Approximation and System Identification Techniques for Stochastic Biomolecular Systems

Abstract

Many biomolecular systems can be modeled as chemical reaction networks with a set of relevant species interacting via chemical reactions. When the molecular counts of the species are small, the inherent stochasticity in the occurrence of the reactions plays an important role in the behavior of the system. This stochasticity presents opportunities for system identification, since when a large population of cells is measured, one has many samples from the underlying distribution of the stochastic model. On the other hand, using the stochastic models of chemical reaction networks, given by continuous time Markov chains with countably infinite state spaces, creates computational and analytical difficulties when performing analysis or system identification. Therefore, approximate models that exploit timescale separation between different sets of chemical reactions to create reduced order models, or deterministic or diffusion approximations that approximate the continuous time Markov chain with an ordinary differential equation or stochastic differential equation respectively must be exploited. This thesis makes contributions in both directions, rigorously justifying such approximations as well as developing the theory to perform system identification on the approximate models.