Reducing a model of sugar metabolism in peach to catch different patterns among genotypes

Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. (2018) to simulate the accumulation of different sugars during peach fruit development. Two major drawbacks of this model are (a) the number of parameters to calibrate and (b) its integration time that can be long due to non-linearity and time-dependent input functions. Together, these issues hamper the use of the model for a large panel of genotypes, for which few data are available. In this paper, we present a model reduction scheme that explicitly addresses the specificity of genetic studies in that: (i) it yields a reduced model that is adapted to the whole expected genetic diversity (ii) it maintains network structure and variable identity, in order to facilitate biological interpretation. The proposed approach is based on the combination and the systematic evaluation of different reduction methods. Thus, we combined multivariate sensitivity analysis, structural simplification and timescale-based approaches to simplify the number and the structure of ordinary differential equations of the model. The original and reduced models were compared based on three criteria, namely the corrected Aikake Information Criterion (AIC_C), the calibration time and the expected error of the reduced model over a progeny of virtual genotypes. The resulting reduced model not only reproduces the predictions of the original one but presents many advantages including a reduced number of parameters to be estimated and shorter calibration time, opening new promising perspectives for genetic studies and virtual breeding. The validity of the reduced model was further evaluated by calibration on 30 additional genotypes of an inter-specific peach progeny for which few data were available.