Spectral solutions to stochastic models of gene expression with bursts and regulation

Abstract

Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches which then require estimating the distributions from many samples. Here we present in detail an alternative method for directly calculating a probability distribution by expanding in the natural eigenfunctions of the governing equation, which is linear. We apply the resulting spectral method to three general models of stochastic gene expression: a single gene with multiple expression states (often used as a model of bursting in the limit of two states), a gene regulatory cascade, and a combined model of bursting and regulation. In all cases we find either analytic results or numerical prescriptions that greatly outperform simulations in efficiency and accuracy. In the last case, we show that bimodal response in the limit of slow switching is not only possible but optimal in terms of information transmission.

arXiv comment20 pages, 5 figures

References in corpus (12)

• Information flow and optimization in transcriptional control
• Growth-rate dependent partitioning of RNA polymerases in bacteria
• Mutual information between in- and output trajectories of biochemical networks
• Signal detection, modularity and the correlation between extrinsic and intrinsic noise in biochemical networks
• Optimal signal processing in small stochastic biochemical networks
• Information capacity of genetic regulatory elements
• Self consistent proteomic field theory of stochastic gene switches
• A stochastic spectral analysis of transcriptional regulatory cascades
• DNA looping provides stability and robustness to the bacteriophage lambda switch
• A variational approach to the stochastic aspects of cellular signal transduction
• The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade
• Quantifying evolvability in small biological networks

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• Extending the dynamic range of transcription factor action by translational regulation
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