Speaker
Description
In many interactions between hosts and pathogens or plants and herbivores, the attacked organism produces a chemical compound to defend itself. The attacker often responds to this by producing a counter defence, e.g. an enzyme that can degrade this defence chemical. Sometimes, the defender responds by producing another chemical, a counter-counter defence, that can inhibit the degrading enzyme. These interactions often attain a steady-state.
In this theoretical study, we analysed under which conditions it is favourable to invest resources into the production of a counter-counter defence and, if so, to what extent. A mathematical model based on enzyme kinetics was developed. For this model, we derived the equation for the steady-state concentration of the defence chemical and solved a resource allocation problem with the goal of maximising this concentration. This revealed that only if the inhibitor shows certain properties it is favourable to develop a counter-counter defence. We also found that it depends on the amount of available resources, whether the production of an inhibitor is beneficial. However, it is never optimal to invest more resources into the inhibitor than into the toxin, provided that their costs are approximately equal. The results can be of interest for calculating the optimal mixing ratios in antibiotics and other drugs that are given for a prolonged time.
