Numerical and Analytic Predictions for Correlations in Gene Expression Noise

In this chapter we develop a mathematical model for stochastic gene regulation that is motivated by previous work on noise in λ cI repressor [19]. Simulated time-series data are used to predict features of cross correlation functions and to understand the effect of active and inactive forms of regulation. We extend the simulation-based analysis by developing analytic solutions to arbitrary cross correlation functions using a linearized approximation of the mathematical model. The analytic framework lends insight into the origins of the cross correlation function shape and simplifies analysis. Two applications are demonstrated: (1) Sensitivity analysis of cross correlation function features reveals which system parameters are most significant. (2) The cross correlation function is calculated for a cascade of arbitrary length to demonstrate generality to larger scale networks. Finally we discuss some limitations of correlation-based analysis methods.