All-atom and coarse-grained molecular dynamics simulations of a membrane protein stabilizing polymer.

Amphipathic polymers called amphipols (APols) have been developed as an alternative to detergents for stabilizing membrane proteins (MPs) in aqueous solutions. APols provide MPs with a particularly mild environment and, as a rule, keep them in a native functional state for longer periods than do detergents. Amphipol A8-35, a derivative of polyacrylate, is widely used and has been particularly well studied experimentally. In aqueous solutions, A8-35 molecules self-assemble into well-defined globular particles with a mass of ∼40 kDa and a R(g) of ∼2.4 nm. As a first step towards describing MP/A8-35 complexes by molecular dynamics (MD), we present three sets of simulations of the pure APol particle. First, we performed a series of all-atom MD (AAMD) simulations of the particle in solution, starting from an arbitrary initial configuration. Although AAMD simulations result in stable cohesive particles over a 45 ns simulation, the equilibration of the particle organization is limited. This motivated the use of coarse-grained MD (CGMD), allowing us to investigate processes on the microsecond time scale, including de novo particle assembly. We present a detailed description of the parametrization of the CGMD model from the AAMD simulations and a characterization of the resulting CGMD particles. Our third set of simulations utilizes reverse coarse-graining (rCG), through which we obtain all-atom coordinates from a CGMD simulation. This allows a higher-resolution characterization of a configuration determined by a long-timescale simulation. Excellent agreement is observed between MD models and experimental, small-angle neutron scattering data. The MD data provides new insight into the structure and dynamics of A8-35 particles, which is possibly relevant to the stabilizing effects of APols on MPs, as well as a starting point for modeling MP/A8-35 complexes.

A coupled polarization-matrix inversion and iteration approach for accelerating the dipole convergence in a polarizable potential function.

A coupled polarization-matrix inversion and iteration (CPII) method is described to achieve and accelerate the convergence of induced dipoles for condensed phase systems employing polarizable intermolecular potential functions (PIPF). The present PIPF is based on the Thole interaction dipole model in which all atomic pair interactions are considered, including those that are directly bonded covalently. Although induced dipoles can be obtained both by inverting a 3N x 3N polarization-matrix where N is the number of polarizable sites, or by a direct iterative approach, the latter approach is more efficient computationally for large systems in molecular dynamics simulations. It was found that induced dipole moments failed to converge in the direct iterative approach if 1-2, 1-3, and 1-4 intramolecular interactions are included in the Thole model. However, it is necessary to include all intramolecular interactions in the Thole model to yield the correct molecular anisotropic polarizability tensor. To solve this numerical stability problem, we reformulated the Thole interaction dipole model in terms of molecular block matrices, which naturally leads to a coupled, preconditioning algorithm that involves a polarization-matrix inversion term to account for intramolecular interactions, and an iterative procedure to incorporate the mutual polarization effects between different molecules. The CPII method is illustrated by applying to cubic boxes of water and NMA molecules as well as an alanine pentapeptide configuration, and it was shown that the CPII method can achieve convergence for the dipole induction polarization rapidly in all cases, whereas the direct iterative approach failed to reach convergence in these cases. In addition, the CPII reduces the overall computational costs by decreasing the number of iteration steps in comparison with the direct iteration approach in which intramolecular bonded interactions are excluded to ensure that induced dipole convergence is obtained.

Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method.

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.

The variational explicit polarization potential and analytical first derivative of energy: Towards a next generation force field.

A previous article proposed an electronic structure-based polarizable potential, called the explicit polarization (X-POL) potential, to treat many-body polarization and charge delocalization effects in polypeptides. Here, we present a variational version of the X-POL potential, in which the wave function of the entire molecular system is variationally optimized to yield the minimum total electronic energy. This allows the calculation of analytic gradients, a necessity for efficient molecular dynamics simulations. In this paper, the detailed derivations of the Fock matrix and analytic force are presented and discussed. The calculations involve a double self-consistent-field procedure in which the wave function of each fragment is self-consistently optimized in the presence of other fragments, and in addition the polarization of the entire system is self-consistently optimized. The variational X-POL potential has been implemented in the Chemistry at Harvard Molecular Mechanics (CHARMM) package and tested successfully for small model compounds.

A Non-Orthogonal Block-Localized Effective Hamiltonian Approach for Chemical and Enzymatic Reactions.

