Implementations of Nosé-Hoover and Nosé-Poincaré thermostats in mesoscopic dynamic simulations with the united-residue model of a polypeptide chain.

Molecular dynamics (MD) simulations generate a canonical ensemble only when integration of the equations of motion is coupled to a thermostat. Three extended phase space thermostats, one version of Nose-Hoover and two versions of Nose-Poincare, are compared with each other and with the Berendsen thermostat and Langevin stochastic dynamics. Implementation of extended phase space thermostats was first tested on a model Lennard-Jones fluid system; subsequently, they were implemented with our physics-based protein united-residue (UNRES) force field MD. The thermostats were also implemented and tested for the multiple-time-step reversible reference system propagator (RESPA). The velocity and temperature distributions were analyzed to confirm that the proper canonical distribution is generated by each simulation. The value of the artificial mass constant, Q, of the thermostat has a large influence on the distribution of the temperatures sampled during UNRES simulations (the velocity distributions were affected only slightly). The numerical stabilities of all three algorithms were compared with each other and with that of microcanonical MD. Both Nose-Poincare thermostats, which are symplectic, were not very stable for both the Lennard-Jones fluid and UNRES MD simulations started from nonequilibrated structures which implies major changes of the potential energy throughout a trajectory. Even though the Nose-Hoover thermostat does not have a canonical symplectic structure, it is the most stable algorithm for UNRES MD simulations. For UNRES with RESPA, the "extended system inside-reference system propagator algorithm" of the RESPA implementation of the Nose-Hoover thermostat was the only stable algorithm, and enabled us to increase the integration time step.