Algebraic tools for chemical reaction network theory

Chemical reaction network theory gives us powerful tools for rigorously understanding chemical reactions. We use these tools to draw conclusions from the mathematical representations of chemical reactions. A frequent issue with mathematical analyses of these systems is the reliance on rates and quantities that cannot be determined experimentally. This can make analysing a chemical reaction network infeasible, depending on its size. One approach towards solving this issue is to work on a subnetwork of the chemical system, analyze the subnetwork, and then lift our conclusions to the broader network of interest.

Gröbner bases, a tool from the mathematical discipline Abstract Algebra, have been successfully employed to obtain useful information about chemical reaction networks. This thesis makes three original contributions in this direction. The first is to give a class of networks for which Göbner basis computations of subnetworks can be used to reconstruct the more expensive Göbner basis computation of the whole network. The second is the computer visualization, including publicly usable software code, of how a network is separated into subnetworks and then reconstructed back. The third is determining when there can be more than one eventual equilibrium for the chemical reaction network, applied to a mathematical model of some core microbial and biochemical interactions in the human gut, adapted from [1].