Zero-eigenvalue bifurcations in Chemical Reaction Networks

• Applicant: Dr. Nicola Vassena
• Subject Area: Mathematics ; Bioinformatics and Theoretical Biology
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 512355535

Chemical reactions turn reactants into products. Several interconnected reactions constitute a chemical reaction network. Multistationarity and oscillations are features of great importance for chemical networks, crucially involved in epigenetic processes such as cell differentiation, in the regulation of metabolic processes and circadian rhythms, and in other important biological functions. The objective of my project is to employ bifurcation analysis to find new efficient criteria to detect multistationarity and oscillations in chemical reaction networks. More specifically, for systems of Ordinary Differential Equations arising from chemical reaction networks, I plan to rigorously establish conditions for equilibria bifurcations involving a zero-eigenvalue of the Jacobian matrix. I plan to address 1. saddle-node bifurcation (simple eigenvalue zero); 2. Takens-Bogdanov bifurcation (algebraically double eigenvalue zero). Saddle-node bifurcations point at parameter regions where multistationarity occurs, while Takens-Bogdanov bifurcations point both at parameter regions where multistationarity and oscillations occur. I will aim at necessary and sufficient network conditions that guarantee the occurrence of such bifurcation phenomena: the analysis will not be confined to any a priori given example. A posteriori, the third goal of the project is 3. applying the results to biochemically relevant networks, in a twofold manner. First, I aim for biochemically meaningful network motifs and patterns indicating possible bifurcation behavior. Second, I intend to use established kinetic models of relevant metabolic networks to explicitly simulate bifurcations.

• DFG Programme: WBP Position