Eugenia Franco: Characterizing the detailed balance property by means of measurements in chemical networks.

Speaker

Eugenia Franco, University of Bonn



Abstract

In this talk I will present a formalism that allows to describe the interactions between different parts of a biochemical system using renewal equations. To formulate a model of a biochemical network using this formalism, only the knowledge of the kernel (or response function) characterizing the renewal equation is needed. We consider then a biochemical network that interacts with the rest of the network exchanging only two substances i and j. The response functions in
this case will be R_{ij}(t) and R_{ji}(t), where the function Rij(t)  is the concentration of the substance j at time t, after the injection of a substance i at time t=0.  We study how to determine if this system satisfies the detailed balance condition using the response functions R_{ij}(t) and R_{ji}(t), without a detailed knowledge of all the reactions taking place in the network. In particular, we obtain a condition involving Rij(t) and Rji(t) that is necessary, but not sufficient for the detailed balance condition to hold in the network. Moreover, we prove that this necessary condition is also sufficient if a topological condition is satisfied, as well as a stability property that guarantees that the chemical rates are not fine-tuned.