Regulation of Irregular Neuronal Firing by Autaptic Transmission

The importance of self-feedback autaptic transmission in modulating spike-time irregularity is still poorly understood. By using a biophysical model that incorporates autaptic coupling, we here show that self-innervation of neurons participates in the modulation of irregular neuronal firing, primarily by regulating the occurrence frequency of burst firing. In particular, we find that both excitatory and electrical autapses increase the occurrence of burst firing, thus reducing neuronal firing regularity. In contrast, inhibitory autapses suppress burst firing and therefore tend to improve the regularity of neuronal firing. Importantly, we show that these findings are independent of the firing properties of individual neurons, and as such can be observed for neurons operating in different modes. Our results provide an insightful mechanistic understanding of how different types of autapses shape irregular firing at the single-neuron level, and they highlight the functional importance of autaptic self-innervation in taming and modulating neurodynamics.Comment: 27 pages, 8 figure

Firing regulation of fast-spiking interneurons by autaptic inhibition

Fast-spiking (FS) interneurons in the brain are self-innervated by powerful inhibitory GABAergic autaptic connections. By computational modelling, we investigate how autaptic inhibition regulates the firing response of such interneurons. Our results indicate that autaptic inhibition both boosts the current threshold for action potential generation and modulates the input-output gain of FS interneurons. The autaptic transmission delay is identified as a key parameter that controls the firing patterns and determines multistability regions of FS interneurons. Furthermore, we observe that neuronal noise influences the firing regulation of FS interneurons by autaptic inhibition and extends their dynamic range for encoding inputs. Importantly, autaptic inhibition modulates noise-induced irregular firing of FS interneurons, such that coherent firing appears at an optimal autaptic inhibition level. Our results reveal the functional roles of autaptic inhibition in taming the firing dynamics of FS interneurons

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