**5. Applying the models**

In this section we describe several applications of our 5-HT and DA terminal models to show how they can be used. The DA terminal model is similar in structure to the 5-HT model, though the details of the kinetics are different (Best et al., 2009).

#### **5.1 Homeostatic effects of the autoreceptors**

It is clear that the 5-HT autoreceptors create homeostasis by providing a kind of end-product inhibition. If firing rate goes up, then e5-HT will go up, which reduces synthesis and release via the autoreceptors. If firing rate goes down, then e5-HT will go down, which increases synthesis and release via the autoreceptors. Thus, the autoreceptors ensure that the average extracellular 5-HT in projections regions due to tonic firing of dorsal raphe neurons does not change very much.

It has been much less remarked in the literature that the autoreceptors provide another kind of homeostasis. The genes for many of the key proteins in the 5-HT system, for example TPH2, SERT, and MAO, have common functional polymorphisms. However, because of the autoreceptors, the polymorphisms have a much smaller effect on e5-HT than one might think. For, example the P449R polymorphism and the R441H polymorphism of TPH2 reduce its 6 Will-be-set-by-IN-TECH

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

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

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

In this section we describe several applications of our 5-HT and DA terminal models to show how they can be used. The DA terminal model is similar in structure to the 5-HT model,

It is clear that the 5-HT autoreceptors create homeostasis by providing a kind of end-product inhibition. If firing rate goes up, then e5-HT will go up, which reduces synthesis and release via the autoreceptors. If firing rate goes down, then e5-HT will go down, which increases synthesis and release via the autoreceptors. Thus, the autoreceptors ensure that the average extracellular 5-HT in projections regions due to tonic firing of dorsal raphe neurons does not

It has been much less remarked in the literature that the autoreceptors provide another kind of homeostasis. The genes for many of the key proteins in the 5-HT system, for example TPH2, SERT, and MAO, have common functional polymorphisms. However, because of the autoreceptors, the polymorphisms have a much smaller effect on e5-HT than one might think. For, example the P449R polymorphism and the R441H polymorphism of TPH2 reduce its

though the details of the kinetics are different (Best et al., 2009).

**5.1 Homeostatic effects of the autoreceptors**

can be found in Best et al. (2010b).

serotonergic system.

serotonergic terminals.

change very much.

**5. Applying the models**

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.

1997; Schildkraut, 1965). This hypothesis led to the development of monoamine oxidase inhibitors (MAOIs), tricyclic anti-depressants and the selective serotonin reuptake inhibitors (SSRIs). The idea of the MAOIs is that by preventing the degradation of 5-HT, more will be available for packaging into synaptic vesicles. The idea of the tri-cyclics and the SSRIs is that they block SERTs and inhibit reuptake of 5-HT from the extracellular space, therefore increasing "serotonergic signaling." These drugs have shown some efficacy in the treatment of depression, but the causal chain of events and the reasons why they benefit some patients

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 413

The simple hypothesis that SSRIs would raise the level of 5-HT in serotonergic synapses by blocking reuptake was thrown into doubt by the discovery that the cell bodies of most 5-HT neurons also release 5-HT and have SERTs. Furthermore, increased e5-HT in the RN decreases the tonic firing rate of those cells via the 5-*HT*1*<sup>A</sup>* autoreceptors (Adell et al., 2002; Gartside et al., 1995). Thus, there are two conflicting effects. Blocking the SERTs in the terminal region would tend to raise e5-HT there, and blocking the SERTs in the raphe nuclei (RN) would tend to decrease e5-HT in the terminal region. The balance between the two effects will depend on the densities of 5-*HT*1*<sup>A</sup>* autoreceptors on different 5-HT populations in the RN and on the densities of SERTs in different projection regions, both quite variable. Thus one would expect that experimental results would depend on dose and on the projection regions being studied, and this was found to be true (Bel & Artigas, 1992; Hervas & Artigas, 1998; Malagie et al., 1995). In some cases, acute doses of SSRIs even decreased e5-HT in projection regions.

