We show how one may analytically compute the stationary density of the
distribution of molecular constituents in populations of cells in the presence
of noise arising from either bursting transcription or translation, or noise in
degradation rates arising from low numbers of molecules. We have compared our
results with an analysis of the same model systems (either inducible or
repressible operons) in the absence of any stochastic effects, and shown the
correspondence between behaviour in the deterministic system and the stochastic
analogs. We have identified key dimensionless parameters that control the
appearance of one or two steady states in the deterministic case, or unimodal
and bimodal densities in the stochastic systems, and detailed the analytic
requirements for the occurrence of different behaviours. This approach
provides, in some situations, an alternative to computationally intensive
stochastic simulations. Our results indicate that, within the context of the
simple models we have examined, bursting and degradation noise cannot be
distinguished analytically when present alone.Comment: 14 pages, 12 figures. Conferences: "2010 Annual Meeting of The
Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010.
"First International workshop on Differential and Integral Equations with
Applications in Biology and Medicine", Aegean University, Karlovassi, Samos
island (Greece), 6-10/09/201
