Parameter identifiability in parallel reaction networks with application to single-walled carbon nanotubes

The class of parameter estimation problems is characterized for which only the ratio of the model parameters can be identified. A mathematical signature is provided for identifying such systems, which include fed-batch reactors commonly operated in the chemical and biotechnology industries, in which reaction networks operate under quasi-steady-state conditions due to limiting addition of a reagent. The theoretical results are demonstrated through application to a single-walled carbon nanotube (SWNT) reaction network relevant to the design of nanobiosensors. Sensitivity analysis implies that such a quasi-steady-state operation of a fed-batch reactor results in the loss of information, in which none of the model parameters can be estimated.