The next hypothesis focused on the 5-*HT*1*<sup>A</sup>* autoreceptors on the RN cell bodies. It was shown that giving 5-*HT*1*<sup>A</sup>* antagonists or knocking out the autoreceptors entirely potentiates the SSRI-induced increase of e5-HT in projection regions. Similarly, 5-*HT*1*<sup>A</sup>* knockouts show increased release in projection regions (Chaput et al., 1986; Knobelman et al., 2001). Furthermore, a number of studies showed that chronic treatment with SSRIs desensitizes the 5-*HT*1*<sup>A</sup>* autoreceptors in the RN (Blier et al., 1987; Chaput et al., 1986; Hervas et al., 2001; Invernizzi et al., 1992). And thus, one could explain the improvements of patients on the time scale of 3-6 weeks by the slow desensitization of autoreceptors. However, when e5-HT was measured in projection regions during the entire course of chronic SSRI treatment, it was found that e5-HT concentrations went up initially and then plateaued or declined somewhat over the course of treatment (Anderson et al., 2005; Smith et al., 2000). Thus the autoreceptor desensitization hypothesis seems unlikely to explain the delay of beneficial effects of SSRI

In (Best et al., 2011) we propose a new hypothesis for the efficacy of SSRIs and provide calculations with the 5-HT terminal model to support our ideas. The 5-HT cells in the RN fire tonically at about 1 Hz and occasionally individual spikes are replaced by short bursts (Feldman et al., 1997; Hajos et al., 1995; Heyn et al., 1982). Our physiological point of view is that tonic firing by the 5-HT neurons in the RN maintains 5-HT tone in target tissues by volume transmission and burst firing conveys specific information to one-on-one synapses that are known to exist (Maley et al., 1990; Parnavelas & Papadopoulos, 1989). Our hypothesis is that chronic treatment of depressed patients with SSRIs returns the response to bursts arriving in terminal regions to normal and we show that this is true in our model. The model behavior depends on the down regulation of SERTs on terminal membranes known to be caused by chronic exposure to SSRIs (Benmansour et al., 2002; Gould et al., 2003; Lau et al.,

2008; Mizra et al., 2007). For details, see (Best et al., 2011).

and not others are unknown.

treatments.

activity to 65% and 19% of wild type, respectively. But the model predicts that e5-HT will decrease to 90% and 45% of wild type in these two cases; see Figure 4 of (Best et al., 2010b). Similarly, we show in (Best et al., 2009) that the D2 autoreceptors make extracellular DA much less sensitive to the expression level or activity of tyrosine hydroxylase (TH).

#### **5.2 Passive stabilization of DA in the striatum**

An interesting and important feature of PD is that symptoms do not appear until a very large percentage (typically 60-90%) of the cells in the SNc have died (Agid, 1991; Zygmond et al., 1990). Animal models have shown that tissue levels of DA in the striatum decline proportionally to cell loss, but eDA remains essentially normal until 85% of the SNc cells have died (Bergstrom & Garris, 2003; Bezard et al., 2001; Dentresangle et al., 2001), and this is widely believed to be the reason that symptoms do not appear until very late in the degeneration of the SNc.

A number of researchers have proposed that this homeostasis of eDA results from active adaptive mechanisms such as increased DA synthesis and the formation of new terminals (Hornykiewicz, 1966; Stanic et al., 2003; Zygmond et al., 1990; 1984). However, Garris and co-workers proposed that the homeostasis is due to passive mechanisms such as release and reuptake and provided some experimental confirmation (Bergstrom & Garris, 2003; Garris et al., 1997; Garris & Wightman, 1994). Their idea is as follows. DA is released in the striatum and is then taken back up into the terminals by the DA transporters (DATs). As the cells in the SNc die the amount of DA released in the striatum decreases proportionally, but the number of DATs available for reuptake has also decreased proportionally. Thus a released DA molecule will spend about the same amount of time in the extracellular space no matter how many SNc cells have died. Garris and co-workers called this "passive stabilization." They did not explain why this homeostasis breaks down when the fraction, *f* , of SNc cells that are alive becomes small.

We investigated these proposals with our mathematical model of a DA terminal (Reed et al., 2009). We found that the passive stabilization mechanism proposed by Garris works as proposed and we determined why the mechanism breaks down when *f* is small. Not all released DA molecules are put back into DA terminals by the DATs. Some are taken up by glial cells or blood vessels and some diffuse out of the striatum. As SNc cells die and the DA terminals in the striatum become more sparse, a greater percentage of released DA is lost through these mechanisms. This is why the Garris passive stabilization mechanism breaks down when *f* is small. We provided quantitative calculations about these effects and showed that passive stabilization itself keeps eDA almost constant when *f* is between <sup>1</sup> <sup>2</sup> and 1. When more than half of the SNc cells have died, the terminal autoreceptors contribute substantially to the homeostasis of eDA. And, only when *f* is as low as .15 or .1 are the combined homeostatic effects of passive stabilization and the autoreceptors overwhelmed by the removal of DA from the striatum by the mechanisms discussed above. For details, see (Reed et al., 2009).

