Title: A Database of Dynamic Signatures for Switching
Speaker: Konstantin Mischaikow
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html
Abstract: Three fundamental problems in systems biology are:
(i) identification of models, (ii) understanding the dynamics of
models as a function of parameters, and (iii) synthetic design of
regulatory systems. Common to these problems is the challenge
that arises from the fact the details of the individual
biochemical reactions is poorly understood. Our understanding of
particular systems or components thereof is often based on
statistical analysis of high throughput experiments as opposed to
first principle chemical or physical analysis. Thus the
mathematical challenge that we are faced with is that of
rigorously analyzing and characterizing the dynamics of a
nonlinear system for which the variables themselves and the
interactions between the variables (let alone the rates of
reactions) are not known with certainty.
In this talk we will describe a new approach to the analysis of
regulatory systems. Under the assumption that the regulatory
control acts as an instantaneous switch we will describe a
mathematically rigorous computational pipeline from regulatory
network to what we call a Database of Dynamic Signatures. This
involves an explicit partition of the entire parameter space into
polytopes, based on relative (not absolute) values of parameter,
and a finite combinatorial/algebraic topological description of
the global dynamics dynamics that is valid over each polytope.
