Coupling kinetic models and advection–diffusion equations. 2. Sensitivity analysis of an advection–diffusion–reaction model

Abstract

Abstract The accompanying paper (Uys et al., in silico Plants, 2021: diab013) presented a core model of sucrose accumulation within the advection–diffusion–reaction framework, which is able to capture the spatio-temporal evolution of the system from a set of initial conditions. This paper presents a sensitivity analysis of this model. Because this is a non-steady-state model based on partial differential equations, we performed the sensitivity analysis using two approaches from engineering. The Morris method is based on a one-at-a-time design, perturbing parameters individually and calculating the influence on model output in terms of elementary effects. Fourier amplitude sensitivity test (FAST) is a global sensitivity analysis method, where all parameters are perturbed simultaneously, oscillating at different frequencies, enabling the calculation of the contribution of each parameter through Fourier analysis. Overall, both methods gave similar results. Perturbations in reactions tended to have a large influence on their own rate, as well as on directly connected metabolites. Sensitivities varied both with the time of the simulation and the position along the sugarcane stalk. Our results suggest that vacuolar sucrose concentrations are most sensitive to vacuolar invertase in the centre of the stalk, but that phloem unloading and vacuolar sucrose uptake also contribute, especially towards the stalk edges. Sucrose in the phloem was most sensitive to phloem loading at the nodes, but most sensitive to phloem unloading in the middle of the internodes. Sink concentrations of sucrose in the symplast were most sensitive to phloem unloading in the middle of the internodes, but at the nodes cytosolic invertase had the greatest effect.