A Continuum Model for Metabolic Gas Exchange in Pear Fruit

Abstract

Exchange of O₂ and CO₂ of plants with their environment is essential for metabolic processes such as photosynthesis and respiration. In some fruits such as pears, which are typically stored under a controlled atmosphere with reduced O₂ and increased CO₂ levels to extend their commercial storage life, anoxia may occur, eventually leading to physiological disorders. In this manuscript we have developed a mathematical model to predict the internal gas concentrations, including permeation, diffusion, and respiration and fermentation kinetics. Pear fruit has been selected as a case study. The model has been used to perform in silico experiments to evaluate the effect of, for example, fruit size or ambient gas concentration on internal O₂ and CO₂ levels. The model incorporates the actual shape of the fruit and was solved using fluid dynamics software. Environmental conditions such as temperature and gas composition have a large effect on the internal distribution of oxygen and carbon dioxide in fruit. Also, the fruit size has a considerable effect on local metabolic gas concentrations; hence, depending on the size, local anaerobic conditions may result, which eventually may lead to physiological disorders. The model developed in this manuscript is to our knowledge the most comprehensive model to date to simulate gas exchange in plant tissue. It can be used to evaluate the effect of environmental stresses on fruit via in silico experiments and may lead to commercial applications involving long-term storage of fruit under controlled atmospheres. Respiration plays an important role in the overall metabolism of plants, and certainly is related to gas exchange of plants with the environment. In roots and bulky storage organs such as fruit and tubers, where the length of the diffusion path may be considerable, anoxic conditions may even occur. This is of particular importance in fruit, which are often stored under low-oxygen conditions to extend their storage life. In this manuscript, we have developed a new mathematical model to describe the gas transport and respiration kinetics in intact pear fruit. Michaelis-Menten kinetics was used to describe the respiration behavior of tissues. Diffusion was the main driving force for gas exchange. Differences in diffusion rates of the different gasses led to total pressure gradients that caused convective exchange as described by Darcy's law. The model incorporates the actual shape of the fruit and was solved using fluid dynamics software. It is a first step towards a multiscale model that addresses all spatial scales relevant to gas transport. These findings can be used to evaluate the effect of environmental stresses on fruit via in silico experiments and may lead to commercial solutions for long-term storage of fruit under controlled atmospheres.