Locating plausible transition paths and enhanced sampling of rare events are fundamental to understanding the functional dynamics of biomolecules. Here, a constraint-based constant advance replicas (CAR) formalism of reaction paths is reported for identifying the most probable transition path (MPTP) between two given states. We derive the temporal-integrated effective dynamics governing the projected subsystem under the holonomic CAR path constraints and show that a dynamical action functional can be defined and used for optimizing the MPTP. We further demonstrate how the CAR MPTP can be located by asymptotically minimizing an upper bound of the CAR action functional using a variational expectation-maximization framework. Essential thermodynamics and kinetic observables are retrieved by integrating the boxed molecular dynamics on the CAR MPTP using a newly proposed adaptive reflecting boundary condition. The efficiency of the proposed method is demonstrated for the Müller potential, the alanine dipeptide isomerization, and the DNA base pairing transition (Watson-Crick to Hoogsteen) in explicit solvent. The CAR representation of transition paths constitutes a robust and extensible platform that can be combined with diverse enhanced sampling methods to aid future flexible and reliable biomolecular simulations.

中文翻译：

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使用 Constant Advance 副本确定最可能的过渡路径。


找到合理的过渡路径和增强罕见事件的采样是理解生物分子功能动力学的基础。在这里，报告了反应路径的基于约束的常进复制 （CAR） 形式，用于识别两个给定状态之间最可能的过渡路径 （MPTP）。我们推导出了在整体 CAR 路径约束下控制投影子系统的时间积分有效动力学，并表明可以定义动力学动作函数并将其用于优化 MPTP。我们进一步展示了如何通过使用变分期望最大化框架渐近最小化 CAR 作用泛函的上限来定位 CAR MPTP。通过使用新提出的自适应反射边界条件在 CAR MPTP 上集成方框分子动力学来检索基本的热力学和动力学可观测值。在显式溶剂中，证明了所提出的方法对 Müller 电位、丙氨酸二肽异构化和 DNA 碱基配对转变（Watson-Crick 到 Hoogsteen）的有效性。过渡路径的 CAR 表示构成了一个强大且可扩展的平台，可以与各种增强的采样方法相结合，以帮助未来灵活可靠的生物分子模拟。