**2. PD and the serotonergic system**

Tremor, rigidity, and bradykinesia, the classical motor symptoms of ideopathic PD, primarily result from loss of dopaminergic neurons in the SNc. However, neural degeneration also occurs in other sites of the brain, ranging from the brain stem to cortex, as the synaptic protein *α*-synuclein accumulates pathologically to form Lewy bodies (LB) or Lewy neurites. The clinical diagnosis of PD is based upon presence of the motor symptoms indicating dopamine deficiency (Chaudhuri et al., 2006; Jankovic, 2008). Postmortem analysis finds LB not only in remaining substantia nigra cells but in other specific brain regions where cells are lost (Gibb & Lees, 1988). Braak and colleagues (Braak et al., 2003) have proposed a scheme of six stages describing the development of ideopathic PD, characterized by the spatial extent of LB inclusions. Braak stage 1 involves LB inclusions in the region of the brain stem; neurodegeneration of the substantia nigra does not begin until stage 3. Braak's hypothesis concerning the progression of PD predicts that symptoms such as diminished olfactory sensitivity (Lim et al., 2009) or REM behavior disorder (Ahlskog, 2004) should precede the cardinal motor symptoms of the disease, a pattern observed in some but not all cases of PD (Linazasoro, 2007). Indeed, the retrospective nature of Braak's study obscures the actual course of progression (Halliday & McCann, 2010). In a longitudinal study, Halliday & McCann (2010) found that approximately half of ideopathic PD cases follow Braak's scheme. In all cases studied by Halliday and McCann, LB occurred not only in the substantia nigra but also in other brain areas including brain stem. Thus, extra-nigral aspects are always present in PD, and their significance can rival that of the cardinal motor symptoms (Chaudhuri et al., 2006).

Ahlskog (2004) reports that LB have been found in pontomedullary neurons of brains without substantia nigra pathology but that the reverse has not been observed. Among the nondopaminergic systems profoundly affected in PD is the serotonergic system. The extent of damage to the serotonergic system in PD is variable and is less severe than the loss of dopamine: Kish found that, while striatal dopamine concentrations decreased by more than 80%, serotonin markers decreased by less than 70% (Kish et al., 2008). It has not been clearly established to what extent this reduction in serotonin markers is due to raphe cell loss 2 Will-be-set-by-IN-TECH

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

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

Tremor, rigidity, and bradykinesia, the classical motor symptoms of ideopathic PD, primarily result from loss of dopaminergic neurons in the SNc. However, neural degeneration also occurs in other sites of the brain, ranging from the brain stem to cortex, as the synaptic protein *α*-synuclein accumulates pathologically to form Lewy bodies (LB) or Lewy neurites. The clinical diagnosis of PD is based upon presence of the motor symptoms indicating dopamine deficiency (Chaudhuri et al., 2006; Jankovic, 2008). Postmortem analysis finds LB not only in remaining substantia nigra cells but in other specific brain regions where cells are lost (Gibb & Lees, 1988). Braak and colleagues (Braak et al., 2003) have proposed a scheme of six stages describing the development of ideopathic PD, characterized by the spatial extent of LB inclusions. Braak stage 1 involves LB inclusions in the region of the brain stem; neurodegeneration of the substantia nigra does not begin until stage 3. Braak's hypothesis concerning the progression of PD predicts that symptoms such as diminished olfactory sensitivity (Lim et al., 2009) or REM behavior disorder (Ahlskog, 2004) should precede the cardinal motor symptoms of the disease, a pattern observed in some but not all cases of PD (Linazasoro, 2007). Indeed, the retrospective nature of Braak's study obscures the actual course of progression (Halliday & McCann, 2010). In a longitudinal study, Halliday & McCann (2010) found that approximately half of ideopathic PD cases follow Braak's scheme. In all cases studied by Halliday and McCann, LB occurred not only in the substantia nigra but also in other brain areas including brain stem. Thus, extra-nigral aspects are always present in PD, and their significance can rival that of the cardinal motor symptoms (Chaudhuri et al.,

Ahlskog (2004) reports that LB have been found in pontomedullary neurons of brains without substantia nigra pathology but that the reverse has not been observed. Among the nondopaminergic systems profoundly affected in PD is the serotonergic system. The extent of damage to the serotonergic system in PD is variable and is less severe than the loss of dopamine: Kish found that, while striatal dopamine concentrations decreased by more than 80%, serotonin markers decreased by less than 70% (Kish et al., 2008). It has not been clearly established to what extent this reduction in serotonin markers is due to raphe cell loss

behavioral issues in PD.

the DA system in PD.

