2017/11/08 by Purushottam D. Dixit, Dixit, Purushottam D., Ken A. Dill +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #FOS: Physical sciences #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Protein Structure and Dynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1711.03043
arxiv created 2017/11/08 · openalex publication_date 2017/11/08 · arxiv updated 2017/11/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Rate processes are often modeled using Markov-State Models (MSM). Suppose you know a prior MSM, and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them, while also giving the wrong overall folding rate, when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C2M2): an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory- based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.