Identifiability and distinguishability of first-order reaction systems

By following the kinetics of a reaction through the use of certain classes of measurable quantities instead of the concentrations of all species, neither the parameter values nor the reaction scheme is necessarily unique. Identifiability deals with the problem of determining whether an experiment is able to supply the desired information on the parameters of an assumed kinetic model, whereas indistinguishability means that two different reaction schemes generate the same values for the observed quantities in any possible experiment. This paper examines these issues for the case of first-order reaction systems, and both problems are solved by the same analytical tools. The method involving Laplace transforms is conceptually simple, is easy to apply, and is also used to derive simple rules to test distinguishability of reaction schemes. Another approach based on similarity transformations is used to generate all the first-order reaction schemes that are indistinguishable from a given one.