2006).

**2. PD and the serotonergic system**

(Jellinger, 1991), serotonergic terminal loss in the striatum, or molecular regulatory changes (Kish et al., 2008).

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 these serotonergic neurons.

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

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., 2008; Nicholson & Brotchie, 2002).

#### **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 to DA and stored in vesicles for synaptic release.

result in large swings in the extracellular concentration of DA. The resulting pulsatile stimulation of striatal DA receptors may be the proximate cause of abnormal movements (de la Fuente-Fernandez et al., 2001) and may induce post-synaptic changes. In animal models of PD, alterations have been identified in the *D*<sup>1</sup> signaling pathway as well as in NMDA and AMPA receptor function and distribution (Bibbiani et al., 2005; Hallett et al., 2005; Robelet et al., 2004), and these changes have been linked to the induction and maintenance of abnormal movements (Gardoni et al., 2006; Hallett et al., 2005; Picconi et al., 2008; Santini et al., 2007). In fact, studies utilizing pumps to provide a fairly continuous dosing with levodopa or

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 409

Changes in gene expression also have been found following treatment with levodopa (Santini et al., 2007), and these may relate to the phenomenon of priming. Some PD patients can be treated with DA receptor agonists without developing dyskinesias. But eventually, as the disease progresses, they generally need to add levodopa in order to achieve relief from symptoms. The phenomenon of priming is that patients started on levodopa and then moved to DA agonists will exhibit dyskinesias even if placed on DA agonists without levodopa

As a first step in using mathematics to help understand the serotonergic and dopaminergic systems, we have created mathematical models of a serotonin terminal (Best et al., 2010b) and a dopamine terminal (Best et al., 2009). Here we briefly describe the model for a serotonin terminal and in the next section give applications. The substrates in the model are indicated in Figure 1 by the pink boxes and the blue ellipses contain the acronyms of enzymes or transporters. Blood tryptophan is considered a (possibly time-varying) input to the model and there are differential equations for the other nine substrates. Each differential equation is just a quantitative expression of mass balance; i.e. the rate of change of the concentration of a substrate is simply the sum of the rates of the reactions by which it is made minus the sum of the rates of the reactions in which it is used. For example, the concentration of

where *V*TPH is the velocity of the TPH reaction and *V*AADC is the velocity of the AADC reaction. One must specify exactly how these velocities depend on the current values of

*Ki* )(*Kbh*<sup>4</sup> + (*bh*4)) ·

The first term on the right is of Michaelis-Menten form and gives the dependence of the velocity on the concentrations of *trp* and *bh*4. The enzyme TPH shows substrate inhibition (Best et al., 2010a; Friedman et al., 1974; McKinney et al., 2005), which is the reason for the (*trp*)<sup>2</sup> term in the denominator. The second term on the right expresses how the concentration of extracellular 5-HT influences the rate of synthesis via the autoreceptors. At normal e5-HT concentration (.768 nM) this factor equals one. As e5-HT goes up the factor can go as low as 0.5

*dt* <sup>=</sup> *<sup>V</sup>*TPH(*trp*, *bh*4,*e*5*ht*) <sup>−</sup> *<sup>V</sup>*AADC(5*htp*) (1)

1.5 <sup>−</sup> (*e*5*ht*)<sup>2</sup>

((.000768)<sup>2</sup> + (*e*5*ht*)2)

. (2)

**4. Mathematical modeling of dopaminergic and serotonergic systems**

DA agonists have found fewer side effects (Nutt et al., 2000).

(Nicholson & Brotchie, 2002).

5-hydroxytryptophan, [5htp], satisfies:

various substrates. *V*TPH is given by:

*d*[5*htp*]

*<sup>V</sup>*TPH <sup>=</sup> *Vmax*(*trp*)(*bh*4) (*Ktrp* + (*trp*) + (*trp*)<sup>2</sup>

