Semi-Implicit Time Integration with Hessian Eigenvalue Corrections for a Larger Time Step in Molecular Dynamics Simulations.

In molecular dynamics simulations, the limited time step size has been a barrier to simulating long-time behaviors. Implicit time integration methods allow markedly larger time steps than the standard explicit time method, although they have major drawbacks such as overheads solving linear systems and instability of Newton iterations. To overcome these issues, we propose a semi-implicit time integration scheme, the semi-implicit Hessian correction (SimHec) scheme, for overdamped Langevin dynamics. The method focuses on the Hessian matrices of bonded and nonbonded interactions, where components with large negative Hessian eigenvalues are cut off in the linear approximation of momentum equations to avoid instability. The narrow band Hessian matrix enables an efficient parallelized linear solution with an overlapping approximation. We tested SimHec for the interdomain fluctuations in adenylate kinase and the powerstroke transition of myosin II using a coarse-grained protein model. SimHec reproduced the same dynamics as the explicit method, although the transition dynamics tended to be accelerated and fluctuations in bonded potentials were slightly reduced. These deviations were corrected using a hybrid method, SimHec-H, which adds explicit time steps after the semi-implicit time step. The proposed scheme allowed us to use time steps 50-200 times larger than those in explicit time integration, which resulted in a speedup factor of 7-30 taking the overhead into account.