#### **5.3 Burst firing in the raphe nuclei and SSRIs**

The etiology of depressive illness remains unknown despite a large body of research. A hypothesis that has been central to much work in pharmacology and electrophysiology is that depression is caused by dysfunction in the serotonergic signaling system (Feldman et al., 8 Will-be-set-by-IN-TECH

activity to 65% and 19% of wild type, respectively. But the model predicts that e5-HT will decrease to 90% and 45% of wild type in these two cases; see Figure 4 of (Best et al., 2010b). Similarly, we show in (Best et al., 2009) that the D2 autoreceptors make extracellular DA much

An interesting and important feature of PD is that symptoms do not appear until a very large percentage (typically 60-90%) of the cells in the SNc have died (Agid, 1991; Zygmond et al., 1990). Animal models have shown that tissue levels of DA in the striatum decline proportionally to cell loss, but eDA remains essentially normal until 85% of the SNc cells have died (Bergstrom & Garris, 2003; Bezard et al., 2001; Dentresangle et al., 2001), and this is widely believed to be the reason that symptoms do not appear until very late in the degeneration of

A number of researchers have proposed that this homeostasis of eDA results from active adaptive mechanisms such as increased DA synthesis and the formation of new terminals (Hornykiewicz, 1966; Stanic et al., 2003; Zygmond et al., 1990; 1984). However, Garris and co-workers proposed that the homeostasis is due to passive mechanisms such as release and reuptake and provided some experimental confirmation (Bergstrom & Garris, 2003; Garris et al., 1997; Garris & Wightman, 1994). Their idea is as follows. DA is released in the striatum and is then taken back up into the terminals by the DA transporters (DATs). As the cells in the SNc die the amount of DA released in the striatum decreases proportionally, but the number of DATs available for reuptake has also decreased proportionally. Thus a released DA molecule will spend about the same amount of time in the extracellular space no matter how many SNc cells have died. Garris and co-workers called this "passive stabilization." They did not explain why this homeostasis breaks down when the fraction, *f* , of SNc cells that are alive

We investigated these proposals with our mathematical model of a DA terminal (Reed et al., 2009). We found that the passive stabilization mechanism proposed by Garris works as proposed and we determined why the mechanism breaks down when *f* is small. Not all released DA molecules are put back into DA terminals by the DATs. Some are taken up by glial cells or blood vessels and some diffuse out of the striatum. As SNc cells die and the DA terminals in the striatum become more sparse, a greater percentage of released DA is lost through these mechanisms. This is why the Garris passive stabilization mechanism breaks down when *f* is small. We provided quantitative calculations about these effects and showed that passive stabilization itself keeps eDA almost constant when *f* is between <sup>1</sup>

1. When more than half of the SNc cells have died, the terminal autoreceptors contribute substantially to the homeostasis of eDA. And, only when *f* is as low as .15 or .1 are the combined homeostatic effects of passive stabilization and the autoreceptors overwhelmed by the removal of DA from the striatum by the mechanisms discussed above. For details, see

The etiology of depressive illness remains unknown despite a large body of research. A hypothesis that has been central to much work in pharmacology and electrophysiology is that depression is caused by dysfunction in the serotonergic signaling system (Feldman et al.,

<sup>2</sup> and

less sensitive to the expression level or activity of tyrosine hydroxylase (TH).

**5.2 Passive stabilization of DA in the striatum**

the SNc.

becomes small.

(Reed et al., 2009).

**5.3 Burst firing in the raphe nuclei and SSRIs**

1997; Schildkraut, 1965). This hypothesis led to the development of monoamine oxidase inhibitors (MAOIs), tricyclic anti-depressants and the selective serotonin reuptake inhibitors (SSRIs). The idea of the MAOIs is that by preventing the degradation of 5-HT, more will be available for packaging into synaptic vesicles. The idea of the tri-cyclics and the SSRIs is that they block SERTs and inhibit reuptake of 5-HT from the extracellular space, therefore increasing "serotonergic signaling." These drugs have shown some efficacy in the treatment of depression, but the causal chain of events and the reasons why they benefit some patients and not others are unknown.

