Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Seminar on Qualitative Theory of Differential Equations - Pavol Bokes (27.10.2016)

Thursday 27.10.2016 at 14:00, Lecture room M/223

13. 10. 2016 13.09 hod.
By: Pavol Quittner

Pavol Bokes:
Using asymptotic approximations of integrals to evaluate noise in gene expression subject to negative feedback

Synthesis of protein molecules in randomly-timed bursts is a major contributor to noise in the expression of individual genes. Negative feedback is a canonical example of a regulatory mechanism by which cells can control noisy gene expression. Here we consider feedback on burst frequency, which causes protein-synthesis bursts to occur less frequently whenever protein concentration exceeds a given threshold. We model protein dynamics by a simple drift-jump Markovian model, which yields an explicit formula for the steady-state protein probability density function. The density can be used, in particular, to calculate the steady-state protein moments (e.g. mean, variance) by numerical integration. In special parametric regimes, namely in the small-noise and the low-threshold regimes, one can use asymptotic approximations of integrals to evaluate these moments analytically. Combining asymptotics with numerical results helps understand the effects of negative feedback on gene-expression noise caused by protein bursting.