Random dynamics of gene transcription activation in single cells
The authors continue to study the qualitative behavior of the master equation for the probabilities \(P_{n,x}(t)\) that a biologically relevant cell system is at the state \(x\) the \(n\)-th time at time \(t\) (quantifying the timing and strength of gene transcription by \(P\) with \(3\) functional states \(x\)). This system describes the gene transcription activity at single cell resolution. The related random transition model was originally suggested by \textit{M. Tang} [The mean and noise of stochastic gene transcription. J. Theor. Biol. 253, 271--280 (2008)]. For their analysis, the study of the properties of the related master operator \(L\) that transforms the probabilities \(P_{n,x}(t)\) into \(P_{n+1,x}(t)\) (e.g., its mollifying property) turns out to be crucial.
scientific article; zbMATH DE number 5608028