A respiration–diffusion model for ‘Conference’ pears I: model development and validation

Abstract A respiration–diffusion model based on Fick's second law of diffusion and Michaelis–Menten kinetics, including non-competitive CO2 inhibition, was developed to predict the internal O2 and CO2 concentrations in ‘Conference’ pears. The ‘respiration-free’ diffusion and ‘diffusion-free’ respiration parameters, determined in previous independent experiments, were incorporated in the respiration–diffusion model. The system of coupled non-linear partial differential equations was solved numerically for a three-dimensional pear geometry, by means of the finite element method. When Michaelis–Menten kinetics are used to describe a process like gas exchange of fruits, which involves both gas diffusion and respiration, the Michaelis–Menten parameters were assigned a higher value than those obtained when respiration was first uncoupled from the diffusion process and then described by means of Michaelis–Menten kinetics. The maximal O2 consumption and fermentative CO2 production were diffusion-independent, but the Michaelis–Menten constants measured on cell protoplasts were considerably smaller when compared with the corresponding apparent Michaelis–Menten constants determined from respiration measurements on intact pears. The model was successfully validated for its prediction of the total pear gas exchange and the gas concentration under the skin, and is suited to simulating three-dimensional internal O2 and CO2 dioxide profiles in pears as a function of the storage atmosphere.