title: Transcription, intercellular variability and correlated random walk.
abstract: We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results.
authors.affiliation: Technische Universität München, Centre for Mathematical Sciences, Boltzmannstrasse 3, 85748 Garching/Munich, Germany. johannes.mueller@mytum.de
authors.forename: Johannes
authors.initials: J
authors.lastname: Müller
authors.forename: Christina
authors.initials: C
authors.lastname: Kuttler
authors.forename: Burkhard A
authors.initials: BA
authors.lastname: Hense
authors.forename: Stefan
authors.initials: S
authors.lastname: Zeiser
authors.forename: Volkmar
authors.initials: V
authors.lastname: Liebscher