带实验约束的深度生成马尔可夫状态模型

中文摘要 AI 辅助

分子建模中的一个核心挑战是如何使模拟与实验可观测量相协调，因为力场的不准确性会扭曲平衡态布居和长时间尺度的动力学。虽然含时约束可以改善模拟动力学，但含时结构可观测量仍然有限。因此，大多数实验数据是时间平均的，它们提供平衡系综的信息，但不直接提供动力学信息。尽管系综细化可以提高热力学精度，但将时间平均可观测量纳入动力学模型仍然困难。在此，我们引入了BICePs重加权的可逆DeepMSMs，结合构象群体贝叶斯推断（BICePs）、马尔可夫过程的变分学习以及最大熵（MaxEnt）/最大通量（MaxCal）原理，以推断一致的热力学和最小扰动的动力学。其核心是一个可逆DeepMSM先验，通过对预训练的动力学模型（如VAMPnet）进行后验正交变换获得。这精确保留了特征谱，同时产生一个非负、行随机且可逆的有效转移矩阵。重加权模型细化了平稳布居、转移动力学和状态条件构象着陆密度。我们使用骨架二面角和J耦合常数，在四阱玩具系统和丙氨酸二肽上验证了该方法。在两个系统中，扰动可观测量会引起平衡系综和相应推断动力学的可预测变化。所得的弛豫时间尺度和动力学模式与分析及MaxCal参考模型高度一致。此外，基于MaxEnt着陆密度训练的扩散生成模型产生了物理上真实的丙氨酸二肽轨迹，这些轨迹再现了热力学和动力学，同时满足所施加的实验约束。

英文摘要

A central challenge in molecular modeling is reconciling simulations with experimental observables, as force-field inaccuracies can distort equilibrium populations and long-timescale kinetics. While time-dependent restraints can improve simulated kinetics, time-dependent structural observables remain limited. Thus, most experimental data are time-averaged, informing equilibrium ensembles but not directly dynamics. Although ensemble refinement can improve thermodynamic accuracy, incorporating time-averaged observables into kinetic models remains difficult. Here, we introduce BICePs-reweighted Reversible DeepMSMs, combining Bayesian Inference of Conformational Populations (BICePs), variational learning of Markov processes, and maximum entropy (MaxEnt)/maximum caliber (MaxCal) principles to infer consistent thermodynamics and minimally perturbed kinetics. At its core is a reversible DeepMSM prior, obtained by applying an orthogonal transformation post-hoc to a pre-trained dynamics model (e.g., VAMPnet). This preserves the eigenspectrum exactly while yielding a valid transition matrix that is nonnegative, row-stochastic, and reversible. The reweighted model refines stationary populations, transition dynamics, and state-conditioned configurational landing densities. We validate the approach on a quadruple-well toy system and alanine dipeptide using backbone dihedral angles and J-coupling constants. In both systems, perturbing the observables induces predictable changes in the equilibrium ensemble and corresponding inferred kinetics. The resulting relaxation timescales and dynamical modes closely agree with analytical and MaxCal reference models. Furthermore, a diffusion-based generative model trained on MaxEnt landing densities produces physically realistic alanine dipeptide trajectories that reproduce thermodynamics and kinetics while satisfying the imposed experimental restraints.

发表机构

• Temple University（天普大学）

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