title: Transcriptional stochasticity in gene expression.
abstract: Due to the small number of copies of molecular species involved, such as DNA, mRNA and regulatory proteins, gene expression is a stochastic phenomenon. In eukaryotic cells, the stochastic effects primarily originate in regulation of gene activity. Transcription can be initiated by a single transcription factor binding to a specific regulatory site in the target gene. Stochasticity of transcription factor binding and dissociation is then amplified by transcription and translation, since target gene activation results in a burst of mRNA molecules, and each mRNA copy serves as a template for translating numerous protein molecules. In the present paper, we explore a mathematical approach to stochastic modeling. In this approach, the ordinary differential equations with a stochastic component for mRNA and protein levels in a single cells yield a system of first-order partial differential equations (PDEs) for two-dimensional probability density functions (pdf). We consider the following examples: Regulation of a single auto-repressing gene, and regulation of a system of two mutual repressors and of an activator-repressor system. The resulting PDEs are approximated by a system of many ordinary equations, which are then numerically solved.
authors.affiliation: Institute of Fundamental Technological Research, Swietokrzyska 21, 00-049 Warsaw, Poland. tomek@rice.edu
authors.forename: Tomasz
authors.initials: T
authors.lastname: Lipniacki
authors.forename: Pawel
authors.initials: P
authors.lastname: Paszek
authors.forename: Anna
authors.initials: A
authors.lastname: Marciniak-Czochra
authors.forename: Allan R
authors.initials: AR
authors.lastname: Brasier
authors.forename: Marek
authors.initials: M
authors.lastname: Kimmel
mesh_terms: D000818:Animals; D005057:Eukaryotic Cells / Q000502:physiology*; D015870:Gene Expression; D005786:Gene Expression Regulation; D006801:Humans; D008957:Models, Genetic; D014176:Protein Biosynthesis; D013269:Stochastic Processes; D014158:Transcription, Genetic; D015533:Transcriptional Activation