**3.2.2 Receptor D4 activity and the attentional focus**

In the next series of experiments, we keep up our focus on the tonic mode of spiking. And, for each imposed SN spike frequency, we examine the effects of changes in the receptor D4 activation. Since the different degrees of D4 activation can be associated to not modeled exogenous or endogenous factors, that are not modeled, this approach makes it possible to speculate plausible outcomes of the dopaminergic agonists (or antagonists) action at the synaptic cleft. The simulations results are summarized in Table 4**.** First, we may note that the results presented in the column relative to *ĝd4* = 1.0 agree with the previous set of experiments. It is more interesting, however, to observe that as the receptor D4 activity diminishes, the thalamic neurons become less active, thus reaching a completely inhibited state. Conversely, as the receptor D4 activity increases, thalamic neurons become more active and tend to spike at the same frequency. Finally, we highlight that, except for the baseline case where the interval between spikes in SN equals 10, when *ĝd4* assumes values lower than 1.0, the differences between *Tx* and *Ty* spiking frequencies disappear. So, the mesothalamic hypoactivity does not impose the attention to focus on the stimulus *Y* anymore.

Mesothalamic Dopaminergic Activity: Implications in Sleep Alterations in Parkinson's Disease 519

100 0.8 Tx and Ty Bursting

50 0.8 all Tonic

40, 30, 20, 10 1.0 all Tonic 5 1.0 TRNx and TRNy Bursting

Fig. 3. Decreases in the receptor D4 activation, under mesothalamic dopaminergic

hypoactivity, turned the tonic state into the burst one in Tx.

Table 5. Distinct dopaminergic activities in presence of similar stimuli.

**3.2.4 Variations in the dopaminergic activity and the oscillatory state** 

(*ĝd4*) Neurons Spike Mode

0.9 all Tonic 1.0 all Tonic

0.9 all Tonic 1.0 all Tonic

In our last series of simulations, we deepen our investigations on the changes in the spiking mode. Now, we repeat the strategy undertaken in Subsection 3.2.1, where a stimulus *X* is presented to the asymmetrical network before a stronger one, *Y.* Through the extended mathematical model we propose in Section 2, here we look for situations where changes in the dopaminergic action lead to the burst mode in neurons of the thalamic complex. In this set of simulations, we examine only extreme cases of dopaminergic alterations. Such option was because all previous experiments indicated these extreme situations as the more plausible to initiate the ionic events that underlie the burst mode occurrence. Table 6

Activity of Dopamine Receptor D4\*

Interval between Spikes in SN

summarizes our results.

(ms)


Table 4. Receptor D4 activity and the thalamic tonic state.

#### **3.2.3 Dopaminergic activity and the oscillatory state**

Next, we simulate the mathematical model described in Section 2 through the extended symmetrical network illustrated in the Figure 1. In this set of experiments, two identical, external stimuli, *X* and *Y*, activate the network simultaneously. As in the previous experiments, we impose different SN spiking frequencies. We observe, in Table 5, that extreme and opposing situations lead to the bursting spiking mode in the thalamic complex: the drastic mesothalamic dopamine hypoactivity caused the oscillatory pattern in the *Tx* and *Ty* neurons, whereas the mesothalamic dopamine hyperactivity made the TRN neurons to spike through bursts. With relation to the *Tx* and *Ty* neurons, the appearance of the bursting mode comes from the strong inhibition they suffered through the GABAergic projection from the TRN neurons, which were over activated due to the low dopaminergic activity. Conversely, the oscillatory behavior of the *TRNx* and *TRNy* neurons originated from the inhibition suffered by the TRN due to the high dopaminergic level. The dynamics of the ionic currents involved in such processes are the same described in Subsection 2.2. Figure 3 illustrates the changes in the *Tx* behavior due to the diminishing of the receptor D4 activation, throughout the dopamine hypoactivity case, described in the first line of Table 5**.** 

Interval between Spikes in SN (ms)

50

30

20

10

5

Spikes in 100ms

Activity of Dopamine Receptor D4 (*ĝd4*)

0.4 0.6 0.8 1.0 1.2 1.4

Tx - 0 2 2 11 14 Ty - 0 2 14 16 19 TRNx - 46 32 14 9 4 TRNy - 46 32 28 15 6

Tx - 0 4 4 12 15 Ty - 0 4 13 17 18 TRNx - 42 30 25 12 2 TRNy - 42 30 25 12 5

Tx - 0 5 7 12 18 Ty - 0 5 13 15 18 TRNx - 40 30 13 10 5 TRNy - 40 30 21 12 2

Tx 0 0 0 10 16 18 Ty 0 6 10 15 17 19 TRNx 52 30 20 5 5 0 TRNy 50 30 30 10 4 0

Tx 0 5 15 18 18 - Ty 0 5 15 19 19 - TRNx 40 25 10 0 0 - TRNy 40 20 5 0 0 -

Next, we simulate the mathematical model described in Section 2 through the extended symmetrical network illustrated in the Figure 1. In this set of experiments, two identical, external stimuli, *X* and *Y*, activate the network simultaneously. As in the previous experiments, we impose different SN spiking frequencies. We observe, in Table 5, that extreme and opposing situations lead to the bursting spiking mode in the thalamic complex: the drastic mesothalamic dopamine hypoactivity caused the oscillatory pattern in the *Tx* and *Ty* neurons, whereas the mesothalamic dopamine hyperactivity made the TRN neurons to spike through bursts. With relation to the *Tx* and *Ty* neurons, the appearance of the bursting mode comes from the strong inhibition they suffered through the GABAergic projection from the TRN neurons, which were over activated due to the low dopaminergic activity. Conversely, the oscillatory behavior of the *TRNx* and *TRNy* neurons originated from the inhibition suffered by the TRN due to the high dopaminergic level. The dynamics of the ionic currents involved in such processes are the same described in Subsection 2.2. Figure 3 illustrates the changes in the *Tx* behavior due to the diminishing of the receptor D4 activation, throughout the dopamine hypoactivity case, described in the first line of Table 5**.** 

Table 4. Receptor D4 activity and the thalamic tonic state.

**3.2.3 Dopaminergic activity and the oscillatory state** 


Table 5. Distinct dopaminergic activities in presence of similar stimuli.