The simple hypothesis that SSRIs would raise the level of 5-HT in serotonergic synapses by blocking reuptake was thrown into doubt by the discovery that the cell bodies of most 5-HT neurons also release 5-HT and have SERTs. Furthermore, increased e5-HT in the RN decreases the tonic firing rate of those cells via the 5-*HT*1*<sup>A</sup>* autoreceptors (Adell et al., 2002; Gartside et al., 1995). Thus, there are two conflicting effects. Blocking the SERTs in the terminal region would tend to raise e5-HT there, and blocking the SERTs in the raphe nuclei (RN) would tend to decrease e5-HT in the terminal region. The balance between the two effects will depend on the densities of 5-*HT*1*<sup>A</sup>* autoreceptors on different 5-HT populations in the RN and on the densities of SERTs in different projection regions, both quite variable. Thus one would expect that experimental results would depend on dose and on the projection regions being studied, and this was found to be true (Bel & Artigas, 1992; Hervas & Artigas, 1998; Malagie et al., 1995). In some cases, acute doses of SSRIs even decreased e5-HT in projection regions.

The next hypothesis focused on the 5-*HT*1*<sup>A</sup>* autoreceptors on the RN cell bodies. It was shown that giving 5-*HT*1*<sup>A</sup>* antagonists or knocking out the autoreceptors entirely potentiates the SSRI-induced increase of e5-HT in projection regions. Similarly, 5-*HT*1*<sup>A</sup>* knockouts show increased release in projection regions (Chaput et al., 1986; Knobelman et al., 2001). Furthermore, a number of studies showed that chronic treatment with SSRIs desensitizes the 5-*HT*1*<sup>A</sup>* autoreceptors in the RN (Blier et al., 1987; Chaput et al., 1986; Hervas et al., 2001; Invernizzi et al., 1992). And thus, one could explain the improvements of patients on the time scale of 3-6 weeks by the slow desensitization of autoreceptors. However, when e5-HT was measured in projection regions during the entire course of chronic SSRI treatment, it was found that e5-HT concentrations went up initially and then plateaued or declined somewhat over the course of treatment (Anderson et al., 2005; Smith et al., 2000). Thus the autoreceptor desensitization hypothesis seems unlikely to explain the delay of beneficial effects of SSRI treatments.

In (Best et al., 2011) we propose a new hypothesis for the efficacy of SSRIs and provide calculations with the 5-HT terminal model to support our ideas. The 5-HT cells in the RN fire tonically at about 1 Hz and occasionally individual spikes are replaced by short bursts (Feldman et al., 1997; Hajos et al., 1995; Heyn et al., 1982). Our physiological point of view is that tonic firing by the 5-HT neurons in the RN maintains 5-HT tone in target tissues by volume transmission and burst firing conveys specific information to one-on-one synapses that are known to exist (Maley et al., 1990; Parnavelas & Papadopoulos, 1989). Our hypothesis is that chronic treatment of depressed patients with SSRIs returns the response to bursts arriving in terminal regions to normal and we show that this is true in our model. The model behavior depends on the down regulation of SERTs on terminal membranes known to be caused by chronic exposure to SSRIs (Benmansour et al., 2002; Gould et al., 2003; Lau et al., 2008; Mizra et al., 2007). For details, see (Best et al., 2011).

lateral inhibition by diffusion of extracellular 5-HT in the RN and a model of the projections

Mathematical Models: Interactions Between Serotonin and Dopamine in Parkinson's Disease 415

Finally, it is well-known that the brain is capable of rewiring itself after injury to use available neurons for new purposes. Note that, in a certain sense, that is what levodopa therapy is stimulating, the use of 5-HT neurons as DA neurons. And, it is known that lesioning the SNc causes hyperinnervation by 5-HT neurons in the striatum (Maeda et al., 2003). Such retraining and rewiring takes time, of course, and it is possible that it can't happen fast enough to compensate for the degeneration in PD, but the possibility is intriguing. Not enough is known presently for mathematical modeling to be helpful here. However, if and when anatomical and electrophysiological information becomes available about such compensatory processes, mathematical models, developed along the lines that we have indicated, could perhaps suggest treatment strategies that would facilitate the compensatory processes.

