Inheritance of behaviours in bio/chemical networks

Murad Banaji, Middlesex University, London. Part of the Leeds applied nonlinear dynamics seminar series.

Understanding the possible behaviours of systems of chemical reactions is at the heart of systems biology. Chemical reaction network (CRN) theory focusses on what can be said about CRNs based on knowledge of the reaction network structure, but without precise data about rates of reaction. Results can be negative: certain behaviours are ruled out for certain reaction networks; or positive: certain behaviours must occur in reaction networks with certain structure.

Within this general theme, a frequent, but imprecise, question is the following. Can the presence of certain "motifs" or "subnetworks" in a CRN be sensibly used to make predictions about dynamical behaviours of the network? The answer turns out to depend on the class of networks studied, the dynamical behaviour of interest and, crucially, the chosen notion of "motif" or "subnetwork". My talk will focus on some recent results where the behaviours in question are multistationarity and oscillation. Network modifications such as adding or deleting reactions, adding or deleting species from reactions, and inserting intermediates into a reaction are considered for their effects on multistationarity and oscillation.  For example, it can be shown that both behaviours are inherited in the induced subnetwork partial ordering on fully open CRNs, but the same does not hold for general CRNs. Under certain mild assumptions, growing a CRN by inserting intermediates into reactions preserves the capacity for multistationarity in a CRN. The theorems are proved using essentially local techniques -- the implicit function theorem and regular and singular perturbation theory -- and hold for various kinetics including (but not exclusively) mass action kinetics.

(The results on multisationarity are joint with Casian Pantea.)