School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.
J Chem Phys. 2013 May 7;138(17):174102. doi: 10.1063/1.4802990.
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation). The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.
研究人员采用 Baker-Campbell-Hausdorff 展开法对最近的工作进行了研究，该方法可以确定与步长相关的构型平均偏差。对于谐振子，某些方案的构型平均是精确的，这可能会提高在建模中对突出键拉伸的生物分子的性能。对于一般系统，可以确定一种具有非常低偏差的最佳方法。对于本文报道的丙氨酸二肽的模拟（包括溶剂化和非溶剂化），在不损失计算效率的情况下，可以获得更高的准确性，同时允许使用大的时间步长，并且不会影响构象探索速率（在模拟中观察到的有效扩散速率）。对于分子采样，最优方案是一种性能更好的统一算法，在真空中可实现的实际时间步长中，整体效率提高了 25%或更多，并且在溶剂化模拟中，在大时间步长下，构型平均误差可降低一个数量级或更多。
