Model of the synthesis of trisporic acid in mucorales showing bistability

An important substance in the signalling between individuals of Mucor-like fungi is trisporic acid (TA). This compound, together with some of its precursors, serves as a pheromone in mating between (+)- and (-)-mating types. Moreover, intermediates of the TA pathway are exchanged between the two mating partners. Based on differential equations, mathematical models of the synthesis pathways of TA in the two mating types of an idealised Mucor-fungus are here presented. These models include the positive feedback of TA on its own synthesis. The authors compare three sub-models in view of bistability, robustness and the reversibility of transitions. The proposed modelling study showed that, in a system where intermediates are exchanged, a reversible transition between the two stable steady states occurs, whereas an exchange of the end product leads to an irreversible transition. The reversible transition is physiologically favoured, because the high-production state of TA must come to an end eventually. Moreover, the exchange of intermediates and TA is compared with the 3-way handshake widely used by computers linked in a network.