Apr 25, 2020

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

BioRxiv : the Preprint Server for Biology
C. CelikA. Singh

Abstract

Regulatory molecules such as transcription factors are often present at relatively small copy numbers in living cells. The copy number of a particular molecule fluctuates in time due to the random occurrence of production and degradation reactions. Here we consider a stochastic model for a self-regulating transcription factor whose lifespan (or time till degradation) follows a general distribution modelled as per a multi-dimensional phase-type process. We show that at steady state the protein copy-number distribution is the same as in a one-dimensional model with exponentially distributed lifetimes. This invariance result holds only if molecules are produced one at a time: we provide explicit counterexamples in the bursty production regime. Additionally, we consider the case of a bistable genetic switch constituted by a positively autoregulating transcription factor. The switch alternately resides in states of up- and downregulation and generates bimodal protein distributions. In the context of our invariance result, we investigate how the choice of lifetime distribution affects the rates of metastable transitions between the two modes of the distribution. The phase-type model, being non-linear and multi-dimensional whilst poss...Continue Reading

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Mentioned in this Paper

Establishment and Maintenance of Localization
Biochemical Pathway
Biological Regulation
Sensory Perception of Chemical Stimulus
Phenylphosphonothioic Acid, 2-Ethyl 2-(4-Nitrophenyl) Ester
Gene Knockdown Techniques
Genes
Caenorhabditis elegans
Diuretic hormone, mealworm
Serotonin Measurement

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