Benoît Roux

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.

The calculation of the potential of mean force using computer simulations

The problem of unbiasing and combining the results of umbrella sampling calculations is reviewed. The weighted histogram analysis method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with molecular dynamics simulations of the alanine dipeptide for one-and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.

Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations

An approach is developed to obtain statistical properties similar to those of an infinite bulk system from computer simulations of a finite cluster. A rigorous theoretical formulation is given for the solvent boundary potential which takes the influence of the surrounding bulk into account. The solvent boundary potential is the configuration‐dependent solvation free energy of an effective cluster composed of an arbitrary solute and a finite number of explicit solvent molecules embedded inside a hard sphere of variable radius; the hard sphere does not act directly on the solute or the explicit solvent molecules, and its radius varies according to the instantaneous configurations. The formulation follows from an exact separation of the multidimensional configurational Boltzmann integral in terms of the solvent molecules nearest to the solute and the remaining bulk solvent molecules. An approximation to the solvent boundary potential is constructed for simulations of bulk water at constant pressure, includin...

Continuum Solvation Model: computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation

A rigorous formulation of the solvation forces (first derivatives) associated with the electrostatic free energy calculated from numerical solutions of the linearized Poisson-Boltzmann equation on a discrete grid is described. The solvation forces are obtained from the formal solution of the linearized Poisson-Boltzmann equation written in terms of the Green function. An intermediate region for the solute-solvent dielectric boundary is introduced to yield a continuous solvation free energy and accurate solvation forces. A series of numerical tests show that the calculated forces agree extremely well with finite-difference derivatives of the solvation free energy. To gain a maximum efficiency, the nonpolar contribution to the free energy is expressed in terms of the discretized grid used for the electrostatic problem. The current treatment of solvation forces can be used to introduce the influence of a continuum solvation model in molecular mechanics calculations of large biological systems.

Control of ion selectivity in potassium channels by electrostatic and dynamic properties of carbonyl ligands.

Potassium channels are essential for maintaining a normal ionic balance across cell membranes. Central to this function is the ability of such channels to support transmembrane ion conduction at nearly diffusion-limited rates while discriminating for K+ over Na+ by more than a thousand-fold. This selectivity arises because the transfer of the K+ ion into the channel pore is energetically favoured, a feature commonly attributed to a structurally precise fit between the K+ ion and carbonyl groups lining the rigid and narrow pore. But proteins are relatively flexible structures that undergo rapid thermal atomic fluctuations larger than the small difference in ionic radius between K+ and Na+. Here we present molecular dynamics simulations for the potassium channel KcsA, which show that the carbonyl groups coordinating the ion in the narrow pore are indeed very dynamic (‘liquid-like’) and that their intrinsic electrostatic properties control ion selectivity. This finding highlights the importance of the classical concept of field strength. Selectivity for K+ is seen to emerge as a robust feature of a flexible fluctuating pore lined by carbonyl groups.

Molecular determinants of gating at the potassium-channel selectivity filter.

We show that in the potassium channel KcsA, proton-dependent activation is followed by an inactivation process similar to C-type inactivation, and this process is suppressed by an E71A mutation in the pore helix. EPR spectroscopy demonstrates that the inner gate opens maximally at low pH regardless of the magnitude of the single-channel-open probability, implying that stationary gating originates mostly from rearrangements at the selectivity filter. Two E71A crystal structures obtained at 2.5 Å reveal large structural excursions of the selectivity filter during ion conduction and provide a glimpse of the range of conformations available to this region of the channel during gating. These data establish a mechanistic basis for the role of the selectivity filter during channel activation and inactivation.

