Changbo Chen: Geometrically Analyzing the Equilibria of Parametric Biochemical Networks Admitting Linear Conservation Laws

In a recent work, we introduced an efficient geometric method, called GeoBlock, for analyzing the equilibria of bi-parametric biological systems by exploiting the block structure. This approach requires that the system defining the equilibria is square and is zero-dimensional for generically chosen parameters. In this paper, by introducing a bipartite graph to describe the correlations between variables and constraints, we show how to adapt GeoBlock to efficiently handle biochemical networks admitting linear conservation laws. The experiments show that the presented geometric approach is a good complementary to the existing algebraic elimination method or the grid sampling approach for solving such systems.