A kinetic inhibition mechanism for maintenance

To fulfil their maintenance costs, most species use mobile pools of metabolites (reserve) in favourable conditions, but can also use less mobile pools (structure) under food-limiting conditions. While some empirical models always pay maintenance costs from structure, the presence of reserve inhibits the use of structure for maintenance purposes. The standard dynamic energy budgets (DEB) model captures this by simply supplementing all costs that could not be paid from reserve with structure. This is less realistic at the biochemical level, and involves a sudden use of structure that can complicate the analysis of the model properties. We here propose a new inhibition formulation for the preferential use of reserve above structure in maintenance that avoids sudden changes in the metabolites use. It is based on the application of the theory for synthesizing units, which can easily become rather complex for demand processes, such as the maintenance. We found, however, a simple explicit expression for the use of reserve and structure for maintenance purposes and compared the numerical behaviour with that of a classical model in oscillating conditions, by using parameters values from a fit of the models to data on yeasts in a batch culture. We conclude that our model can better handle variable environments. This new inhibition formulation has a wide applicability in modelling metabolic processes.