Michael Feig

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.

Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations.

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure–function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc‐pVxZ//MP2/6‐31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc‐pVQZ//MP2/6‐31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone ϕ, ψ dihedral crossterms or a ϕ, ψ grid‐based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the ϕ, ψ dihedral parameters along with the grid‐based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of ϕ and ψ in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid‐based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.

Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures

This study compares generalized Born (GB) and Poisson (PB) methods for calculating electrostatic solvation energies of proteins. A large set of GB and PB implementations from our own laboratories as well as others is applied to a series of protein structure test sets for evaluating the performance of these methods. The test sets cover a significant range of native protein structures of varying size, fold topology, and amino acid composition as well as nonnative extended and misfolded structures that may be found during structure prediction and folding/unfolding studies. We find that the methods tested here span a wide range from highly accurate and computationally demanding PB‐based methods to somewhat less accurate but more affordable GB‐based approaches and a few fast, approximate PB solvers. Compared with PB solvation energies, the latest, most accurate GB implementations were found to achieve errors of 1% for relative solvation energies between different proteins and 0.4% between different conformations of the same protein. This compares to accurate PB solvers that produce results with deviations of less than 0.25% between each other for both native and nonnative structures. The performance of the best GB methods is discussed in more detail for the application for force field‐based minimizations or molecular dynamics simulations.

New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations

In a recent article (Lee, M. S.; Salsbury, F. R. Jr.; Brooks, C. L., III. J Chem Phys 2002, 116, 10606), we demonstrated that generalized Born (GB) theory provides a good approximation to Poisson electrostatic solvation energy calculations if one uses the same definitions of molecular volume for each. In this work, we present a new and improved analytic method for reproducing the Lee–Richards molecular volume, which is the most common volume definition for Poisson calculations. Overall, 1% errors are achieved for absolute solvation energies of a large set of proteins and relative solvation energies of protein conformations. We also introduce an accurate SASA approximation that uses the same machinery employed by our GB method and requires a small addition of computational cost. The combined methodology is shown to yield an efficient and accurate implicit solvent representation for simulations of biopolymers.

An Implicit Membrane Generalized Born Theory for the Study of Structure, Stability, and Interactions of Membrane Proteins

Exploiting recent developments in generalized Born (GB) electrostatics theory, we have reformulated the calculation of the self-electrostatic solvation energy to account for the influence of biological membranes. Consistent with continuum Poisson-Boltzmann (PB) electrostatics, the membrane is approximated as an solvent-inaccessible infinite planar low-dielectric slab. The present membrane GB model closely reproduces the PB electrostatic solvation energy profile across the membrane. The nonpolar contribution to the solvation energy is taken to be proportional to the solvent-exposed surface area (SA) with a phenomenological surface tension coefficient. The proposed membrane GB/SA model requires minor modifications of the pre-existing GB model and appears to be quite efficient. By combining this implicit model for the solvent/bilayer environment with advanced computational sampling methods, like replica-exchange molecular dynamics, we are able to fold and assemble helical membrane peptides. We examine the reliability of this model and approach by applications to three membrane peptides: melittin from bee venom, the transmembrane domain of the M2 protein from Influenza A (M2-TMP), and the transmembrane domain of glycophorin A (GpA). In the context of these proteins, we explore the role of biological membranes (represented as a low-dielectric medium) in affecting the conformational changes in melittin, the tilt of transmembrane peptides with respect to the membrane normal (M2-TMP), helix-to-helix interactions in membranes (GpA), and the prediction of the configuration of transmembrane helical bundles (GpA). The present method is found to perform well in each of these cases and is anticipated to be useful in the study of folding and assembly of membrane proteins as well as in structure refinement and modeling of membrane proteins where a limited number of experimental observables are available.

