Biologists are often interested in how small subnetworks ("motifs") might influence the dynamical behaviors of larger networks in which they are embedded. For chemical reaction networks (CRNs) we can sometimes pose such questions precisely, and answer them. We can, for example, often guarantee that a mass action CRN admits some interesting behavior, such as multiple nondegenerate equilibria or stable oscillation, by finding appropriate smaller subnetworks with this behavior. These smaller networks may be obtained from the larger one by deleting reactions and/or species, or via more complex operations such as collapsing multiple reactions into a single step. Such results often rely on perturbation theory; roughly, we show that the dynamics of the full network reduces to that of the subnetwork in a suitable (often singular) limit. I'll list some results in this direction, give some examples of their application, and hint at the proofs.
Which enlargements of a reaction network preserve its capacity for nontrivial behaviors?
2022. 03. 01. 16:00
Murad Banaji (Middlesex University London)