title: Stochastic gene expression with delay.
abstract: The expression of genes usually follows a two-step procedure. First, a gene (encoded in the genome) is transcribed resulting in a strand of (messenger) RNA. Afterwards, the RNA is translated into protein. We extend the classical stochastic jump model by adding delays (with arbitrary distributions) to transcription and translation. Already in the classical model, production of RNA and protein comes in bursts by activation and deactivation of the gene, resulting in a large variance of the number of RNA and proteins in equilibrium. We derive precise formulas for this second-order structure with the model including delay in equilibrium.
authors.affiliation: University Medical Center Freiburg, Institute of Clinical Chemistry and Laboratory Medicine, Hugstetter Straße 55, 79106 Freiburg, Germany. Electronic address: martin.jansen@uniklinik-freiburg.de.
authors.forename: Martin
authors.initials: M
authors.lastname: Jansen
authors.affiliation: University of Freiburg, Abteilung für Mathematische Stochastik, Eckerstr. 1, 79104 Freiburg, Germany. Electronic address: p.p@stochastik.uni-freiburg.de.
authors.forename: Peter
authors.initials: P
authors.lastname: Pfaffelhuber
mesh_terms: D000818:Animals; D001419:Bacteria; D001665:Binding Sites; D003198:Computer Simulation; D020869:Gene Expression Profiling; D005786:Gene Expression Regulation; D008390:Markov Chains; D008957:Models, Genetic; D009991:Oscillometry; D016012:Poisson Distribution; D014176:Protein Biosynthesis; D011506:Proteins / Q000737:chemistry; D012313:RNA / Q000737:chemistry; D013269:Stochastic Processes; D014158:Transcription, Genetic
chemical_list: D011506:Proteins; D012313:RNA
keywords: Chemical reaction network; Poisson process