Abstract
We discuss effects of stochasticity and time delays in simple models of population dynamics. In social-type models, where individuals react to the information concerning the state of the population at some earlier time, sufficiently large time delays may cause oscillations. In biological-type models, where some changes already take place in the population at an earlier time, oscillations might not be present for any time delay. We illustrate this idea in models of delayed random walks, gene expression, and population dynamics of evolutionary game theory.
Highlights
Regulation of gene expression is a chemical process involving many coupled elementary chemical reactions modelled usually by systems of differential equations describing time evolution of molecular concentrations
Our results show that translational repression results in a higher noise than repression on the promoter level [2]
For small time delays the system evolves into its stationary state with damped oscillations observed in transient states
Summary
Regulation of gene expression is a chemical process involving many coupled elementary chemical reactions modelled usually by systems of differential equations describing time evolution of molecular concentrations. We will review a simple model of protein production which can be completely solved, that is one can obtain analytical expressions for the expected value and the variance of the number of protein molecules [1]. We will discuss specific models of mRNA- and protein-regulated networks. We will discuss contributions of regulatory factors to gene expression noise in four basic mechanisms of negative gene expression control: 1) transcriptional regulation by a protein repressor, 2) translational repression by a protein, 3) transcriptional repression by RNA, and 4), RNA
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