Multistationarity and Hopf-bifurcations in families of ODE models of N-site phosphorylation

• Applicant: Professor Dr.-Ing. Carsten Conradi
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 517274113

Phosphorylation is a biochemical mechanism underlying important biological processes. Biochemically a protein is altered by adding (or removing) a phosphate group at a designated binding site. Proteins often have more than one binding site. If spatial effects may be neglected, these models come in the form of systems of Ordinary Differential Equations with polynomial right-hand side. Mathematically one can distinguish three families of models parameterized by N, the number of binding sites. Measuring individual concentration variables is prohibitively expensive and technically challenging. Hence parameter values can only be given with large error bounds, if at all. In studying phosphorylation networks therefore, the following mathematical question arises naturally: are there (positive) parameter values, such that the ODEs admit a solution with property xyz - for some or all (positive) initial conditions. Here we will focus on the following three properties (i) uniqueness of steady states, (ii) existence of multiple steady states and (iii) existence of Hopf bifurcations. These are mathematically interesting and challenging and, at the same time, of interest in systems biology and medicine. In essence, we propose to establish (i), (ii) or (iii) in three families of ODEs with polynomial right-hand side and unknown but positive parameters and initial conditions.

• DFG Programme: Research Grants