Abstract:  In this talk we first introduce the mathematical framework of chemical reaction networks. To study steady states of a chemical reaction network one needs to study the solutions to a parameterized system of polynomial equations. Here is where we encounter Gröbner bases. It is well-known that computing Gröbner bases is usually a computationally expensive task. In this work we consider reaction networks with intermediates and with enzymes. Specifically, given a core reaction network and an extension of it, obtained by adding intermediates or enzymes, we study how the Gröbner bases of the steady state ideal of the core reaction network relate to the Gröbner bases of the steady state ideal of extended networks. We use this to find Gröbner bases of large networks from Grböner bases of simplified versions of them, thereby reducing substantially the computational cost. We finish this talk comparing the current algorithms of computing Gröbner basis with our algorithm for the ideals arising in the chemical reaction network context.

Contact: Yasemin Şengül