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

This paper introduces a novel high order interface scheme, the matched interface and boundary (MIB) method, for solving elliptic equations with discontinuous coefficients and singular sources on Cartesian grids. By appropriate use of auxiliary line and/or fictitious points, physical jump conditions are enforced at the interface. Unlike other existing interface schemes, the proposed method disassociates the enforcement of physical jump conditions from the discretization of the differential equation under study. To construct higher order interface schemes, the proposed MIB method bypasses the major challenge of implementing high order jump conditions by repeatedly enforcing the lowest order jump conditions. The proposed MIB method is of arbitrarily high order, in principle. In treating straight, regular interfaces we construct MIB schemes up to 16th-order. For more general elliptic problems with curved, irregular interfaces and boundary, up to 6th-order MIB schemes have been demonstrated. By employing the standard high-order finite difference schemes to discretize the Laplacian, the present MIB method automatically reduces to the standard central difference scheme when the interface is absent. The immersed interface method (IIM) is regenerated for a comparison study of the proposed method. The robustness of the MIB method is verified against the large magnitude of the jump discontinuity across the interface. The nature of high efficiency and low memory requirement of the MIB method is extensively validated via solving various elliptic immersed interface problems in two- and three-dimensions. ee-dimensions.

Sodium and chlorine ions as part of the DNA solvation shell.

The distribution of sodium and chlorine ions around DNA is presented from two molecular dynamics simulations of the DNA fragment d(C(5)T(5)). (A(5)G(5)) in explicit solvent with 0.8 M additional NaCl salt. One simulation was carried out for 10 ns with the CHARMM force field that keeps the DNA structure close to A-DNA, the other for 12 ns with the AMBER force field that preferentially stabilizes B-DNA conformations (, Biophys. J. 75:134-149). From radial distributions of sodium and chlorine ions a primary ion shell is defined. The ion counts and residence times of ions within this shell are compared between conformations and with experiment. Ordered sodium ion sites were found in minor and major grooves around both A and B-DNA conformations. Changes in the surrounding hydration structure are analyzed and implications for the stabilization of A-DNA and B-DNA conformations are discussed.

A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes.

Reliable computer simulations of complex biological environments such as integral membrane proteins with explicit water and lipid molecules remain a challenging task. We propose a modification of the standard generalized Born theory of homogeneous solvent for modeling the heterogeneous dielectric environments such as lipid/water interfaces. Our model allows the representation of biological membranes in the form of multiple layered dielectric regions with dielectric constants that are different from the solute cavity. The proposed new formalism is shown to predict the electrostatic component of solvation free energy with a relative error of 0.17% compared to exact finite-difference solutions of the Poisson equation for a transmembrane helix test system. Molecular dynamics simulations of melittin and bacteriorhodopsin are carried out and performed over 10 ns and 7 ns of simulation time, respectively. The center of melittin along the membrane normal in these stable simulations is in excellent agreement with the relevant experimental data. Simulations of bacteriorhodopsin started from the experimental structure remained stable and in close agreement with experiment. We also examined the free energy profiles of water and amino acid side chain analogs upon membrane insertion. The results with our implicit membrane model agree well with the experimental transfer free energy data from cyclohexane to water as well as explicit solvent simulations of water and selected side chain analogs.

CHARMM36m: an improved force field for folded and intrinsically disordered proteins

The all-atom additive CHARMM36 protein force field is widely used in molecular modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.

Implicit solvation based on generalized Born theory in different dielectric environments.

In this paper we are investigating the effect of the dielectric environment on atomic Born radii used in generalized Born (GB) methods. Motivated by the Kirkwood expression for the reaction field of a single off-center charge in a spherical cavity, we are proposing extended formalisms for the calculation of Born radii as a function of external and internal dielectric constants. We demonstrate that reaction field energies calculated from environmentally dependent Born radii lead to much improved agreement with Poisson-Boltzmann solutions for low dielectric external environments, such as biological membranes or organic solvent, compared to previous methods where the calculation of Born radii does not depend on the environment. We also examine how this new approach can be applied for the calculation of transfer free energies from vacuum to a given external dielectric for a system with an internal dielectric larger than one. This has not been possible with standard GB theory but is relevant when scoring minimized or average structures with implicit solvent.