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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

On reaction dynamics at dopamine synapses

Henry Tuckwell


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. We focus attention on the fundamental reaction which 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 non-essential. 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 non-essential cofactor is more complex and it is shown for the first time how this leads to reaction rate formulas which depend explicitly on the concentrations of the enzyme and cofactor. The extended Michaelis-Menten formulas are applied to the above-mentioned reaction with tyrosine hydroxylase as enzyme and biopterin as cofactor. The results are useful in constructing accurate models of dopamine synapses


Related publications

2007 Repository Open Access
Henry C. Tuckwell

On reaction dynamics at dopamine synapses

In: The international journal of neuroscience, 117 (2007) 5, pp. 667-679