Attentional Focus Modulated by Mesothalamic Dopamine: Consequences in Parkinson’s Disease and Attention Deficit Hyperactivity Disorder

Abstract

In this work, we propose a mathematical model that describes how the mesothalamic dopamine pathway modulates the attentional focus via the thalamocortical loop, and how mesothalamic dopamine alterations can promote inattention symptoms in patients with Parkinson’s disease (PD) and attention deficit hyperactivity disorder (ADHD). We model the thalamocortical loop with a neuronal network where each thalamic neuron is described by a system of coupled differential equations reflecting neurophysiological properties. The computational simulations reflect neurochemical features of PD and ADHD. Our results suggest that the mesothalamic dopamine hypoactivity causes difficulties in attentional shifting. Conversely, the mesothalamic dopamine hyperactivity hinders the attentional focus consolidation. Furthermore, regardless of the amount of mesothalamic dopamine activity, the mesocortical dopamine hypoactivity leads to loss of attentional focus. Finally, we identify a unique neuronal mechanism underlying attention deficits in PD and ADHD and relate different inattention symptoms in ADHD to different dopaminergic levels in the brain circuit modeled.

Appendices

Appendix A

Some Analytical Considerations

Here, we summarize some relevant properties of our model. We first present in a concise fashion the system of equations described in “The Modeled Neural Network”—these are the equations for the thalamic and TRN cell dynamics:

$$ C{\frac{dv}{dt}} = I_{k} + I_{c} + I_{\text{syn}} + I_{l} $$

$$ I_{k} = g_{k} \left( {E_{k} - V} \right), $$

$$ I_{c} = \left\{ {\begin{array}{*{20}c} {g_{c} \, \left( {E_{k} - V} \right),} & {{\text{for the }}TRN\,{\text{neuron}}} \\ {0,} & {{\text{for the }}T_{x} {\text{ and }}T_{y \, } {\text{neurons}},} \\ \end{array} } \right. $$

$$ I_{\text{syn}} = g_{\text{syn}} \left( {E_{\text{syn}} - V} \right), $$

$$ I_{l} = g_{l} \left( {E_{l} -V} \right), $$

$$ {\frac{{{\text{d }}g_{k} }}{{{\text{d}}t}}} = {\frac{{s \, \beta_{k} - g_{k} }}{{\tau_{k \, } }}} $$

$$ s(V) = \left\{ {\begin{array}{*{20}c} {1,} & {{\text{if }}V \ge \theta } \\ {0,} & {{\text{if }}V < \theta } \\ \end{array} } \right. $$

$$ g_{c} = \hat{g}_{c} D_{4}^{*} S\left( {\left[ {\text{Ca}} \right]} \right), $$

$$ D_{ 4}^{*} = \hat{g}_{d4} \, \sum\limits_{j = 1}^{N} {\left( {t - t_{j} } \right){ \exp }\left[ { - \left( {t - t_{j} } \right)/t_{pd} } \right],} $$

$$ S\left( {\left[ {\text{Ca}} \right]} \right) = 1/\left[ { 1+ { \exp }\left( { - a \, [{\text{Ca}}]} \right)} \right], $$

$$ {\frac{{{\text{d }}[{\text{Ca}}]}}{{{\text{d}}t}}} = {\frac{{s \, \beta_{\text{Ca}} - [{\text{Ca}}]}}{{\tau_{\text{Ca}} }}}, $$

$$ g_{\text{syn}} = \hat{g}\sum\limits_{j = 1}^{N} {\left( {t - t_{j} } \right)\left[ {{ \exp } - \left( {t - t_{j} } \right)/t_{p} } \right],} $$

where V(0) = −40, g _k (0) = 0.5, [Ca](0) = 1.0, and C, E _k , E _syn, E _l , g _l , β _k , τ _k , ĝ _c , ĝ _d4 t _pd , a, β _Ca, τ _Ca , ĝ, and t _p are constants. All used parameters are described in Table 5.

Table 5 Glossary of parameters

Increasing C makes V less vulnerable to fluctuations in I _k , I _c , I _syn, and I _l . Also, if g _k increases, then I _k decreases and that makes V more negative. The behavior of I _c in the TRN neuron is under the influence of [Ca], S, and D ^* ₄ . Therefore, whenever s is nonzero, [Ca] increases proportionally to the magnitude of β _Ca. The influence that [Ca] exerts on g _c is described by the sigmoid function S. The receptor D ^* ₄ is a function of the dopaminergic inputs which occur in the N time steps t _j —and decay exponentially with respect to time—and D ^* ₄ modulates the influence of S on g _c . Hence, g _c increases as the frequency of inputs increases. The higher g _c the more negative I _c becomes, diminishing V.

