Speaker: 唐晓弦副教授，北京航空航天大学

Inviter: 李伟

Title: The Smallest Multistable Zero-one Reaction Networks

Language: Chinese

Time & Venue: 2024.12.06 14:00-15:00 思源楼 515

Abstract: Zero-one reaction networks play key roles in cell signaling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a key dynamics feature enabling decision-making in cells. Since multistability can be lifted from a ``subnetwork" (a network with less species and fewer reactions) to large networks, we aim to explore the multistability problem of small zero-one networks. We prove the following main results: 1. any zero-one network with a one-dimensional stoichiometric subspace admits at most one (stable) positive steady state, and all the one-dimensional zero-one networks can be classified according to if they indeed admits a (stable) positive steady state or not; 2. any two-dimensional zero-one network with up to three species either admits only degenerate positive steady states, or admits at most one nondegenerate (stable) positive steady state; 3. the smallest (by ``smallest" we mean the network contains species as few as possible) zero-one networks that admit nondegenerate multistationarity/multistability contain three species and five/six reactions, and they are three-dimensional. In these proofs, we use the theorems based on the Brouwer degree theory and the theory of real algebraic geometry. Moreover, applying the tools of computational real algebraic geometry, we provide a systematical way for detecting the zero-one networks that admit nondegenerate multistationarity/multistability.