Mathematical Insights into the Effects of Levodopa

Parkinson’s disease has been traditionally thought of as a dopaminergic disease in which cells of the substantia nigra pars compacta (SNc) die. However, accumulating evidence implies an important role for the serotonergic system in Parkinson’s disease in general and in physiological responses to levodopa therapy, the first line of treatment. We use a mathematical model to investigate the consequences of levodopa therapy on the serotonergic system and on the pulsatile release of dopamine (DA) from dopaminergic and serotonergic terminals in the striatum. Levodopa competes with tyrosine and tryptophan at the blood-brain barrier and is taken up by serotonin neurons in which it competes for aromatic amino acid decarboxylase. The DA produced competes with serotonin (5HT) for packaging into vesicles. We predict the time courses of LD, cytosolic DA, and vesicular DA in 5HT neurons during an LD dose. We predict the time courses of DA and 5HT release from 5HT cell bodies and 5HT terminals as well as the changes in 5HT firing rate due to lower 5HT release. We compute the time course of DA release in the striatum from both 5HT and DA neurons and show how the time course changes as more and more SNc cells die. This enables us to explain the shortening of the therapeutic time window for the efficacy of levodopa as Parkinson’s disease progresses. Finally, we study the effects 5HT1a and 5HT1b autoreceptor agonists and explain why they have a synergistic effect and why they lengthen the therapeutic time window for LD therapy. Our results are consistent with and help explain results in the experimental literature and provide new predictions that can be tested experimentally.