**2. The model**

508 Etiology and Pathophysiology of Parkinson's Disease

Conversely, under the burst state thalamic neurons are no more reliable channels through which neural representations from sensorial inputs reach the cerebral cortex. As a matter of fact, this mode of activity underlies the thalamic behavior during sleep (Steriade et al., 1993; Pace-Schott & Hobson, 2002). In this case, the environmental stimuli are not perceived consciously as it occurs throughout wakefulness (Carvalho, 1994). The thalamic burst mode also permeates epileptic episodes during which environmental information is not processed reliably (Jeanmonod et al., 1996; Llinás et al., 1999). The dynamics of the ionic channels under the burst mode are different from the ones underlying the thalamic tonic state. That is why, under the burst mode, thalamic neurons spike quite autonomously, in such a way that

Since the inattention symptoms addressed in (Madureira et al., 2010) concerned awakened people, the model considered the behavior of thalamic neurons under the tonic state. In the present work, we go further with the matter and scrutinize relationships between the MDA and the oscillatory state of neurons in the thalamic complex. Doing so, it becomes possible to widen the investigation to examine a possible MDA contribution to sleep alterations in PD

Clinical evidences indicating a variety of sleep alterations in PD suggest that this class of symptoms should not be considered as a secondary one: on the contrary, sleep problems certainly pertain to the core symptoms that define PD (De Cock et al., 2008; Arnulf & Leu-Semenescu, 2009). Such sleep alterations involve daytime sleepiness, inappropriate intrusion of REM sleep episodes throughout the day, and nocturne movement. In other words, parkinsonism disrupts the control of the sleep-wake cycle (Jancovic, 2002; Arnulf & Leu-

The question thus that naturally arises concerns the dopaminergic role in the sleep-wake cycle control. Given the clinical evidence from sleep impairments in PD, a disease whose basic neural origins is the dopaminergic neurons degeneration, we tend to conclude that

Up to recently, the above mentioned clinical observations have been quite disregarded. If, through PD, the dopaminergic participation in the control of the sleep cycle may be inferred (Rye, 2004), there is, on the other hand, a number of neuroscientific studies showing that the variation in the dopaminergic level throughout the sleep-wake cycle is too small to be taken

A series of experiments undertaken by (Dzirasa et al., 2006), however, illuminated this controversy. They were capable of demonstrating that sleep-wake states are also controlled by dopamine. This seminal work shows the importance of the dopaminergic influence in the sleep regulation – even under small variations. In addition, they emphasize the relationship

Here, we address – through a neurocomputational approach – the interference of SN neurons, particularly the degenerated ones, in the thalamocortical spiking modes. Our goal consists in investigating if the PD dopaminergic disruption alters the typical spiking patterns associated

We now outline the contents of this chapter. In Section 2 we introduce our hypothesis of dopaminergic influence on the control of the sleep-wake cycle, and describe the model. In Section 3, we explain how the computational simulations of the model are designed, and present the computational results. Finally, we conclude by discussing the consequences of our results in terms of sleep alterations in PD, in the context of the neuroscience of sleep.

to sleep and wake states, thus compromising the normal sleep-wake cycle in PD.

and, to look at attention focusing aspects under a little more detailed point of view.

their pattern of activity does not represent the input information.

dopamine does participate in the sleep regulation. Is it the case?

between dopaminergic alterations and sleep impairments in PD.

Semenescu, 2009).

into account (Jancovic, 2002).

In (Madureira et al., 2010), we proposed a mathematical model indicating how the mesothalamic dopamine influences the thalamocortical loop, through the TRN, and thus modulates the attentional focus formation. In particular, we investigated relationships between alterations in this dopaminergic pathway and attention deficits in PD and ADHD.

Here, we extend this model to address how dopamine influences the emergence of distinct spiking modes in thalamic neurons. Since the thalamic modes of spiking are specifically related to sleep and wake neuron states, our modeling enables us to discuss if and how dopaminergic alterations in PD are related to the sleep problems observed in the disease.

