Indistinguishability and identifiability of kinetic models for the Mur C reaction in peptidoglycan biosynthesis

An important question in Systems Biology is the design of experiments to allow discrimination between two (or more) competing pathway models or biological mechanisms. In chemical kinetics a common assumption when studying reactions which release several products is to assume that they are all released in one step. A structural indistinguishability analysis is performed between two different models describing the kinetic mechanism of the Mur C reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable both in the full version and under quasi-steady-state assumptions. A structural identifiability analysis is carried out for both models to ensure that the model output uniquely determines the unknown parameters. Similar analyses (indistinguishability and identifiability) are performed using other model simplifications (using conservation equations) and comparisons made with the results of the full model. The analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis.