Abstract
Dopamine neurons play a key role in normal and pathological cognitive processes as well as in the effects of certain drugs of addiction. Models of the synapses of such neurons include transporter mechanisms and reaction dynamics. This article focuses attention on the fundamental reaction that converts tyrosine to DOPA, which involves a cofactor. The Michaelis-Menten formula for the rate of an enzymatic reaction is modified by the presence of cofactors, which may be either essential or nonessential. In the essential case, the reaction rate is found to depend on the relative magnitudes of the concentrations of the primary enzyme and the cofactor. The case of a nonessential cofactor is more complex and it is shown for the first time how this leads to reaction rate formulas that depend explicitly on the concentrations of the enzyme and cofactor. The extended Michaelis-Menten formulas are applied to the aforementioned reaction with tyrosine hydroxylase as enzyme and biopterin as cofactor. The results are useful in constructing accurate models of dopamine synapses.
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