(190c) Analysis of Complex Biochemical Reaction Network Behavior: Recent Advances in Species-Reaction Graph Theory

Analysis of Complex Biochemical Reaction Network 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
³Javelin Medical Ltd., 4 Pekeris St., Rehovot 76702, Israel

When studying biological systems, predicting their dynamical properties is more readily inferred from knowledge of only the reaction network, as detailed kinetic information is often not 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.  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 cannot.  The foundation for these results is the Species-Reaction, or SR graph, which is an intuitive method of displaying a reaction network not dissimilar from 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.

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