Spike‐and‐wave discharges of absence seizures in a sleep waves‐constrained corticothalamic model

Abstract Aims Recurrent network activity in corticothalamic circuits generates physiological and pathological EEG waves. Many computer models have simulated spike‐and‐wave discharges (SWDs), the EEG hallmark of absence seizures (ASs). However, these models either provided detailed simulated activity only in a selected territory (i.e., cortical or thalamic) or did not test whether their corticothalamic networks could reproduce the physiological activities that are generated by these circuits. Methods Using a biophysical large‐scale corticothalamic model that reproduces the full extent of EEG sleep waves, including sleep spindles, delta, and slow (<1 Hz) waves, here we investigated how single abnormalities in voltage‐ or transmitter‐gated channels in the neocortex or thalamus led to SWDs. Results We found that a selective increase in the tonic γ‐aminobutyric acid type A receptor (GABA‐A) inhibition of first‐order thalamocortical (TC) neurons or a selective decrease in cortical phasic GABA‐A inhibition is sufficient to generate ~4 Hz SWDs (as in humans) that invariably start in neocortical territories. Decreasing the leak conductance of higher‐order TC neurons leads to ~7 Hz SWDs (as in rodent models) while maintaining sleep spindles at 7–14 Hz. Conclusion By challenging key features of current mechanistic views, this simulated ictal corticothalamic activity provides novel understanding of ASs and makes key testable predictions.

provided detailed simulated activity only in a selected territory (i.e., cortical or thalamic) or did not test whether their corticothalamic networks could reproduce physiological activities that are known to be generated by these circuits. 22Here, we used our corticothalamic model (Figure S1) that faithfully simulates EEG waves of natural sleep, that is, sleep spindles, delta, and slow (<1 Hz) waves 23 (Figure S2), to investigate whether single abnormal voltage-or transmitter-gated conductances bring about SWDs of ASs.
In particular, we show that an increase in the tonic GABA-A inhibition of first-order thalamocortical (TC FO ) neurons, a decrease in cortical phasic GABA-A inhibition, an increase in cortical AMPA receptor function, or an increase in the T-type Ca 2+ conductance of higher-order thalamocortical (TC HO ) neurons generates ~4 Hz SWDs (as observed in humans with ASs 2,5 ) that invariably start in the neocortex.

| Corticothalamic network model
We used our biophysical model of the corticothalamic network (Figure S1) that faithfully reproduces the typical EEG waves of natural sleep (Figure S2). 23Briefly, our corticothalamic model contains 900 model neurons and is organized into six sectors (Figure S1): four cortical layers, including layers 2/3 (L2/3), 4 (L4), 5 (L5), and 6 (L6), and a first-and a higher-order thalamic nucleus with their thalamocortical neurons (TC FO and TC HO , respectively) which are reciprocally connected to inhibitory NRT neurons (NRT FO and NRT HO , respectively). 24Each cortical layer is divided into two subsectors, each with 100 excitatory and 50 inhibitory neurons.
The full model is a two-dimensional stack of subsector neuron rows.The neuron position within a subsector was determined pseudo-randomly. 23

| Model network connectivity
Connections were organized topographically with sources and targets located in matching regions of their corresponding structures.A neuron did not synapse onto itself and could only form a single synapse on its target neuron.The number of contacts that a source neuron could form in a target structure was defined by the parameter P (a projection radius).Other key connectivity parameters (e.g., connection weight, postsynaptic potential shape, synaptic transmission latency, and synaptic receptors) are described in detail in Dervinis and Crunelli. 23Similarly, the numerical values of the various intrinsic and synaptic conductances of the different neuronal populations are detailed in Dervinis and Crunelli.

| Data analyses
Simulation data were analyzed and visualized with the help of custom-written Matlab (MathWorks Inc.) routines.The raw EEG signal was filtered and cross-correlated as described in Dervinis and Crunelli. 23SWD Hilbert transform phase was calculated by bandpass filtering raw EEG traces using Butterworth filter with the following parameters: passband and stopband frequencies centered at ±2 Hz and ±4 Hz around the SWD oscillation frequency (~4 or ~7 Hz), respectively, and passband ripple and stopband attenuation being 0.5 and 65 dB, respectively.The filtered EEG signal was then subjected to Matlab's hilbert function.Hilbert phase synchronization index (PSI) 25 was calculated for two filtered signals obtained using the same filtering parameters as above and then smoothed using a moving average window of 1 s duration (for additional data analyses, see Appendix S1 in Dervinis and Crunelli 23 ).

