Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes

• Published in: Journal of chemical theory and computation Vol. 11; no. 11; pp. 5464 - 5472
• Main Authors: Dixit, Purushottam D, Jain, Abhinav, Stock, Gerhard, Dill, Ken A
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 10-11-2015
• Subjects: Entropy; Gene Expression; Markov processes; Mathematical analysis; Metastable state; Networks; Peptides - chemistry; Populations; Promoter Regions, Genetic - physiology; RNA, Messenger - genetics; Thermodynamics; Transportation networks
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.5b00537

We are interested inferring rate processes on networks. In particular, given a network’s topology, the stationary populations on its nodes, and a few global dynamical observables, can we infer all the transition rates between nodes? We draw inferences using the principle of maximum caliber (maximum path entropy). We have previously derived results for discrete-time Markov processes. Here, we treat continuous-time processes, such as dynamics among metastable states of proteins. The present work leads to a particularly important analytical result: namely, that when the network is constrained only by a mean jump rate, the rate matrix is given by a square-root dependence of the rate, k ab ∝ (π b /π a )1/2, on π a and π b , the stationary-state populations at nodes a and b. This leads to a fast way to estimate all of the microscopic rates in the system. As an illustration, we show that the method accurately predicts the nonequilibrium transition rates in an in silico gene expression network and transition probabilities among the metastable states of a small peptide at equilibrium. We note also that the method makes sensible predictions for so-called extra-thermodynamic relationships, such as those of Bronsted, Hammond, and others.