Making High-Dimensional Molecular Distribution Functions Tractable through Belief Propagation on Factor Graphs

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with five and nine residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Second, we directly use the belief propagation-based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.

Automated summary

This study utilizes tools from probabilistic graphical modeling to develop a factor graph trained through belief propagation, which helps factorize high-dimensional molecular dynamics simulation data into a more manageable form. Through analysis of peptide conformational dynamics and validation through intervention schemes, the study demonstrates the potential for enhanced sampling by using approximate probability distributions as static bias. This work introduces a useful approach for dealing with high-dimensional molecular simulations.