Abstract
Cellular processes are “noisy”. In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry.
Highlights
Stochastic modeling of gene expression has typically relied on forward simulations of time courses, for example via Gillespie algorithms [20,21] or numerical solution of stochastic differential equations (SDEs) [4,22,23]
When using a chemical model for some aspect of cellular function, one needs to consider two sources of variability: intrinsic variability, which results from the reactions proceeding as in the model but naturally varying because of the finite number of molecules in the cells and their random behavior; and extrinsic variability, which results from other kinds of variation not accounted for in the specific, deterministic model
Our methods provide advantages in speed, accuracy, and scope of mechanisms modeled, and we apply them to experimental data, demonstrating the nature of intrinsic and extrinsic noise in those systems
Summary
Flow cytometry and fluorescence microscopy currently allow for access to increasingly rich data on approximately steady-state distributions of gene expression. These distributions arise biologically when a set of reactions proceeds much faster than environmental changes, and observing such data provides a step towards understanding some aspects of the underlying cellular network. To assess how such data can be informative, we need to compute or simulate aspects of the steady-state distribution
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