Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation

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.Synopsis: Delay processes are ubiquitous in the biological sciences but are not always well-represented in mathematical models attempting to describe these biological processes. Additional issues arise when attempting to capture the uncertainty (intrinsic noise) associated with chemical kinetics in dealing with when and in what order reactions take place. Complicating the situation further are important instances when certain key molecules occur only in small numbers, so that it is not meaningful to talk about concentrations.