Inferring Transition Rates from Stationary Distributions within Complex Networks

I will introduce an approach for estimating the transition rates between discrete states of a stationary Markov process. In general, when given the birth and death rates of a process, one can obtain its stationary distribution. In the “inverse problem”, we aim to reconstructing biochemical rates from observed stationary data. The method is general, and can be applied to other processes as well. For a given reaction network, our method allows us to extract the reactions rates between system components only from a “snapshot” of the concentration of the relevant species. This approach has three key features; First, we use for the birth-rate inference only the stationary PDF, without any dynamical information. Second, the production rate of a given molecule might depend on the number of other molecules in the system. Third, the structure/topology of the entire reaction network may remain arbitrary, thus the only specified part of the network is for the relevant species. We examine the validity of the approach for different properties of the systems.