Extend layered mixed matrix theory to reaction networks with conserved quantities

Extend the tools of layered mixed matrix theory to reaction networks with conserved quantities, in particular to networks whose Jacobian determinant is identically zero because of linear conservation laws, in order to obtain corresponding sensitivity results in the non-invertible setting.

Background

The paper restricts its main algebraic and sensitivity results to invertible layered mixed matrices and, correspondingly, to reaction networks whose symbolic Jacobian determinant is not identically zero. This nondegeneracy assumption excludes reaction networks with linear conserved quantities, which are common in applications.

The authors note that sensitivity results already exist in the more general setting with conserved quantities, but the layered mixed matrix tools developed in the paper are not extended to that case. Developing such an extension would broaden the applicability of the combinatorial canonical form, inverse-structure, buffering-structure, and influence-graph framework.