Structure, energetics, and dynamics of lipid–protein interactions: A molecular dynamics study of the gramicidin A channel in a DMPC bilayer

The microscopic details of lipid–protein interactions are examined using molecular dynamics simulations of the gramicidin A channel embedded in a fully hydrated dimyristoyl phosphatidylcholine (DMPC) bilayer. A novel construction protocol was used to assemble the initial configurations of the membrane protein complex for the simulations. Three hundreds systems were constructed with different initial lipid placement and conformations. Seven systems were simulated with molecular dynamics. One system was simulated for a total of 600 psec, four were simulated for 300 psec, and two for 100 psec. Analysis of the resulting trajectories shows that the bulk solvent–membrane interface region is much broader than traditionally pictured in simplified continuum theories: its width is almost 15 Å. In addition, lipid–protein interactions are far more varied, both structurally and energetically, than is usually assumed: the total interaction energy between the gramicidin A and the individual lipids varies from 0 to −50 kcal/mol. The deuterium quadrupolar splittings of the lipid acyl chains calculated from the trajectories are in good agreement with experimental data. The lipid chains in direct contact with the GA are ordered but the effect is not uniform due to the irregular surface of the protein. Energy decompositions shows that the most energetically favorable interactions between lipid and protein involve nearly equal contributions from van der Waals and electrostatic interactions. The tryptophans, located near the bulk–membrane interface, appear to be particularly important in mediating both hydrogen bonding interactions with the lipid glycerol backbone and water and also in forming favorable van der Waals contacts with the hydrocarbon chains. In contrast, the interactions of the leucine residues with the lipids, also located near the interface, are dominated by van der Waals interactions with the hydrocarbon lipid chains.

Energetics of ion conduction through the gramicidin channel

The free energy governing K+ conduction through gramicidin A channels is characterized by using over 0.1 μs of all-atom molecular dynamics simulations with explicit solvent and membrane. The results provide encouraging agreement with experiments and insights into the permeation mechanism. The free energy surface of K+, as a function of both axial and radial coordinates, is calculated. Correcting for simulation artifacts due to periodicity and the lack of hydrocarbon polarizability, the calculated single-channel conductance for K+ ions is 0.8 pS, closer to experiment than any previous calculation. In addition, the estimated single ion dissociation constants are within the range of experimental determinations. The relatively small free energy barrier to ion translocation arises from a balance of large opposing contributions from protein, single-file water, bulk electrolyte, and membrane. Mean force decomposition reveals a remarkable ability of the single-file water molecules to stabilize K+ by –40 kcal/mol, roughly half the bulk solvation free energy. The importance of the single-file water confirms the conjecture of Mackay et al. [Mackay, D. H. J., Berens, P. H., Wilson, K. R. & Hagler, A. T. (1984) Biophys. J. 46, 229–248]. Ion association with the channel involves gradual dehydration from approximately six to seven water molecules in the first shell, to just two inside the narrow pore. Ion permeation is influenced by the orientation of the single-file water column, which can present a barrier to conduction and give rise to long-range coupling of ions on either side of the pore. Small changes in the potential function, including contributions from electronic polarization, are likely to be sufficient to obtain quantitative agreement with experiments.

High-resolution polypeptide structure in a lamellar phase lipid environment from solid state NMR derived orientational constraints.

BACKGROUND Solid-state nuclear magnetic resonance (NMR) spectroscopy provides novel structural constraints from uniformly aligned samples. These orientational constraints orient specific atomic sites with respect to the magnetic field direction and the unique molecular axis of alignment. Solid-state NMR is uniquely and ideally suited for providing such structural constraints on polypeptides and proteins in a lamellar phase lipid environment. Membrane protein structure represents a great challenge for structural biologists; a new approach for characterizing high resolution three-dimensional structure in such an environment is needed. RESULTS The optimal use of orientational constraints for defining three-dimensional structures is demonstrated with the elucidation of the gramicidin A channel structure at high resolution. Initial structures are refined against both the experimental constraints and the CHARMM energy using a novel simulated-annealing protocol to define torsion angle solutions with an error bar of approximately +/- 5 degrees. CONCLUSIONS This analysis results in the determination of a high-resolution, time averaged structure of gramicidin A obtained in a lipid bilayer environment above the gel-to-liquid crystalline phase transition temperature. It is demonstrated that solid-state NMR can be used to establish polypeptide, and potentially protein, structures in such an environment. Furthermore, this high-resolution structure is demonstrated to provide new insights into polypeptide function. For the gramicidin A channel the roles of the indole groups that facilitate ion transport and details of the cation solvation environment provided by the amide oxygens are characterized.