(747d) A Path Entropy-Based Approach to Predict Transition Rates from Limited Information

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 path entropy. We maximize the entropy of the distribution over all possible paths a dynamical system can take subject to stationary and dynamical constraints. 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 ∝ (Ï€b/Ï€a)1/2, on Ï€a and Ï€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 transition probabilities among the metastable states of a small peptides as well as proteins at equilibrium.