Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically improves the time scale separation of the slowest processes. Additionally, constraining the forward and backward rates between metastable states leads to slight improvement of their relative stabilities and, thus, refined equilibrium properties of the resulting model. Finally, we find that difficulties in simultaneously describing both the simulated data and the provided constraints can help identify specific limitations of the underlying simulation approach.
The Journal of Chemical Physics (JCP) article collection on Markov Models of Molecular Kinetics (MMMK) features recent advances developing and using Markov State Models (MSMs) in atomistic molecular simulations and related applications. This editorial provides a brief overview of the state of the art in the field and relates it to the articles in this JCP collection.
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular simulations. The characterization of kinetic properties, such as diffusion coefficients, of molecular systems with significantly high energy barriers, on the other hand, has received less attention. Among others, Markov state models, in which the long-time statistical dynamics of a system is approximated by a Markov chain on a discrete partition of configuration sp…
The weighted ensemble (WE) simulation strategy provides unbiased sampling of non-equilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady state behavior. Unfortunately, WE simulations of sufficiently complex systems will not relax to steady state on observed simulation times. Here we show that a post-simulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community, can yield unbiased kinetics from WE data before steady-state convergence of the WE simulati…
A novel approach to simulate simple protein-ligand systems at large time- and length-scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes; is limited to isotropic ligands in a single conformational state, and is lacking a multi-particle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parametrize th…
MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
分子动力学（MD）模拟可以模拟大分子之间的相互作用，具有高时空分辨率，但在一个高的计算成本。通过将高通量MD与马尔可夫状态模型（MSM）相结合，现在可以获得小到中等生物分子和复合物的长时间尺度行为。为了模拟大尺度下许多分子的相互作用，基于粒子的反应扩散（RD）模拟更合适，但缺乏分子细节。因此，耦合MSM和RD模拟（MSM/RD）将是非常可取的，因为它们可以有效地产生模拟在大的时间和长度尺度，同时仍然保存在原子细节观察到的相互作用的特征。虽然这样的耦合看起来很简单，但基本问题仍然是开放的：MSM状态的定义是合适的？在缔合/解离反应中，哪种合并和分裂RD粒子的方案将保持正确的双分子动力学和热力学？在本文中，我们向MSM/RD迈出了第一步，通过布局耦合的一般理论，并提出了第一个实施的关联/解离的蛋白质与一个小的配体（A + B <-->C）。应用玩具模型和CO扩散到血红素腔肌红蛋白的报告。
Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typi…
How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability. Here, we present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. We apply our method to polymer systems, to determine (i) the first…
The process of RNA base fraying (i.e. the transient opening of the termini of a helix) is involved in many aspects of RNA dynamics. We here use molecular dynamics simulations and Markov state models to characterize the kinetics of RNA fraying and its sequence and direction dependence. In particular, we first introduce a method for determining biomolecular dynamics employing core-set Markov state models constructed using an advanced clustering technique. The method is validated on previously reported simulations. We then use the method to analyze extensive trajectories for four different RNA mo…
Markov State Models (MSM) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations, for example produced by enhanced sampling techniques, is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the stat…
