Speaker
Description
We investigate the identifiability of non-autocatalytic mass-action reaction networks using dynamical observations of species concentrations and individual reaction rates. Our main objective is to determine whether these observations uniquely specify the underlying reaction network or whether different networks can produce identical data. We establish that the reactant complexes and the associated rate constants are uniquely recoverable from the available observations. Therefore, any possible non-identifiability can arise only from the product complexes of reactions that share the same reactant complex.
For each such collection of reactions, we construct an associated integer lattice. Using results from the theory of finitely generated abelian groups, we characterize all alternative networks that are observationally indistinguishable from the original network. The requirement that product stoichiometric coefficients remain nonnegative further ensures that only finitely many such alternative networks can exist.
Our characterization also demonstrates that non-identifiability is possible only when the rate constants satisfy exact arithmetic relations. These relations occur on exceptional subsets of the parameter space having Lebesgue measure zero. Consequently, for almost every choice of rate constants, the mass-action reaction network is uniquely identifiable from concentration and reaction rate data.