| RE SULTS
As shown in the preceding paper, 23 our thalamocortical model is capable of smoothly transitioning between wakefulness (as evident from a low-amplitude, high-frequency EEG) and different EEG waves of natural sleep (depending on the input resistance of its constituent neurons) and it does not enter an overly synchronous activitymode typical of seizures.However, one particular state of the model is prone to generate ictal states, that is, the transition between sleep and wakefulness.When the model is in this state, different single-membrane conductance changes in either cortical or thalamic neurons do lead to an EEG waveform typical of SWDs of ASs, as described below.Notably, all the changes in different conductances that lead to simulated SWDs have a minimal impact on sleep waves (not shown).

| Selective increase in tonic GABA-A inhibition of TC FO neurons generates SWDs
8][29] Moreover, higher levels of GABA were found in the thalamus of a child with ASs, 30 and drugs that are known to increase GABA levels, that is, vigabatrin and tiagabine, can induce or aggravate ASs in humans. 31,32Increasing (by 5%) the leak conductance (g KL ) in TC FO neurons (in order to mimic the increased tonic GABA-A inhibition observed in genetic AS models 27,28 ) led to the appearance of SWDs at ~4 Hz (Figure 1A 1 ,B 1 ; Table S1), a frequency similar to that in humans with ASs. 2,5Further increases in g KL did not change the SWD frequency and duration though decreased and then prolonged the interictal period (Figure 1A 2 ,A 3 ; Table S1).
At the single-cell level, almost all neuronal populations increased their total firing during SWDs except TC FO neurons which showed a decrease (Figures 1B 1 ,B 2 and 2A).The same was observed for ictal burst firing, whereas tonic, single action potential (AP) firing decreased (Figure 2B,C).Indeed, burst firing was the highest contributor to ictal activity in all excitatory and inhibitory cortical neurons (independent from their layer location), but was absent in TC FO neurons and similar to tonic firing in all NRT neurons (Figure 2D).Notably, all cortical and NRT neurons were never silent during SWDs, whereas both TC FO and TC HO neurons were mostly silent ictally or fired tonically (Figure 2D).
When considering the firing dynamics of all ictal APs, all neuronal populations fired at or just after the SWD spike except TC FO and TC HO neurons that fired ~30 and 20 ms, respectively, prior to the SWD spike (Figure 2E 1 ,F 1 ).This is also reflected in the firing phase evolution throughout the SWD with TC FO and TC HO cells showing a positive phase through most of the SWD (leading) while cortical cells showing zero or slightly negative phase over the same period (lagging) (Figure 2G 1 ).However, when only the first AP of an SWD cycle was considered, all neurons fired ~10 ms before the SWD spike (Figure 2E 2 ), and almost all neuron types had a smaller peak ~80 ms prior to the SWD spike (Figure 2F 2 ).We then analyzed the temporal dynamics of firing synchrony within and between neuronal populations in the interictal and ictal periods (Figure 3).Within a given neural type, the stronger progressive increase in synchrony from interictal to ictal periods was observed in NRT FO and NRT HO neurons while the smallest increase occurred in TC FO and TC HO neurons (Figure 3A 1,2 ).Among different populations, those involving all possible pairs of thalamic neurons showed the highest progressive synchrony as did the layer 5 pyramidal neurons (L5PY) pairs with either NRT or TC neurons, whereas the synchrony between L4PY and TC HO neurons gradually decreased (Figure 3B 3 ).Thus, in summary, the temporal dynamics of increased synchrony progress from thalamic and cortical neuron pairs to NRT neuron pairs and then to cortical and NRT neuron pairs (Figure 3C).