The action of the synaptic currents is gathered in I _syn. Similarly, to the analysis for D ^*₄ , in the expression governing g _syn, the influence of each input decays exponentially, as function of the difference between the current time step, t, and the instant in which each of the N inputs occurred, t _j .

Next we examine how the previously mentioned modeling details underlie the behavior of our modeled dopamine-modulated thalamocortical circuit. As depicted in Fig. 2, T _x receives excitatory projections from X and the PFC, whose neural activities are codified as temporal sequences representing their respective spiking times. Such temporal patterns feed g _syn and consolidate through I _syn, the synaptic component that affects the membrane potential of T _x .

When these excitatory stimuli are capable of bringing V to the threshold, θ, making the step function s nonzero, g _k increases dramatically forcing I _k to be quite negative, and that brings V to a negative value. Such series of events makes up the neural spiking phenomenon. As long as the excitatory inputs keep occurring, the membrane potential starts arising again, leading to the repetition of the whole process and repetitive firing takes place.

Turning back to the Fig. 2, we observe that TRN receives excitatory projections from T _x and the PFC, and an inhibitory one from SN. The synaptical influence from T _x depends on the temporal sequence of spiking times produced by such neuron, according to the process previously described. And, as in the PFC, the neural activity in SN is represented by a previously adjusted pattern of spiking frequencies.

Although the already mentioned properties underling T _x are present in TRN, its relevant feature comes from the action of I _c —which suffers the dopaminergic influence, according to our model. Indeed, g _c depends on the level of [Ca]; besides, the frequency of the SN spiking modulates the [Ca] influence. A high neural activity in SN, for instance, is capable of promoting a strong increase in g _c , no matter how large [Ca] is. And, a high valued g _c strongly inhibits the neuron.

Finally and according to Fig. 2, we see that T _y receives excitatory inputs from Y and the PFC and an inhibitory projection from TRN. The dynamics underlying the evolution of its membrane potential follows the lines described for T _x . On the other hand, the behavior of T _y also suffers the inhibitory effect of the TRN spiking frequencies.

Summarizing, the degree by which the TRN inhibits T _y is a consequence of the degree by which SN inhibits TRN. In other words, if dopamine modulates g _c in the TRN—as we propose here -, then, the dopaminergic action in TRN exerts a powerful role in thalamocortical mechanisms underlying the control of attention.

Appendix B

Next, we present alternative ways of investigating the dopamine action in the TRN, through the proposed model.

First, we address the degree of influence the SN exerts on the activity of receptor D ^*₄ , through the term ĝ _d4 in Equation (2), “TRN Neuron”. Indeed, ĝ _d4 is supposed to mean the weight of the connection between the SN and TRN neurons. Then, ĝ _d4 tells us how much the dopaminergic receptor D ^*₄ , in the TRN, is affected by the dopamine release enhanced by a nerve impulse from SN.

Here, we simulate different values of ĝ _d4 in three situations: normal condition, drastic mesothalamic hypo and hyper activities. Figure 8 illustrates that, as expected, increases in ĝ _d4 enhance the inhibitory state of TRN. More sophisticated modelings of ĝ _d4 may account for the complex dynamics underlying the D ^*₄ activity and, possibly, are a further way of investigating how alterations in the receptor D4 function lead to attention deficits.

Fig. 8

Mesothalamic dopamine action in the TRN influenced by variations in ĝ _d4

Another approach concerns how the decay time of the released nigral dopamine affects the receptor D ^*₄ in the TRN. A plausible way of addressing such question, through our model, consists in examining the term t _pd , also in Equation (2), “TRN Neuron”.

Again, we simulate three situations—normal condition, drastic mesothalamic hypo and hyper activities—in which one different values of t _pd are imposed. As we observe in Fig. 9, the more the value of t _pd , the more inhibited the TRN neuron becomes. Or, longer dopamine decay times enhance the TRN inhibition.

Fig. 9

Mesothalamic dopamine action in the TRN influenced by variations in t _pd