Welcome to the q-bio Summer School and Conference!

Finite State Projection Solutions to the CME Arising in Gene Regulatory Networks

From Q-bio

Brian Munsky, UC Santa Barbara

Abstract
The cell is a noisy environment in which random molecular events can dominate the dynamics of cellular constituents. This intrinsic noise can determine the outcomes of stochastic switches, result in stochastic and coherence resonance, and/or amplify signals via stochastic focusing. Given the prevalence of such fluctuations in the cell, stochastic modeling and analysis is of paramount importance for the understanding and synthesis of biological networks. Such systems are frequently modeled with jump Markov processes, whose dynamics cannot be fully described by individual trajectories. Instead, these systems are better characterized by probability distributions that evolve according to the Chapman-Kolmogorov equation often known as the Chemical Master Equation (CME). The CME is typically an infinite dimensional ordinary differential equation that has no known computationally tractable solution. In this talk we present a new approach to the solution to the CME. We show that by projecting the CME to a suitable finite dimensional subspace, we can often approximate its solution to an exceptional degree of accuracy. We present the intuition behind the underlying Finite State Projection (FSP) algorithm and demonstrate the power of the FSP approach to (1) provide approximations to the CME with strict accuracy guarantees; and (2) enable exact computations of certain important quantities such as switch rates. Finally, we illustrate the FSP approach on a stochastic model of the lambda phage switch.

Back to The First q-bio Conference.