Peter A. Kollman

Development and testing of a general amber force field.

We describe here a general Amber force field (GAFF) for organic molecules. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most organic and pharmaceutical molecules that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited number of atom types, but incorporates both empirical and heuristic models to estimate force constants and partial atomic charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallographic structures were compared to GAFF minimized structures, with a root‐mean‐square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, respectively). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermolecular energies were compared to MP2/6‐31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, respectively. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, respectively), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to experiment) is about 0.5 kcal/mol. GAFF can be applied to wide range of molecules in an automatic fashion, making it suitable for rational drug design and database searching.

A Point-Charge Force Field for Molecular Mechanics Simulations of Proteins Based on Condensed-Phase Quantum Mechanical Calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third‐generation point‐charge all‐atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc‐pVTZ//HF/6‐31G** quantum mechanical methods. The main‐chain torsion parameters were obtained by fitting to the energy profiles of Ace‐Ala‐Nme and Ace‐Gly‐Nme di‐peptides calculated using MP2/cc‐pVTZ//HF/6‐31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of ε = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed‐phase simulations of proteins. Initial tests on peptides demonstrated a high‐degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace‐Gly‐Nme and Ace‐Ala‐Nme di‐peptides. Some highlights of our results include (1) well‐preserved balance between the extended and helical region distributions, and (2) favorable type‐II poly‐proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand‐binding calculations. Test simulations on a large set of proteins are also discussed.

An all atom force field for simulations of proteins and nucleic acids

We present an all atom potential energy function for the simulation of proteins and nucleic acids. This work is an extension of the CH united atom function recently presented by S.J. Weiner et al. J. Amer. Chem. Soc., 106, 765 (1984). The parameters of our function are based on calculations on ethane, propane, n−butane, dimethyl ether, methyl ethyl ether, tetrahydrofuran, imidazole, indole, deoxyadenosine, base paired dinucleoside phosphates, adenine, guanine, uracil, cytosine, thymine, insulin, and myoglobin. We have also used these parameters to carry out the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach.

How Well Does a Restrained Electrostatic Potential (RESP) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules

In this study, we present conformational energies for a molecular mechanical model (Parm99) developed for organic and biological molecules using the restrained electrostatic potential (RESP) approach to derive the partial charges. This approach uses the simple “generic” force field model (Parm94), and attempts to add a minimal number of extra Fourier components to the torsional energies, but doing so only when there is a physical justification. The results are quite encouraging, not only for the 34‐molecule set that has been studied by both the highest level ab initiomodel (GVB/LMP2) and experiment, but also for the 55‐molecule set for which high‐quality experimental data are available. Considering the 55 molecules studied by all the force field models for which there are experimental data, the average absolute errors (AAEs) are 0.28 (this model), 0.52 (MM3), 0.57 (CHARMm [MSI]), and 0.43 kcal/mol (MMFF). For the 34‐molecule set, the AAEs of this model versus experiment and ab initio are 0.28 and 0.27 kcal/mol, respectively. This is a lower error than found with MM3 and CHARMm, and is comparable to that found with MMFF (0.31 and 0.22 kcal/mol). We also present two examples of how well the torsional parameters are transferred from the training set to the test set. The absolute errors of molecules in the test set are only slightly larger than in the training set (differences of <0.1 kcal/mol). Therefore, it can be concluded that a simple “generic” force field with a limited number of specific torsional parameters can describe intra‐ and intermolecular interactions, although all comparison molecules were selected from our 82‐compound training set. We also show how this effective two‐body model can be extended for use with a nonadditive force field (NAFF), both with and without lone pairs. Without changing the torsional parameters, the use of more accurate charges and polarization leads to an increase in average absolute error compared with experiment, but adjustment of the parameters restores the level of agreement found with the additive model. After reoptimizing the Ψ, Φ torsional parameters in peptides using alanine dipeptide (6 conformational pairs) and alanine tetrapeptide (11 conformational pairs), the new model gives better energies than the Cornell et al. ( J Am Chem Soc 1995, 117, 5179–5197) force field. The average absolute error of this model for high‐level ab initio calculation is 0.82 kcal/mol for alanine dipeptide and tetrapeptide as compared with 1.80 kcal/mol for the Cornell et al. model. For nucleosides, the new model also gives improved energies compared with the Cornell et al. model. To optimize force field parameters, we developed a program called parmscan, which can iteratively scan the torsional parameters in a systematic manner and finally obtain the best torsional potentials. Besides the organic molecules in our test set, parmscan was also successful in optimizing the Ψ, Φ torsional parameters in peptides to significantly improve agreement between molecular mechanical and high‐level ab initio energies.

AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules

We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a number of the powerful tools of modern computational chemistry-molecular dynamics and free energy calculations.

