Seminar 3.12.2020: Pavol Bokes

[quittner]

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

Thursday 3.12.2020 at 14:00

Pavol Bokes (KAMŠ FMFI UK):
Effects of large distributed delays on noisy genetic feedback circuits

MS-teams link:
https://teams.microsoft.com/l/meetup-jo ... 0ff7%22%7d

Abstract:
Bursty protein production is an important source of stochastic noise
in the expression of individual genes. In the first part of the talk,
we will review basic Markovian models of non-bursty and bursty gene expression.
We will emphasise that the non-bursty model admits Poissonian protein distributions,
whereas the bursty model generates super-Poissonian noise in protein level.
We will argue that extending a bursty model with a large distributed production
delay buffers the super-Poissonian protein noise down to Poissonian levels.
In the second part of the talk, the delayed bursty production model will be extended
by feedback in burst frequency and analysed with Wentzel--Kramers--Brillouin
(WKB)/large-deviation-theory (LDT) methods. An ordinary differential equation
will be formulated that captures the model's limiting deterministic behaviour;
the equation will be extended by an additional dimension into a planar Hamiltonian system
that characterises stochastically-driven transitions between deterministic equilibria.
In the presence of multiple equilibria, the protein distribution will be approximated
by a mixture of Poisson modes; the WKB/LDT analysis thereby quantifies the mixture weights.