Critical Roles of the Direct GABAergic Pallido-cortical Pathway in Controlling Absence Seizures

<div><p>The basal ganglia (BG), serving as an intermediate bridge between the cerebral cortex and thalamus, are believed to play crucial roles in controlling absence seizure activities generated by the pathological corticothalamic system. Inspired by recent experiments, here we systematically investigate the contribution of a novel identified GABAergic pallido-cortical pathway, projecting from the globus pallidus externa (GPe) in the BG to the cerebral cortex, to the control of absence seizures. By computational modelling, we find that both increasing the activation of GPe neurons and enhancing the coupling strength of the inhibitory pallido-cortical pathway can suppress the bilaterally synchronous 2–4 Hz spike and wave discharges (SWDs) during absence seizures. Appropriate tuning of several GPe-related pathways may also trigger the SWD suppression, through modulating the activation level of GPe neurons. Furthermore, we show that the previously discovered bidirectional control of absence seizures due to the competition between other two BG output pathways also exists in our established model. Importantly, such bidirectional control is shaped by the coupling strength of this direct GABAergic pallido-cortical pathway. Our work suggests that the novel identified pallido-cortical pathway has a functional role in controlling absence seizures and the presented results might provide testable hypotheses for future experimental studies.</p></div

Absence seizures induced by strong coupling of the cortico-thalamic pathway and slow dynamics of GABA_B receptors in TRN.

<p>A, B: Two-dimensional state analysis (A) and frequency analysis (B) in the (<i>v_se</i>, <i>τ</i>) panel. Here <i>v_se</i> represents the excitatory coupling strength of the cortico-thalamic pathway emitting from the pyramidal neurons to SRN, whereas <i>τ</i> denotes the GABA_B delay. Similar to previous work, four types of dynamical state regions are observed: the saturation region (I), the SWD oscillation region (II), the simple oscillation region (III) and the low firing region (IV). The asterisk (“*”) regions surrounded by black dashed lines in (A) and (B) represent the typical SWD oscillation regions falling into the 2–4 Hz frequency range. C-F: Typical time series of <i>ϕ</i>_<i>e</i> correspond to the above four dynamical states. Four symbols in the state analysis diagram (A) are linked to parameter values used for different typical time series in (C)-(F): I (“∘”), II (“◇”), III (“◻”), and IV (“▿”). Note that we set <i>v</i>_<i>cp</i>₂ = −0.05 mV s for all simulations.</p

Default parameter values used in this study, which are adapted from previous modelling studies [21, 28–37].

<p>Default parameter values used in this study, which are adapted from previous modelling studies [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004539#pcbi.1004539.ref021" target="_blank">21</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004539#pcbi.1004539.ref028" target="_blank">28</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004539#pcbi.1004539.ref037" target="_blank">37</a>].</p

Effects of direct GPe-related pathways on regulating absence seizures.

<p>A, B: Two dimensional state analysis (A) and frequency analysis (B) in different parameter spaces. Here we consider three direct GPe-related pathways: the excitatory STN-GPe pathway (A₁, B₁), the inhibitory GPe recurrent pathway (A₂, B₂) and the inhibitory striatal D2-GPe pathway (A₃, B₃), corresponding to parameter spaces (−<i>v</i>_<i>cp</i>₂, <i>v</i>_<i>p</i>₂<i>ζ</i>), (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_{<i>p</i>₂<i>p</i>₂}) and (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_{<i>p</i>₂<i>d</i>₂}), respectively. In (A₁)–(A₃), two dynamical state regions are observed: the SWD oscillation region (II) and the low firing region (IV). The suppression of SWDs appears to the right of the white dashed line in (A₁) and (A₂), where the arrows denote the suppression directions of SWDs. The red lines in (A₁)-(A₃) represent the default coupling strengths of these direct GPe-related pathways. The asterisk (“*”) regions surrounded by black dashed lines in (B₁)-(B₃) denote the typical 2–4 Hz SWD oscillation regions. C: The triggering mean firing rate (TMFR) as a function of −<i>v</i>_<i>cp</i>₂ for the excitatory STN-GPe pathway (C₁) and inhibitory GPe recurrent pathway (C₂). D: The relative ratios (RRs) as a function of −<i>v</i>_<i>cp</i>₂ for the excitatory STN-GPe pathway (D₁) and inhibitory GPe recurrent pathway (D₂). E: Typical time series of <i>ϕ</i>_<i>e</i> by changing −<i>v</i>_<i>cp</i>₂ under two conditions of the inhibitory striatal D2-GPe pathway (“default” and “block”). The pink region in (E) denotes the suppression of SWDs by increasing −<i>v</i>_<i>cp</i>₂. Obviously, blockade of the inhibitory striatal D2-GPe pathway does not impact the model dynamics significantly.</p

