Seminar 27.10.2016: Pavol Bokes

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 27.10.2016: Pavol Bokes

Postby quittner » Thu Oct 13, 2016 12:42 pm

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Štvrtok 27.10.2016 o 14:00, poslucháreň M-223

Pavol Bokes (KAMŠ FMFI UK):
Using asymptotic approximations of integrals to evaluate noise
in gene expression subject to negative feedback


Abstract:
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.
quittner
 
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