Abstract
We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.
Highlights
Gene circuits are sets of interacting genes and proteins
The results presented in this paper indicate that stochastic effects due to small gene copy numbers play an important role in the dynamics of oscillatory gene networks
Many of these networks are described by models whose behavior is ‘‘excitable.’’ That is, in the absence of stochastic fluctuations, the model may predict timeindependent steady state concentrations of messenger RNAs (mRNAs) and the associated proteins
Summary
Gene circuits are sets of interacting genes and proteins (and perhaps other biological molecules). These stochastic fluctuations may explain some aspects of phenotype behavior: how differentiated cells emerge from cells with identical genetic makeup and identical environments, many other so-called epigenetic effects such as DNA methylation, histone modification, and small interfering RNAs play a role in differentiation and inheritance of differentiated characteristics [7,8,9] These fluctuations, always present when gene copy numbers and the numbers of resulting messenger RNAs (mRNAs) and proteins are small, must be taken into account to understand the dynamics of genetic oscillators such as circadian clock networks. We focus on the dynamics of gene circuits
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