Abstract of Cofactor Modifications To Michaelis Menten Kinetics

Research Report SRR95-001

Cofactor Modifications To Michaelis Menten Kinetics

Henry C. Tuckwell

Abstract: In order to construct mathematical models for the dynamical operation of central nervous system synapses, accurate chemical kinetic theory is required for enzymatic reactions. The Michaelis-Menton formula for the rate of an enzymatic reaction is modified when there are cofactors involved. We distinguish the cases of essential and non-essential cofactors. In the case of an essential cofactor, the formula for the reaction rate is found to depend on the relative magnitudes of the concentrations of the primary enzyme and the cofactor, extending a result previously employed by various authors. The case of a non-essential cofactor is more complex and leads to reaction rate formulas which depend explicitly on the concentration of both the primary enzyme and the cofactor. The relative magnitudes of the concentrations of the latter two substances again determines the functional dependence of the reaction rate on these quantities. Simplified expressions are obtained under certain assumptions on a parameter describing the relative efficacies of the enzyme alone and the enzyme with cofactor. An example is given which arises from a mathematical model of a dopaminergic synapse, namely the conversion of tyrosine to DOPA via tyrosine hydroxylase and its biopterin cofactor.

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