Parameter inference to motivate asymptotic model reduction: An analysis of the gibberellin biosynthesis pathway

We focus on the particular example of biosynthesis of the plant hormone gibberellin (GA), which controls plant growth and has been mutated in many current crop varieties. This pathway comprises two parallel series of enzyme-substrate reactions, which have previously been modelled using the law of mass action (Middleton et al., 2012). Considering the GA20ox-mediated steps, we analyse the identifiability of the model parameters using published experimental data; the analysis reveals the ratio between enzyme and GA levels to be small and motivates us to perform a quasi-steady state analysis to derive a reduced model. Fitting the parameters in the reduced model reveals additional features of the pathway and motivates further asymptotic analysis which produces a hierarchy of reduced models. Calculating the Akaike information criterion and parameter confidence intervals enables us to select a parsimonious model with identifiable parameters. As well as demonstrating the benefits of combining parameter estimation and asymptotic analysis, the analysis shows how GA biosynthesis is limited by the final GA20ox-mediated steps in the pathway and generates a simple mathematical description of this part of the GA biosynthesis pathway.