Effects of indirect GPe-related pathways on regulating absence seizures.

<p>A, B: Two-dimensional state analysis (A) and frequency analysis (B) in the combined (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_{<i>ζp</i>₂}) and (−<i>v</i>_<i>cp</i>₂, −<i>v</i>_<i>ζe</i>) parameter spaces. Two considered indirect GPe-related pathways are: the inhibitory GPe-STN pathway (A₁, B₁) and the excitatory hyperdirect pathway from pyramidal neurons to STN (A₂, B₂). Three dynamical state regions are observed in the state analysis diagrams: the saturation region (I), the SWD oscillation region (II) and the low firing region (IV). In (A₁) and (A₂), the red dashed lines stand for the default coupling strengths of these two indirect GPe-related pathways, the white dashed lines represent the boundaries of suppression regions of SWDs, and the arrows denote the suppression directions of SWDs. In (B₁) and (B₂), the asterisk (“*”) regions surrounded by black dashed lines are the SWD oscillation regions falling into the 2–4 Hz frequency range. C: The TMFR as a function of −<i>v</i>_<i>cp</i>₂ for the inhibitory GPe-STN pathway (C₁) and the excitatory hyperdirect pathway (C₂). D: The RR as a function of −<i>v</i>_<i>cp</i>₂ for the inhibitory GPe-STN pathway (D₁) and the excitatory hyperdirect pathway (D₂). Compared to the results in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004539#pcbi.1004539.g004" target="_blank">Fig 4</a>, these two indirect GPe-related pathways have relatively weak effects on controlling absence seizures.</p

Control of absence seizures by the direct GABAergic pallido-cortical pathway.

<p>A: Bifurcation diagrams of <i>ϕ</i>_<i>e</i> as a function of the inhibitory coupling strength of the GABAergic pallidocortical pathway −<i>v</i>_<i>cp</i>₂ (A₁) and the external stimulation <i>V</i>_stim to GPe neurons (A₂). It can be seen that both increasing the values of −<i>v</i>_<i>cp</i>₂ and <i>V</i>_stim push the model dynamics from the SWD oscillation region (II) into the low firing region (IV). B: The dominant frequency of neural oscillations as a function of −<i>v</i>_<i>cp</i>₂ (B₁) and <i>V</i>_stim (B₂). C: The mean firing rates (MFRs) of several key neural populations as a function of −<i>v</i>_<i>cp</i>₂ (C₁) and V_stim (C₂). Here four neural populations are considered: GPe (“▵”), excitatory pyramidal neurons (“*”), SRN (“∘”) and TRN (“◻”). Note that the gray regions in (A)–(C) denote the SWD oscillations falling into the typical 2–4 Hz.</p

Bidirectional control of absence seizures due to the competition between the SNr-TRN and SNr-SRN pathways.

