Biochemical reaction systems: multistationarity, persistence, and identifiability

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Biochemical reaction networks are the fundamental engines of life, giving rise to biological processes ranging from photosynthesis to digestion. The objective of this research is to analyze such networks endowed with mass-action kinetics. These dynamical systems model various biological mechanisms, and they will be studied using algebraic, geometric, and combinatorial methods. The investigator is pursuing the following aims directly related to reaction networks: (1) determining how the combinatorial geometry of a given reaction network informs the long-term dynamics of the resulting dynamical system, (2) classifying and analyzing multistationary reaction networks, and (3) parametrizing multistationarity in post-translational modification systems (important signaling motifs in biology) using techniques from real algebraic geometry such as real root counting. In a fourth research direction, the investigator is analyzing Grobner bases of certain elimination ideals with the aim of developing criteria for identifiability, which is the question of whether parameters can be uniquely recovered from data. This investigation will occur both in the context of quasi-steady-state approximations in chemical reaction systems and in the setting of graphical models in algebraic statistics. This research seeks to provide new insights about the dynamical behavior of medically relevant biochemical reaction networks. Indeed, the reaction systems studied in this research are widely used models for biomolecular activities; examples include pharmacological models of drug interaction, signal transduction models, and enzymatic mechanisms. In particular, this research will yield insight into the long-term behavior of reaction systems and provide a better understanding of multistationary networks.