Academic Commons

Articles

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

Mugler, Andrew; Walczak, Aleksandra M.; Wiggins, Chris H.

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.

Files

Also Published In

Title
Physical Review E
DOI
https://doi.org/10.1103/PhysRevE.80.041921

More About This Work

Academic Units
Applied Physics and Applied Mathematics
Publisher
American Physical Society
Published Here
September 19, 2014
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.