Symplectic integration of closed chain rigid body dynamics with internal coordinate equations of motion

Internal coordinate molecular dynamics (ICMD) is a recent efficient method for modeling polymer molecules which treats them as chains of rigid bodies rather than ensembles of point particles as in Cartesian MD. Unfortunately, it is readily applicable only to linear or tree topologies without closed flexible loops. Important examples violating this condition are sugar rings of nucleic acids, proline residues in proteins, and also disulfide bridges. This paper presents the first complete numerical solution of the chain closure problem within the context of ICMD. The method combines natural implicit fixation of bond lengths and bond angles by the choice of internal coordinates with explicit constraints similar to Cartesian dynamics used to maintain the chain closure. It is affordable for large molecules and makes possible 3–5 times faster dynamics simulations of molecular systems with flexible rings, including important biological objects like nucleic acids and disulfide-bonded proteins.

[1]  A. Mazur.  Quasi‐Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers , 1997 .

[2]  M. Sundaralingam,et al.  Conformational analysis of the sugar ring in nucleosides and nucleotides. A new description using the concept of pseudorotation. , 1972, Journal of the American Chemical Society.

[3]  J. H. Weiner,et al.  Brownian dynamics study of a polymer chain of linked rigid bodies , 1979 .

[4]  Alexey K. Mazur,et al.  The Hierarchy of Fast Motions in Protein Dynamics , 1998, physics/9801022.

[5]  A. Brünger,et al.  Torsion angle dynamics: Reduced variable conformational sampling enhances crystallographic structure refinement , 1994, Proteins.

[6]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1977, Journal of molecular biology.

[7]  R. Abagyan,et al.  New methodology for computer-aided modelling of biomolecular structure and dynamics. 1. Non-cyclic structures. , 1989, Journal of biomolecular structure & dynamics.

[8]  R A Abagyan,et al.  New methodology for computer-aided modelling of biomolecular structure and dynamics. 2. Local deformations and cycles. , 1989, Journal of biomolecular structure & dynamics.

[9]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[10]  E. Haug,et al.  A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems , 1987 .

[11]  N. Go,et al.  Ring Closure and Local Conformational Deformations of Chain Molecules , 1970 .

[12]  A. Mazur,et al.  Investigation of conformational equilibrium of polypeptides by internal coordinate stochastic dynamics. Met5-enkephalin. , 1993, Journal of biomolecular structure & dynamics.

[13]  Abhinandan Jain,et al.  A Spatial Operator Algebra for Manipulator Modeling and Control , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[14]  Henry A. Gabb,et al.  Efficient conformational space sampling for nucleosides using internal coordinate Monte Carlo simulations and a modified furanose description , 1995, J. Comput. Chem..

[15]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[16]  Alexey K. Mazur.  Common Molecular Dynamics Algorithms Revisited , 1997 .

[17]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[18]  Guillermo Rodríguez-Ortiz,et al.  Spatial operator factorization and inversion of the manipulator mass matrix , 1992, IEEE Trans. Robotics Autom..

[19]  V. Arnold,et al.  Mathematical aspects of classical and celestial mechanics , 1997 .

[20]  Alexey K. Mazur,et al.  Accurate DNA Dynamics without Accurate Long-Range Electrostatics , 1998 .

[21]  S. Roe,et al.  Atomic resolution (0.83 A) crystal structure of the hydrophobic protein crambin at 130 K. , 1993, Journal of molecular biology.

[22]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997 .

[23]  A. Mazur,et al.  Investigation of the conformational properties of a β-(1 → 3) branched β-(1 → 6) heptasaccharide elicitor and its analogues by internal coordinate stochastic dynamics , 1995 .

[24]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[25]  Abhinandan Jain.  Unified formulation of dynamics for serial rigid multibody systems , 1991 .

[26]  Abhinandan Jain,et al.  A fast recursive algorithm for molecular dynamics simulation , 1993 .

[27]  A T Brünger,et al.  Torsion-angle molecular dynamics as a new efficient tool for NMR structure calculation. , 1997, Journal of magnetic resonance.

[28]  Giuseppe Rodriguez,et al.  Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics , 1987, IEEE Journal on Robotics and Automation.

[29]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[30]  D S Moss,et al.  Segmented anisotropic refinement of bovine ribonuclease A by the application of the rigid-body TLS model. , 1989, Acta crystallographica. Section A, Foundations of crystallography.