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 4.9× in single-threaded executions and up to 76× 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.
This work has been partially supported by the Spanish Ministry of Science and Innovation MCIN/AEI/10.13039/501100011033 (contracts PID2019-107255GB-C21, PID2019-105660RB-C21, and PID2019-107293GB-I00), by the Generalitat de Catalunya (contract 2017-SGR-1328), by the Gobierno de Aragón (E45_20R T58_20R research groups), and by Lenovo-BSC Contract-Framework Contract (2020). Santiago Marco was supported by the Agencia Estatal de Investigación (Spain) under Juan de la Cierva fellowship grant IJC2020-045916-I. Miquel Moretó was partially supported by the Agencia Estatal de Investigación (Spain) under Ramón y Cajal fellowship number RYC-2016-21104. Carl Christian Kjelgaard Mikkelsen is supported by eSSENCE, a collaborative e-Science programme funded by the Swedish Research Council within the framework of the strategic research areas designated by the Swedish Government.
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