Symplectic quaternion scheme for biophysical molecular dynamics

Abstract

Massively parallel biophysical molecular dynamics simulations, coupled with efficient methods, promise to open biologically significant time scales for study. In order to promote efficient fine-grained parallel algorithms with low communication overhead, the fast degrees of freedom in these complex systems can be divided into sets of rigid bodies. Here, a novel Hamiltonian form of a minimal, nonsingular representation of rigid body rotations, the unit quaternion, is derived, and a corresponding reversible, symplectic integrator is presented. The novel technique performs very well on both model and biophysical problems in accord with a formal theoretical analysis given within, which gives an explicit condition for an integrator to possess a conserved quantity, an explicit expression for the conserved quantity of a symplectic integrator, the latter following and in accord with Calvo and Sanz-Sarna, Numerical Hamiltonian Problems (1994), and extension of the explicit expression to general systems with a flat phase space.