Comparison with other methods in the literature.

The row that corresponds to “admissible kinetics” asks about the functional form of the reaction rates for which the method is applicable. “Global attractor” asks whether the method is able to provide guarantees for the global convergence to an attractor. “Uniqueness with i/o perturbations” asks whether the method can guarantee uniqueness of steady states with respect to arbitrary addition of inflows and outflows to the network (i.e., “homogeneous CFSTR” in the terminology of [45]). Rows that correspond to “PTM cycle” and “Kinetic proofreading” ask whether the method can tackle the networks (9) and (15), respectively. We have picked these two networks as non-trivial examples that are pertinent to systems biology. The question of a global attractor for HJF-type networks is marked by an asterisk (*) since a proof has been proposed in a preprint [46] but is not formally published yet. (See [47] also).