Spindle Oscillation Emerges at the Critical State of the Electrically Coupled Network in Thalamic Reticular Nucleus

Spindle Oscillations Emerge at the Critical State of Electrically Coupled Networks in the Thalamic Reticular Nucleus | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Spindle Oscillations Emerge at the Critical State of Electrically Coupled Networks in the Thalamic Reticular Nucleus Shangyang Li , Chaoming Wang , Si Wu doi: https://doi.org/10.1101/2023.12.31.573769 Shangyang Li 1 School of Psychological and Cognitive Sciences, Beijing Key Laboratory of Behavior and Mental Health,, IDG/McGovern Institute for Brain Research, Center of Quantitative Biology,, Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University , Beijing, 100871, China 2 Guangdong Institute of Intelligence Science and Technology , Hengqin, Zhuhai, 519031, Guangdong, China Find this author on Google Scholar Find this author on PubMed Search for this author on this site Chaoming Wang 1 School of Psychological and Cognitive Sciences, Beijing Key Laboratory of Behavior and Mental Health,, IDG/McGovern Institute for Brain Research, Center of Quantitative Biology,, Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University , Beijing, 100871, China 2 Guangdong Institute of Intelligence Science and Technology , Hengqin, Zhuhai, 519031, Guangdong, China Find this author on Google Scholar Find this author on PubMed Search for this author on this site Si Wu 1 School of Psychological and Cognitive Sciences, Beijing Key Laboratory of Behavior and Mental Health,, IDG/McGovern Institute for Brain Research, Center of Quantitative Biology,, Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University , Beijing, 100871, China 2 Guangdong Institute of Intelligence Science and Technology , Hengqin, Zhuhai, 519031, Guangdong, China Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: siwu{at}pku.edu.cn Abstract Full Text Info/History Metrics Preview PDF SUMMARY Spindle oscillation is a waxing-and-waning neural oscillation observed in the brain, initiated at the thalamic reticular nucleus (TRN) and typically occurring at 7-15 Hz. Experiments have shown that in the adult brain, electrical synapses, rather than chemical synapses, dominate between TRN neurons, suggesting that the traditional view of spindle generation via chemical synapses may need reconsideration. Based on known experimental data, we develop a computational model of the TRN network, where heterogeneous neurons are connected by electrical synapses. The model shows that the interplay between synchronizing electrical synapses and desynchro-nizing heterogeneity leads to multiple synchronized clusters with slightly different oscillation frequencies, whose summed activity produces spindle oscillation as seen in local field potentials. Our results suggest that during spindle oscillation, the network operates at the critical state, which is known for facilitating efficient information processing. This study provides insights into the underlying mechanism of spindle oscillation and its functional significance. INTRODUCTION Spindle oscillation refers to a waxing-and-waning oscillatory event occurring at a frequency of 7-15 Hz 1 , 2 . This phenomenon has been widely observed in various mammals, including the cat 3 , 4 , mice 5 , 6 , rat 7 , 8 , ferret 9 , 10 , dog 11 , 12 , sheep 13 , macaque 14 , 15 , and human 16 , 17 . Extensive experimental studies have established a strong correlation between spindle oscillation and learning and memory processes in the brain 18 . For example, research has shown that the density and amplitude of spindle oscillation increase during post-learning sleep, both for declarative memory tasks 19 – 21 and procedural memory tasks 22 , 23 . Manipulation studies conducted on humans and rodents have provided causal evidence supporting the role of spindle oscillation in memory consolidation 24 , 25 . Despite the recognized importance of spindle oscillation in brain functions, the neural mechanism underlying spindle generation remains a subject of debate. The conventional understanding of spindle generation has suggested that spindles are generated in the thalamus 1 , 2 , 17 , 26 . For example, early investigations on anesthetized cats revealed that the decorticated thalamus alone could produce waxing-and-waning spindle rhythms 27 , 28 . In vitro studies using thalamic slices further demonstrated that the synaptic connectivity between thalamocortical (TC) relay neurons and thalamic reticular nucleus (TRN) neurons played a crucial role in spindle rhythm generation 9 , 10 , 29– , 32 . According to this framework, low-threshold bursts from TRN cells transiently inhibit TC neurons, and upon release from inhibition, TC cells generate Ca 2+ -dependent post-inhibitory rebound bursts, which drive subsequent spike bursts in TRN neurons 26 , 33 – 36 . However, experimental findings have challenged this “ping-pong” model of spindle generation. These inconsistencies include: 1) optogenetic stimulation of TRN neurons triggering cortical spindles that are not observed in the corresponding TC site 37 ; 2) the generation of sleep spindles in the mouse thalamus in the absence of T-type Ca 2+ channels and burst firing of TC neurons, both in vivo and in vitro 38 ; and 3) administration of a Ca 2+ channel blocker in the corticothalamic network reducing spindles at higher frequencies (approximately 14 Hz) while enhancing the power of slow spindles (approximately 10 Hz) 39 . These findings strongly suggest that the involvement of TC cells is not the necessary condition for spindle generation 33 . TRN neurons are intrinsic GABAergic cells that encompass the entire thalamus 40 , 41 . They receive glutamate excitatory inputs from TC and corticothalamic (CT) neurons 40 , 42 , as well as extensive inhibitory projections from subcortical areas, including the basal forebrain 43 – 46 , the substantia nigra pars reticulata 47 , the globus pallidus 48 – 50 , and the hypothalamus 51 . Experimental studies have suggested that the TRN can generate oscillations at the spindle frequency without relying on the inputs from the cortex and thalamus 4 , 52 , 53 . Earlier experiments involving local glutamate application revealed that TRN neurons in rodents younger than 2 weeks of age are interconnected through inhibitory chemical synapses 54 – 58 . Subsequent computational modeling demonstrated that a TRN network with neurons connected by inhibitory chemical synapses can generate various types of network oscillations at frequencies of 7-10 Hz 34 , 59 – 61 . However, these models rely on low-threshold Ca 2+ -dependent bursts, which either require a sufficiently negative reversal potential of inhibitory synapses 34 , 59 , 60 or a hyperpolarized resting membrane potential 61 . These assumptions are not consistent with the biological properties of TRN neurons, which include: 1) TRN cells have a depolarized chloride reversal potential (E GABA = − 62 mV) compared to TC neurons, resulting in postsynaptic depolarizations rather than strong inhibition upon receiving GABAergic inputs 62 – 64 . 2) Spindles can be generated from TRN slices with a more depolarized resting potential (−63.8 ± 1.2 mV) 29 , 31 . Moreover, experimental findings have shown that electrical synapses dominate the connectivity between TRN neurons after two weeks of age. Paired recordings from TRN neurons in rats and mice across different ages have revealed the presence of electrical synapses but rare chemical transmission between TRN neurons 65 – 69 . Optogenetic stimulation of layer 6 CT neurons or neighboring TRN neurons failed to evoke inhibitory postsynaptic currents (IPSCs) in TRN neurons in mice older than two weeks 70 – 72 . Genetic deletion of vesicular GABA transporters from TRN neurons only reduced GABAergic transmission in TC neurons but not TRN neurons 72 . These findings indicate that the electrically coupled TRN network, without direct inputs from TC neurons, is sufficient for the generation of spindle oscillations. Notably, sleep spindles begin to emerge around 2-3 months of age in humans and during the third to fourth postnatal weeks in rodents 73 , which aligns with the dominance of electrical couplings in the TRN at later developmental stages. Thus, the traditional mechanism based on chemical synapses for spindle generation in the TRN suggests a reconsideration. Motivated by recent experimental evidence, the present study investigates the generation of spindle oscillation by the electrically coupled TRN neurons. Here, sleep spindle oscillations in the TRN are defined as oscillatory events in the frequency range of 7-15 Hz and with a typical duration of 0.5-3 seconds. They are characterized by a waxing-and-waning pattern in the os-cillatory activity, as identified through visual inspection of the waveform filtered between 0.3-35 Hz. We develop a computational model that incorporates the latest findings regarding TRN neurons, specifically the prevalence of electrical synapses between neurons and the presence of neuronal heterogeneity. These factors have opposing effects on network dynamics, as electrical coupling tends to synchronize neurons while neuronal heterogeneity tends to desynchronize them. Our results suggest that the interplay between electrical coupling and neuronal hetero-geneity leads to the self-organization of the TRN network into the critical state. In this state, neurons form multiple synchronized clusters, each oscillating at slightly different frequencies. The superposition of these neuronal activities, mimicking the local field potential (LFP) recorded in experiments, exhibits characteristic spindle oscillations. Overall, our modeling study suggests a natural emergence of spindle oscillations in the TRN network when it operates in the critical state — a condition known to facilitate efficient information processing in complex systems 74 . These findings provide insights into the underlying mechanisms of spindle generation and offer further understanding of the functional role of the TRN in regulating thalamocortical activity. RESULTS An electrically coupled heterogeneous TRN network We built a TRN network model based on physiological data collected from ferrets, cats, mice, and rats. Specifically, we considered that the TRN network is a two-dimensional grid ( Figure 1A ), on which N neurons are uniformly distributed and connected with each other by electrical synapses 65 , 66 , 68 , 69 , 72 according to a Gaussian probability connection profile (this reflects the fact that neighboring TRN neurons tend to be connected by electrical synapses 68 , see details in STAR). Each neuron in the network receives two kinds of external synaptic inputs: excitatory synaptic projections from the thalamus and cortex 40 , and inhibitory inputs from subcortical brain areas 43 – 51 . The dynamics of a single TRN neuron is given by 75 , where V is the membrane potential and τ the membrane time constant. I L , I Na , I K , I T and I KL denote, respectively, the leaky channel current, the sodium channel current, the potassium channel current, the low-threshold calcium channel current, and the potassium leaky current. I gap denotes the recurrent gap junctional current from other TRN neurons. I inh and I exc denote the subcortical inhibitory current 50 , 51 and the thalamic and cortical excitatory current 40 , 42 , respectively. For the detailed form of each current, see STAR. Download figure Open in new tab Figure 1. The TRN network model. (A) The network structure. TRN neurons are uniformly distributed on a two-dimensional sheet and connected with electrical synapses. The connection probability between neurons follows a distance-dependent Gaussian distribution. Each neuron receives an excitatory thalamic and cortical input and an inhibitory subcortical input.. (B) The distribution of the conductance g T of T-type Ca 2+ channels of all TRN neurons.. (C) The spontaneous activity of a TRN neuron changes from the resting state, subthreshold oscillation, to bursting firing when increasing the conductance g T .. (D) The distribution of the number of spikes per burst in TRN neurons. Each burst was triggered by injecting a negative current followed by abrupt current removal 83 .. (E) The relationship between the coupling coefficient (CC) and the conductance of electrical synapse J e . For CC in the range of (0.05 − 0.2), J e is in the range of (0.0005 S , 0.005 S ). The shaded region represents the standard error of the mean (SEM) calculated from n = 10 independent simulations.. (F) The relationship between