Abstract
Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.
Highlights
The mathematical modelling and simulation of genetic regulatory networks can provide insights into the complicated biological and chemical processes associated with genetic regulation
Xðt þ sÞ 1⁄4 XðtÞ þ vk t1⁄4tþs else if j is not a delayed reaction else record time; tþhþs; for delayed reaction j t1⁄4tþh end Parameter Exploration and Model Comparison we present a selection of delay differential equations (DDE) solutions and delay stochastic simulation algorithm (DSSA) trajectories displaying the dynamical properties of model 1
As for the DSSA, what we present are single simulations of just one particular strong solution based on a particular path generated by the random variables
Summary
The mathematical modelling and simulation of genetic regulatory networks can provide insights into the complicated biological and chemical processes associated with genetic regulation. An important aspect associated with genetic regulation is that mRNA and protein expression levels can be quite low, and so continuous models, as described by ordinary differential equations, may be inappropriate. Processes such as transcription and translation do not occur instantaneously and may have considerable delays associated with them.
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