| SWD generation by other selective alterations in inhibitory and excitatory conductances
We first checked whether SWDs could be generated by an increase in conductance of the extrasynaptic GABA-A receptors (g eGABAa ) of TC FO neurons instead of indirectly increasing the g KL of these neurons.As shown in Figure 4B 1-4 , progressive enhancement of this conductance reliably elicited SWDs.Moreover, selectively decreasing (by 10% and 25%) the conductance of the phasic GABA-A inhibition (g GABAa ) in all cortical neurons led to SWDs (as observed in vivo experiments [33][34][35][36] ) of progressively larger amplitude and increasingly longer interictal periods (Figure 4C 1-3 ; Table S2).Compared to the SWDs generated by an increase in thalamic tonic GABA-A inhibition, stronger synchrony was observed between L5PY and all NRT neuron pairs as well as between L4PY and TC HO neuron pairs in the simulated activity induced by a decreased cortical g GABAa (Figure 4C 4 ).
A higher number of cortical strongly intrinsically bursting (SIB) neurons have been reported in genetic rat models of ASs 37,38 : its implementation in the model indeed generated SWDs although of a small amplitude compared to changes in other conductances (Figure 4E 1-3 ; Table S2) and with a characteristic interictal-to-ictal decrease in synchrony in L4PY-TC HO , L5PY-TC HO , NRT HO -TC FO , and NRT HO -TC HO neuron pairs (Figure 4E 4 ).
Finally, increasing the conductance of the T-type Ca 2+ channels (g T ) in all NRT neurons, as it has been observed in both humans and experimental models of ASs, 39,40 led to brief, small-amplitude SWDs, which, notably, were abolished by a further increase in this conductance (Figure 4F 1-4 ).Moreover increasing (by 5% and 10%) g T in TC HO neurons (Table S2) generated progressively longer SWDs, ultimately leading to absence status (Figure 4G 1,3 ), and a gradual increase in synchrony among almost all neuronal pairs (Figure 4G 4 ).

| Critical conductances of simulated SWDs
Having established that our model reproduces SWDs elicited by either increasing thalamic tonic or decreasing cortical phasic GABA-A inhibition, we next studied which effect other conductances have on these simulated SWDs.Removing g T from TC FO neurons did not abolish SWDs, as recently reported, 41 but actually increased their amplitude and decreased the interictal period duration (Figure 5B 1,2 ).
In contrast, removing g T from TC HO neurons abolished SWDs elicited by both increased thalamic tonic and decreased cortical phasic GABA-A inhibition (Figure 5C 1,2 ) as did g T removal from all types of NRT neurons (Figure 5D 1,2 ).
3][44][45] In contrast, increasing g GABAb in cortical neurons decreased the amplitude of SWDs and markedly increased their duration (Figure 5H 1,2 ).Enhancing g GABAb in TC FO neurons increased the amplitude and the interictal period of SWDs elicited by the increased thalamic tonic GABA-A inhibition (Figure 5I 1 ), whereas it decreased the interictal period of the SWDs simulated by a decreased cortical phasic GABA-A inhibition (Figure 5I 2 ).Finally, increasing g GABAb in TC HO neurons led to absence status in both models (Figure 5J 1,2 ).
Next, we investigated which conductance was critical for determining the simulated intra-SWD frequency as it represents a major difference between ASs in human and animal models.[5] Finally, since the non-selective cation conductance (g CAN ) plays a key role in some EEG waves of natural [46][47][48] and simulated 23 sleep and its involvement in ASs has not been studied before, we investigated whether it is necessary for simulated SWDs.Removing g CAN from all TC neurons had little effect on SWDs (Figure 6G 1,2 ).In contrast, removal of (g CAN ) from all NRT neurons led to absence status in the model with increased g KL of TC FO neurons (Figure 6H 1 ) and markedly prolonged SWDs in the model with decreased g GABAa in cortical neurons (Figure 6H 2 ).

| DISCUSS ION
The main finding of this study is the ability to faithfully reproduce SWDs at the 4 Hz frequency observed in human ASs by single modifications of neocortical or thalamic conductances in a corticothalamic model that faithfully reproduces the intrinsic and network activity observed in neocortical and thalamic territories during natural sleep. 23To the best of our knowledge, this is the most detailed large-scale model dedicated to simulating SWDs, and its component parts and their connectivity patterns were replicated with a high degree of fidelity to experimental data. 22Constructing a multipurpose model guards against an implementation bias of favoring a particular (patho)physiological regime.In fact, no previous attempt at modeling SWDs had this level of physiological validity.

