Abstract
For quantitative understanding of probabilistic behaviors of living cells, it is essential to construct a correct mathematical description of intracellular networks interacting with complex cell environments, which has been a formidable task. Here, we present a novel model and stochastic kinetics for an intracellular network interacting with hidden cell environments, employing a complete description of cell state dynamics and its coupling to the system network. Our analysis reveals that various environmental effects on the product number fluctuation of intracellular reaction networks can be collectively characterized by Laplace transform of the time-correlation function of the product creation rate fluctuation with the Laplace variable being the product decay rate. On the basis of the latter result, we propose an efficient method for quantitative analysis of the chemical fluctuation produced by intracellular networks coupled to hidden cell environments. By applying the present approach to the gene expression network, we obtain simple analytic results for the gene expression variability and the environment-induced correlations between the expression levels of mutually noninteracting genes. The theoretical results compose a unified framework for quantitative understanding of various gene expression statistics observed across a number of different systems with a small number of adjustable parameters with clear physical meanings.
- Received 9 November 2014
DOI:https://doi.org/10.1103/PhysRevX.5.031014
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Published by the American Physical Society
Popular Summary
Live cells with the same DNA produce different numbers of protein molecules, which results in variations in the biological behaviors of a clonal population of cells. Quantitatively understanding intracellular chemical fluctuations and their impact on the probabilistic behaviors of living cells is one of the most challenging goals of modern biophysical science. To achieve the goal, it is necessary to construct a correct mathematical model of intracellular networks interacting with cell environment, which has remained a formidable task because cell environments and their coupling to the system network are too complex to be fully represented by conventional models. Here, we present a novel model and stochastic kinetics optimized for intracellular networks; we treat the cell state dynamics and their coupling to the system network in an implicit and exact manner while modeling the system network explicitly.
Taking a new theoretical approach, we discover a general principle governing the chemical fluctuations produced by intracellular networks. On the basis of our results, we propose an efficient method for quantitatively analyzing intracellular chemical fluctuations. By applying our approach to the gene expression network, we obtain simple analytic results for the gene expression level variation among a clonal population of cells. Our results provide excellent quantitative explanations of the various gene expression statistics observed across a number of different gene expression systems in E. coli and S. cerevisiae in a unified manner.
Our results present a new paradigm for a quantitative understanding of intracellular chemical fluctuations.