Abstract

A central dilemma in studying reaction networks that arise is molecular system biology is that the ‘quantitative’ or ‘parametric’ description of the network is scarce and uncertain compared to the widely available ‘qualitative’ or ‘graphical’ description. Hence, a central problem in this realm is the extraction of information regarding the asymptotic behaviour of the network from the graphical description solely.

This talk presents a new approach that uncovers a new class of networks that can be analysed from the graphical information only. Using intuitions from the graphical representation of the network, the talk introduces the class of ‘piecewise linear in rates’ Lyapunov functions and the associated class of ‘graphically stable networks’. Several algorithms for the construction of such functions will be given.

The ‘robust’ stability properties of the new class will be discussed. In addition, it will be shown that the proposed approach has strong implications and connections to linear differential inclusions, ‘robust’ uniqueness of equilibria, contraction analysis, and ‘structural’ persistence. Finally, the talk presents the application of the results to several important biochemical examples.