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.

20 pages, 5 figures

References in corpus (5)

• Growth-rate dependent partitioning of RNA polymerases in bacteria
• A stochastic spectral analysis of transcriptional regulatory cascades
• 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

Cited by in corpus (7)

• Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback
• Telling time with an intrinsically noisy clock
• Poisson channel with binary Markov input and average sojourn time constraint
• Kinetic foundation of the zero-inflated negative binomial model for single-cell RNA sequencing data
• Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection toward hierarchical architectures
• Dissipation in non-steady state regulatory circuits
• Exact derivation and practical application of a hybrid stochastic simulation algorithm for large gene regulatory networks