Tutorial: Stochastic Gene Expression in Systems Biology

By Brian Munsky (Los Alamos National Laboratory) and Mustafa H. Khammash (University of California, Santa Barbara).

Abstract

Random motion of genetic particles imbues the cellular environment with intrinsic noise that frequently causes cell to cell variability and even significant phenotypic differences within a clonal cell population. In some instances, fluctuations are suppressed downstream through intricate dynamical networks that act as noise filters. Yet in other important instances, noise induced fluctuations are exploited to the cell's advantage. Researchers are just now beginning to understand that the richness of stochastic phenomena in biology depends directly upon the interactions of dynamics and noise and upon the mechanisms through which these interactions occur.

Tutorial Description: In this tutorial we review a number of approaches for the analysis of stochastic fluctuations in gene expression. We will discuss the intuition underlying various analytical and computational methods for the analysis of stochasticity in living cells and explore examples of gene regulatory networks that suppress or exploit noise.

Specific topics include: Introduction to stochastic gene expression; Deterministic vs. stochastic models; The stochastic chemical kinetics framework; A derivation of the chemical master equation. Linear vs. nonlinear propensities; Monte Carlo simulations; Gillespie's Stochastic Simulation Algorithm; Variants of the SSA; Direct methods for the solution of the Chemical Master Equation; Finite State Projections; Moment computations; Linear noise approximations; Moment Closure methods. Propagation of noise in cell networks: Noise suppression in cells; The role of feedback; How cells exploit noise; Noise focusing; Coherence resonance; Bimodality and stochastic switches.

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