Autoregulatory feedback loops are one of the most common network motifs. A wide variety of
stochastic models have been constructed to understand how the fluctuations in protein …

In the mathematical modeling of biochemical reactions, a convenient standard approach is
to use ordinary differential equations (ODEs) that follow the law of mass action. However …

This paper considers the behavior of discrete and continuous mathematical models for gene
expression in the presence of transcriptional/translational bursting. We treat this problem in …

We study the response of an autoregulated gene to a range of concentrations of signal
molecules. We show that transcriptional leakage and noise due to translational bursting …

Propensity functions of the Hill type are commonly used to model transcriptional regulation
in stochastic models of gene expression. This leads to an effective reduced master equation …

In a stochastic process, noise often modifies the picture offered by the mean-field dynamics.
In particular, when there is an absorbing state, the noise erases a stable fixed point of the …

We study a stochastic model of gene expression, in which protein production has a form of
random bursts whose size distribution is arbitrary, whereas protein decay is a first-order …

Using an analytically solvable stochastic model, we study the properties of a simple genetic
circuit consisting of multiple copies of a self-regulating gene. We analyse how the variation …

Biochemical reaction networks are subjected to large fluctuations attributable to small
molecule numbers, yet underlie reliable biological functions. Thus, it is important to …

The deterministic rate equation has been considered as an approximate description of the
dynamics of the gene regulatory network, derived in the limit of vanishing stochastic …