Identification of Markov Chains From Distributional Measurements and Applications to Systems Biology

Abstract

In this paper, we are concerned with doing system identification for biological systems using time series distributional measurements and Markov chain models. By distributional measurements, we mean measurements provided by assays such as flow cytometry or FISH (fluorescence in situ hybridization) that allow us to make the same single cell measurements over a number of different cells. We focus here on the problem of estimating the transition probabilities of a Markov chain from distributional measurements. We set this problem up using Bayes' rule and make simplifying assumptions to reduce the problem to a non-convex optimization problem over finitely many variables. We propose methods for locally solving this non-convex optimization problem. For a special case, we discuss necessary and sufficient conditions for the Markov chain to be identifiable. Finally, we demonstrate our procedure on instructive toy examples as well as on simulated stochastic data for a genetic toggle switch. [Gardner et al. (2000)].