This work was supported by NSF grants DMS-061670 (MR,HFN) and EF-1038593 (HFN,MR), NSF CAREER grant DMS-0956057 (JB), and NSF agreement 0112050 through the Mathematical Biosciences Institute (JB, MR). JB is an Alfred P. Sloan Research Foundation

Adell, A., Celada, P., Abella, M. T. & Artigasa, F. (2002). Origin and functional role of the extracellular serotonin in the midbrain raphe nuclei, *Brain Res Rev* 39: 154–180.

Ahlskog, J. E. (2004). Challenging conventional wisdom: The etiologic role of dopamine oxidative stress in Parkinson's disease, *Movement Disorders* 20(3): 271–282. Ahlskog, J. E. & Muenter, M. D. (2001). Frequency of levodopa-related dyskinesias and

Anderson, G. M., Barr, C. S., Lindell, S., Durham, A. C., Shifrovich, I. & Higley, J. D. (2005).

Bel, N. & Artigas, F. (1992). Fluoxetine preferentially increases extracellular

Benmansour, S., Owens, W. A., Cecchi, M., Morilak, D. & Frazer, A. (2002). Serotonin clearance

Bergstrom, B. & Garris, P. (2003). 'Passive stabilization' of striatal extracellular dopamine

motor fluctuations as estimated from the cumulative literature, *Movement Disorders*

Time course of the effects of the serotonin-selective reuptake inhibitor sertraline on central and peripheral serotonin neurochemistry in the rhesus monkey, *Phycopharma*

5-hydroxytryptamine in the raphe nuclei: an in vivo microdialysis study, *Eur.*

in vivo is altered to a greater extent by antidepressant-induced downregulation of the serotonin transporter than by acute blockade of the transporter, *J. Neurosci.*

across the lesion spectrum encompassing the presymptomatic phase of Parkinson's disease: a voltametric study in the 6-OHDA-lesioned rat, *J. Neurochem* 87: 1224–36. Best, J. A., Nijhout, H. F. & Reed, M. C. (2009). Homeostatic mechanisms in dopamine synthesis and release: a mathematical model, *Theor Biol Med Model* 6: 21.

Fellow. The authors thank Shira Rubin for a close reading of the manuscript.

Agid, Y. (1991). Parkinson's disease: pathophysiology, *Lancet* 337: 1321–1324.

to the mPFC with negative feedback from the mPFC to the RN.

**7. Acknowledgements**

16(3): 448–458.

178: 339–346.

*J. Pharmacol.* 229: 101–103.

22(15): 6766–6772.

**8. References**

#### **6. Future work**

We indicate briefly here some of the ideas that we plan to pursue. We plan to use our current model of a 5-HT terminal described above to investigate the consequences of levodopa uptake by 5-HT terminals. Both 5-HTP and levodopa will compete for AADC that will turn them into 5-HT and DA respectively, and the monoamine transporter will package them together into vesicles. Since there is leakage out of the vesicles driven by concentration gradients, the competition will limit the amounts of 5-HT and DA available for release. Our physiological point of view is that normal 5-HT or DA neurons maintain 5-HT or DA tone in target tissues by volume transmission and convey specific information via burst firing. The autoreceptors on DA neurons inhibit release when the extracellular concentration of DA goes up due to a burst, bringing the concentration back to the normal tonic level rapidly. However, levodopa therapy partially turns 5-HT neurons into DA neurons that do not have DA autoreceptors and one expects that stimulation of the 5-HT system will therefore cause larger than normal swings in extracellular DA in the striatum after levodopa therapy. This effect will be compounded by the fact that cell death in the SNc implies that there will be many fewer DATs in the striatum to take up the released DA. We plan to investigate this situation with our model. Finally, we are currently extending our models to include the competition between tyrosine, tryptophan, leucine, isoleucine, and valine at the blood-brain barrier. When this is completed we can study the tryptophan depletion and tryptophan loading experiments described in (Scholtissen et al., 2006).

We are particularly interested in how levodopa therapy could produce dyskinesis and have some ideas that can be tried out through mathematical modeling. (Carta et al., 2007) provided strong evidence that release of DA from 5-HT neurons causes LID by showing that 5-*HT*1*<sup>A</sup>* agonists that reduce RN firing and/or 5-*HT*1*<sup>B</sup>* agonists that reduce release in the striatum both reduce the incidence of LID in an animal model. We plan to extend our 5-HT terminal model to include the cell body in the RN so that we can study release of DA in the striatum in the presence of either 5-*HT*1*<sup>A</sup>* or 5-*HT*1*<sup>B</sup>* agonists (or both) after cell death in the SNc reduces the number of DATs. This will provide a platform for trying out *in silico* the experiments in (Carta et al., 2007).

