| Abstract | Biochemical reaction network models give rise to dynamical systems that are usually high dimensional, nonlinear, and have many unknown parameters. Due to the presence of unknown parameters (such as reaction rate constants) and to the wide diversity of kinetic laws (such as mass-action, Michaelis-Menten, or Hill law) direct numerical simulation of the chemical dynamics is practically impossible. On the other hand, we will show that important properties of these systems are often determined only by the network structure, and do not depend on the unknown parameters. For example, some reaction networks may give rise to multiple positive equilibria (i.e., they may function as a "biochemical switch") while others cannot exhibit multiple equilibria for any values of the reaction rate parameters and any type of kinetics. We will point out connections between the capacity of a reaction network to function as a biochemical switch, and properties of signed graphs and digraphs that encode the combinatorics of matrix sign patterns of the associated dynamical system. This is a joint work with Murad Banaji. |
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