A Cycle of Enzymatic Reactions that Behaves like a Neuronal Circuit

A cycle of four enzymatic reactions with repression or allosteric inhibition of the enzymes has been proposed by analogy to a neural oscillator. The system is analysed in a situation remote from full symmetry. Asymmetry has been introduced by treating one of the reagents as a reservoir substance with constant concentration and having essentially different rate constants for forward and backward reactions. It is demonstrated that, for certain values of parameters, the system can work as a strength of stimulus to frequency transducer. For other values of the parameters, it acquires the features of an excitable system.