Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models

Abstract

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are also used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of Adenylate Kinase.

Quantifying Multiscale Noise Sources in Single-Molecule Time Series

“…The differences in dynamical responses can also be attributed in part to “unresolved orthogonal coordinates”. , For example, it is known that the number of hydrogen bonds in the molecule correlates heavily with its mechanical strength. ,, Other possible “unresolved orthogonal coordinates” can be related to collective conformational degrees of freedom. For example, collective motions associated with allosteric motion are known to modulate the dynamical response of simple low-dimensional models. , These types of collective coordinates are typically associated with relatively slow time scales. Explicitly including a deterministic memory kernel in a scalar model, as in the spirit of the generalized Langevin equation, may not be able capture the effects of these unresolved collective coordinates.…”

“…The root-mean-square displacement (rmsd) partially characterizes the conformational state of the protein. This type of quantity is not usually accessible in dynamic SM experiments, but the rmsd variability can heavily influence the distribution of an end-to-end coordinate and cause heavily skewed histograms of the latter. ,,− Furthermore, unobservable conformational transitions can occur on time scales which are fairly slow relative to the experiment. These considerations substantially complicate using a single low-dimensional model to approximate the stochastic dynamics of the entire population of SM experiments.…”

Estimating Error in Diffusion Coefficients Derived from Molecular Dynamics Simulations

“…The problem of estimating the diffusion coefficients is non-trivial for systems with slowly evolving conformational degrees of freedom and research to address these issues are being reported in the literature 9,10 . In fact, it may not even be appropriate to represent the dynamics with a single estimate of the diffusion depending on the system under study.…”

Quantifying Transient 3D Dynamical Phenomena of Single mRNA Particles in Live Yeast Cell Measurements

“…The unresolved latent features often induce substantial “heterogeneity” in the dynamics 7,10,16,48,49 . No pair of trajectories are exactly alike, but researchers in biophysics and cell biology are interested in accurately quantifying / understanding this heterogeneity 7,10 .…”