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Tutorial: Challenges in the study of algebraic models of biochemical reaction networks

Banff International Research Station for Mathematical Innovation and Discovery

In the context of (bio)chemical reaction networks, the dynamics of the concentrations of the chemical species over time are often modelled by a system of parameter-dependent ordinary differential equations, which are typically polynomial or described by rational functions. The polynomial structure of the system allows the use of techniques from algebra (e.g., real algebraic geometry) to study properties of the system around steady states, for all parameter values. In this talk I will start by presenting the formalism of the theory of reaction networks. Afterwards I will outline the qualitative questions one would like to address, which include deciding upon the existence of multiple equilibrium points or periodic orbits, and their stability. If time permits, I will discuss selected methods with emphasis on their limitations.

Mathematics; Mathematical logic and foundations; Algebraic geometry

video/mp4

Author affiliation: University of Copenhagen

2020-11-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76614

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/