title: Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes.
abstract: 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, kab ∝ (πb/πa)(1/2), on πa and πb, 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.
authors.affiliation: Department of Systems Biology, Columbia University , New York, New York 10032, United States.
authors.forename: Purushottam D
authors.initials: PD
authors.lastname: Dixit
authors.affiliation: Institute of Physics and Freiburg Institute for Advanced Studies (FRIAS), Albert Ludwigs University , 79104 Freiburg, Germany.
authors.forename: Abhinav
authors.initials: A
authors.lastname: Jain
authors.affiliation: Institute of Physics and Freiburg Institute for Advanced Studies (FRIAS), Albert Ludwigs University , 79104 Freiburg, Germany.
authors.forename: Gerhard
authors.initials: G
authors.lastname: Stock
authors.affiliation: Laufer Center for Quantitative Biology, Department of Chemistry, and Department of Physics and Astronomy, Stony Brook University , Stony Brook, New York 11790, United States.
authors.forename: Ken A
authors.initials: KA
authors.lastname: Dill
mesh_terms: D015870:Gene Expression; D010455:Peptides / Q000737:chemistry*; D011401:Promoter Regions, Genetic / Q000502:physiology; D012333:RNA, Messenger / Q000235:genetics; D013816:Thermodynamics
chemical_list: D010455:Peptides; D012333:RNA, Messenger