the resting membrane potential and the potassium leaky conductance g KL .. (G) The spontaneous activity of a TRN neuron changes from the resting state, bursting firing, to the resting state when increasing the neuromodulation level g KL . In the experiments, spindle oscillation was observed in the local field potential (LFP). Similar to previous works 76 , we considered that the simulated LFP in our model represents the averaged membrane potential of all TRN neurons, which is calculated to be, where V i is the membrane potential of the i -th neuron, and the summation runs over all TRN neurons. We also calculated LFP using a different method called the spatial lowpass filter and obtained the same results (see STAR). In our model, the generation of spindle oscillation is influenced by three crucial factors: neuron heterogeneity, electrical couplings between neurons, and neuromodulation levels. In the below, we will discuss the settings of these factors in the model and explore their effects on the neural dynamics. Heterogeneity of TRN neurons TRN neurons are distinguished by their abundant T-type Ca 2+ channels 77 . In our model, we computed the T-type Ca 2+ channel current using the equation I T = g T f ( V ) (refer to Equation 5 for the specific form of f ( V )), where g T represents the channel conductance. It is important to note that TRN neurons exhibit significant heterogeneity. Different TRN neurons display distinctive firing patterns, which have been linked to variations in sleep rhythms across sensory cortices 78 , 79 . One of the primary sources of this heterogeneity is the varied distribution of T-type Ca 2+ channels among TRN neurons 78 – 83 . Therefore, in our model, we assigned different values of g T to individual neurons to reflect this heterogeneity (see Figure 1B ). We explored how g T affects the dynamics of a single neuron. By varying g T , we observed that ( Figure 1C ): 1) for g T < 2.32 mS / cm 2 , the neuron is in the resting state; 2) for 2.32 mS / cm 2 < g T 3.19 mS / cm 2 , the neuron generates bursting spikes. To match with the experimental data, we considered that the values of g T for all neurons are randomly sampled from a truncated normal distribution as illustrated in Figure 1B . In the biological experiment, the number of spikes per offset burst of TRN neurons was measured and was found to approximately satisfy a normal distribution (Fig.3d in 83 ). Following the same protocol as in 83 , we injected a negative current to a TRN neuron followed by a sudden current removal to induce bursting firing of the neuron. We set the distribution of g T appropriately, such that the numbers of spikes in bursts generated by all TRN neurons exhibit a similar distribution as observed in the experiment ( Figure 1D ). Electrical couplings between TRN neurons Another remarkable feature of TRN neurons is their electrical couplings 65 , 66 , 72 . In the model, we set the electrical synapse current between neurons ( i, j ) to be I gap = J e ( V j − V i ) (see STAR for details), with J e the coupling conductance. The strength of electrical couplings can be quantified by the coupling coefficient (CC) between TRN neurons. To correlate the electrical synapse conductance J e with the CC, we calculated how the average CC varies with J e (see Figure 1E ). To be consistent with the experimental finding that the average CC in TRN varies in the range of (0.05 − 0.2) 66 , 84 , we set the conductance J e of electrical synapse in the range of (0.0005 S , 0.005 S ) in all later computational experiments. Modulation by neuromodulators It is known that subcortical neuromodulators, such as acetyl-choline and norepinephrine, influence oscillatory activities in the thalamus 85 , 86 . To model this neuromodulation effect, we included a potassium leaky current I KL = g KL ( E KL − V ) in the neuronal dynamics (see Equation 5 for more details), where g KL is the conductance controlled by neuromodulators. At the single neuron level, g KL shows a great impact on the membrane resting potential, i.e., the value of resting potential decreases with g KL ( Figure 1G ). Neuromodulation also affects neuronal firing patterns. As illustrated in Figure 1F , a TRN neuron tends to oscillate at an intermediate g KL value and rest when g KL is small or large. Spindle oscillation emerges in the TRN network Experimental studies have revealed varied oscillation behaviors in the TRN network during different sleep and awake conditions 87 . To validate our network model, we first identify the parameter ranges in which TRN spindles occur. Specifically, we manipulate the parameter g KL , which reflects the levels of neuromodulation in different sleep and awake conditions, while keeping all other parameters constant at appropriate values (see STAR). Furthermore, when modeling the sleep condition, we incorporate an inhibitory current I inh from subcortical regions, while excluding any excitatory current I exc from the thalamic and cortical regions. Conversely, in the awake condition, we include both I inh and I exc . Deep sleep condition In deep sleep, i.e., N3 NREM sleep, the neuromodulation level is low 88 , we set g KL to be a large value. In such a state, most TRN neurons are hyperpolarized and they predominantly generate strong bursting activities with high-frequency inter-burst spikes ( Figure 2A ). Together with electrical couplings between neurons, the whole network generates highly synchronized responses, resulting in strong LFP ( Figure 2D ), and the oscillation frequency is around 4 Hz ( Figure 2G ), agreeing with the delta oscillation (1 − 4 Hz) observed in the experiment 89 . Download figure Open in new tab Figure 2. Oscillation behaviors of the TRN Network. (A-C) Raster plots of neurons’ firings in deep sleep, light sleep, and alertness conditions, respectively.. (D-F) LFP in deep sleep, light sleep, and alertness conditions, respectively.. (G-I) The spectrum of LFP in deep sleep, light sleep, and alertness conditions, respectively.. (J) The phase diagram of the network state with respect to the neuromodulation level g KL .. (K) The statistical properties of the spindle oscillation cycle in experiments 7 and our model. Upper panel: the experimental data. Lower panel: the model simulation data.. (L) The statistical properties of the spindle oscillation duration in experiments 7 and our model. Upper panel: the experimental data. Lower panel: the model simulation data. Light sleep condition: spindle oscillation occurs In light sleep, i.e., N2 NREM sleep, the neuromodulation level is at the medium level 88 , we set g KL to be a mediate value. In this state, TRN neurons are less hyperpolarized (−65.5 ∼ −63.5 mV) and produce weak bursts ( Figure 2B ). A single burst typically contains only one or two spikes, and such bursts can be easily interrupted (see the discontinuous spiking of a TRN neuron in Figure 2B ). Under this condition, the whole TRN network generates oscillations of the waxing-and-waning shape in LFP ( Figure 2E ) with a frequency of 7 Hz ( Figure 2H ), which is in the range of spindle oscillation (7 − 15 Hz) 18 . We also calculated LFP using a different method and obtained the similar results (see Figure S12). We carried out ablation studies to illustrate the impact of model parameters on spindle generation. First, by removing the subcortical synaptic inputs (i.e, setting I inh = 0), the waxing-and-waning oscillation disappears in the network (see Figure S10). Second, by removing or blocking the low-threshold Ca 2+ channel currents (i.e., setting I T = 0), spindle oscillation also disappears (see Figure S11). These results are in line with the experimental findings, which are: 1) the TRN slice in vitro without subcortical projections could not produce spindle oscillation 31 ; 2) the power of spindle oscillations was significantly reduced in Ca 2+ channel knockout mice, and the spindle rhythmogenesis in major sensory cortical areas depended on low-threshold Ca 2+ currents 79 , 90 , 91 . Alertness condition In the alertness condition, i.e., REM sleep or awake state, the neuromodulation level is high 88 , we set g KL to be small. In such a case, TRN neurons have depolarized resting membrane potentials ( Figure 1C ). Furthermore, in the REM sleep state, we set the excitatory input I exc = 0. Consistent with experimental finding 88 , a significantly weak LFP signal is seen in our TRN network (Figure S4B). Moreover, TRN neurons show small voltage fluctuations and uncorrelated activities (Figure S4C) and TRN neurons under such a state present nearly no spiking activity. In the awake state, we set I exc ≠ 0 representing the excitatory input from the thalamus and cortex, and we found that TRN neurons show irregular spiking ( Figure 2F ) and have no dominating oscillation frequency ( Figure 2I ). Phase diagram of the TRN network In summary, Figure 2J presents how the TRN network undergoes three different states of oscillation as a function of the neuromodulation level parameter g KL . As g KL decreases (i.e., the neuromodulation level increases), the TRN network transitions from the regular low-frequency delta oscillation (3 −6 Hz), to the waxing-and-waning spindle oscillation (6 − 8 Hz), and finally to irregular firings. These states correspond to the physiological states of deep sleep, light sleep, and alertness, respectively. The resting membrane potentials of individual neurons also change accordingly, rising from (−65.5 ∼ −75mV), to (−65.5 ∼ −63.5mV), and to ( > −63.5 mV). Our model reproduces the experimental finding 52 that the resting membrane potential in spindle oscillation is more depolarized than that in delta oscillation. Statistical properties of spindle oscillations The experimental data has shown that spindle oscillations are characterized as 0.5 − 3s long oscillation sequences in LFP which have the waxing-and-waning profile and oscillate at 7 − 15 Hz 18 . The density, duration, and amplitude of spindle oscillations, all display statistical characteristics, and they are highly correlated with memory performance 92 , problem-solving ability 93 , and mental diseases 94 . We found that our model can reproduce the statistical properties of spindle oscillations observed in human 95 – 97 and animal 7 , 38 . By using multichannel silicon-probe recording on the thalamus of urethane-anesthetized and sleeping rats, it was found that both the spindle oscillation cycle and the duration exhibit uni-modal distributions with biases to small values (refer to the upper panels in Figure 2K and L ) 7 . Consistent with these results, our network model generates spindle oscillations having similar statistical distributions (refer to the lower panels in Figure 2K and L ), with the majority of spindle oscillations having 5 −13 oscillation cycles and a duration of 0.5 − 1.5s. These results are also in line with the observations in human 95 and mice 38 . The mechanism of spindle generation In the below, we further explore the underlying mechanism of spindle generation in our TRN network. Specifically, we show that the interplay between electrical coupling and neuronal heterogeneity produces spindle oscillations. Effects of electrical coupling The role of electrical coupling in regulating TRN oscillation has been highlighted in the experiments 98 , 99 . Here, we systematically investigated the effects of electrical coupling on the dynamics of the TRN network. We fixed all other parameters of the model except the conductance of electrical synapse J e . The parameter g KL reflecting neuromodulation is set to be of an intermediate value which allows the generation of spindle oscillation (see Section). We first examined the relationship between the conductance of electrical synapse J e and the cross-correlation (CC) among neurons in the network. As depicted in Figure S6A, we observed that CC increases as J e rises. This phenomenon can be attributed to the synchronization of neuronal responses facilitated by electrical couplings. To further explore the impact of J e on spindle generation, we conducted measurements and documented the probability of spindle occurrence at different J e values (refer to STAR). The results, illustrated in Figure S6B, reveal an initial increase followed by a subsequent decrease in the probability of spindle generation with increasing J e . This pattern suggests that an appropriate range of electrical coupling strength is required for the spindle generation. This observation aligns with our intuition: when J e is too small, neurons in the network fire independently, resulting in a lack of coherent oscillation in the local field potential (LFP); conversely, when J e is too large, all neurons fire synchronously, leading to LFP oscillation at a single frequency. The subsequent sections provide a more detailed analysis of the mechanics underlying spindle generation. We further conducted an analysis on the clustering phenomenon within the network. In this context, a cluster represents a group of interconnected neurons that fire at the same frequency. Our observations reveal that by increasing the electrical coupling conductance ( J e ), the network state can be categorized into three distinct phases ( Figure 3 ). These phases include: 1) the asynchronous firing phase (AFP, depicted in Figure 3A-C ), where neuronal firings are largely independent of each other, the network lacks obvious large firing clusters, and the LFP does not exhibit clear oscillation during this phase; 2) the multiple cluster phase (MCP, illustrated in Figure 3D-F ), characterized by the formation of multiple clusters within the network, varying in size and oscillating at slightly different frequencies. The LFP during this phase displays spindle oscillation; 3) the synchronized firing phase (SFP, shown in Figure 3G-I ), where the majority of neurons in the network synchronize their firing, resulting in the LFP oscillating at a single dominant frequency. Notably, the occurrence of spindle oscillation is associated with the MCP, and this phenomenon of multiple clustering has also been reported in a current clamp experiment conducted on the rat TRN slice 66 . Download figure Open in new tab Figure 3. The mechanism of spindle generation. (A-C) Histogram of neuronal oscillation frequency, heat map of neuronal oscillation frequency, and LFP signal. The parameters are: J e = 0 and Var( g T ) = 1.0.. (D-E) The same as in (A-C), except J e = 0.001 and Var( g T ) = 1.0.. (G-I) The same as in (A-C), except J e = 0.003 and Var( g T ) = 1.0.. (J-L) The same as in (A-C), except J e = 0.001 and Var( g T ) = 2.4.. (M-O) The same as in (A-C), except J e = 0.001 and Var( g T ) = 0.. (P) Phase diagram of the TRN network with respect to the electrical coupling strength J e and the neuronal heterogeneity Var( g T ).. (Q) Two sine waves having slightly different oscillation frequencies, where y 1 ( t ) = sin(2.2 πt ) and y 2 ( t ) = sin(2.4 πt ).. (R) Superposition of two sine waves, y ( t ) = y 1 ( t ) + y 2 ( t ).. (S) Superposition of 100 sine waves by their frequencies corresponding to the oscillation fre-quencies of TRN neurons during spindle generation. In the above, we have assumed a constant electrical synapse conductance between all neurons for simplicity. However, empirical evidence suggests that the strength of electrical synapses between TRN neurons exhibit significant variability 100 , 101 . To investigate the impact of electrical coupling variability on spindle oscillations, we conducted an additional experiment incorporating heterogeneous synapse strengths. We modeled the electrical synapse strengths using an exponential decay distribution, reflecting the biological tendency for spatially proximate neurons to form stronger connections (see Figure S5A and B). Despite this added heterogeneity, our model continued to generate robust spindle oscillations (see Figure S5C and E). This finding highlights that our simplified models effectively capture the essential role of electrical synapses in spindle generation. Effects of neuronal heterogeneity We conducted further investigation into the impact of neuronal heterogeneity on the dynamics of the TRN network. Neuronal heterogeneity, quantified by the variance of the T-type Ca 2+ conductance ( g T ) denoted as Var( g T ) (while keeping the mean of g T fixed), plays a significant role in shaping the distinctive behavior of individual neurons and contributes to the desynchronization of their activities. This is evident in the decrease of cross-correlation between neurons as Var( g T ) increases (Figure S6C). We also observed that the probability of spindle generation initially increases with Var( g T ) and then decreases (Figure S6D). This observation can be intuitively understood. When Var( g T ) is very small, neurons in the network exhibit synchronous firing, resulting in a single-frequency oscillation in the LFP. Conversely, when Var( g T ) is very large, neurons fire independently, leading to the absence of coherent oscillation in the LFP. Similar to the impact of electrical coupling, the clustering phenomenon within the TRN network also undergoes three distinct phases in response to neuronal heterogeneity. However, in the case of heterogeneity, these phases appear in the reverse order as Var( g T ) increases, namely, SFP ( Figure 3M-O ), MCP ( Figure 3D-F ), and AFP ( Figure 3J-L ). The reason behind this ordering is straightforward: as the heterogeneity represented by Var( g T ) increases, neuronal firings become progressively more desynchronized, resulting in a transition from a single cluster to multiple clusters, and eventually to the absence of clustering. Once again, we observed that spindle oscillations occur specifically during the MCP. We also inspected the statistical properties of spindles when the neuronal heterogeneity varies. With the decrease of Var( g T ), the averaged cluster size (i.e., the averaged number of neurons in a synchronized cluster) increases. Figure S7A displays how the spindle probability (measured as the number of spindles occurring in a fixed time interval) varies with the averaged cluster size. It shows that the spindle probability takes the maximum value when the averaged cluster size has an intermediate value, i.e., the neuronal heterogeneity Var( g T ) takes an intermediate value. With the increase of Var( g T ), the variance of individual neuronal oscillation frequency increases. Figure S7B shows that the spindle modulation frequency increases with the variance of neuronal oscillation frequency. This can be intuitively understood from the below simple mathematical analysis (see Equation 3 ), which shows that the spindle modulation frequency is determined by the difference between neuronal oscillation frequency. The above two statistical properties can be checked in experiments to validate our model. Up to now, we have considered that the TRN neurons form a homogeneous group for simplicity. However, the experiments have identified three distinct tiers within the TRN, where central cells exhibit a higher tendency to burst, while edge cells favor tonic spiking 82 , 83 , 102 , 103 . To reflect this heterogeneity, we carried out an additional experiment, in which we extended the model by including distinct T-type calcium conductance profiles for edge and central cells. Specifically, the edge cells were represented by two 2×10 subnetworks, whereas the central cells were modeled as a 10×10 subnetwork (Figure S8A). We adjusted the means of g KL in the edge and central tiers to align with the experimental measurements of the distribution of the number of spikes in rebound bursting (see Figure S8B and Figure. 3d in 83 ). We confirmed that with this extra heterogeneity in the cell type distribution, our model can still produce robust spindle oscillations (Figure S8C-G), with spindles predominantly occurring in the central part of the network which has the higher mean value of g KL . In summary, our results suggest that electrical coupling and neuronal heterogeneity exert contrasting effects on the dynamics of the TRN network. Electrical coupling promotes synchronization, whereas neuronal heterogeneity contributes to desynchronization. The interplay between these two factors gives rise to a diverse range of dynamics within the TRN network. Notably, when the amplitudes of electrical coupling and neuronal heterogeneity are appropriately balanced, spindle oscillation emerges. Figure 3P illustrates the phase diagram of the TRN network concerning the electrical coupling and neuronal heterogeneity. Mathematical analysis of spindle generation In the above, we have established that spindle oscillations emerge when the network state resides in the MCP. The MCP state is distinguished by the coexistence of multiple clusters with varying sizes and slightly different oscillation frequencies. In the below, we describe how the MCP state gives rise to the characteristic waxing-and-waning LFP pattern. Let us first consider two harmonic oscillators with the same amplitude but slightly different frequencies (see the example illustrated in Figure 3Q ), denoted, respectively, as y 1 ( t ) = A cos (2 πω 1 t ) and y 2 ( t ) = A cos (2 πω 2 t ), with | ω 1 − ω 2 | ≪ ( ω 1 + ω 2 ) / 2. The superposition of the two oscillators y ( t ) = y 1 ( t ) + y 2 ( t ) can be expressed as We see that the superposition of two oscillators displays a waxing-and-waning shaped oscillation. Specifically, the variable y ( t ) oscillates at a high frequency of ( ω 1 + ω 2 ) / 2, while its amplitude 2 A |cos [ π ( ω 1 − ω 2 ) t ]| oscillates at a much slower frequency of | ω 1 − ω 2 | (see Figure 3R ). When considering multiple harmonic oscillators with their frequencies randomly sampled from a limited range, their superposition exhibits the characteristics of spindle oscillation. To confirm this, we extracted the oscillation frequencies of clusters in the TRN network at the MCP state (Figure S9), and used them as the frequencies of corresponding harmonic oscillators. Subsequently, we calculated the superposition of these harmonic oscillators. Our observations confirmed that the superposed activities indeed display the features of spindle oscillation, including rapid oscillation enveloped by waxing-and-waning amplitudes, as well as variations in spindle duration, amplitude, and inter-spindle interval (see Figure S9B and E). On the other hand, when we constructed harmonic oscillators using the oscillation frequencies of clusters in the phases of AFP and SFP, their superposed activities do not exhibit spindle oscillation, but rather demonstrate stochastic responses (Figure S9C and D) or regular oscillation (Figure S9A and F). In the TRN network, we can regard a synchronized cluster as a harmonic oscillator. At the MCP state, all clusters represent distinct harmonic oscillators with slightly varying oscillation frequencies. Consequently, the collective activity of these clusters, reflected in the LFP, displays spindle oscillations, as described earlier (refer to Figure 2E and Figure 3D-F ). Spindle oscillations occur at the critical state In the previous sections, we observed that spindle oscillations occur when the TRN network is in the MCP state, characterized by the formation of multiple synchronized clusters among the network’s neurons. Interestingly, this state aligns with the critical state of a dynamical system, a common feature of complex dynamical systems 74 . The critical state is known to emerge as a result of the interplay between synchronization and desynchronization forces within the system. When the synchronization force dominates, the system exhibits high order, with few synchronized clusters. Conversely, when the desynchronization force dominates, the system becomes highly disordered, lacking large-size clusters. The critical state arises when these two forces are balanced, resulting in the coexistence of multiple synchronized clusters within the network. Extensive theoretical studies have highlighted the significance of criticality as the optimal condition for large systems, including neuronal networks, to process information efficiently 74 . In the TRN network, the synchronization force arises from electrical couplings between neurons, while the desynchronization force stems from neuronal heterogeneity. We have demonstrated that the interplay between these forces drives the TRN network into the MCP state, exhibiting the characteristic of criticality. In this section, we examine the correspondence between the MCP state and the critical state of the TRN network by computing relevant indicators of criticality. Firstly, we examined the distribution of avalanche size in the TRN network. We began by calculating the spike times for all neurons and computing the average inter-spike interval (ISI) of these merged spike times. Using this ISI (typically 1-4 ms in our experiments) as the bin size, we divided the merged spike train into small bins and counted the number of spikes in each bin (see Figure 4A ). We defined an avalanche as a series of consecutive bins, each containing at least one spike, separated by silent bins with no spike. The size of an avalanche was determined by the total number of spikes it contained (see the illustration in Figure 4A and STAR). It was observed that the distribution of avalanche sizes exhibited a power-law pattern exclusively in the MCP state ( Figure 4D ), suggesting criticality. In contrast, other states deviated from the power-law distribution ( Figure 4C and E ). Download figure Open in new tab Figure 4. The criticality analysis of the spindle oscillation state. (A) The time is divided into small bins of equal length. The bin size Δ t is set to be the averaged inter-spike interval (ISI) of the merged spike train of all neurons, which is typically 1-4ms. An avalanche is defined as a sequence of bins with each of them containing at least one spike (marked by gray), and distinct avalanches are separated by silent bins. The size of an avalanche is the total number of spikes it contains, and the lifetime is the number of bins it spans.. (B) The DFA analysis of network oscillation behaviors. The x-axis represents the window width ( w ), while the y-axis the root-mean-squared fluctuation ( F ( w )) of the detrended time series of firing rate. The slope of the log-log plot is approximately 1.2, 0.85, and 0.5 in the state of SFP, MCP and AFP, respectively. Error bars represent the standard error of the mean (SEM) calculated from n = 10 independent simulations.. (C-E) The log-log plot of the distribution of avalanche size in three TRN states: the AFP state (C), the MCP state (D), and the SFP state (E).. (F-H) The log-log plot of the distribution of avalanche lifetime in three TRN states: the AFP state (F), the MCP state (G), and the SFP state (H). Secondly, we measured the distribution of avalanche lifetime, which was defined as the number of bins an avalanche spans (see the illustration in Figure 4A and STAR). Only in the MCP state did the lifetime distribution exhibit a power-law pattern ( Figure 4G ), indicating criticality; while in other states, the power-law distribution was not satisfied ( Figure 4F and H ). Thirdly, we assessed the long-range temporal correlation of oscillatory signals using detrended fluctuation analysis (DFA) 104 . DFA allows us to quantify the decay rate of auto-correlation in the network fluctuation F ( w ) (see STAR). If F ( w ) exhibits a slowly decaying auto-correlation structure, DFA yields a power-law form F ( w ) ∼ w α , where α ≈ 0.5 corresponds to a disordered pattern, 0.5 < α 1 reflects a highly correlated pattern. In the MCP state, we obtained 0.5 < α < 1, indicating that the network operates at the critical state ( Figure 4B ). Conversely, in AFP, α 1 ( Figure 4B ), suggesting deviations from criticality. In summary, our results suggest that the TRN network operates at the critical state when spindle oscillations occur. However, it is important to note that the critical state alone is insufficient to generate spindle oscillation. For instance, if we counterbalance electrical coupling with stochastic noises instead of neuronal heterogeneity, we can achieve the criticality of the network state. Nevertheless, in such a case, all clusters within the network oscillate at the same frequency, and spindle oscillation will not manifest in the LFP. To generate spindle oscillation, the inclusion of neuronal heterogeneity is necessary since neuronal heterogeneity leads to clusters oscillating at slightly different frequencies, and their superposition gives rise to the waxing-and-waning shaped oscillation (refer to the analysis in Mathematical analysis of spindle generation). Conclusion and Discussion The latest TRN experiments revealed that TRN neurons are highly heterogeneous and connected dominantly with electrical synapses. This suggests a reconsideration of the classical view of spindle generation via chemical synapses in the TRN network. In this work, by building a computational model capturing the updated properties of the TRN network, we re-examined the mechanism of spindle generation. We found that the waxing-and-waning spindle oscillations naturally emerge in the TRN network as a consequence of the competition between two driving forces: electrical synapses tending to synchronize neurons while heterogeneity tending to de-synchronize neurons. The interplay between two forces drives the TRN network to fall into a state where multiple synchronized clusters with slightly different oscillation frequencies coexist. The superposition of multiple local TRN clusters thus gives rise to spindle oscillation in the recorded LFP. Our research suggests that the TRN network operates at a critical state during spindle oscillations. This critical state represents a balance between order and disorder 74 and allows the TRN network to integrate various inputs and coordinate neural activities across brain regions. These findings provide insights into spindle oscillation mechanisms and their potential role in learning and memory. Experimental evidence of the model Our model has reproduced a number of experimental findings, including the statistical properties of the duration and the cycle number of spindle oscillations as observed in experiments 7 , 38 , 95 . It reconciles two conflicting experimental findings regarding the generation of TRN spindles. Steriade et al. 3 , 4 , 52 found that the deafferented TRN in vivo , lacking thalamic and cortical projections, can generate and sustain spindle oscillations. On the other hand, von Krosigk et al. 31 found that isolated TRN in vitro , devoid of any thalamic, cortical, and subcortical connections, fails to generate spindles. Our modeling supports both in vivo and in vitro experiments by highlighting that subcortical inhibitory projections in vivo serve as the excitatory drive for spindle generation, and this excitation arises due to the depolarized reversal potentials of TRN GABA A receptors ( E GABA ≈ −45 mV found in 63 and E GABA = −62 ± 3.0 mV obtained in 64 ). Additionally, our model underscores the importance of electrical synapses and neuronal heterogeneity in spindle generation, corroborating recent experimental findings. For example, blocking electrical synapses suppresses spindle oscillation 105 , while reducing neuronal excitability by knocking out T-type Ca 2+ channels diminishes spindle generation 38 , 79 . Moreover, experimental studies have provided crucial insights into the synchronized behavior of TRN neurons under electrical couplings. Long et al. 66 and Lee et al. 68 observed clustered, synchronized responses in these neurons. Long et al. 66 observed that when a subpopulation of TRN cells was activated by the nonspecific metabotropic glutamate receptor (mGluR) agonist ACPD, they generated synchronized rhythms in the 5-15 Hz range via electrical synapses, which is highly consistent with our modeling. Finally, our model posits that neuronal heterogeneity is crucial for TRN spindle oscillation. Particularly, we incorporate two key aspects of this heterogeneity: variations in T-type Ca 2+ conductance and the resulting diverse firing patterns, both of which are well-documented in experimental studies 81– , 83 , 102 . This heterogeneity is evident in the diverse morphology, neurochemistry, and electrophysiology of TRN neurons 78 . Research has identified distinct neuronal types 106 , synaptic projection patterns 107 , 108 , and neurochemical markers 37 , 109 , 110 , as well as genetic subtypes with varying firing properties 82 , 83 , 102 . These findings provide essential evidence supporting our model’s focus on neuronal heterogeneity. Predictions of the model Our model produces predictions that can be tested through experiments (please also refer to STAR for the detailed analysis of model parameter influences on spindle oscillation properties). One of our key predictions is the significant role of electrical synapses in spindle generation and regulation. To validate this, we propose experiments that manipulate electrical synapse strength and observe the resulting effects on spindle oscillations. One such experiment involves measuring spindle oscillations in mice with Connexin 36 (Cx36) knockdown. Cx36 is the primary protein responsible for forming gap junctions in TRN [1,2]. Our model predicts that Cx36 knockdown mice will exhibit impaired spindle oscillations compared to wild-type mice. Our model also suggests that neuronal heterogeneity, especially the variability in T-type calcium conductance and resultant firing patterns, is crucial for the desynchronization within the TRN network, leading to the characteristic waxing-and-waning spindle oscillations. To empirically test this hypothesis, we propose developing transgenic animal models with altered TRN neuronal heterogeneity and comparing their spindle oscillations to those of wild-type animals. A relevant study by Michael et al. 111 reported diminished SK2 currents and neuronal bursting in TRN neurons of Ptchd1 -knockout mice, with consequent reductions in sleep spindle counts. While this supports our model, the findings are limited by their in vivo context, which may include extraneous interactions between the thalamus and TRN. A more direct validation could be achieved by analyzing spindle oscillations in TRN slices from these knockout mice, thereby focusing solely on intrinsic TRN dynamics and eliminating external influences. Additionally, our model postulates a universal mechanism for spindle-like oscillations, suggesting that the interplay between synchronizing and desynchronizing forces could generate similar oscillations across various neural circuits, not limited to the TRN. This hypothesis posits that waxing-and-waning oscillations could be a general feature of neural dynamics, observable across different brain regions and networks, reflecting a fundamental aspect of how neural systems transition between states of synchronization and desynchronization. Limitations of the study Although our model successfully demonstrates the generation of spindle oscillations in an electrically coupled heterogeneous TRN network, there are several issues that require further investigation. Firstly, the TRN is part of the larger corticothalamic system, influenced by excitatory inputs from thalamic and cortical areas and inhibitory inputs from subcortical regions. While our current focus was on the role of subcortical projections in spindle generation, the contribution of thalamo-cortical interactions is well-documented and crucial for the initiation, modulation, and termination of spindles 17 . Future enhancements of the model will incorporate these cortical influences to provide a more comprehensive understanding of spindle dynamics. Secondly, the plasticity and asymmetry of electrical synapses between TRN neurons, which are believed to play significant roles in network oscillations, were not addressed in our current study 84 , 112 , 113 . In future work, we plan to extend our current model to investigate the roles of plasticity and asymmetry in spindle generation. Thirdly, our analysis concentrates on thalamic spindles with frequencies in the slow range (7 − 12 Hz), yet spindle activity encompasses both slow and fast spindles, with the latter typically ranging from 12 − 15 Hz 114 . Our model primarily reproduces slow spindles, driven by the intrinsic oscillation frequencies of TRN neuron clusters. The rhythmic burst firing frequency of TRN neurons, influenced by voltage and temperature, generally matches this range. However, our simulated spindle frequencies are slightly slower than those recorded in experiments, where thalamic spindles often exceed 12 Hz 7 . This discrepancy may stem from our model’s exclusion of thalamic and cortical excitatory inputs, suggesting a need for further investigation into the factors that modulate spindle frequency in the thalamus. Future research should investigate the factors influencing thalamic spindle frequency to address this difference. Spindle oscillation at the critical state Our modeling suggests that spindle oscillations emerge naturally in the electrically coupled TRN network when it self-organizes into the critical state due to the balance between electrical coupling and neuronal heterogeneity. Thus, we hypothesize that this critical state may play a functional role in efficient neural information processing within the thalamocortical system through two key aspects. Firstly, the TRN has been suggested to play a strong functional control in attentional filtering 111 , 115 – 118 and regulating oscillations 7 , 37 , 102 , 119 in the brain. This functional role necessitates that the TRN network operates as a coherent whole while maintaining fine-grained control over individual neuronal units. Operating at criticality satisfies this requirement, as it allows the system to be exquisitely sensitive to inputs while enabling efficient signal propagation over long distances 74 . During spindle oscillations, this critical state likely allows for dynamic information processing from diverse subcortical and cortical inputs, with the coexistence of dynamically synchronized clusters acting as functional units to selectively gate or route information streams through the thalamus to the cortex. Secondly, substantial experimental evidence from developmental and memory studies points to a fundamental role for sleep spindle oscillations in brain learning, plasticity, and memory 19 – 25 . Critical dynamics are known to enhance network adaptability and learning capabilities 120 . Therefore, the spindle critical state may optimize synaptic plasticity processes related to memory consolidation during sleep. By operating at criticality, the TRN network can efficiently coordinate and route relevant information streams from subcortical and cortical regions to support sleepdependent memory consolidation and reorganization. However, further experimental and theoretical studies are needed to directly test these hypothesized roles of the spindle critical state within the thalamocortical circuits (please refer to Section for limitations of the current model). The multifaceted origin of spindle generation Recent experimental findings challenge the traditional perspective that spindle oscillations primarily originate from the thalamus 3 , 31 , 121 , 122 , suggesting that spindle oscillations may have diverse origins within the brain 33 . For example, evidence from EEG and MEG studies suggests a differentiation in their genesis: EEG spindles likely originate from matrix (nonspecific) thalamic nuclei, while MEG spindles stem from core (specific) thalamic pathways 123 – 125 . This distinction implies that various thalamic regions may contribute to specific types of spindle oscillations. Furthermore, recent pharmacological studies in humans have shown that ion channel antagonists differentially affect fast and slow spindles 114 . Notably, the administration of a Ca 2+ blocker selectively suppresses fast spindles, while leaving slow spindles intact. These findings collectively reinforce the hypothesis that spindle oscillations arise from multiple, distinct neurophysiological mechanisms. Although the model is based on the TRN site, our modeling suggests a general mechanism for the genesis of spindle-like oscillations, where self-organized synchronization and desynchronization forces create the critical state. In this state, neuronal clusters dynamically appear and disappear, corresponding to the waxing-and-waning phase of spindles, respectively. This mechanism may extend beyond the TRN, potentially implemented through various neural circuits. For instance, the interplay between cortical and thalamic inputs also plays a significant role in this process. For example, cortical feedback and thalamic projections modulate TRN neurons during the cortical slow oscillation cycles, where the upstate phases enhance synchronization and the downstate phases promote desynchronization 40 , 126 . Related works Various mechanisms for spindle oscillations have been proposed previously. As noted in introduction, much of the previous research has focused on the role of mutual inhibition via chemical synapses between TRN neurons in generating spindles 34 , 59 – 61 . Another significant line of computational work explores the “ping-pong” interaction between TC and TRN neurons. These studies highlight how different connectivity patterns 35 , 124 , 127 , ion channel dynamics 36 , neuromodulation effects 128 , and short-term plasticity dynamics 129 can lead to different types of spindle oscillations. Moreover, direct spindle-like modulation inputs have been investigated as another mechanism influencing spindle activities. For example, studies by Yazdanbakhsh et al. 130 have demonstrated how spindle-like inputs can shape the activity patterns in the TRN. The most relevant work to our study is a pioneering model developed by Fuentealba et al. 105 , in which TRN neurons were interconnected via both inhibitory chemical synapses and electrical synapses. However, in Fuentealba et al. 105 , spindles arise from the mutual inhibition and rebound bursting of TRN neurons. Supplemental information index Figures S1-S12 and their legends in a PDF Author contributions Conceptualization, S.L., C.W., and S.W.; Methodology, S.L., C.W., and S.W.; Writing, S.L., C.W., and S.W. Funding Acquisition, S.W.; Supervision, S.W. Declaration of interests The authors declare no competing interests. All Cell Press life science journals and iScience use the STAR Methods format for reporting materials and methods. Other Cell Press journals use an experimental procedures format; for those journals, please delete the contents of this page from the template and refer instead to the experimental procedures template on page 2. The following headings are mandatory and must be included exactly as they are written here: Key resources table, Resource availability (including subheadings Lead contact, Materials availability, and Data and code availability), and Method details. Please do not alter the mandatory headings. All other headings are optional. Please refer to the full STAR Methods guide for authors for further information: Cell authors should download the guide for Cell authors available here All other journal authors should use this version of the guide STAR METHODS Key resources table To create the KRT, please use the KRT webform or the Word template and upload this file separately . Resource availability Lead contact Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Si Wu ( siwu{at}pku.edu.cn ). Materials availability The study did not generate new unique reagents. Data and code availability All data reported in this paper can be accessed through the open-access repository at DOI 10.5281/zenodo.13377848. The source code, processed data, and statistical analyses supporting the findings of this study are available at the open-access repository https://github.com/shangyangli/TRN-spindl and have been archived at DOI 10.5281/zenodo.13377848. Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request. Experimental model and study participant details This study does not involve any experimental models or human participants. Instead, a computational neuroscience model was developed and used to conduct the research. Therefore, there are no species, genotypes, ages, sexes, or maintenance and care information to report. Method details Network structure To mimic a 1 × 1 mm of TRN slice, we modeled a tier of TRN network which contains 100 (10 × 10) neurons (see Figure 1A ). The TRN network is placed in a two-dimensional grid with a periodic boundary, in which neurons are electrically coupled with each other by a Gaussian probability connection pattern. The connection probability for each pair of neurons ( i, j ) obeys where d ij is the Euclidean distance between two neurons, and G is a 2-dimensional Gaussian function centered at 0 with the standard deviation σ , and σ controls the connection width of each neuron. In addition to the electrical couplings between neurons, each neuron may receive two other kinds of synaptic projections (see Figure 1A ). To mimic the physiological condition of the TRN network in vivo , a neuron receives the inhibitory projections from the subcortical structures 50 , 51 , 118 . This inhibitory projection is modeled as a train of Poisson spikes conveying currents onto the neuron with GABA A synapse. To model the synaptic connections from the thalamus and cortex in the awake state, a neuron receives a spike train with excitatory AMPA synapse. Particularly, the firing rates of both excitatory and inhibitory background inputs used in our model are 50 Hz. TRN neuron model For the convenience of analysis, we used the previously developed reduced TRN neuron model 75 . It is biologically grounded, capable of reproducing characteristic TRN bursts and tonic discharges, and allows easy dynamical analysis. Specifically, the TRN neuron is modeled as a single-compartment Hodgkin-Huxley model, with a minimal set of active channels that are sufficient to produce the tonic and bursting spiking dynamics. It contains three active ionic currents: a fast sodium current ( I Na ) and a delayed rectifier ( I K ) for spiking generation and a low-threshold Ca 2+ current ( I T ) for rebound bursting. Moreover, it has two passive leaky channels: a potassium leaky current ( I KL ) for modeling the neuromodulation effect, and a leaky current ( I L ). The dynamics of the TRN neuron model is given by where τ = C/ρ V is the membrane time constant, I syn is the received synaptic current that normalized by the membrane area A = 1.43 × 10 − 4 cm 2 , I Na , I K and I T are the currents mediated by the sodium, potassium and low-threshold calcium channels, respectively, I L is the leakage current, I KL is the potassium leaky current controlled by neuromodulators like acetylcholine and norepinephrine, C = 1 µ F / cm 2 is the membrane capacitance, ρ V is the reduction coefficient of the membrane potential V 75 , y and z are two reduced equivalent potentials 75 , ρ h , ρ n and ρ p are reduction coefficients 75 , ϕ h = 1, ϕ n = 1, ϕ p = 6.9 and ϕ q = 3.7 are temperature factors, τ x ( x ∈ { h, n, p, q }) are time constant functions of each variable, and x ∞ ( x ∈ { h, n, p, q }) are steadystate functions. The detail expressions of reduction coefficients (including ρ V , ρ h , ρ n , ρ p , ρ q ), time constant functions (including τ h , τ n , τ p , τ q ), and steady-state functions (including h ∞ , n ∞ , p ∞ , q ∞ ) can be obtained in 75 . For the sodium current I Na , we set the maximal conductance g Na = 100 mS / cm 2 , the reversal potential E Na = 50 mV, and the spike adjusting threshold mV. For the potassium current I K , we set mV, E K = −100 mV, and g K = 10 mS / cm 2 . For the low-threshold calcium current I T , we set g T = 2.25 mS / cm 2 , and mV. For the leakage current I L , we used the leakage channel conductance g L = 0.06 mS / cm 2 and the leakage reversal potential E L = −70 mV. For the potassium leaky current I KL , we set the potassium leakage channel conductance g KL = 0.0065 mS / cm 2 and the reversal potential E KL = −100 mV. The synaptic current of the TRN neuron i is decomposed into three components: where I gap is the electrical synapse current, I inh the inhibitory GABA A current, and I exc the excitatory AMPA current. They are described in the following. Electrical synapse model The electrical synapse current flowing into the TRN neuron i is computed as where J e is the conductance of electrical synapses, and N gj ( i ) denotes the collection of neurons that are electrically coupled with the neuron i . Subcortical inhibitory synapse model The inhibitory synaptic current to the neuron i from the transmission of a subcortical spike is computed as the GABA A synapse model. Specifically, it is modeled as: where denotes the maximum GABA A synaptic conductance, the synaptic re-versal potential, and s the fraction of open channels. Moreover, s is modeled by the first-order activation scheme where [ T ] is the concentration of neurotransmitter modeled as a brief pulse (0.3 ms duration, 0.5 mM amplitude) after pre-synaptic neuron generating an action potential 36 , and α and β are the channel forward and backward binding rates given by α = 10 ms − 1 and β = 0.18 ms − 1 , respectively 36 , 129 , 131 . Thalamic and cortical excitatory synapse model The excitatory synaptic current to the neuron i when receiving a thalamic or cortical spike is computed as the AMPA synapse model. Specifically, the AMAP current is modeled as where denotes the maximum AMPA synaptic conductance, and E AMPA the synaptic reversal potential. Similar to GABA A model, s is modeled by Equation 9 , except that α = 10.5 ms − 1 and β = 0.166 ms − 1 36 , 129 , 131 . Simulation tool The network model was coded with the BrainPy library in Python 132 , 133 . All simulations were performed by using the fourth-order Runge-Kutta method (RK4) with a fixed time step of 0.01 ms. A shorter simulation time step does not change the results. The model source code is available on the GitHub. Local field potential We measured the local field potential by averaging the membrane potentials across the whole TRN neuron group 76 , which is written as, We then used a finite impulse response (FIR) filter (mne.filter.filter_data(), a built-in function implemented in MNE-Python toolbox 134 ) to calculate the broadband filtered LFP signal (0.5 ∼30 Hz) LFP bf and the spindle band filtered signal (6 ∼10 Hz) LFP spin . The power spectrum of the LFP was obtained by a fast Fourier transform (FFT) on LFP bf . The peak spectral frequency was chosen as the network oscillation frequency. In addition to the standard method of calculating the local field potential (LFP) by averaging the membrane potentials across the whole TRN neuron group, we also employed a spatial lowpass filter to compute the LFP. This method takes into account the spatial distribution of neurons and their respective distances, providing a more nuanced representation of the neuronal activity 135 , 136 . The spatial lowpass filter method involves the following steps: 1 Distance Matrix Calculation We first calculate the spatial distance matrix, D , where each element D ij represents the Euclidean distance between neuron i and neuron j . The positions of neurons are assumed to be in a two-dimensional space. 2 Weight Matrix Calculation A Gaussian function is used to calculate the weight matrix, W , based on the distances. The weight for each pair of neurons i and j is given by: where σ is a parameter that controls the spread of the Gaussian function. The weights are then normalized so that the sum of the weights for each neuron is equal to 1: 3 LFP Calculation Using the weight matrix, the LFP is calculated as a weighted sum of the membrane potentials, V : where N is the total number of neurons, and V j ( t ) is the membrane potential of neuron j at time t . The comparison between the standard LFP method and the spatial lowpass filter method is illustrated in Supplementary Materials (Figure S12). Automatic spindle detection Spindles are automatically detected, with the method inspired by the A7 algorithm described in 137 and the YASA spindle algorithm presented in 138 . Specifically, four thresholds are used: Relative spindle power RelSpinPow The first threshold is computed as the relative power in the spindle frequency range, which aims to ensure the increase of the power is specific to the spindle oscillation range and not due to a global oscillation power increase. The threshold is set to RelSpinPow ≥ 0.9. Root mean square RMS In order to detect the energy power increase in the spindle frequency band, the moving RMS of LFP spin with a window size of 100 ms and a step size of 50 ms is used. The threshold is exceeded whenever a sample has a RMS ≥ RMS threshold , where RMS threshold = RMS mean + 0.1RMS std . Spindle correlation SpinCorr In order to characterize the causal influence of LFP spin power increase on LFP bf rise, SpinCorr is computed by the Pearson correlation coefficient between LFP spin and LFP bf with a moving sliding window of 300 ms and a step of 100 ms. The threshold is exceeded whenever a sample has a correlation value SpinCorr ≥ 0.9. Gaussian kernel fitting errors err p When the above three parameters exceed their respective thresholds, a candidate spindle event can be selected. However, the morphologies of such events extracted by three thresholds may not be waxing and waning. Therefore, we fit the cycle peaks in each spindle candidate with a Gaussian kernel to filter out the false alarm event. The standard deviation errors (err p ) on the parameters { A, µ, σ } after curve fitting are used for the threshold judgment. Once one of the errors exceeds 10, we reject this candidate event. Cross correlation The cross-correlation between a pair of neurons is calculated as follows. Denoting the spike trains of a pair of neurons to be S i ( t ) and S j ( t ), for S i ( t ), S j ( t ) = 0 or 1, and t = 1, 2, …, T , the CC between the neuron pair is calculated to be For a network, the overall cross-correlation is given by, where the summation runs over all neuron pairs. Coupling coefficient To assess the strength of the electrical synapse connection, we utilized the steady-state coupling coefficient (CC) as a measure. This involved injecting long polarizing current pulses into one of the paired neurons. The injection of current induced a voltage drop in the presynaptic cell (V pre ), which typically caused a change in the membrane potential of the coupled postsynaptic cell (V post ). The duration of the current pulses was intentionally extended to overcome the initial attenuation of the membrane potential caused by the passive properties of the postsynaptic membrane’s filtering characteristics. Consequently, we were able to measure voltage changes in a stable state. Quantitatively, the strength of coupling was determined by calculating the coupling coefficient, defined as the ratio between the voltage deflections observed in the post- and presynaptic cells: Critical state analysis Data Preprocessing for Avalanche Analysis Following the classical analysis of criticality in spiking activity 139 , we counted the number of spikes in each bin of length Δ t (measured in milliseconds) for the merged spike train of all neurons. An avalanche is defined as a sequence of consecutive bins containing spikes, separated from other avalanches by silent bins. In this study, we defined the size of an avalanche S as the total number of spikes it contains, and the lifetime T as the number of bins it spans. We selected the average inter-spike interval of the merged spiking train as the bin size Δ t . Critical exponents estimation First, we inspected the distributions of avalanche size and lifetime. For distributions exhibiting characteristics of a power law, we used a doubly truncated algorithm based on maximum likelihood estimation 140 , 141 for analysis. Denote x the size or life-time of an avalanche. We fit a discrete power-law distribution: where x min is the smallest avalanche size or lifetime, and x max is the upper bound. Assume identical and independent distribution of avalanches, the value of α can be calculated by maximizing the likelihood function, which is, where N is the number of avalanches. To assess the goodness of fit and determine if a power law adequately describes the data, we used several evaluation techniques 142 . First, we employed bootstrapping and the Kolmogorov-Smirnov test to generate a p -value for an individual fit. Second, we used the log-likelihood ratio to compare two fits and identify the better one. The p -value from the Kolmogorov-Smirnov test represents the significance level of the fit. Comparing the log-likelihood ratio between two candidate distributions helps determine if the data is more likely to follow one distribution over the other. A positive log-likelihood ratio indicates that the data is more likely to adhere to the first distribution, while a negative value suggests a greater likelihood for the second distribution 142 . Detrended Fluctuation Analysis In analyzing the scale-invariant long-range time correlation, we employed detrended fluctuation analysis (DFA) 104 . This method works as follows: 1) we first calculated an integrated zero-mean version of the original time series z , denoted as y ( k ), by summing the deviations from the mean up to the k -th point, i.e., ; 2) we then divided the entire time period into consecutive non-overlapping window of width w (in milliseconds or seconds, as appropriate) and fit a local linear trend y w in each window; 3) finally, we calculated the fluctuation F ( w ) at a given time-scale w using the following equation: where N is the total number of time windows. The scaling exponent α is determined by linearly fitting log F ( w ) vs log w . The interpretation of α is as follows: α < 0.5: anti-correlation in the time-series. α = 0.5: absence of correlation (white noise). 0.5 < α < 1: positive correlation in the time series, indicating that the neural network operates in the critical regime, where small fluctuations can propagate and lead to complex, system-wide response. α ≈ 1: 1/f-noise, pink noise. α > 1: positive correlation often seen in highly structured systems. Analysis of the TRN neuron model Diverse firing patterns, including different degrees of bursting 143 – 146 and tonic spiking 80 , 119 , 143 , 147 , have been observed in TRN neurons in vivo and in vitro . To understand the neuronal mechanism of TRN’s characteristic burst and tonic discharges, we previously developed a reduced three-variable TRN neuron model 75 which allows us to perform bifurcation analysis of its spiking dynamics (see the following text). Despite its simple form, this neuron model can reproduce the discharge patterns as seen in TRN oscillatory activities 4,7,31,38,52,145,148 (see Figure S1). Our reduced model shows different degrees of rhythmic bursts under different resting potentials (Figure S1A). Under the depolarized states (like V r = −61 or −65 mV), the cell exhibits burst firings with the spindle frequency (7-15 Hz). While hyperpolarization of neurons to −70 and −75 mV results in a decrease in interburst frequency and a substantial increase of spike number in a burst. Similarly, this neuron model shows consistent tonic spiking (Figure S1B) as seen in biological observations 7 . More hyperpolarization of the neuron needs a larger size of excitatory current to elicit a TRN spike. What’s more, as shown in Figure S1C, our single neuron model can exhibit different degrees of rebound bursting as observed in biological experiments 82 , 83 , 146 . Specifically, neurons with larger g T conductance show higher intrinsic bursting, while small g T conductance results in a few spikes per rebound burst. Diverse discharge patterns of the TRN neuron occur conditionally, depending on the conductance of low-threshold Ca 2+ current g T , the conductance of potassium leaky current g KL , and the external inputs. The intrinsic bursting oscillations in the TRN neuron are more obvious when g T becomes larger (Figure S1D). It can oscillate with small values of g KL , i.e., at high resting membrane potential, when g T is large, implying that the larger size of g T increases the intrinsic excitability of the model. However, when the cell has small values of g T , the intrinsic oscillation of the model disappears no matter how g KL changes (Figure S1E). Instead, the subthreshold oscillation as reported in the experiments 66 occurs when g KL lies in the intermediate value regime. Superposition of harmonic waves We superpose two simple harmonic waves with the same direction and frequency. Suppose the two simple harmonic waves with the same direction and frequency are: Their summation is calculated to be, where, It can be seen that the superposition of two simple harmonic waves with the same direction and frequency is still simple harmonic. We next examined the superposition of two simple harmonic waves with slightly different frequencies. Consider the two simple harmonics are: Further assume A 1 = A 2 and | ω 1 − ω 2 | << ω 1 + ω 2 , the superposition of two waves are: where A = 2 A 1 | cos( ω 2 − ω 1)t / 2| is the amplitude of the superimposed wave. Since | ω 2 − ω 1 ≪ ω 1 + ω 2 , the superposed signal x ( t ) exhibits the wax-and-waning shape. The influence of model parameters on spindle oscillation properties To understand the properties of spindles generated in the TRN network, we quantitatively studied the influence of network parameters on the simulated spindle activities. We focused on the electrical synapse strength (corresponds to the average CC, see Figure S2A, D, G and Figure S3 A1-A6), the neuromodulation control level (corresponds to the potassium leaky conductance g KL , see Figure S2B, E, H and Figure S3B1-B6), and the heterogeneity of neuronal firing patterns (corresponds to the variance of Ca 2+ channel conductance g T , see Figure S2C, F, I and Figure S3C1-C6). We analyzed various metrics of spindle oscillation using the YASA spindles detection algorithm 138 . These metrics provide valuable insights into the characteristics of spindles. The specific metrics we examined include: Frequency: This metric represents the median instantaneous frequency of the spindle, measured in Hz. It is derived from a Hilbert transform of the filtered signal. Duration: This metric indicates the duration of spindle oscillation, measured in seconds. Amplitude: The amplitude metric represents the peak-to-peak amplitude of the detrended spindle in the raw data. It is measured in microvolts ( µ V). AbsPower: This metric quantifies the median absolute power of the spindle, measured in log 10 µV 2 . It is calculated from the Hilbert-transformed filtered signal. Oscillations: This metric denotes the number of oscillations, which is equivalent to the number of positive peaks in the spindle. Peak: This metric indicates the time at the most prominent spindle peak, measured in seconds. RelPower: Similar to the AbsPower metric, this metric represents the median absolute power of the spindle in log 10 µV 2 . It is derived from the Hilbert-transformed filtered signal. RMS: This metric stands for root-mean-square and is measured in microvolts ( µ V). Symmetry: This metric indicates the location of the most prominent peak of the spindle, normalized on a scale from 0 (start) to 1 (end). An ideal value for this metric is close to 0.5, indicating that the most prominent peak is located halfway through the spindle. The average CC of the TRN network was observed to have a great impact on the spindle oscillation frequency (Figure S2A) and amplitude (Figure S2G). With the increasing average CC, the TRN generates spindles at a lower frequency (Figure S2A). Higher CC values induce more synchronized network spiking, resulting in spindle oscillations with a higher amplitude (Figure S2G) and stronger absolute power in simulated LFPs (Figure S3A). The increased oscillation amplitude and power are associated with higher RMS values of the spindle signal (Figure S3A5), indicating that larger CC results in greater variance in spindle LFP activity. Moreover, increasing CC slightly increased the duration (Figure S2B) and the number of oscillation cycles (Figure S3A2). The effect of neuromodulation on spindle rhythms showed different profiles. Increasing the neuromodulation level, i.e., decreasing g KL and increasing the resting membrane potential of each TRN neuron, augmented the oscillation frequency of spindle activity (Figure S2B), as depolarized resting potentials increased single-neuron burst frequencies (see Figure 1 ). Meanwhile, the depolarized membrane potential inactivated the Ca 2+ channel and reduced burst strength in individual TRN neurons, leading to a reduction in oscillation amplitude (Figure S2H), oscillation power (Figure S2B1), and LFP signal variance (Figure S3E) with smaller values of g KL . Unlike the network average CC, no consistent impact of g KL on spindle duration (Figure S2B5), oscillation cycles (Figure S3B2), and relative oscillation powers (Figure S3B4) was observed. Increasing the variance of g T in TRN neurons had the opposite effect on spindle activity compared to increasing CC. A higher g T variance means more TRN neurons exhibit higher g T values, leading to more frequent bursting ( Figure 1 ). As a result, increasing g T variance led to spindles with higher oscillation frequencies (Figure S2C). However, the increase in g T variance also led more neurons to have lower g T values, which caused these neurons to spontaneously oscillate at subthreshold levels. Consequently, the TRN network generated spindle activities with lower amplitude as g T variance increased (Figure S2I). Correspondingly, we observed that absolute oscillation power and RMS decreased with higher g T variance (Figure S3C1 and C5). In contrast to electrical coupling strength, increased heterogeneity among TRN neurons slightly decreased spindle oscillation duration (Figure S2F) and oscillation cycles (Figure S3C2). Interestingly, a substantial increase in relative oscillation power at the spindle band was observed (Figure S3C4), implying that spindle activity dominated network oscillations with increased TRN cell heterogeneity. Overall, these three parameters were observed to modulate different aspects of TRN spindle rhythms. However, no consistent influence of these parameters on spindle oscillation shape, including oscillation peak and symmetry, was observed (see Figure S3A3, B3, C3 and Figure S3A5, B5, C5). These properties may be shaped by other network parameters and warrant further investigation. Acknowledgments This work was supported by the Science and Technology Innovation 2030-Brain Science and Brain-inspired Intelligence Project (No. 2021ZD0200204, SW), the Young Scientists Fund of the National Natural Science Foundation of China (No. 32400937, CMW), the China Postdoctoral Science Foundation (No. 2024M750076, CMW), and the Postdoctoral Fellowship Program of CPSF (No. GZC20230106, CMW). The authors thank all members of the lab for their support. Footnotes ↵ 3 Lead contact: Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Si Wu ( siwu{at}pku.edu.cn ). Spindle oscillation is a waxing-and-waning neural oscillation observed in the brain, initiated at the thalamic reticular nucleus (TRN) and typically occurring at 7-15 Hz. Experiments have shown that in the adult brain, electrical synapses, rather than chemical synapses, dominate between TRN neurons, suggesting that the traditional view of spindle generation via chemical synapses may need reconsideration. Based on known experimental data, we develop a computational model of the TRN network, where heterogeneous neurons are connected by electrical synapses. The model shows that the interplay between synchronizing electrical synapses and desynchronizing heterogeneity leads to multiple synchronized clusters with slightly different oscillation frequencies, whose summed activity produces spindle oscillation as seen in local field potentials. Our results suggest that during spindle oscillation, the network operates at the critical state, which is known for facilitating efficient information processing. This study provides insights into the underlying mechanism of spindle oscillation and its functional significance. References 1. ↵ Lüthi , A. ( 2014 ). Sleep spindles: where they come from, what they do . The Neuroscientist 20 , 243 – 256 . doi: 10.1177/1073858413500854 . OpenUrl CrossRef PubMed 2. ↵ Clawson , B. C. , Durkin , J. , and Aton , S. J. ( 2016 ). Form and function of sleep spindles across the lifespan . Neural Plasticity . doi: 10.1155/2016/6936381 . OpenUrl CrossRef PubMed 3. ↵ Steriade , M. , Deschenes , M. , Domich , L. , and Mulle , C. ( 1985 ). Abolition of spindle oscillations in thalamic neurons disconnected from nucleus reticularis thalami . Journal of neurophysiology 54 , 1473 – 1497 . doi: 10.1152/jn.1985.54.6.1473 . OpenUrl CrossRef PubMed Web of Science 4. ↵ Steriade , M. , Domich , L. , Oakson , G. , and Deschenes , M. ( 1987 ). The deafferented reticular thalamic nucleus generates spindle rhythmicity . Journal of neurophysiology 57 , 260 – 273 . doi: 10.1152/jn.1987.57.1.260 . OpenUrl CrossRef PubMed Web of Science 5. ↵ Thankachan , S. , Katsuki , F. , McKenna , J. T. , Yang , C. , Shukla , C. , Deisseroth , K. , Uygun , D. S. , Strecker , R. E. , Brown , R. E. , McNally , J. M. et al. ( 2019 ). Thalamic reticular nucleus parvalbumin neurons regulate sleep spindles and electrophysiological aspects of schizophrenia in mice . Scientific reports 9 , 1 – 16 . doi: 10.1038/s41598-019-50338-0 . OpenUrl CrossRef 6. ↵ Halassa , M. M. , Chen , Z. , Wimmer , R. D. , Brunetti , P. M. , Zhao , S. , Zikopoulos , B. , Wang , F. , Brown , E. N. , and Wilson , M. A. ( 2014 ). State-dependent architecture of thalamic reticular subnetworks . Cell 158 , 808 – 821 . doi: 10.1016/j.cell.2014.06.025 . OpenUrl CrossRef PubMed Web of Science 7. ↵ Barthó , P. , Slézia , A. , Mátyás , F. , Faradzs-Zade , L. , Ulbert , I. , Harris , K. D. , and Acsády , L. ( 2014 ). Ongoing network state controls the length of sleep spindles via inhibitory activity . Neuron 82 , 1367 – 1379 . doi: 10.1016/j.neuron.2014.04.046 . OpenUrl CrossRef PubMed 8. ↵ Eschenko , O. , Mölle , M. , Born , J. , and Sara , S. J. ( 2006 ). Elevated sleep spindle density after learning or after retrieval in rats . Journal of Neuroscience 26 , 12914 – 12920 . doi: 10.1523/JNEUROSCI.3175-06.2006 . OpenUrl Abstract / FREE Full Text 9. ↵ Bal , T. , von Krosigk , M. , and McCormick , D. A. ( 1995 ). Synaptic and membrane mechanisms underlying synchronized oscillations in the ferret lateral geniculate nucleus in vitro . The Journal of physiology 483 , 641 – 663 . doi: 10.1113/jphysiol.1995.sp020612 . OpenUrl CrossRef PubMed Web of Science 10. ↵ Kim , U. , Bal , T. , and McCormick , D. A. ( 1995 ). Spindle waves are propagating synchronized oscillations in the ferret lgnd in vitro . Journal of Neurophysiology 74 , 1301 – 1323 . doi: 10.1152/jn.1995.74.3.1301 . OpenUrl CrossRef PubMed Web of Science 11. ↵ Iotchev , I. B. , Reicher , V. , Kovács , E. , Kovács , T. , Kis , A. , Gácsi , M. , and Kubinyi , E. ( 2020 ). Averaging sleep spindle occurrence in dogs predicts learning performance better than single measures . Scientific Reports 10 , 1 – 6 . doi: 10.1038/s41598-020-70693-0 . OpenUrl CrossRef 12. ↵ Bódizs , R. , Kis , A. , Gácsi , M. , and Topál , J. ( 2020 ). Sleep in the dog: comparative, behavioral and translational relevance . Current Opinion in Behavioral Sciences 33 , 25 – 33 . doi: 10.1016/j.cobeha.2019.12.005 . OpenUrl CrossRef 13. ↵ Schneider , W. T. , Vas , S. , Nicol , A. U. , and Morton , A. J. ( 2020 ). Characterizing sleep spindles in sheep . Eneuro 7 . doi: 10.1523/ENEURO.0057-20.2020 . OpenUrl Abstract / FREE Full Text 14. ↵ Takeuchi , S. , Murai , R. , Shimazu , H. , Isomura , Y. , Mima , T. , and Tsujimoto , T. ( 2016 ). Spatiotemporal organization and cross-frequency coupling of sleep spindles in primate cerebral cortex . Sleep 39 , 1719 – 1735 . doi: 10.5665/sleep.6106 . OpenUrl CrossRef 15. ↵ Sritharan , S. Y. , Contreras-Hernández , E. , Richardson , A. G. , and Lucas , T. H. ( 2020 ). Primate somatosensory cortical neurons are entrained to both spontaneous and peripherally evoked spindle oscillations . Journal of neurophysiology 123 , 300 – 307 . doi: 10.1152/jn.00453.2019 . OpenUrl CrossRef 16. ↵ Loomis , A. L. , Harvey , E. N. , and Hobart , G. ( 1935 ). Potential rhythms of the cerebral cortex during sleep . Science . doi: 10.1126/science.81.2111.597 . OpenUrl FREE Full Text 17. ↵ Fernandez , L. M. , and Lüthi , A. ( 2020 ). Sleep spindles: mechanisms and functions . Physiological reviews 100 , 805 – 868 . doi: 10.1152/physrev.00042.2018 . OpenUrl CrossRef PubMed 18. ↵ Peyrache , A. , and Seibt , J. ( 2020 ). A mechanism for learning with sleep spindles . Philosophical Transactions of the Royal Society B 375 , 20190230 . doi: 10.1098/rstb.2019.0230 . OpenUrl CrossRef 19. ↵ Gais , S. , Mölle , M. , Helms , K. , and Born , J. ( 2002 ). Learning-dependent increases in sleep spindle density . Journal of Neuroscience 22 , 6830 – 6834 . doi: 10.1523/JNEUROSCI.22-15-06830.2002 . OpenUrl Abstract / FREE Full Text 20. Schabus , M. , Gruber , G. , Parapatics , S. , Sauter , C. , Klösch , G. , Anderer , P. , Klimesch , W. , Saletu , B. , and Zeitlhofer , J. ( 2004 ). Sleep spindles and their significance for declarative memory consolidation . Sleep 27 , 1479 – 1485 . doi: 10.1093/sleep/27.8.1479 . OpenUrl CrossRef PubMed Web of Science 21. ↵ Clemens , Z. , Fabó , D. , and Halász , P. ( 2005 ). Overnight verbal memory retention correlates with the number of sleep spindles . Neuroscience 132 , 529 – 535 . doi: 10.1016/j.neuroscience.2005.01.011 . OpenUrl CrossRef PubMed Web of Science 22. ↵ Barakat , M. , Carrier , J. , Debas , K. , Lungu , O. , Fogel , S. , Vandewalle , G. , Hoge , R. D. , Bellec , P. , Karni , A. , Ungerleider , L. G. et al. ( 2013 ). Sleep spindles predict neural and behavioral changes in motor sequence consolidation . Human brain mapping 34 , 2918 – 2928 . doi: 10.1002/hbm.22110 . OpenUrl CrossRef PubMed 23. ↵ Laventure , S. , Fogel , S. , Lungu , O. , Albouy , G. , Sévigny-Dupont , P. , Vien , C. , Sayour , C. , Carrier , J. , Benali , H. , and Doyon , J. ( 2016 ). Nrem2 and sleep spindles are instrumental to the consolidation of motor sequence memories . PLoS biology 14 , e1002429 . doi: 10.1371/journal.pbio.1002429 . OpenUrl CrossRef 24. ↵ Marshall , L. , Helgadóttir , H. , Mölle , M. , and Born , J. ( 2006 ). Boosting slow oscillations during sleep potentiates memory . Nature 444 , 610 – 613 . doi: 10.1038/nature05278 . OpenUrl CrossRef PubMed Web of Science 25. ↵ Lustenberger , C. , Boyle , M. R. , Alagapan , S. , Mellin , J. M. , Vaughn , B. V. , and Fröhlich , F. ( 2016 ). Feedback-controlled transcranial alternating current stimulation reveals a functional role of sleep spindles in motor memory consolidation . Current Biology 26 , 2127 – 2136 . doi: 10.1016/j.cub.2016.06.044 . OpenUrl CrossRef PubMed 26. ↵ Fogerson , P. M. , and Huguenard , J. R. ( 2016 ). Tapping the brakes: cellular and synaptic mechanisms that regulate thalamic oscillations . Neuron 92 , 687 – 704 . doi: 10.1016/j.neuron.2016.10.024 . OpenUrl CrossRef PubMed 27. ↵ Morison , R. , and Bassett , D. ( 1945 ). Electrical activity of the thalamus and basal ganglia in decorticate cats . Journal of Neurophysiology 8 , 309 – 314 . doi: 10.1152/jn.1945.8.5.309 . OpenUrl CrossRef Web of Science 28. ↵ Timofeev , I. , and Steriade , M. ( 1996 ). Low-frequency rhythms in the thalamus of intactcortex and decorticated cats . Journal of neurophysiology 76 , 4152 – 4168 . doi: 10.1152/jn.1996.76.6.4152 . OpenUrl CrossRef PubMed Web of Science 29. ↵ Huguenard , J. , and Prince , D. ( 1994 ). Intrathalamic rhythmicity studied in vitro: nominal t-current modulation causes robust antioscillatory effects . Journal of Neuroscience 14 , 5485 – 5502 . doi: 10.1523/JNEUROSCI.14-09-05485.1994 . OpenUrl Abstract / FREE Full Text 30. Warren , R. A. , Agmon , A. , and Jones , E. G. ( 1994 ). Oscillatory synaptic interactions between ventroposterior and reticular neurons in mouse thalamus in vitro . Journal of Neurophysiology 72 , 1993 – 2003 . doi: 10.1152/jn.1994.72.4.1993 . OpenUrl CrossRef PubMed Web of Science 31. ↵ von Krosigk , M. , Bal , T. , and McCormick , D. A. ( 1993 ). Cellular mechanisms of a synchronized oscillation in the thalamus . Science 261 , 361 – 364 . doi: 10.1126/science.8392750 . OpenUrl Abstract / FREE Full Text 32. ↵ Bal , T. , von Krosigk , M. , and McCormick , D. A. ( 1995 ). Role of the ferret perigeniculate nucleus in the generation of synchronized oscillations in vitro . The Journal of physiology 483 , 665 – 685 . doi: 10.1113/jphysiol.1995.sp020614 . OpenUrl CrossRef PubMed Web of Science 33. ↵ Timofeev , I. , and Chauvette , S. The spindles: are they still thalamic? ( 2013 ). doi: 10.5665/sleep.2704 . OpenUrl CrossRef PubMed Web of Science 34. ↵ Golomb , D. , Wang , X.