Accurate and efficient constrained molecular dynamics of polymers using Newton?s method and special purpose code

In molecular dynamics simulations we can often increase the time step by imposing constraints on bond lengths and bond angles. This allows us to extend the length of the time interval and therefore the range of physical phenomena that we can afford to simulate. We examine the existing algorithms and software for solving nonlinear constraint equations in parallel and we explain why it is necessary to advance the state-of-the-art. We present ILVES-PC, a new algorithm for imposing bond constraints on proteins accurately and efficiently. It solves the same system of differential algebraic equations as the celebrated SHAKE algorithm, but ILVES-PC solves the nonlinear constraint equations using Newton's method rather than the nonlinear Gauss-Seidel method. Moreover, ILVES-PC solves the necessary linear systems using a specialized linear solver that exploits the structure of the protein. ILVES-PC can rapidly solve constraint equations as accurately as the hardware will allow. The run-time of ILVES-PC is proportional to the number of constraints. We have integrated ILVES-PC into GROMACS and simulated proteins of different sizes. Compared with SHAKE, we have achieved speedups of up to 4.9x in single-threaded executions and up to 76x in shared-memory multi-threaded executions. Moreover, ILVES-PC is more accurate than P-LINCS algorithm. Our work is a proof-of-concept of the utility of software designed specifically for the simulation of polymers. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).

Automated summary

In molecular dynamics simulations, constraints on bond lengths and angles can increase the time step and expand the range of physical phenomena that can be simulated. We propose ILVES-PC, a new algorithm that accurately and efficiently imposes bond constraints on proteins using Newton's method. Integrated into GROMACS, ILVES-PC achieves significant speedups compared to SHAKE and higher accuracy than P-LINCS algorithm. This work serves as a proof-of-concept for the utility of software designed for polymer simulation.