As the number of remaining dopaminergic cells continues to decrease, the levodopa may increasingly be taken up by other cell types including serotonergic neurons and glial cells. Serotonergic cells may play a special role here, as they also express the enzymes used in dopaminergic cells to convert levodopa to DA (amino acid aromatic decarboxylase, AADC) and to package DA into vesicles (vesicular monoamine transporter 2, MAT). Indeed, experiments have verified that serotonergic cells can store and release DA in vivo and in vitro (Nicholson & Brotchie, 2002). Evidence that serotonergic cells may be playing a role in LID comes from animal models of PD. (Tanaka et al., 1999) showed that, in levodopa treatment of a hemiparkinsonian rat, extracellular DA (eDA) decreased substantially when the serotonergic system was lesioned. Glial cells also contain AADC and so could contribute to the conversion of levodopa to DA; however, experiments by Kannari et al. (2000) in which he used reserpine to block vesicular packaging showed a great reduction of eDA, suggesting that most of the levodopa-derived DA is released by exocytosis of vesicles rather than by glia, at least at physiological levels of levodopa administration. Carta et al. (2007) have provided further evidence implicating serotonergic cells in LID in a rat model by showing that either toxic lesion of the serotonergic system or pharmacological impairment of the system with selective serotonin autoreceptor (5-*HT*1*<sup>A</sup>* and 5-*HT*1*B*) agonists resulted in a nearly complete elimination of LID.

The observation that LID becomes increasingly problematic as the disease progresses suggests that LID may result from the fact that DA released from serotonergic cells is not subject to the DA homeostatic mechanisms present in dopaminergic cells. Many approaches to eliminating LID therefore tend to focus instead on manipulating factors that regulate serotonergic cell activity, such as serotonergic autoreceptors that participate in serotonergic homeostatic mechanisms. Simply decreasing serotonergic cell activity by administering serotonin autoreceptor agonists has the drawback of also reducing the amount of dopamine released into the extracellular space, tending to worsen PD symptoms (Iravani et al., 2006). Carta et al. (2008) argue that it is reasonable to use 5-HT autoreceptor agonists especially because the DA intermixed with the 5-HT released by the serotonergic cell effectively lowers the binding of 5-HT to 5-HT autoreceptors and induces the cells to be over-active. A more detailed look at the serotonergic system, using mathematical models, may help suggest more nuanced approaches.

There are many types of serotonin receptors. 5-*HT*1*<sup>A</sup>* receptors are present on the cell body and dendrites of serotonergic neurons in the dorsal and median raphe; they function as autoreceptors and they decrease firing as extracellular 5-HT (e5-HT) goes up. 5-*HT*1*<sup>B</sup>* receptors are present on axon terminals in serotonin projection regions where they function as autoreceptors and decrease the release of serotonin as e5-HT goes up in the terminal region. Applying agonists only to 5-*HT*1*<sup>A</sup>* or only to 5-*HT*1*<sup>B</sup>* autoreceptors in a rat model of PD treated with levodopa can partially reduce LID (Bibbiani et al., 2001; Jackson et al., 2004). Carta et al. (2007) found that providing subthreshold doses of both 5-*HT*1*<sup>A</sup>* and 5-*HT*1*<sup>B</sup>* agonists (that is, doses that would have little or no effect alone) could completely eliminate LID. This is very strong evidence that the absence of the normal control mechanisms by the DA autoreceptors is connected to LID.

Post-synaptic mechanisms may play a role in LID. Given that serotonergic cells may be responsible for releasing much of the levodopa-derived DA in advanced PD and that these cells lack DA homeostatic mechanisms, the intermittent administration of levodopa may 4 Will-be-set-by-IN-TECH

As the number of remaining dopaminergic cells continues to decrease, the levodopa may increasingly be taken up by other cell types including serotonergic neurons and glial cells. Serotonergic cells may play a special role here, as they also express the enzymes used in dopaminergic cells to convert levodopa to DA (amino acid aromatic decarboxylase, AADC) and to package DA into vesicles (vesicular monoamine transporter 2, MAT). Indeed, experiments have verified that serotonergic cells can store and release DA in vivo and in vitro (Nicholson & Brotchie, 2002). Evidence that serotonergic cells may be playing a role in LID comes from animal models of PD. (Tanaka et al., 1999) showed that, in levodopa treatment of a hemiparkinsonian rat, extracellular DA (eDA) decreased substantially when the serotonergic system was lesioned. Glial cells also contain AADC and so could contribute to the conversion of levodopa to DA; however, experiments by Kannari et al. (2000) in which he used reserpine to block vesicular packaging showed a great reduction of eDA, suggesting that most of the levodopa-derived DA is released by exocytosis of vesicles rather than by glia, at least at physiological levels of levodopa administration. Carta et al. (2007) have provided further evidence implicating serotonergic cells in LID in a rat model by showing that either toxic lesion of the serotonergic system or pharmacological impairment of the system with selective serotonin autoreceptor (5-*HT*1*<sup>A</sup>* and 5-*HT*1*B*) agonists resulted in a nearly complete