The effective Hamiltonian-molecular orbital and valence bond (EH-MOVB) method based on non-orthogonal block-localized fragment orbitals has been implemented into the program CHARMM for molecular dynamics simulations of chemical and enzymatic reactions, making use of semiempirical quantum mechanical models. Building upon ab initio MOVB theory, we make use of two parameters in the EH-MOVB method to fit the barrier height and the relative energy between the reactant and product state for a given chemical reaction to be in agreement with experiment or high-level ab initio or density functional results. Consequently, the EH-MOVB method provides a highly accurate and computationally efficient QM/MM model for dynamics simulation of chemical reactions in solution. The EH-MOVB method is illustrated by examination of the potential energy surface of the hydride transfer reaction from trimethylamine to a flavin cofactor model in the gas phase. In the present study, we employed the semiempirical AM1 model, which yields a reaction barrier that is more than 5 kcal/mol too high. We use a parameter calibration procedure for the EH-MOVB method similar to that employed to adjust the results of semiempirical and empirical models. Thus, the relative energy of these two diabatic states can be shifted to reproduce the experimental energy of reaction, and the barrier height is optimized to reproduce the desired (accurate) value by adding a constant to the off-diagonal matrix element. The present EH-MOVB method offers a viable approach to characterizing solvent and protein-reorganization effects in the realm of combined QM/MM simulations.

X-Pol Potential: An Electronic Structure-Based Force Field for Molecular Dynamics Simulation of a Solvated Protein in Water.

A recently proposed electronic structure-based force field called the explicit polarization (X-Pol) potential is used to study many-body electronic polarization effects in a protein, in particular by carrying out a molecular dynamics (MD) simulation of bovine pancreatic trypsin inhibitor (BPTI) in water with periodic boundary conditions. The primary unit cell is cubic with dimensions ~54 × 54 × 54 Å(3), and the total number of atoms in this cell is 14281. An approximate electronic wave function, consisting of 29026 basis functions for the entire system, is variationally optimized to give the minimum Born-Oppenheimer energy at every MD step; this allows the efficient evaluation of the required analytic forces for the dynamics. Intramolecular and intermolecular polarization and intramolecular charge transfer effects are examined and are found to be significant; for example, 17 out of 58 backbone carbonyls differ from neutrality on average by more than 0.1 electron, and the average charge on the six alanines varies from -0.05 to +0.09. The instantaneous excess charges vary even more widely; the backbone carbonyls have standard deviations in their fluctuating net charges from 0.03 to 0.05, and more than half of the residues have excess charges whose standard deviation exceeds 0.05. We conclude that the new-generation X-Pol force field permits the inclusion of time-dependent quantum mechanical polarization and charge transfer effects in much larger systems than was previously possible.

The Design of a Next Generation Force Field: The X-POL Potential.

An electronic structure-based polarization method, called the X-POL potential, has been described for the purpose of constructing an empirical force field for modeling polypeptides. In the X-POL potential, the internal, bonded interactions are fully represented by an electronic structure theory augmented with some empirical torsional terms. Non-bonded interactions are modeled by an iterative, combined quantum mechanical and molecular mechanical method, in which the molecular mechanical partial charges are derived from the molecular wave functions of the individual fragments. In this paper, the feasibility of such an electronic structure force field is illustrated by small model compounds. A method has been developed for separating a polypeptide chain into peptide units and its parameterization procedure in the X-POL potential is documented and tested on glycine dipeptide. We envision that the next generation of force fields for biomolecular polymer simulations will be developed based on electronic structure theory, which can adequately define and treat many-body polarization and charge delocalization effects.

Development of a polarizable intermolecular potential function (PIPF) for liquid amides and alkanes.

A polarizable intermolecular potential function (PIPF) employing the Thole interacting dipole (TID) polarization model has been developed for liquid alkanes and amides. In connection with the internal bonding terms of the CHARMM22 force field, the present PIPF-CHARMM potential provides an adequate description of structural and thermodynamic properties for liquid alkanes and for liquid amides through molecular dynamics simulations. The computed heats of vaporization and liquid density are within 1.4% of experimental values. Polarization effects play a major role in liquid amides, which are reflected by an increase of 1.5 to 1.8 D in molecular dipole moment for primary and secondary amides. Furthermore, the computed polarization energies contribute to the total intermolecular interaction energy by 6 to 24%. The ability of the PIPF-CHARMM force field to treat protein backbone structures is tested by examining the potential energy surface of the amide bond rotation in N-methylacetamide and the Ramachandran surface for alanine dipeptide. The agreement with ab initio MP2 results and with the original CHARMM22 force field is encouraging, suggesting the PIPF-CHARMM potential can be used as a starting point to construct a complete polarizable force field for proteins.