Application of the multimolecule and multiconformational RESP methodology to biopolymers: Charge derivation for DNA, RNA, and proteins

We present the derivation of charges of ribo‐ and deoxynucleosides, nucleotides, and peptide fragments using electrostatic potentials obtained from ab initio calculations with the 6‐31G* basis set. For the nucleic acid fragments, we used electrostatic potentials of the four deoxyribonucleosides (A, G, C, T) and four ribonucleosides (A, G, C, U) and dimethylphosphate. The charges for the deoxyribose nucleosides and nucleotides are derived using multiple‐molecule fitting and restrained electrostatic potential (RESP) fits,1,2 with Lagrangian multipliers ensuring a net charge of 0 or ± 1. We suggest that the preferred approach for deriving charges for nucleosides and nucleotides involves allowing only C1′ and H1′ of the sugar to vary as the nucleic acid base, with the remainder of sugar and backbone atoms forced to be equivalent. For peptide fragments, we have combined multiple conformation fitting, previously employed by Williams3 and Reynolds et al.,4 with the RESP approach1,2 to derive charges for blocked dipeptides appropriate for each of the 20 naturally occuring amino acids. Based on our results for propyl amine,1,2 we suggest that two conformations for each peptide suffice to give charges that represent well the conformationally dependent electrostatic properties of molecules, provided that these two conformations contain different values of the dihedral angles that terminate in heteroatoms or hydrogens attached to heteroatoms. In these blocked dipeptide models, it is useful to require equivalent N—H and CO charges for all amino acids with a given net charge (except proline), and this is accomplished in a straightforward fashion with multiple‐molecule fitting. Finally, the application of multiple Lagrangian constraints allows for the derivation of monomeric residues with the appropriate net charge from a chemically blocked version of the residue. The multiple Lagrange constraints also enable charges from two or more molecules to be spliced together in a well‐defined fashion. Thus, the combined use of multiple molecules, multiple conformations, multiple Lagrangian constraints, and RESP fitting is shown to be a powerful approach to deriving electrostatic charges for biopolymers.

MULTIDIMENSIONAL FREE-ENERGY CALCULATIONS USING THE WEIGHTED HISTOGRAM ANALYSIS METHOD

The recently formulated weighted histogram analysis method (WHAM)1 is an extension of Ferrenberg and Swendsens multiple histogram technique for free‐energy and potential of mean force calculations. As an illustration of the method, we have calculated the two‐dimensional potential of mean force surface of the dihedrals gamma and chi in deoxyadenosine with Monte Carlo simulations using the all‐atom and united‐atom representation of the AMBER force fields. This also demonstrates one of the major advantages of WHAM over umbrella sampling techniques. The method also provides an analysis of the statistical accuracy of the potential of mean force as well as a guide to the most efficient use of additional simulations to minimize errors.

Computational alanine scanning of the 1:1 human growth hormone–receptor complex

The MM‐PBSA (Molecular Mechanics–Poisson–Boltzmann surface area) method was applied to the human Growth Hormone (hGH) complexed with its receptor to assess both the validity and the limitations of the computational alanine scanning approach. A 400‐ps dynamical trajectory of the fully solvated complex was simulated at 300 K in a 101 Å×81 Å×107 Å water box using periodic boundary conditions. Long‐range electrostatic interactions were treated with the particle mesh Ewald (PME) summation method. Equally spaced snapshots along the trajectory were chosen to compute the binding free energy using a continuum solvation model to calculate the electrostatic desolvation free energy and a solvent‐accessible surface area approach to treat the nonpolar solvation free energy. Computational alanine scanning was performed on the same set of snapshots by mutating the residues in the structural epitope of the hormone and the receptor to alanine and recomputing the ΔGbinding. To further investigate a particular structure, a 200‐ps dynamical trajectory of an R43A hormone–receptor complex was simulated. By postprocessing a single trajectory of the wild‐type complex, the average unsigned error of our calculated ΔΔGbinding is ∼1 kcal/mol for the alanine mutations of hydrophobic residues and polar/charged residues without buried salt bridges. When residues involved in buried salt bridges are mutated to alanine, it is demonstrated that a separate trajectory of the alanine mutant complex can lead to reasonable agreement with experimental results. Our approach can be extended to rapid screening of a variety of possible modifications to binding sites.

Water–water and water–ion potential functions including terms for many body effects

We have developed potential functions for water–water and water–ion interactions that include terms to model nonadditive or many body effects. Using these potential functions, we have obtained good agreement with experimental results for gas phase and condensed phase water calculations and excellent results for gas phase ion hydration enthalpies. Some gas phase ion–water cluster display unusual geometries such as the sodium complex with six waters, where four water molecules bind directly to sodium and the two remaining water molecules form hydrogen bonds with the first four water molecules. The chloride complex with four waters is also interesting in that all four waters cluster on the same side of the anion and form weak hydrogen bonds with each other in addition to the linear hydrogen bond each forms with the anion. We have also used the potentials to estimate solvation enthalpies and coordination numbers for several ionic species Na+, K+, Mg++, and Cl−, again obtaining good overall agreement with expe...

The development/application of a ‘minimalist’ organic/biochemical molecular mechanic force field using a combination of ab initio calculations and experimental data

In this chapter, we present an overview on our approach to developing a molecular mechanical model for organic and biological molecules and our opinions on what are the most important issues that go into the development of such a model. Since molecular mechanical models are more thoroughly reviewed by Hunenberger et al. [1], it is not inappropriate that we focus more on general principles and philosophy here. The main focus on new results presented here are consequences of some recent high-level ab initio calculations carried out by Beachy et al. [2]. This leads to a slight modification of our previously presented force field; we call this new model C96.