solution

Since the publication of Cornell et al., the force field was extended by Junmei Wang and Kollman to include additional dihedral parameters for organic molecules. Chris Bayly and his student Araz Jakalian recently developed a simpler and faster model for charge derivation—the AM1-BCC model. This is useful, for example, for generating charges for large databases of small molecules. More recently, a third-generation force field has been published which was developed in Peter’s lab in collaboration with Yong Duan and co-workers. This new force field is based on charges derived in condensed phase and is backwards-compatible with the second-generation force field.

Before Peter’s untimely death in 2001, his lab was working on more complicated force fields which included off-center charges to simulate non-isotropic atomic charge distributions around heteroatoms and polarizability. Other labs also have been working on polarizable force fields for a number of years, however, they are not yet well validated and there is not one in common use. This has been somewhat surprising, given the length of time such research has been going on. At the time the manuscript for this work was submitted, we expected that the polarizable force fields would have supplanted the effective two-body versions by now. Recently, quantum chemical (qm) calculations have been carried out on entire proteins, which has raised the provocative question of whether polarizable force fields will ever be widely used or if all-qm or mixed qm/mm models will be a more effective alternative.

In the next several years, we can imagine the research in this field going in any or all of the following directions:

1. The absolute free energies derived using this force field will be much more easily available and calculable.
2. There is a need to develop more realistic force field parameterization for the polysaccharides and lipids.
3. The force field still needs some improvement in phi/psi dihedral angles for amino acids in order to perform more realistic modeling and structure prediction of proteins. The force field for nucleic acids can also be improved.
4. The force field will be applied to realistically model very large systems, such as membranes with their components, glyco-proteins, nucleic acid-protein complexes, and many other systems containing more than 100,000 atoms. Also, modeling processes in much longer time scales will be available. This is needed in the field of protein folding and modeling of large molecular domain movements.
5. The simulations of enzymatic reactions will become more popular with advances in the field of hybrid classical/quantum simulations.
6. There is also a need to go beyond class I (diagonal) type force fields and to take into account cross terms, higher-order energy terms, polarization, charge transfer, and other additive or non-additive effects in molecular simulations.