<p>A, B: The state analysis (A) and frequency analysis (B) in the (<i>K</i>, <i>v</i>_{<i>p</i>₁<i>ζ</i>}) panel. Here <i>K</i> is the scale factor, and <i>v</i>_{<i>p</i>₁<i>ζ</i>} is the excitatory coupling strength of the STN-SNr pathway. The BGCT model mainly exhibits three types of dynamical states: the SWD oscillation region (II), the simple oscillation region (III) and the low firing region (IV), but occasionally displays the saturation state in the large <i>K</i> and strong <i>v</i>_{<i>p</i>₁<i>ζ</i>} region. For intermediate scale factor <i>K</i>, both increase and decrease in the activation level of SNr can inhibit the SWDs (double arrow, bidirectional suppression). In (A), the black dashed line represents the demarcation between the bidirectional (double arrow) and unidirectional suppression (single arrow) regions. The asterisk (“*”) region surrounded by dashed lines in (B) denotes the SWD oscillation region that falls into the 2–4 Hz frequency range. C: The low and high TMFRs of SNr neurons as a function of <i>K</i>. D: The low and high RRs of the STN-SNr pathway as a function of <i>K</i>. In all simulations, we set <i>τ</i> = 45 ms and <i>v</i>_<i>cp</i>₂ = −0.06 mV s.</p

Roles of several GPe-related pathways in the regulation of absence seizures, through modulating the activation level of GPe neurons.

<p>Roles of several GPe-related pathways in the regulation of absence seizures, through modulating the activation level of GPe neurons.</p

Framework of the basal ganglia-corticothalamic (BGCT) network used in this work.

<p>The BGCT network contains three components: (I) the cerebral cortex, (II) the thalamus and (III) the basal ganglia. Neural populations include: <i>e</i> = excitatory pyramidal neurons, <i>i</i> = inhibitory interneurons, <i>s</i> = SRN, <i>r</i> = TRN, <i>d</i>₁ = striatal D1 neurons, <i>d</i>₂ = striatal D2 neurons, <i>p</i>₁ = SNr/GPi, <i>p</i>₂ = GPe and ζ = STN. Parameter <i>ϕ</i>_<i>n</i> denotes the non-specific external inputs to SRN. Excitatory projections are mediated by glutamate, which are shown by the red lines with square heads. Inhibitory projections are mediated by GABA_A and GABA_B, which are represented by the solid and dashed blue lines with arrow heads, respectively. Compared with the BGCT networks developed in previous studies, a new efferent pathway representing direct connection from the GPe to the cerebral cortex is incorporated in our current BGCT model.</p

Shaping effects of the direct GABAergic pallido-cortical pathway on the bidirectional control of absence seizures by the BG.

<p>A, B: Tow-dimensional state analysis (A) and frequency analysis (B) in the (<i>K</i>, <i>v</i>_{<i>p</i>₁<i>ζ</i>}) panel for different values of <i>v</i>_<i>cp</i>₂. Similar to the results in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004539#pcbi.1004539.g006" target="_blank">Fig 6A</a>, our BGCT model mainly exhibits three types of dynamical states: the SWD oscillation region (II), the simple oscillation region (III) and the low firing region (IV), but occasionally displays the saturation state in the large <i>K</i> and strong <i>v</i>_{<i>p</i>₁<i>ζ</i>} region. In (A₁)-(A₄), the double arrows denote the bidirectional suppression and the single arrows represent the unidirectional suppression. The black dashed lines in (A₁) and (A₂) stand for the demarcations between the bidirectional and unidirectional suppression regions. In (B₁)-(B₄), the asterisk (“*”) regions surrounded by dashed lines denote the regions of 2–4 Hz SWDs. From left to right, the strengths of direct GABAergic pallido-cortical pathway are: <i>v</i>_<i>cp</i>₂ = −0.05 mV s (A₁, B₁), <i>v</i>_<i>cp</i>₂ = −0.055 mV s (A₂, B₂), <i>v</i>_<i>cp</i>₂ = −0.065 mV s (A₃, B₃), and <i>v</i>_<i>cp</i>₂ = −0.07 mV s (A₄, B₄), respectively. In all simulations, we set <i>τ</i> = 45 ms.</p