| Model limitations
Notwithstanding, our model has a number of limitations (see Dervinis and Crunelli 23 for details).In the absence of direct measurements, the T-type Ca 2+ current implemented in various types of neocortical neurons was guided by the ability of these neurons to faithfully reproduce intrinsic slow (<1 Hz) waves. 23Moreover, although no detailed parameters exist for the persistent Na + current in NRT neurons, this current (with biophysical properties similar to those reported for TC neurons 46 ) had to be introduced in NRT neurons in order to faithfully reproduce the intrinsic slow (<1 Hz) waves observed in in vitro studies. 48[51][52]

| Simulation strength
The solidity of our simulated SWDs is supported by two major findings.First, our model faithfully reproduces the three main EEG waves generated by corticothalamic networks during sleep, that is, spindle, delta, and slow (<1 Hz) waves, 23 and these natural rhythms are only minimally affected by the different changes in single voltage-and transmitter-gated conductances that lead to SWDs.Second, our model is capable of reproducing many experimental findings after implementing the different abnormalities that are known to be present in humans with, and genetic models of, ASs.
In particular, our model generates ~4 Hz SWDs following: 1. blockade of neocortical phasic GABA-A inhibition, as shown experimentally following intracortical injection of the weak and potent GABA-A antagonists penicillin and bicuculline, respectively [33][34][35][36][53][54][55] ; F I G U R E 1 Selective increase in tonic GABA-A inhibition of TC FO neurons elicits SWDs.(A 1 ) EEG traces show the induction of spontaneous SWDs at ~4 Hz after progressive increases in g KL of TC FO neurons, mimicking the constitutively high tonic GABA-A inhibition reported in AS models.The control condition shows simulated desynchronized state typical of relaxed wakefulness.The SWD in the shaded area is expanded in B 1 .(A 2 ) Cross-correlations between APs of all neurons and the EEG calculated over a 20 min simulation period.Shaded regions represent 95% confidence intervals.2. increase in the tonic GABA-A inhibition of TC FO neurons, by directly increasing the function of extrasynaptic GABA-A receptors or indirectly increasing the g KL of these neurons, as shown in different genetic models of ASs, 27 that is, the GAERS (Genetic Absence Epilepsy Rats from Strasbourg) rats and the stargazer and lethargic mouse models; 3. enhancement of GABA-B inhibition in either thalamic or cortical territory, as shown by the generation and aggravation of SWDs in normal mice and rats and genetic AS models, respectively, following systemic, intracortical, and intrathalamic injection of GABA-B receptor agonists [42][43][44][45] ; F I G U R E 3 Time evolution of interictal and ictal firing synchrony for SWDs elicited by increased tonic GABA-A inhibition of TC FO neurons.(A 1 ) Ictal and interictal mean phase synchronization index (PSI) of APs within a neuronal population (color-code as in Figure 2E 2 ).Ictal and interictal periods were linearly scaled to their average durations.Dashed vertical black lines indicate different parts of ictal and interictal periods: i 1 marks a section from 1/6 to 1/3 of the interictal period, i 2 marks the 1/3 to 2/3 section, i 3 marks the final third of the interictal period, and the last two lines indicate the start and end of the ictal period.(A 2 ) Changes in PSI during interictal and ictal periods.For each indicated neuronal population, the left bar is the PSI change between i 1 and i 2 (i 1 → i 2 ), the middle bar between i 2 and i 3 (i 2 → i 3 ), and the right bar between i 3 and the ictal period (i 3 → SWD).(B 1,2 ) Evolution of ictal and interictal PSI between different cortical (B 1 ) and thalamic (B 2 ) populations (color-code on the right).Vertical dashed black lines demarcate the same regions as in (A 1 ).(B 3 ) Changes in PSI of different neuronal populations over interictal and ictal periods.For each neuronal population pair, the three bars are as in (A 2 ).(C) Schematic representation of the evolution of PSI.Brian areas and their connections shaded in yellow show increase in PSIs between i 1 and i 2 and represent the initial synchronization stage (corresponding to bar 1 in all comparison groups of A 2 and B 3 ).Orange and red colors mark PSI increases during the second synchronization stage (between i 2 and i 3 ) and the final synchronization stage (between i 3 and the ictal period), respectively.and the GAERS genetic models of ASs. 38r simulations also show that SWDs are abolished or reduced following (1) blockade of cortical or thalamic GABA-B receptors as observed in different genetic and pharmacological models of ASs following systemic, intracortical, or intrathalamic injection of selective GABA-B receptor antagonists [40][41][42][43] ; and (2) removal of T-type Ca 2+ channels in NRT neurons, as seen following intra-NRT infusion of TTA-P2, 39 a potent and selective blocker of these channels, 56 in GAERS rats.In contrast, simulated SWDs are unaffected by blocking T-type Ca 2+ channels in TC FO neurons as reported by McCafferty et al. 41 Notably, an increase in g T of all NRT neurons, as observed in humans and models of ASs, 39,40 only led to brief, small-amplitude SWDs, clearly indicating that this thalamic abnormality is not capable alone to induce a solid absence phenotype.
Finally, the strength of our results is also supported by their similarities with the following experimental findings: 1. TC FO neurons, as those in the ventrobasal thalamus, are mostly silent during SWDs 41,57 ; 2. burst firing of NRT and cortical neurons increases during SWDs 41,58 ; 3. tonic firing is reduced in all types of cells, as shown experimentally, 41  ).For each neuronal population pair, the left bar is the PSI change between i 1 and i 2 (i 1 → i 2 ), the middle bar between i 2 and i 3 (i 2 → i 3 ), and the right bar between i 3 and the ictal period (i 3 → SWD), as indicated in Figure 3A  Smaller-amplitude, almost continuous SWDs are elicited when g GABAb is increased in neocortical neurons.(I 1,2 ) the SWD amplitude and the interictal period are increased when g GABAb is increased in TC FO neurons.(J 1,2 ) Absence status is generated when g GABAb is increased in TC HO neurons.

