RU Seminar - 07.07.21 Peter Sollich "Coarse-graining biology: subnetwork dynamics in protein interaction and gene regulation networks"

 

Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase in size and complexity, detailed dynamical models become cumbersome, making them difficult to explore and decipher. This necessitates the application of simplifying coarse-graining techniques in order to derive explanatory insight.

In this talk I will review our work on using projection methods to reduce the dimensionality of dynamical networks by focussing on a subnetwork. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. It turns out that memory functions can be calculated systematically for such situations; I will describe methods that initially capture the near-steady state dynamics of binary reaction networks that can model protein interactions, progressing to strongly nonlinear gene regulation dynamics and finally to memory functions that are nonlinear themselves. Examples from developmental biology will be used to illustrate how memory functions can identify qualitative features that cannot easily be detected by e.g. direct simulation of the overall network.

To get the invitation link for the videoconference, please contact: simone.ortolf@physik.uni-freiburg.de