Linearity relations for nonzero-deficiency reaction networks

Develop other forms of linearity for chemical reaction networks with nonzero deficiency.

Background

The paper proves mutual linearity of stationary complex activities for mass-action chemical reaction networks with zero deficiency and a single linkage class when one non-bridge reaction is controlled. The resulting coefficients are independent of the controlled rate constants, conservation laws, initial state, and complex stoichiometry.

The authors note that the established relation can fail when the deficiency is nonzero, as illustrated by a network in which replacing one complex increases the deficiency to one. They leave unresolved whether alternative forms of linearity may nevertheless exist for nonzero-deficiency networks.