Mathematical Models of Dopamine Metabolism in Parkinson’s Disease

As discussed in Chap. 1 and elsewhere in this volume, a feature of Parkinson’s disease (PD) is a reduction in dopamine concentration in the striatum, caused by progressive loss of dopamine neurons in the substantia nigra pars compacta. Dopamine is a crucial neurotransmitter that is involved in numerous physiological functions, and its role in PD has been studied extensively. However, the dynamics of dopamine in situ are not fully understood because it is affected by a large number of metabolites, other biological components, and an ill-characterized spectrum of environmental and genetic factors. This chapter describes the state of the art in mathematical models of dopamine metabolism and signal transduction. First, the topology of the dopamine pathway is reviewed. Second, the construction of two types of models is discussed. The first of these models targets dopamine metabolism in the presynaptic terminal, while the second describes dopamine-based signal transduction at the synapse and signal integration in the postsynaptic target neurons. The construction phase of symbolic models is followed by numerical configurations based on data. The resulting parameterized models are then compared with experimental and clinical observations as a means of testing their validity and predictive power. The best model is utilized to analyze ill-understood aspects of the role of dopamine in PD and to identify critical molecules and processes that might be potential therapeutical targets. Simulations of drugs targeting these sites are presented and evaluated with respect to their benefits, possible side effects, and downstream effects of perturbations in dopamine dynamics.