Many proteins in cells are capable of sensing and responding to piconewton-scale forces, a regime in which conformational changes are small but significant for biological processes. In order to efficiently and effectively sample the response of these proteins to small forces, enhanced sampling techniques will be required. In this work, we derive, implement, and evaluate an efficient method to simultaneously sample the result of applying any constant pulling force within a specified range to a molecular system of interest. We start from simulated tempering in force, whereby force is added as a linear bias on a collective variable to the system’s Hamiltonian, and the coefficient is taken as a continuous auxiliary degree of freedom. We derive a formula for an average collective-variable-dependent force, which depends on a set of weights learned on-the-fly throughout a simulation, that reflect the limit where force varies infinitely quickly. Simulation data can then be used to retroactively compute averages of any observable at any force within the specified range. This technique is based on recent work deriving similar equations for infinite switch simulated tempering in temperature, which showed that the infinite switch limit is the most efficient for sampling. Here, we demonstrate that our method accurately samples molecular systems at all forces within a user defined force range simultaneously and show how it can serve as an enhanced sampling tool for cases where the pulling direction destabilizes states that have low free-energy at zero-force. This method is implemented in and freely distributed with the PLUMED open-source sampling library, and hence can be readily applied to problems using a wide range of molecular dynamics software packages.

中文翻译：

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无限开关模拟有效回火（FISST）。

细胞中的许多蛋白质都能够感知并响应皮微尺度的作用力，这种作用的构象变化很小，但对生物学过程却很重要。为了有效地和有效地采样这些蛋白质对小力的反应，将需要增强的采样技术。在这项工作中，我们得出，实施和评估一种有效的方法，以便同时对在指定范围内对目标分子系统施加任何恒定拉力的结果进行采样。我们从模拟的回火开始，其中将力作为线性偏差添加到系统的哈密顿量的集合变量上，并将系数作为连续的辅助自由度。我们推导了一个平均的集体变量相关力的公式，它取决于整个模拟过程中动态学习的一组权重，反映了力无限快速变化的极限。然后，可以使用模拟数据来追溯计算指定范围内任何作用力下任何可观察到的平均值。该技术基于最近的工作，该工作为温度的无限开关模拟回火推导了类似的方程式，这表明无限开关极限对于采样是最有效的。在这里，我们证明了我们的方法可以同时准确地在用户定义的力范围内的所有力下对分子系统进行采样，并展示了它在拉力方向使零力下具有低自由能的状态不稳定的情况下如何用作增强的采样工具。该方法在PLUMED开源采样库中实现并随其自由分发，