There is another intriguing possibility that we plan to investigate by modeling. Recall that the 5-HT neurons in the raphe nuclei release 5-HT from their cell bodies when they fire. The released 5-HT binds to the 5-*HT*1*<sup>A</sup>* autoreceptors on the cell bodies and inhibits RN firing (Adell et al., 2002). This is a kind of lateral inhibition in the RN that limits total firing. However, in the presence of levodopa, the cell bodies will release a combination of 5-HT and DA, and the lower extracellular concentration of 5-HT will provide much less lateral inhibition. Thus is it likely that the 5-HT neurons in the RN fire more frequently after levodopa therapy and there is evidence for altered firing patterns (Zhang et al., 2007). This would have the effect of releasing more DA in the striatum. Notice, however, that raphe neurons project to many brain regions that send inhibitory projections back to the RN (for example the mPFC; see (Celada et al., 2001)). Such negative feedback systems often exhibit oscillations if they are forced hard enough, and such oscillations would mean periodic oscillations in the amount of firing of 5-HT neurons in the RN and thus periodic oscillations in the amount of DA released in the striatum. It is tempting to speculate that such oscillations may contribute to LID and that they could be initiated by intermittent levodopa therapy (Nutt et al., 2000; Olanow et al., 2006; 2000). We plan to investigate this hypothesis by developing mathematical models of the lateral inhibition by diffusion of extracellular 5-HT in the RN and a model of the projections to the mPFC with negative feedback from the mPFC to the RN.

Finally, it is well-known that the brain is capable of rewiring itself after injury to use available neurons for new purposes. Note that, in a certain sense, that is what levodopa therapy is stimulating, the use of 5-HT neurons as DA neurons. And, it is known that lesioning the SNc causes hyperinnervation by 5-HT neurons in the striatum (Maeda et al., 2003). Such retraining and rewiring takes time, of course, and it is possible that it can't happen fast enough to compensate for the degeneration in PD, but the possibility is intriguing. Not enough is known presently for mathematical modeling to be helpful here. However, if and when anatomical and electrophysiological information becomes available about such compensatory processes, mathematical models, developed along the lines that we have indicated, could perhaps suggest treatment strategies that would facilitate the compensatory processes.

#### **7. Acknowledgements**

This work was supported by NSF grants DMS-061670 (MR,HFN) and EF-1038593 (HFN,MR), NSF CAREER grant DMS-0956057 (JB), and NSF agreement 0112050 through the Mathematical Biosciences Institute (JB, MR). JB is an Alfred P. Sloan Research Foundation Fellow. The authors thank Shira Rubin for a close reading of the manuscript.

#### **8. References**

10 Will-be-set-by-IN-TECH

We indicate briefly here some of the ideas that we plan to pursue. We plan to use our current model of a 5-HT terminal described above to investigate the consequences of levodopa uptake by 5-HT terminals. Both 5-HTP and levodopa will compete for AADC that will turn them into 5-HT and DA respectively, and the monoamine transporter will package them together into vesicles. Since there is leakage out of the vesicles driven by concentration gradients, the competition will limit the amounts of 5-HT and DA available for release. Our physiological point of view is that normal 5-HT or DA neurons maintain 5-HT or DA tone in target tissues by volume transmission and convey specific information via burst firing. The autoreceptors on DA neurons inhibit release when the extracellular concentration of DA goes up due to a burst, bringing the concentration back to the normal tonic level rapidly. However, levodopa therapy partially turns 5-HT neurons into DA neurons that do not have DA autoreceptors and one expects that stimulation of the 5-HT system will therefore cause larger than normal swings in extracellular DA in the striatum after levodopa therapy. This effect will be compounded by the fact that cell death in the SNc implies that there will be many fewer DATs in the striatum to take up the released DA. We plan to investigate this situation with our model. Finally, we are currently extending our models to include the competition between tyrosine, tryptophan, leucine, isoleucine, and valine at the blood-brain barrier. When this is completed we can study the tryptophan depletion and tryptophan loading experiments described in (Scholtissen et al.,

