Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Seminár z kvalitatívnej teórie diferenciálnych rovníc - Pavol Bokes (27.10.2016)

vo štvrtok 27.10.2016 o 14:00 hod. v miestnosti M/223

13. 10. 2016 13.03 hod.
Od: Pavol Quittner

Prednášajúci: Pavol Bokes (KAMŠ FMFI UK)

Názov prednášky: Using asymptotic approximations of integrals to evaluate noise in gene expression subject to negative feedback

Termín: 27.10.2016, 14:00 hod., M/223


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.

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