Good and bad children in metabolic networks

Abstract

Equilibrium bifurcations arise from sign changes of Jacobian determinants, as parameters are varied. Therefore we address the Jacobian determinant for metabolic networks with general reaction kinetics. Our approach is based on the concept of Child Selections: each (mother) metabolite is mapped, injectively, to one of those (child) reactions that it drives as an input. Our analysis distinguishes reaction network Jacobians with constant sign from the bifurcation case, where that sign depends on specific reaction rates. In particular we distinguish "good" Child Selections, which do not affect the sign, from more interesting and mischievous "bad" children, which gang up towards sign changes, instability, and bifurcation.