Martin Karplus

All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins †

New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent-solvent, solvent-solute, and solute-solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volumes, and crystal pressures and structures were used in the optimization. The resulting protein parameters were tested by applying them to noncyclic tripeptide crystals, cyclic peptide crystals, and the proteins crambin, bovine pancreatic trypsin inhibitor, and carbonmonoxy myoglobin in vacuo and in crystals. A detailed analysis of the relationship between the alanine dipeptide potential energy surface and calculated protein φ, χ angles was made and used in optimizing the peptide group torsional parameters. The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in solution and in crystals. Extensive comparisons between molecular dynamics simulations and experimental data for polypeptides and proteins were performed for both structural and dynamic properties. Energy minimization and dynamics simulations for crystals demonstrate that the latter are needed to obtain meaningful comparisons with experimental crystal structures. The presented parameters, in combination with the previously published CHARMM all-atom parameters for nucleic acids and lipids, provide a consistent set for condensed-phase simulations of a wide variety of molecules of biological interest.

CHARMM: The biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model‐building capabilities. The CHARMM program is applicable to problems involving a much broader class of many‐particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical‐molecular mechanical force fields, to all‐atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Contact Electron‐Spin Coupling of Nuclear Magnetic Moments

The valence‐bond theory for the contact electron‐spin coupling of nuclear magnetic moments is used to calculate the proton‐proton, proton‐fluorine, and fluorine‐fluorine coupling constants in ethanic and ethylenic molecules. A considerable simplification is introduced into the theory by approximations which reduce the problem to one involving only a small number of electrons and canonical structures. The agreement between calculated and experimental values is such as to demonstrate that the mechanism considered is the one of primary importance for the nuclear coupling in the compounds studied. Of particular interest is the theoretical confirmation of the observation that in ethylenic compounds the trans coupling between nuclei (HH, HF, FF) is considerably larger than cis coupling.

Crystallographic R Factor Refinement by Molecular Dynamics

Molecular dynamics was used to refine macromolecular structures by incorporating the difference between the observed crystallographic structure factor amplitude and that calculated from an assumed atomic model into the total energy of the system. The method has a radius of convergence that is larger than that of conventional restrained least-squares refinement. Test cases showed that the need for manual corrections during refinement of macromolecular crystal structures is reduced. In crambin, the dynamics calculation moved residues that were misplaced by more than 3 angstroms into the correct positions without human intervention.

Effective Energy Function for Proteins in Solution

A Gaussian solvent‐exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self‐energy contribution is accounted for primarily by the exclusion model. Ionic side‐chains are neutralized, and a distance‐dependent dielectric constant is used to approximate the charge–charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high‐temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins. Proteins 1999;35:133–152.

Computational Complexity, Protein Structure Prediction, and the Levinthal Paradox

A protein molecule is a covalent chain of amino acid residues. Although it is topologically linear, in physiological conditions it folds into a unique (though flexible) three-dimensional structure. This structure, which has been determined by x-ray crystallography and nuclear magnetic resonance for many proteins (Bernstein et al., 1977; Abola et al., 1987), is referred to as the native structure. As demonstrated by the experiments of Anfinsen and co-workers (Anfinsen et al., 1961; Anfinsen, 1973), at least some protein molecules, when denatured (unfolded) by disrupting conditions in their environment (such as acidity or high temperature) can spontaneously refold to their native structures when proper physiological conditions are restored. Thus, all of the information necessary to determine the native structure can be contained in the amino acid sequence.

Simulation of activation free energies in molecular systems

A method is presented for determining activation free energies in complex molecular systems. The method relies on knowledge of the minimum energy path and bases the activation free energy calculation on moving along this path from a minimum to a saddle point. Use is made of a local reaction coordinate which describes the advance of the reaction in each segment of the minimum energy path. The activation free energy is formulated as a sum of two terms. The first is due to the change in the local reaction coordinate between the endpoints of each segment of the path. The second is due to the change in direction of the minimum energy path between consecutive segments. Both contributions can be obtained by molecular dynamics simulations with a constraint on the local reaction coordinate. The method is illustrated by applying it to a model potential and to the C7eq to C7ax transition in the alanine dipeptide. It is found that the term due to the change of direction in the reaction path can make a substantial con...

Proteins : a theoretical perspective of dynamics, structure, and thermodynamics

Potential Functions. Dynamical Simulation Methods. Thermodynamic Methods. Atom and Sidechain Motions. Rigid-Body Motions. Larger-Scale Motions. Solvent Influence on Protein Dynamics. Thermodynamic Aspects. Experimental Comparisons and Analysis. Concluding Discussion. References. Index.

Exchange Reactions with Activation Energy. I. Simple Barrier Potential for (H, H2)

A quasiclassical procedure for the examination of the collision dynamics of atom—diatomic‐molecule reactions with activation energy is introduced. By means of Monte Carlo averages over a large number of appropriately chosen three‐dimensional classical trajectories, the total reaction cross section (Sr) and other reaction attributes can be determined as a function of the initial relative velocity (Vr) and the initial molecular rotation‐vibration state (J, ν).The method is applied to the exchange reaction resulting from a hydrogen atom and a hydrogen molecule moving on a simple barrier potential of the London—Eyring—Polanyi—Sato type. It is found that Sr is a monotonically increasing function of relative velocity that rises smoothly from a threshold at ∼0.9×106 cm/sec to its asymptotic value of ∼4.5a02 at ∼1.8×106 cm/sec. The zero‐point vibrational energy of the molecule contributes to the energy required for reaction, but the rotational energy does not. The reaction probability, which depends on VR, ν, and...

A hierarchy of timescales in protein dynamics is linked to enzyme catalysis

The synergy between structure and dynamics is essential to the function of biological macromolecules. Thermally driven dynamics on different timescales have been experimentally observed or simulated, and a direct link between micro- to milli-second domain motions and enzymatic function has been established. However, very little is understood about the connection of these functionally relevant, collective movements with local atomic fluctuations, which are much faster. Here we show that pico- to nano-second timescale atomic fluctuations in hinge regions of adenylate kinase facilitate the large-scale, slower lid motions that produce a catalytically competent state. The fast, local mobilities differ between a mesophilic and hyperthermophilic adenylate kinase, but are strikingly similar at temperatures at which enzymatic activity and free energy of folding are matched. The connection between different timescales and the corresponding amplitudes of motions in adenylate kinase and their linkage to catalytic function is likely to be a general characteristic of protein energy landscapes.