The observation that LID becomes increasingly problematic as the disease progresses suggests that LID may result from the fact that DA released from serotonergic cells is not subject to the DA homeostatic mechanisms present in dopaminergic cells. Many approaches to eliminating LID therefore tend to focus instead on manipulating factors that regulate serotonergic cell activity, such as serotonergic autoreceptors that participate in serotonergic homeostatic mechanisms. Simply decreasing serotonergic cell activity by administering serotonin autoreceptor agonists has the drawback of also reducing the amount of dopamine released into the extracellular space, tending to worsen PD symptoms (Iravani et al., 2006). Carta et al. (2008) argue that it is reasonable to use 5-HT autoreceptor agonists especially because the DA intermixed with the 5-HT released by the serotonergic cell effectively lowers the binding of 5-HT to 5-HT autoreceptors and induces the cells to be over-active. A more detailed look at the serotonergic system, using mathematical models, may help suggest more

There are many types of serotonin receptors. 5-*HT*1*<sup>A</sup>* receptors are present on the cell body and dendrites of serotonergic neurons in the dorsal and median raphe; they function as autoreceptors and they decrease firing as extracellular 5-HT (e5-HT) goes up. 5-*HT*1*<sup>B</sup>* receptors are present on axon terminals in serotonin projection regions where they function as autoreceptors and decrease the release of serotonin as e5-HT goes up in the terminal region. Applying agonists only to 5-*HT*1*<sup>A</sup>* or only to 5-*HT*1*<sup>B</sup>* autoreceptors in a rat model of PD treated with levodopa can partially reduce LID (Bibbiani et al., 2001; Jackson et al., 2004). Carta et al. (2007) found that providing subthreshold doses of both 5-*HT*1*<sup>A</sup>* and 5-*HT*1*<sup>B</sup>* agonists (that is, doses that would have little or no effect alone) could completely eliminate LID. This is very strong evidence that the absence of the normal control mechanisms by the DA autoreceptors

Post-synaptic mechanisms may play a role in LID. Given that serotonergic cells may be responsible for releasing much of the levodopa-derived DA in advanced PD and that these cells lack DA homeostatic mechanisms, the intermittent administration of levodopa may

elimination of LID.

nuanced approaches.

is connected to LID.

result in large swings in the extracellular concentration of DA. The resulting pulsatile stimulation of striatal DA receptors may be the proximate cause of abnormal movements (de la Fuente-Fernandez et al., 2001) and may induce post-synaptic changes. In animal models of PD, alterations have been identified in the *D*<sup>1</sup> signaling pathway as well as in NMDA and AMPA receptor function and distribution (Bibbiani et al., 2005; Hallett et al., 2005; Robelet et al., 2004), and these changes have been linked to the induction and maintenance of abnormal movements (Gardoni et al., 2006; Hallett et al., 2005; Picconi et al., 2008; Santini et al., 2007). In fact, studies utilizing pumps to provide a fairly continuous dosing with levodopa or DA agonists have found fewer side effects (Nutt et al., 2000).

Changes in gene expression also have been found following treatment with levodopa (Santini et al., 2007), and these may relate to the phenomenon of priming. Some PD patients can be treated with DA receptor agonists without developing dyskinesias. But eventually, as the disease progresses, they generally need to add levodopa in order to achieve relief from symptoms. The phenomenon of priming is that patients started on levodopa and then moved to DA agonists will exhibit dyskinesias even if placed on DA agonists without levodopa (Nicholson & Brotchie, 2002).

#### **4. Mathematical modeling of dopaminergic and serotonergic systems**

As a first step in using mathematics to help understand the serotonergic and dopaminergic systems, we have created mathematical models of a serotonin terminal (Best et al., 2010b) and a dopamine terminal (Best et al., 2009). Here we briefly describe the model for a serotonin terminal and in the next section give applications. The substrates in the model are indicated in Figure 1 by the pink boxes and the blue ellipses contain the acronyms of enzymes or transporters. Blood tryptophan is considered a (possibly time-varying) input to the model and there are differential equations for the other nine substrates. Each differential equation is just a quantitative expression of mass balance; i.e. the rate of change of the concentration of a substrate is simply the sum of the rates of the reactions by which it is made minus the sum of the rates of the reactions in which it is used. For example, the concentration of 5-hydroxytryptophan, [5htp], satisfies:

$$\frac{d[5htp]}{dt} = V\_{\rm TPH}(trp, bh4, e5ht) - V\_{\rm AADC}(5htp) \tag{1}$$

where *V*TPH is the velocity of the TPH reaction and *V*AADC is the velocity of the AADC reaction. One must specify exactly how these velocities depend on the current values of various substrates. *V*TPH is given by:

$$V\_{\rm TPH} = \frac{V\_{\rm max}(trp)(bh4)}{(K\_{trp} + (trp) + \frac{(trp)^2}{K\_l})(K\_{bh4} + (bh4))} \cdot \left(1.5 - \frac{(e5ht)^2}{((.000768)^2 + (e5ht)^2)}\right) . \tag{2}$$

The first term on the right is of Michaelis-Menten form and gives the dependence of the velocity on the concentrations of *trp* and *bh*4. The enzyme TPH shows substrate inhibition (Best et al., 2010a; Friedman et al., 1974; McKinney et al., 2005), which is the reason for the (*trp*)<sup>2</sup> term in the denominator. The second term on the right expresses how the concentration of extracellular 5-HT influences the rate of synthesis via the autoreceptors. At normal e5-HT concentration (.768 nM) this factor equals one. As e5-HT goes up the factor can go as low as 0.5

Fig. 1. Steady state concentrations and fluxes in the 5-HT terminal model. The figure shows the reactions in the model. The pink rectangular boxes indicate substrates and blue ellipses contain the acronyms of enzymes or transporters; steady state values in the model are indicated. Concentrations (red) have units of *μ*M and rates (blue) have units of *μ*M/hr. Full names of the substrates are: bh2, dihydrobiopterin; bh4, tetrahydrobiopterin; trp, tryptophan; btrp, serum tryptophan; 5htp, 5-hydroxytryptophan; c5ht, cytosolic 5-HT; v5ht, vesicular 5-HT; e5ht; extracellular 5-HT; 5-hiaa, 5-hydroxyindoleacetic acid; *trp*−*pool*, the tryptophan pool. Names of enzymes and transporters are: Trpin, neutral amino acid transporter; DRR, dihydrobiopterin reductase; TPH, tryptophan hydroxylase; AADC, aromatic amino acid decarboxylase; MAT, vesicular monoamine transporter; SERT, 5-HT reuptake transporter; auto, 5-HT autoreceptors; MAO, monoamine oxidase; ALDH, aldehyde dehydrogenase. Removal means uptake by capillaries or glial cells or diffusion out of the system.

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 411

and as e5-HT goes down, the factor can go as high as 1.5. We chose *Km* and *Ki* values from the literature and chose the *Vmax* so that the normal velocity of the the TPH reaction is in the range given by experiments. The form of the second factor is more speculative. Though it is certain that increasing extracellular concentrations of 5-HT inhibit synthesis via the autoreceptors (Adell et al., 2002), there is relatively little information in the literature about the range of e5-HT concentrations over which the effect takes place and about the strength of the effect in the low nanomolar range. Here, as in other choices of parameters and functional forms, we base our choices as much as possible on the experimental literature. Full details of the model can be found in Best et al. (2010b).

The model can be used to show how the steady state values of concentrations and rates change if parameters, like serotonin transporter (SERT) density, or inputs, like serum tryptophan, change. One can also compute the time courses of the concentrations and rates on long time scales (hours) or very short time scales (msec) as the system responds to the release of 5-HT due to individual action potentials. However, the model has limitations. Various physiological processes known to be important are not included, for example the movement of vesicles or SERTs from the interior of the terminal to and from the synaptic membrane. The detailed biophysics of the autoreceptors is not included; instead the model has terms that represent the effect of e5-HT on TPH and on release from the vesicles. And finally, this is a model for a terminal and thus has limited value in studying network questions about the full serotonergic system.

It is important to keep in mind that there is no such thing as *the* serotonergic terminal. Important parameters vary considerably from one projection region to another. For example, SERT density (which corresponds roughly to the *Vmax* of *V*SERT) varies by about a factor of 5 (Bunin et al., 1998; Daws et al., 2005; Lin et al., 2004). And, functional polymorphisms for the TPH, SERT, and MAO genes are known to exist. Indeed, one of the strengths of the model is that it can be used to study the likely effects of such variations on the functional behavior of serotonergic terminals.
