Cooke Ben, Schmidler Scott C
Department of Mathematics, Duke University, Durham, North Carolina 27708-0251, USA.
J Chem Phys. 2008 Oct 28;129(16):164112. doi: 10.1063/1.2989802.
We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic.
基于基础等温分子动力学（MD）模拟中数值积分器的性质，我们考虑了副本交换分子动力学（REMD）[杉田和冈本，《化学物理快报》314, 141 (1999)]的收敛行为。我们表明，分子动力学从业者青睐的用于生物分子恒温模拟的多种确定性算法，要么不具有测度不变性，要么不具有不可约性，因此不是遍历的。然后我们表明，使用这些算法的REMD也不是遍历的。结果，即使在无限长的模拟中，整个构型空间也可能无法被探索，并且模拟可能不会收敛到所需的平衡玻尔兹曼系综。此外，我们的分析表明，对于具有不利能量的初始构型，系统可能无法到达围绕最低能量构型的区域。我们针对三个小系统展示了REMD算法的这些失败情况：高斯分布（简谐振子动力学）、高斯分布的双峰混合物以及丙氨酸二肽。对所得相图和平衡构型密度的检查表明，REMD模拟生成的系综存在显著误差。我们基于随机混合蒙特卡罗校正描述了一种简单的修改方法来解决这些失败情况，并证明其是遍历的。
