(199h) Connecting Complex Biochemical Reaction Network Structure to Dynamical Behavior: Recent Advances in Species-Reaction Graph Theory

Connecting Complex Biochemical Reaction Network Structure to Dynamical Behavior: Recent Advances in Species-Reaction Graph Theory

Daniel Knight¹, G. Shinar³, Martin Feinberg^1,2

¹Department of Chemical and Biomolecular Engineering and the ²Department of Mathematics, Ohio State University, Columbus, Ohio
³Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel

In the analysis of biological systems, it is often preferred to be able to predict their dynamical properties from knowledge of only the reaction network, as detailed kinetic information is rarely available with confidence. Our goal is to be able to make powerful statements about what dynamic behavior a (potentially very complex) system might admit based only on the network structure, provided the kinetics falls within a very general and natural class (including those that permit product inhibition). In particular, we wish to distinguish in a precise way between networks that might provide the basis for a bistable switch, and networks – even very intricate ones – that are restricted to relatively dull, stable dynamics. The foundation for these results is the Species-Reaction, or SR graph, which is an intuitive method of displaying a reaction network, similar to classical biological network representations. Improvements have been made to recent results^1,2, drawing a stronger connection between the properties of a network’s SR graph and its capacity to exhibit interesting dynamical features, such as multiple steady states. This new theorem will be given, and a few example networks will be discussed.

1.  G. Shinar and M. Feinberg.  “Concordant Chemical Reaction Networks.” Math. Biosci. 240.2 (2012): 92-113. In print.

2.  G. Shinar and M. Feinberg.  “Concordant Chemical Reaction Networks and the Species-Reaction Graph.” Math. Biosci. 241 (2013): 1-23.  In print.