Mathematics of cellular control processes I. Negative feedback to one gene

Repression of mRNA synthesis is discussed for situations in which the repressor is either the protein encoded by the mRNA or a metabolite formed under the catalytic control of that protein. Following Goodwin (1965), plausible physicochemical equations are set up. They contain a non-linear element. Standard methods of the theory of non-linear equations are used to determine the properties of these equations for general values of the parameters contained therein. Undamped oscillations in the concentrations of the components can never occur for any values of the parameters when the repression is accomplished by the protein. Such oscillations are possible when repression is due to the metabolite, but only when there is a co-operative repression of such a high order as to be unlikely in practice.