Parameter estimation for models of chemical reaction networks from experimental data of reaction rates

For the purpose of precise mathematical modelling of chemical reaction networks, useful techniques for estimating their parameters from experimental data are necessary. In this manuscript, we propose a new parameter estimation method for enzymatic chemical reaction networks from time-series experimental data of reaction rates. The main idea is based on retrieving time-series data of the species' concentrations from the available experimental data of reaction rates by making use of parametric Bézier curves. The least-squares method is applied to these retrieved data in order to determine the best-fitting values of the parameters in the corresponding mathematical model. Subsequently, we demonstrate the applicability of our parameter estimation method on three examples of enzymatic chemical reaction networks, including a model of ryanodine receptor adaptation and a model of protein kinase cascades. We also address the issue of identifiability of chemical reaction network models from reaction rates.