Stochastic approximation for regulating circadian cycles, a precision medicine viewpoint

Circadian cycles and other self-regulatory biological processes are the result of complex interactions between gene expression and molecular interactions. In this paper we study a Petri net model of the circadian clock and use gradient estimation methods for finding optimal input rates.The significance of our research is the potential early identification of pathologies caused by aberrant cycles, and the discovery of those rates that are of main importance for the control of the cycles, enabling specific cures for people, in accordance with personalized (or precision) medicine. We use SPSA to drive the simulation to the optimal rates that result in a desired period, then propose a surrogate model for gradient estimation that evaluates the exact gradient for an “aggregate” system described by ODEs. Our hybrid model for gradient estimation addresses the high-dimensionality problem and can potentially increase the efficiency of the optimization method by at least one order of magnitude.