2. 3 |
SimulationsAll simulations were carried out in NEURON on a desktop computer or one of the following computing clusters: the Neuroscience Gateway (NSG) Portal for Computational Neuroscience or the Cardiff University School of Biosciences Biocomputing Hub HPC/ Cloud infrastructure.
GABA-A inhibition of TC FO neurons moved the peak of the first AP in each cycle to the left and the right in TC FO and layer 4 pyramidal (L4/PY) neurons, respectively (Figure 2E 3 ,F 3 ).Spike-triggered action potential (STAP) histograms, however, do not decisively show which structures are leading during individual oscillation cycles.The temporal evolution of the phase of the first APs indicates that their phases do not remain stable (Figure 2G 2 ).Indeed, whereas the cortex is leading during the initial few seconds of the SWD (Figure 2G 3 ), the TC FO cells briefly catch up and then gradually fall behind the cortical cells again (Figure 2G 2 ,G 4 ).

(A 3 )
Schematic timeline showing ictal and interictal periods for different g KL values.Color code as in (A 2 ).(B 1 ) Top trace: EEG.Panels below show the membrane potential (upper trace) of the indicated neuron and a color-coded graph of the membrane potential of all neurons of the indicated population.Red bars on the membrane potential traces indicate −60 mV.Red arrowheads in the color-coded graphs mark the neuron shown in the corresponding membrane potential trace.(B 2 ) Same as (B 1 ), shows the expanded SWD cycle highlighted in (B1).Vertical red dotted line marks the peak of the SWD spike.L4 PY, Pyramidal neuron in cortical layer 4; L5 PY, pyramidal neuron in cortical layer 5; L5 IN, interneuron in cortical layer 5; TC FO , first-order TC neuron; TC HO , higher-order TC neuron; NRT FO , first-order NRT neuron; NRT HO , higher-order NRT neuron.F I G U R E 2 Firing properties during SWDs elicited by increased tonic GABA-A inhibition of TC FO neurons.(A-C) Interictal and ictal time evolution of total, burst, and tonic firing frequency for the indicated neuron types.Ictal and interictal periods were linearly scaled to their average durations.The shaded regions represent 95% confidence intervals.Dashed vertical black lines represent the onset and offset of the averaged SWD.Color-code as in (E 2 ).(D) Mean proportion of the indicated neurons showing burst and tonic firing (B and T column, respectively) and those that are silent (S column).Error bars indicate 95% confidence intervals.(E 1 ) Cross-correlations between all APs of different neuronal types and the SWD spike (SWD spike-triggered action potentials: STAPs).Shaded regions are 95% confidence intervals.Dashed vertical line indicates the peak of the SWD spike.Color-code as in (E 2 ).(E 2 ) Same as (E 1 ) but only for the first AP in an SWD cycle.(E 3 ) Same as (E 2 ) but only for L4PY and TC FO neurons for the three color-coded g KL values indicated in (F 3 ) and Figure 1A 2 .Arrows indicate the shift of the firing peaks as g KL is increased.(F 1-3 ) Cumulative AP probability corresponding to (E 1-3 ).(G 1 ) Hilbert transform mean phase of APs of all cell types with respect to the SWD spike.Different SWDs were linearly scaled to the average duration SWD.Dashed vertical lines indicate the SWD onset and offset.Shaded regions represent 95% confidence intervals.Color code as in (E 2 ).(G 2 ) Same as (G 1 ) but only for the first AP in an SWD cycle.(G 3,4 ) Same as (G 2 ) showing the enlarged regions circled in (G 2 ).L2/3 PY, pyramidal neuron in cortical layers 2 and 3; L2/3 IN, interneuron in cortical layers 2 and 3; L4 PY, pyramidal neuron in cortical layer 4; L4 IN, interneuron in cortical layer 4; L5 PY, pyramidal neuron in cortical layer 5; L5 IN, interneuron in cortical layer 5; L6 PY, pyramidal neuron in cortical layer 6; L6 IN, interneuron in cortical layer 6; TC FO , first-order TC neuron; TC HO , higher-order TC neuron; NRT FO , first-order NRT neuron; NRT HO , higher-order NRT neuron.

