Dataset Information

Equipartition Principle for Internal Coordinate Molecular Dynamics.

ABSTRACT: The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has ½kT of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordinates and includes cross-terms. Due to this coupled structure, no such equipartition principle holds for ICMD models. In this paper we introduce non-canonical modal coordinates to recover some of the structural simplicity of Cartesian models and develop a new equipartition principle for ICMD models. We derive low-order recursive computational algorithms for transforming between the modal and physical coordinates. The equipartition principle in modal coordinates provides a rigorous method for initializing velocities in ICMD simulations thus replacing the ad hoc methods used until now. It also sets the basis for calculating conformational entropy using internal coordinates.

SUBMITTER: Jain A

PROVIDER: S-EPMC3549275 | biostudies-literature | 2012 Aug

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Equipartition Principle for Internal Coordinate Molecular Dynamics.

Jain Abhinandan A Park In-Hee IH Vaidehi Nagarajan N

Journal of chemical theory and computation 20120705 8

The principle of equipartition of (kinetic) energy for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has ½kT of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordina ...[more]

PMID: 23341754

Similar Datasets

Project description:The Internal Coordinate Molecular Dynamics (ICMD) method is an attractive molecular dynamics (MD) method for studying the dynamics of bonded systems such as proteins and polymers. It offers a simple venue for coarsening the dynamics model of a system at multiple hierarchical levels. For example, large scale protein dynamics can be studied using torsional dynamics, where large domains or helical structures can be treated as rigid bodies and the loops connecting them as flexible torsions. ICMD with such a dynamic model of the protein, combined with enhanced conformational sampling method such as temperature replica exchange, allows the sampling of large scale domain motion involving high energy barrier transitions. Once these large scale conformational transitions are sampled, all-torsion, or even all-atom, MD simulations can be carried out for the low energy conformations sampled via coarse grained ICMD to calculate the energetics of distinct conformations. Such hierarchical MD simulations can be carried out with standard all-atom forcefields without the need for compromising on the accuracy of the forces. Using constraints to treat bond lengths and bond angles as rigid can, however, distort the potential energy landscape of the system and reduce the number of dihedral transitions as well as conformational sampling. We present here a two-part solution to overcome such distortions of the potential energy landscape with ICMD models. To alleviate the intrinsic distortion that stems from the reduced phase space in torsional MD, we use the Fixman compensating potential. To additionally alleviate the extrinsic distortion that arises from the coupling between the dihedral angles and bond angles within a force field, we propose a hybrid ICMD method that allows the selective relaxing of bond angles. This hybrid ICMD method bridges the gap between all-atom MD and torsional MD. We demonstrate with examples that these methods together offer a solution to eliminate the potential energy distortions encountered in constrained ICMD simulations of peptide molecules.

Project description:We present an extension of the all-atom internal-coordinate force field, ICMFF, that allows for simulation of heterogeneous systems including hexopyranose saccharides and glycan chains in addition to proteins. A library of standard glycan geometries containing α- and β-anomers of the most common hexapyranoses, i.e., d-galactose, d-glucose, d-mannose, d-xylose, l-fucose, N-acetylglucosamine, N-acetylgalactosamine, sialic, and glucuronic acids, is created based on the analysis of the saccharide structures reported in the Cambridge Structural Database. The new force field parameters include molecular electrostatic potential-derived partial atomic charges and the torsional parameters derived from quantum mechanical data for a collection of minimal molecular fragments and related molecules. The ϕ/ψ torsional parameters for different types of glycosidic linkages are developed using model compounds containing the key atoms in the full carbohydrates, i.e., glycosidic-linked tetrahydropyran-cyclohexane dimers. Target data for parameter optimization include two-dimensional energy surfaces corresponding to the ϕ/ψ glycosidic dihedral angles in the disaccharide analogues, as determined by quantum mechanical MP2/6-31G** single-point energies on HF/6-31G** optimized structures. To achieve better agreement with the observed geometries of glycosidic linkages, the bond angles at the O-linkage atoms are added to the internal variable set and the corresponding bond bending energy term is parametrized using quantum mechanical data. The resulting force field is validated on glycan chains of 1-12 residues from a set of high-resolution X-ray glycoprotein structures based on heavy atom root-mean-square deviations of the lowest-energy glycan conformations generated by the biased probability Monte Carlo (BPMC) molecular mechanics simulations from the native structures. The appropriate BPMC distributions for monosaccharide-monosaccharide and protein-glycan linkages are derived from the extensive analysis of conformational properties of glycoprotein structures reported in the Protein Data Bank. Use of the BPMC search leads to significant improvements in sampling efficiency for glycan simulations. Moreover, good agreement with the X-ray glycoprotein structures is achieved for all glycan chain lengths. Thus, average/median RMSDs are 0.81/0.68 Å for one-residue glycans and 1.32/1.47 Å for three-residue glycans. RMSD from the native structure for the lowest-energy conformation of the 12-residue glycan chain (PDB ID 3og2) is 1.53 Å. Additionally, results obtained for free short oligosaccharides using the new force field are in line with the available experimental data, i.e., the most populated conformations in solution are predicted to be the lowest energy ones. The newly developed parameters allow for the accurate modeling of linear and branched hexopyranose glycosides in heterogeneous systems.

Dataset Information

Equipartition Principle for Internal Coordinate Molecular Dynamics.

Publications

Equipartition Principle for Internal Coordinate Molecular Dynamics.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets