### Seminar 27.10.2016: Pavol Bokes

Posted:

**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.

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.