| 9 of 12 DERVINIS and CRUNELLI 4 .
increase in the T-type Ca 2+ channel function in TC HO neurons, as reported by Gorji et al.49 and Seidenbecher et al.50 ; 5. increase in the T-type Ca 2+ channel function in NRT neurons, as reported by Chen et al.39 and Cain et al.40 ; and 6. enhancement of the number of intrinsically bursting cells in layers 5/6, as observed in the Wistar Albino Glaxo Rats from Rijswijk37 except in TC HO cells for which no data are available at present; F I G U R E 4 Thalamic and cortical abnormalities can independently induce SWDs.(A) EEG showing a period of simulated desynchronized state.(B 1 ) SWDs elicited by progressive increases in the extrasynaptic GABA-A conductance (g eGABAa ) of TC FO neurons.(B 2 ) Crosscorrelations between APs of all cells and EEG (over a 20 min simulation period) with increased TC FO neuron g eGABAa .Color code as in B1.Shaded regions represent 95% confidence intervals.(B 3 ) Schematic SWD timeline showing SWD duration and frequency of occurrence for different TC FO neuron g eGABAa levels.(B 4 ) Change in the firing PSI between the indicated neuronal populations in (G 4 2 .(C 1-4 ) same as (B 1-4 ) but showing SWDs following decreases in GABA-A conductance (g GABAa ) of all cortical neurons.(D 1-4 ) same as (B 1-4 ) but showing SWDs following increases in the cortical AMPA receptor conductance (g AMPA ).(E 1-4 ) same as (B 1-4 ) but showing SWDs elicited by the addition of strongly intrinsically bursting (SIB) neurons in cortical layer 5 (L5) only or in both L5 and cortical layer 6 (L6).(F 1-4 ) same as (B 1-4 ) but showing SWDs after increases in the T-type Ca 2+ conductance (g T ) of NRT cells.(G 1-4 ) same as (B 1-4 ) but showing SWDs after increases in the T-type Ca 2+ conductance (g T ) of TC HO cells.Note the absence status reached the highest increase of g T in these thalamic neurons.F I G U R E 5Essential contribution of various voltage-and transmitter-gated conductances to simulated SWDs.(A 1 ) Control SWDs elicited by increased g KL in TC FO neurons.(A 2 ) Control SWDs elicited by decreased neocortical g GABAa .(B 1,2 ) SWDs persist after blocking g T in TC FO neurons.(C 1,2 ) SWDs are not generated when g T is blocked in TC HO neurons.(D 1,2 ) SWDs are not elicited when g T is blocked in all NRT neurons.(E 1,2 ) SWDs are blocked after removing g GABAb in all neocortical neurons.(F 1,2 ) SWDs are blocked after removing g GABAb in TC FO neurons.(G 1,2 ) SWDs are blocked after removing g GABAb in TC HO neurons.(H 1,2 )