**Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease**

Janet Best1, Grant Oakley1, Michael Reed2 and H. Frederik Nijhout2 <sup>1</sup>*Ohio State University* <sup>2</sup>*Duke University USA*

#### **1. Introduction**

404 Etiology and Pathophysiology of Parkinson's Disease

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Parkinson's disease (PD) has traditionally been thought of as a dysfunction in the dopamine (DA) signaling system caused primarily by cell death in the substantia nigra pars compacta (SNc). However, strong evidence has been accumulating that the serotonin (5-HT) signaling system is also involved. First, 5-HT influences normal motor function through a dense innervation of the striatum. Second, substantial cell death of serotonergic neurons occurs in PD and in some cases may occur earlier than DA cell death. And, finally, there are indications that interactions between the 5-HT system and the DA system may be responsible for some of the symptoms of PD and some of the side effects of treatment by levodopa. Some of the evidence for these assertions is reviewed below.

The 5-HT system is itself very complex. The serotonergic neurons in the raphe nuclei (RN) send ascending projections to a large number of different brain regions including medial prefrontal cortex (mPFC), motor cortex, hypothalamus, hippocampus, amygdala, and the basal ganglia. And, some of these brain regions, substantia nigra, amygdala, mPFC, and hypothalamus send projections back to the RN (Monti, 2010). Thus it is not surprising that 5-HT is linked to so many behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders (Feldman et al., 1997). Since the pharmacology and the electrophysiology of both the serotonergic and the dopaminergic systems are only partially understood, it is a daunting task to understand how these two systems affect one another. This is particularly true in the presence of a degenerative disease that involves massive cell death in both systems.

In this complicated situation, mathematical models can potentially provide insight into mechanisms and interactions. The purpose of the models is not to summarize what is already known. The purpose is to provide a platform for *in silico* biological experimentation. Using models one can try out ideas, validate or refute hypotheses, settle disputes in the literature, and sometimes discover new phenomena. Of course, to be useful the models have to be well-grounded in real physiology and the creation of such models is not easy. However, if one

(Jellinger, 1991), serotonergic terminal loss in the striatum, or molecular regulatory changes

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 407

In post-mortem analyses of brains from PD patients, Kish et al. (2008) found that serotonin and dopamine have substantially different patterns of loss within the striatum. Serotonin markers show greater loss in the caudate than in putamen, while the dopamine loss is greater in the putamen. Thus the striatal subdivision with the more severe dopamine loss (putamen) was less affected by loss of serotonin markers, possibly reflecting compensatory sprouting of 5-HT terminals (Maeda et al., 2003). Serotonergic responses to dopamine depletion may also be evident in changes in the electrical activity of serotonergic neurons. Zhang et al. (2007) reports that, in an animal model of PD, raphe neurons have altered firing rates and fire bursts more frequently. Under levodopa administration, DA may also be released in bursts from

One of the clearest and best-studied involvements of 5-HT in PD symptoms is in the motor symptoms, including tremor and especially levodopa induced dyskinesias (LID). Experiments have found that the serotonergic system plays an essential role in both symptoms. Brooks (2007) reports that in order to generate tremors with the characteristic PD frequency of 3-5 Hz in animal models it is necessary to lesion not just nigro-striatal dopaminergic projections but also the midbrain tegmentum, which contains serotonergic cell bodies in the median raphe, rubrospinal, and dentatothalamic tracts. He also notes that loss of midbrain serotonin 5-*HT*1*<sup>A</sup>* binding correlates with tremor severity in PD, unlike loss of striatal dopaminergic function. He speculates that this may explain why some parkinsonian tremors are relatively resistant to dopaminergic medications. 5-HT may not be equally involved in all motor symptoms of PD: it has been observed clinically that rigidity and bradykinesia are more responsive to

Upon diagnosis of PD, patients can often use levodopa to effectively relieve symptoms for several years. However, more than 50% of patients develop motor complications in response to levodopa administration within 5 years (Olanow et al., 2000); after 10 years, the percentage is approximately 90% (Ahlskog & Muenter, 2001). These complications include a narrowing of the temporal window of efficacy (*i.e.*, the duration of benefit after a given dose of levodopa becomes progressively shorter until it approximates the plasma half-life of levodopa) (Olanow et al., 2006), sudden failures of efficacy known as "on-off fluctuations" (Nicholson & Brotchie, 2002) and, most troublesome, the appearance of involuntary movements (LID) (Carta et al.,

**3. Possible mechanisms of serotonergic involvement in PD motor symptoms**

In order to understand the emergence of LID, it is useful to first review how levodopa may achieve therapeutic effect. The idea of administering levodopa is to provide dopamine replacement therapy. Dopamine itself is unable to pass the blood brain barrier, but its immediate precursor, levodopa, is able to reach the brain following peripheral administration when given in combination with a decarboxylase inhibitor to prevent metabolism while in the blood stream (Carta et al., 2008). The motor symptoms of PD typically emerge when a sufficient proportion of dopaminergic cells in SNc have been lost that dopaminergic terminals in the striatum are no longer able to maintain a high enough concentration of extracellular DA. Supplemental levodopa can be taken into the remaining dopaminergic terminals, converted

(Kish et al., 2008).

these serotonergic neurons.

dopaminergic drugs than is tremor (Fox et al., 2009).

2008; Nicholson & Brotchie, 2002).

to DA and stored in vesicles for synaptic release.

has a model that represents (part of) the underlying physiology well, then *in silico* experiments are quick and inexpensive. The model provides a quantitative way of thinking about the phenomena being investigated and may suggest new hypotheses that can be checked by animal experiments. Thus, modeling, when combined with animal experiments and clinical trials, can shed some light on the complicated pharmacological, electrophysiological, and behavioral issues in PD.

In Section 2, we discuss the evidence for the role of 5-HT in PD and the side effects of levodopa therapy and in Section 3 we discuss possible mechanisms. In Section 4, we describe a mathematical model that we recently created to study homeostatic mechanisms in serotonergic signaling. In Section 5 we use the model, and a previous model of a DA terminal, to discuss the effects of gene polymorphisms, the stability of extracellular DA in the striatum in the face of cell death in the substantia nigra, and the mechanism of action of selective serotonin reuptake inhibitors. Finally, in Section 6 we outline how we plan to use existing models and new models to investigate the interactions between the 5-HT system and the DA system in PD.
