Quasi-Hamiltonian Equations of Motion for Internal Coordinate Molecular Dynamics of Polymers

摘要

Conventional molecular dynamics simulations macromolecules require longcomputational times because the most interesting motions are very slow comparedwith the fast oscillations of bond lengths and bond angles that limit theintegration time step. Simulation of dynamics in the space of internalcoordinates, that is with bond lengths, bond angles and torsions as independentvariables, gives a theoretical possibility to eliminate all uninteresting fastdegrees of freedom from the system. This paper presents a new method forinternal coordinate molecular dynamics simulations of macromolecules. Equationsof motion are derived which are applicable to branched chain molecules with anynumber of internal degrees of freedom. Equations use the canonical variablesand they are much simpler than existing analogs. In the numerical tests theinternal coordinate dynamics are compared with the traditional Cartesiancoordinate molecular dynamics in simulations a 56 residue globular protein. Itis shown that the traditional and internal coordinate dynamics require the sametime step size for the same accuracy and that in the standard geometryapproximation of amino acids, that is with fixed bond lengths, bond angles andrigid aromatic groups, the characteristic step size is 4 fsec, that is twotimes higher than with fixed bond lengths only. The step size can be increasedup to 11 fsec when rotation of hydrogen atoms is suppressed.