Throughout the sleep-wake cycle, complex chemical and electrical networks of events occur in the thalamocortical neural circuit. They give rise to distinct patterns of neural behavior that underlies the different brain rhythms specifically associated to different sleep phases and also to the wake state (Pace-Schott & Hobson, 2002; Hobson & Pace-Schott, 2002; Diekelmann & Born, 2010).

The variety of brain rhythms extensively studied by the neuroscience of sleep (Steriade et al., 2003; De Gennaro & Ferrara, 2003; Llinás & Steriade, 2006; Steriade, 2006; Pace-Schott & Hobson, 2002; Hobson & Pace-Schott, 2002; Hobson, 2009; Diekelmann & Born, 2010) reflects the behavior of neural groups. Indeed, such brain rhythms, e.g. spindles, slow oscillation and theta activity, are measurements of field potential oscillations captured by EEGs experiments – not by single cell recordings. Therefore, they provide information from a scale above the cellular one.

Our model, on the other hand, addresses the dynamics of ionic and synaptic currents. It thus deals with information at the same level of single cell recordings, in particular, variations in the membrane electric potential.

Under this approach, it is reasonable to examine sleep issues by mathematically modeling neurons in the thalamocortical loop, and computationally simulating the action of neuromodulators throughout this brain area.

As an outcome of our neurocomputational model, we conjecture that the inhibitory action of mesothalamic dopamine in the thalamic reticular nucleus (TRN) (Florán et al., 2004) affects the spiking mode of thalamocortical neurons. This is possible whenever the dopaminergic action leads to a period of neuron hyperpolarization that activates the calcium conductance, thus changing the way by which the neuron behaves (Carvalho, 1994). Next, we present the model and develop such ideas more deeply.

### **2.1 The neural network**

We model a thalamocortical circuit with a dopaminergic projection from SN to the TRN, according to Figure 1. We can note the excitatory and inhibitory connections in the modeled neural network. Thalamocortical and corticothalamic projections are excitatory, mediated by glutamate. Both areas send glutamatergic excitatory collateral axons to the TRN. Conversely, efferent projections from the TRN to thalamus are GABAergic inhibitory (Guillery & Harting, 2003).

With relation to the dopaminergic action, the architecture of the network incorporates results gathered together from Freeman et al. (2001) and Florán et al. (2004), which reveal the inhibitory dopaminergic projection from SN to the TRN, or the mesothalamic dopaminergic pathway. The explanation we suggest for the dopaminergic action in TRN is

Mesothalamic Dopaminergic Activity: Implications in Sleep Alterations in Parkinson's Disease 511

In the following, we describe the systems of equations that model the behaviors of *Tx*, *Ty*, *TRNx* and *TRNy*. The neural activities of the SN and the PFC, as well as the excitatory projections from *X* and *Y* are codified as temporal sequences representing their respective spiking times. As this work takes further the model presented in (Madureira et al., 2010), throughout the next section we examine specially the particular aspects of

To better investigate alternate thalamic states, this model incorporates physiological features related to the tonic and the bursting modes of thalamic spikes. Thus, we address the neuron spike by considering the sodium, *INa*, and the calcium, *ICa*, currents, which depolarize the neuron, and the potassium current, *IK*, which restores the cellular membrane potential (Kandel, 2000). With relation to the patterns of intervals between spikes, associated to different potassium currents (McCormick et al., 1995), our model incorporates the calcium dependent-potassium current, *Ic*, particularly, in the *TRN* neurons: it is a transient current, whose amplitude increases with intracellular calcium concentration, and it suffers dopaminergic influence (Florán et al., 2004; Madureira et al., 2010). Essentially associated to the bursting mode, the *Iahp*, a current that underlies neural hyperpolarization, is modeled as

The model deals with a network of ionic and synaptic events that leads to a specific mode of spiking. Particularly, under this approach we examine if dopamine is able to influence the spikes of thalamic neurons. In this model we assume that a high inhibitory dopamine action on D4 receptors in TRN neurons hyperpolarizes such cells, thus facilitating the activation of calcium currents. As a consequence, and according to thalamic properties (Carvalho, 1994), even a small membrane depolarization is capable of triggering an action potential, due to the low threshold calcium-currents. Whenever the inflow of Ca2+ in the cell, due to spikes, increases the Ca2+ concentration above a threshold, then the hyperpolarizing current *Iahp*, becomes activated, hyperpolarizing the neuron. Therefore, the calcium currents become activate – or remain activated, depending on their previous state – and a cyclic or oscillatory behavior takes place in the TRN neuron. This is the burst thalamic mode of spiking, associated to sleep states (Steriade et al., 1993; Llinás & Steriade, 2006). It may be interrupted due to the calcium currents inactivation, which occurs whenever the neuron does not suffer

Based on this model, we speculate another possibility that is directly related to the PD origins: the generation of bursting in thalamic neurons, due to a strong inhibition imposed by TRN neurons. Such situation is plausible to occur in case of mesothalamic hypodopaminergy, which allows the inhibitory TRN neurons to become atypically over

Because of the dopaminergic modulation in the TRN, two types of neurons are modeled: the thalamic ones, *Tx* and *Ty*, and the *TRN* neurons. Both are single point spiking and are

We define a simplified neuron model with a single compartment where dendrites, soma and axons are concentrated, and whose electric potential is *V*. The neural membrane is modeled

this extension.

**2.2 Ionic currents** 

described below.

presented next.

**2.2.1 Thalamic neurons** 

according to the equation:

hyperpolarization for around 100ms.

stimulated (Madureira et al., 2010, Florán et al., 2004).

that dopamine acts on the calcium dependent potassium channels, possibly by increasing its conductance. By this way, the level of potassium that leaves the cell increases, which consequently inhibits neuron spiking. Thus, the GABA release becomes inhibited – for more details see (Madureira et al., 2010).

Given such a structure, external stimuli *X* and *Y* are projected through excitatory pathways to neighboring thalamic regions, *Tx* and *Ty*, respectively. Once stimulated, *Tx* activates *TRNx* beyond collaterals of an ascending glutamatergic projection, whose final destiny is the PFC. Since our work does not model the PFC explicitly, such excitatory projection ends up in *TRN* in the model. Also, through an excitatory glutamatergic descending pathway, the cortical region enhances the activation of *Tx*, and also sends collateral axons to *TRNx*. Thus, once activated, the *TRNx* inhibits the thalamic region *Ty* through a GABAergic inhibitory projection. Summarizing, the thalamocortical circuit activation by an external stimulus *X* excites a central thalamic region *Tx* and inhibits its neighborhood, represented by the neuron *Ty*. As the mesothalamic dopamine inhibits neurons in *TRN,* a rise in the dopaminergic level contributes to deactivating such cells. This leads to a more active thalamic region *Ty*. Conversely, a reduction in the dopaminergic level activates *TRN*, and increases the inhibition of *Ty*. A symmetrical case involves the *Ty* and *TRNy* neurons, as illustrated in Figure 1.

Fig. 1. The modeled thalamocortical network architecture: excitatory glutamatergic synapses (arrows), inhibitory GABAergic synapse (black sphere), inhibitory dopaminergic synapse (white sphere).

In the following, we describe the systems of equations that model the behaviors of *Tx*, *Ty*, *TRNx* and *TRNy*. The neural activities of the SN and the PFC, as well as the excitatory projections from *X* and *Y* are codified as temporal sequences representing their respective spiking times. As this work takes further the model presented in (Madureira et al., 2010), throughout the next section we examine specially the particular aspects of this extension.
