Experimental Design for Parameter Estimation in Kinetic Models of Metabolism

In kinetic models of metabolism, the parameter values determine the dynamic behaviour predicted by these models. Estimating parameters from in vivo experimental data requires the parameters to be structurally identifiable, and the data to be informative enough to estimate these parameters. Existing methods to determine the structural identifiability of parameters in kinetic models of metabolism can only be applied to models of small metabolic networks due to their computational complexity. Additionally, a priori experimental design, a necessity to obtain informative data for parameter estimation, also does not account for using steady state data to estimate parameters in kinetic models. We present a scalable methodology to structurally identify parameters for each flux in a kinetic model of metabolism based on the availability of steady state data. We determine the number and nature of experiments for generating steady state data to estimate the enzyme kinetic parameters in a kinetic model of a small metabolic network. We show that most parameters in fluxes expressed by mechanistic enzyme kinetic rate laws (Michaelis-Menten, Monod-Wyman-Changeux and Hill kinetics) can be identified using steady state data. We also show that the requisite steady state data can be obtained from experiments involving both substrate and enzyme level perturbations. While substrate perturbation experiments are necessary for estimating parameters of uptake fluxes, enzyme level perturbation experiments may be necessary to estimate parameters of intracellular fluxes. The proposed methodology can be used in combination with other identifiability and experimental design algorithms that use dynamic data in order to determine the most informative experiments requiring the least resources to perform.