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bioRxiv · 10.1101/2021.04.22.440897

Protein noise and distribution in a two-stage gene-expression model extended by an mRNA inactivation loop

Celik, C.·Bokes, P.·Singh, A.
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Abstract

Chemical reaction networks involving molecular species at low copy numbers lead to stochasticity in protein levels in gene expression at the single-cell level. Mathematical modelling of this stochastic phenomenon enables us to elucidate the underlying molecular mechanisms quantitatively. Here we present a two-stage stochastic gene expression model that extends the standard model by an mRNA inactivation loop. The extended model exhibits smaller protein noise than the original two-stage model. Interestingly, the fractional reduction of noise is a non-monotonous function of protein stability, and can be substantial especially if the inactivated mRNA is stable. We complement the noise study by an extensive mathematical analysis of the joint steady-state distribution of active and inactive mRNA and protein species. We determine its generating function and derive a recursive formula for the protein distribution. The results of the analytical formula are cross-validated by kinetic Monte-Carlo simulation.

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Celik, C., Bokes, P., Singh, A.. 2021-04-22. Protein noise and distribution in a two-stage gene-expression model extended by an mRNA inactivation loop. https://doi.org/10.1101/2021.04.22.440897

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