Eastwood Michael P, Stafford Kate A, Lippert Ross A, Jensen Morten Ø, Maragakis Paul, Predescu Cristian, Dror Ron O, Shaw David E
D. E. Shaw Research, New York, New York 10036.
J Chem Theory Comput. 2010 Jul 13;6(7):2045-58. doi: 10.1021/ct9002916.
Since the behavior of biomolecules can be sensitive to temperature, the ability to accurately calculate and control the temperature in molecular dynamics (MD) simulations is important. Standard analysis of equilibrium MD simulations-even constant-energy simulations with negligible long-term energy drift-often yields different calculated temperatures for different motions, however, in apparent violation of the statistical mechanical principle of equipartition of energy. Although such analysis provides a valuable warning that other simulation artifacts may exist, it leaves the actual value of the temperature uncertain. We observe that Tolman's generalized equipartition theorem should hold for long stable simulations performed using velocity-Verlet or other symplectic integrators, because the simulated trajectory is thought to sample almost exactly from a continuous trajectory generated by a shadow Hamiltonian. From this we conclude that all motions should share a single simulation temperature, and we provide a new temperature estimator that we test numerically in simulations of a diatomic fluid and of a solvated protein. Apparent temperature variations between different motions observed using standard estimators do indeed disappear when using the new estimator. We use our estimator to better understand how thermostats and barostats can exacerbate integration errors. In particular, we find that with large (albeit widely used) time steps, the common practice of using two thermostats to remedy so-called hot solvent-cold solute problems can have the counterintuitive effect of causing temperature imbalances. Our results, moreover, highlight the utility of multiple-time step integrators for accurate and efficient simulation.
由于生物分子的行为对温度敏感，因此在分子动力学（MD）模拟中准确计算和控制温度的能力很重要。然而，对平衡MD模拟的标准分析——即使是长期能量漂移可忽略不计的恒能模拟——通常会针对不同运动得出不同的计算温度，这明显违反了能量均分的统计力学原理。尽管这种分析提供了一个有价值的警示，即可能存在其他模拟假象，但它使温度的实际值不确定。我们观察到，对于使用速度Verlet或其他辛积分器进行的长时间稳定模拟，托尔曼广义均分定理应该成立，因为模拟轨迹被认为几乎完全是从由影子哈密顿量生成的连续轨迹中采样得到的。由此我们得出结论，所有运动应该共享一个单一的模拟温度，并且我们提供了一种新的温度估计器，我们在双原子流体和溶剂化蛋白质的模拟中对其进行了数值测试。使用标准估计器观察到的不同运动之间明显的温度变化在使用新估计器时确实消失了。我们使用我们的估计器来更好地理解恒温器和恒压器如何加剧积分误差。特别是，我们发现，对于大的（尽管广泛使用）时间步长，使用两个恒温器来解决所谓的热溶剂 - 冷溶质问题的常见做法可能会产生导致温度失衡的反直觉效果。此外，我们的结果突出了多时间步积分器在准确高效模拟方面的效用。
