A cycle of enzymatic reactions with some properties of neuronal circuits
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A cycle of four methylation and four demethylation reactions with repression or allosteric inhibition of enzymes is considered. The corresponding dynamical system is characterised by two parameters: the sum of reagent concentrations (C) and the ratio of rate constants of forward and backward reactions (k). In a symmetrical case (k=1) the system has a unique equilibrium. At C>4 the equilibrium is unstable and the system has oscillatory solutions. At k essentially different from 1, the system becomes excitable or behaves as a bistable trigger.
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