We are particularly interested in how levodopa therapy could produce dyskinesis and have some ideas that can be tried out through mathematical modeling. (Carta et al., 2007) provided strong evidence that release of DA from 5-HT neurons causes LID by showing that 5-*HT*1*<sup>A</sup>* agonists that reduce RN firing and/or 5-*HT*1*<sup>B</sup>* agonists that reduce release in the striatum both reduce the incidence of LID in an animal model. We plan to extend our 5-HT terminal model to include the cell body in the RN so that we can study release of DA in the striatum in the presence of either 5-*HT*1*<sup>A</sup>* or 5-*HT*1*<sup>B</sup>* agonists (or both) after cell death in the SNc reduces the number of DATs. This will provide a platform for trying out *in silico* the experiments in

There is another intriguing possibility that we plan to investigate by modeling. Recall that the 5-HT neurons in the raphe nuclei release 5-HT from their cell bodies when they fire. The released 5-HT binds to the 5-*HT*1*<sup>A</sup>* autoreceptors on the cell bodies and inhibits RN firing (Adell et al., 2002). This is a kind of lateral inhibition in the RN that limits total firing. However, in the presence of levodopa, the cell bodies will release a combination of 5-HT and DA, and the lower extracellular concentration of 5-HT will provide much less lateral inhibition. Thus is it likely that the 5-HT neurons in the RN fire more frequently after levodopa therapy and there is evidence for altered firing patterns (Zhang et al., 2007). This would have the effect of releasing more DA in the striatum. Notice, however, that raphe neurons project to many brain regions that send inhibitory projections back to the RN (for example the mPFC; see (Celada et al., 2001)). Such negative feedback systems often exhibit oscillations if they are forced hard enough, and such oscillations would mean periodic oscillations in the amount of firing of 5-HT neurons in the RN and thus periodic oscillations in the amount of DA released in the striatum. It is tempting to speculate that such oscillations may contribute to LID and that they could be initiated by intermittent levodopa therapy (Nutt et al., 2000; Olanow et al., 2006; 2000). We plan to investigate this hypothesis by developing mathematical models of the

**6. Future work**

2006).

(Carta et al., 2007).


de la Fuente-Fernandez, R., Lu, J.-Q., Sossi, V., Jivan, S., Schulzer, M., Holden, J. E., Lee, C. S.,

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**19** 

*Belgium* 

**Dopaminergic Control of the Neurotransmitter** 

A critical role of the subthalamic nucleus (STN) in the control of movement has been proposed based on the observations that its lesion or high-frequency stimulation, aimed at altering its activity, is effective in alleviating clinical features of Parkinson's disease (Bergman et al,. 1990; Bennazouz et al., 1993; Pollak et al., 1993, Benazzouz et al., 2000). Indeed, overactivity of the subthalamic neurons due to the loss of midbrain dopaminergic neurons is believed to be a key feature in Parkinson's disease. Several studies indicate that the activity of STN neurons can be influenced directly by dopamine and its receptor agonists/antagonists. Indeed, the STN receives a direct dopaminergic input arising in the substantia nigra pars compacta (SNc) and both dopamine D1- and D2-like receptors are present in the STN (Canteras et al., 1990; Hassani et al., 1997; Flores et al., 1999). Understanding the position of the STN within the basal ganglia and the possible direct effects of dopamine and its ligands at the level of this nucleus in normal and parkinsonian states may be important in the development of new therapies for Parkinson's disease. The purpose of this chapter is to give an overview of the current position of the STN in the basal ganglia motorloop and to clarify the role of dopamine at the level of the STN in both normal

Despite the small size of this biconvex-shaped structure, the STN has an important role in the modulation of the basal ganglia output and thus movement control (DeLong & Wichmann, 2007; Obeso et al., 2008; Gubbelini et al., 2009). Indeed, together with the striatum, the STN forms the major input to the basal ganglia and is considered an important relay nucleus of the indirect pathway. In this section, the role of the STN within the basal

The basal ganglia consist of five interconnected nuclei including the caudate nucleus, the putamen [which forms together with the caudate nucleus the striatum], the globus pallidus (pars interna (GPi) and externa (GPe)) the SN (SNc and substantia nigra pars reticulata (SNr))

conditions and in parkinsonian experimental animal models.

**2.1 The subthalamic nucleus as a part of the basal ganglia** 

**2. The subthalamic nucleus and its connections** 

ganglia and its connections are described.

**1. Introduction** 

**Release in the Subthalamic Nucleus: Implications for Parkinson's Disease** 

Ben Ampe, Anissa El Arfani, Yvette Michotte and Sophie Sarre

**Treatment Strategies** 

*Vrije Universiteit Brussel,* 

