Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks

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. Author Summary: Variability from one cell to another is a pronounced and universal trend in living organisms; much of this variability is related to varying concentrations of proteins and other chemical species across the cells. Understanding this variability is necessary if we are to fully understand cellular functions, particularly the ways in which cells differ from each other and in which cells with the same origin behave in different ways (e.g. in human development and cancer). 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. We present new methods to model and compute both kinds of variability, to facilitate the study of cellular variability as a whole. 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.