Modelling ethylene regulated changes in ‘Hass’ avocado quality

Abstract

Temperature and exogenous ethylene are two important factors that determine the rate of quality change in ‘Hass’ avocado. The aim of this study was to quantify this effect and to build a mathematical model that will assist in predicting the effect of temperature, exogenous ethylene, and time on quality outcomes of ‘Hass’ avocado. A mathematical model was developed to describe autocatalytic ethylene production, and coupled to models describing softening and colour changes via ethylene. The effect of exogenous ethylene was incorporated by addition of a diffusion term, while temperature effect was modelled by expressing rate constants as a function of temperature using the Arrhenius equation. The model was calibrated using data on ethylene efflux rate, firmness and skin hue collected on ‘Hass’ avocado fruit stored at 5, 10, or 20°C, in atmospheres containing <0.05μLL−1 (air), 1μLL−1 or 10μLL−1 ethylene in air. Effect of ethylene on softening was greater than on colour change, with clear firmness separation of the different ethylene treated fruit evident even during ripening at 20°C. The high dependency of softening on ethylene was revealed in the Michaelis-Menten constant for the regulation of the softening enzyme by ethylene, which was about 15 times larger than that for the colour degrading enzymes. The model was successfully validated on a sub-dataset.