-J. , and Rinzel , J. ( 1994 ). Synchronization properties of spindle oscillations in a thalamic reticular nucleus model . Journal of neurophysiology 72 , 1109 – 1126 . doi: 10.1152/jn.1994.72.3.1109 . OpenUrl CrossRef PubMed Web of Science 35. ↵ Wang , X. , Golomb , D. , and Rinzel , J. ( 1995 ). Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms . Proceedings of the National Academy of Sciences 92 , 5577 – 5581 . doi: 10.1073/pnas.92.12.5577 . OpenUrl Abstract / FREE Full Text 36. ↵ Destexhe , A. , Bal , T. , McCormick , D. A. , and Sejnowski , T. J. ( 1996 ). Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices . Journal of neurophysiology 76 , 2049 – 2070 . doi: 10.1152/jn.1996.76.3.2049 . OpenUrl CrossRef PubMed Web of Science 37. ↵ Halassa , M. M. , Siegle , J. H. , Ritt , J. T. , Ting , J. T. , Feng , G. , and Moore , C. I. ( 2011 ). Selective optical drive of thalamic reticular nucleus generates thalamic bursts and cortical spindles . Nature neuroscience 14 , 1118 – 1120 . doi: 10.1038/nn.2880 . OpenUrl CrossRef PubMed 38. ↵ Lee , J. , Song , K. , Lee , K. , Hong , J. , Lee , H. , Chae , S. , Cheong , E. , and Shin , H.-S. ( 2013 ). Sleep spindles are generated in the absence of t-type calcium channel-mediated lowthreshold burst firing of thalamocortical neurons . Proceedings of the National Academy of Sciences 110 , 20266 – 20271 . doi: 10.1073/pnas.1314168110 . OpenUrl Abstract / FREE Full Text 39. ↵ Ayoub , A. , Aumann , D. , Hörschelmann , A. , Kouchekmanesch , A. , Paul , P. , Born , J. , and Marshall , L. ( 2013 ). Differential effects on fast and slow spindle activity, and the sleep slow oscillation in humans with carbamazepine and flunarizine to antagonize voltage-dependent na+ and ca2+ channel activity . Sleep 36 , 905 – 911 . doi: 10.5665/sleep.2720 . OpenUrl CrossRef PubMed Web of Science 40. ↵ Pinault , D. ( 2004 ). The thalamic reticular nucleus: structure, function and concept . Brain Research Reviews 46 , 1 – 31 . doi: 10.1016/j.brainresrev.2004.04.008 . OpenUrl CrossRef PubMed Web of Science 41. ↵ Halassa , M. M. , and Acsády , L. ( 2016 ). Thalamic inhibition: diverse sources, diverse scales . Trends in Neurosciences 39 , 680 – 693 . doi: 10.1016/j.tins.2016.08.001 . OpenUrl CrossRef PubMed 42. ↵ Crabtree , J. W. ( 2018 ). Functional diversity of thalamic reticular subnetworks . Frontiers in systems neuroscience 12 , 41 . doi: 10.3389/fnsys.2018.00041 . OpenUrl CrossRef PubMed 43. ↵ Asanuma , C. ( 1989 ). Axonal arborizations of a magnocellular basal nucleus input and their relation to the neurons in the thalamic reticular nucleus of rats . Proceedings of the National Academy of Sciences 86 , 4746 – 4750 . doi: 10.1073/pnas.86.12.4746 . OpenUrl Abstract / FREE Full Text 44. Asanuma , C. , and Porter , L. ( 1990 ). Light and electron microscopic evidence for a gabaergic projection from the caudal basal forebrain to the thalamic reticular nucleus in rats . Journal of comparative neurology 302 , 159 – 172 . doi: 10.1002/cne.903020113 . OpenUrl CrossRef PubMed Web of Science 45. Bickford , M. , Günlük , A. , Van Horn , S. , and Sherman , S. ( 1994 ). Gabaergic projection from the basal forebrain to the visual sector of the thalamic reticular nucleus in the cat . Journal of Comparative Neurology 348 , 481 – 510 . doi: 10.1002/cne.903480403 . OpenUrl CrossRef PubMed Web of Science 46. ↵ Sun , Y.-G. , Rupprecht , V. , Zhou , L. , Dasgupta , R. , Seibt , F. , and Beierlein , M. ( 2016 ). mglur1 and mglur5 synergistically control cholinergic synaptic transmission in the thalamic reticular nucleus . Journal of Neuroscience 36 , 7886 – 7896 . doi: 10.1523/JNEUROSCI.1083-16.2016 . OpenUrl Abstract / FREE Full Text 47. ↵ Paré , D. , Hazrati , L.-N. , Parent , A. , and Steriade , M. ( 1990 ). Substantia nigra pars reticulata projects to the reticular thalamic nucleus of the cat: a morphological and electrophys-iological study . Brain research 535 , 139 – 146 . doi: 10.1016/0006-8993(90)91820-2 . OpenUrl CrossRef PubMed Web of Science 48. ↵ Hazrati , L.-N. et al. ( 1991 ). Projection from the external pallidum to the reticular thalamic nucleus in the squirrel monkey . Brain research 550 , 142 – 146 . doi: 10.1016/0006-8993(91)90502-R . OpenUrl CrossRef PubMed Web of Science 49. Asanuma , C. ( 1994 ). Gabaergic and pallidal terminals in the thalamic reticular nucleus of squirrel monkeys . Experimental brain research 101 , 439 – 451 . doi: 10.1007/BF00227345 . OpenUrl CrossRef PubMed Web of Science 50. ↵ Govindaiah , G. , Wang , T. , Gillette , M. U. , Crandall , S. R. , and Cox , C. L. ( 2010 ). Regulation of inhibitory synapses by presynaptic d4 dopamine receptors in thalamus . Journal of neurophysiology 104 , 2757 – 2765 . doi: 10.1152/jn.00311.2010 . OpenUrl CrossRef PubMed Web of Science 51. ↵ Herrera , C. G. , Cadavieco , M. C. , Jego , S. , Ponomarenko , A. , Korotkova , T. , and Adamantidis , A. ( 2016 ). Hypothalamic feedforward inhibition of thalamocortical network controls arousal and consciousness . Nature neuroscience 19 , 290 – 298 . doi: 10.1038/nn.4209 . OpenUrl CrossRef PubMed 52. ↵ Contreras , D. , Curró Dossi , R. , and Steriade , M. ( 1993 ). Electrophysiological properties of cat reticular thalamic neurones in vivo . The Journal of Physiology 470 , 273 – 294 . doi: 10.1113/jphysiol.1993.sp019861 . OpenUrl CrossRef PubMed Web of Science 53. ↵ Fuentealba , P. , and Steriade , M. ( 2005 ). The reticular nucleus revisited: intrinsic and network properties of a thalamic pacemaker . Progress in neurobiology 75 , 125 – 141 . doi: 10.1016/j.pneurobio.2005.01.002 . OpenUrl CrossRef PubMed Web of Science 54. ↵ Ahlsén , G. , and Lindström , S. ( 1982 ). Mutal inhibition between perigeniculate neurones . Brain research 236 , 482 – 486 . doi: 10.1016/0006-8993(82)90527-0 . OpenUrl CrossRef PubMed Web of Science 55. Sanchez-Vives , M. V. , Bal , T. , and McCormick , D. A. ( 1997 ). Inhibitory interactions between perigeniculate gabaergic neurons . Journal of Neuroscience 17 , 8894 – 8908 . doi: 10.1523/JNEUROSCI.17-22-08894.1997 . OpenUrl Abstract / FREE Full Text 56. Shu , Y. , and McCormick , D. A. ( 2002 ). Inhibitory interactions between ferret thalamic reticular neurons . Journal of Neurophysiology 87 , 2571 – 2576 . doi: 10.1152/jn.2002.87.5.2571 . OpenUrl CrossRef PubMed Web of Science 57. Deleuze , C. , and Huguenard , J. R. ( 2006 ). Distinct electrical and chemical connectivity maps in the thalamic reticular nucleus: potential roles in synchronization and sensation . Journal of Neuroscience 26 , 8633 – 8645 . doi: 10.1523/JNEUROSCI.4679-05.2006 . OpenUrl Abstract / FREE Full Text 58. ↵ Lam , Y.-W. , Nelson , C. S. , and Sherman , S. M. ( 2006 ). Mapping of the functional interconnections between thalamic reticular neurons using photostimulation . Journal of Neurophysiology 96 , 2593 – 2600 . doi: 10.1152/jn.00510.2006 . OpenUrl CrossRef PubMed Web of Science 59. ↵ Wang , X.-J. , and Rinzel , J. ( 1993 ). Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons . Neuroscience 53 , 899 – 904 . doi: 10.1016/0306-4522(93)90253-C . OpenUrl CrossRef PubMed Web of Science 60. ↵ Destexhe , A. , Contreras , D. , Sejnowski , T. J. , and Steriade , M. ( 1994 ). A model of spindle rhythmicity in the isolated thalamic reticular nucleus . Journal of neurophysiology 72 , 803 – 818 . doi: 10.1152/jn.1994.72.2.803 . OpenUrl CrossRef PubMed Web of Science 61. ↵ Bazhenov , M. , Timofeev , I. , Steriade , M. , and Sejnowski , T. ( 1999 ). Self-sustained rhythmic activity in the thalamic reticular nucleus mediated by depolarizing gaba a receptor potentials . Nature neuroscience 2 , 168 – 174 . doi: 10.1038/5729 . OpenUrl CrossRef PubMed Web of Science 62. ↵ Ulrich , D. , and Huguenard , J. R. ( 1997 ). Nucleus-specific chloride homeostasis in rat thalamus . Journal of Neuroscience 17 , 2348 – 2354 . doi: 10.1523/JNEUROSCI.17-07-02348.1997 . OpenUrl Abstract / FREE Full Text 63. ↵ Sun , Y.-G. , Wu , C.-S. , Renger , J. J. , Uebele , V. N. , Lu , H.-C. , and Beierlein , M. ( 2012 ). Gabaergic synaptic transmission triggers action potentials in thalamic reticular nucleus neurons . Journal of Neuroscience 32 , 7782 – 7790 . doi: 10.1523/JNEUROSCI.1038-12.2012 . OpenUrl Abstract / FREE Full Text 64. ↵ Klein , P. M. , Lu , A. C. , Harper , M. E. , McKown , H. M. , Morgan , J. D. , and Beenhakker , M. P. ( 2018 ). Tenuous inhibitory gabaergic signaling in the reticular thalamus . Journal of Neuroscience 38 , 1232 – 1248 . doi: 10.1523/JNEUROSCI.2548-17.2017 . OpenUrl Abstract / FREE Full Text 65. ↵ Landisman , C. E. , Long , M. A. , Beierlein , M. , Deans , M. R. , Paul , D. L. , and Connors , B. W. ( 2002 ). Electrical synapses in the thalamic reticular nucleus . Journal of Neuroscience 22 , 1002 – 1009 . doi: 10.1523/JNEUROSCI.22-03-01002.2002 . OpenUrl Abstract / FREE Full Text 66. ↵ Long , M. A. , Landisman , C. E. , and Connors , B. W. ( 2004 ). Small clusters of electrically coupled neurons generate synchronous rhythms in the thalamic reticular nucleus . Journal of Neuroscience 24 , 341 – 349 . doi: 10.1523/JNEUROSCI.3640-03.2004 . OpenUrl Abstract / FREE Full Text 67. Parker , P. R. , Cruikshank , S. J. , and Connors , B. W. ( 2009 ). Stability of electrical coupling despite massive developmental changes of intrinsic neuronal physiology . Journal of Neuroscience 29 , 9761 – 9770 . doi: 10.1523/JNEUROSCI.0764-09.2009 . OpenUrl Abstract / FREE Full Text 68. ↵ Lee , S.-C. , Patrick , S. L. , Richardson , K. A. , and Connors , B. W. ( 2014 ). Two functionally distinct networks of gap junction-coupled inhibitory neurons in the thalamic reticular nucleus . Journal of Neuroscience 34 , 13170 – 13182 . doi: 10.1523/JNEUROSCI.2127-14.2014 . OpenUrl Abstract / FREE Full Text 69. ↵ Zolnik , T. A. , and Connors , B. W. ( 2016 ). Electrical synapses and the development of inhibitory circuits in the thalamus . The Journal of physiology 594 , 2579 – 2592 . doi: 10.1113/JP270671 . OpenUrl CrossRef PubMed 70. ↵ Cruikshank , S. J. , Urabe , H. , Nurmikko , A. V. , and Connors , B. W. ( 2010 ). Pathway-specific feedforward circuits between thalamus and neocortex revealed by selective optical stimulation of axons . Neuron 65 , 230 – 245 . doi: 10.1016/j.neuron.2009.12.025 . OpenUrl CrossRef PubMed Web of Science 71. Crandall , S. R. , Cruikshank , S. J. , and Connors , B. W. ( 2015 ). A corticothalamic switch: controlling the thalamus with dynamic synapses . Neuron 86 , 768 – 782 . doi: 10.1016/j.neuron.2015.03.012 . OpenUrl CrossRef 72. ↵ Hou , G. , Smith , A. G. , and Zhang , Z.-W. ( 2016 ). Lack of intrinsic gabaergic connections in the thalamic reticular nucleus of the mouse . Journal of Neuroscience 36 , 7246 – 7252 . doi: 10.1523/JNEUROSCI.0633-16.2016 . OpenUrl Abstract / FREE Full Text 73. ↵ Murata , Y. , and Colonnese , M. T. ( 2019 ). Thalamic inhibitory circuits and network activity development . Brain research 1706 , 13 – 23 . doi: 10.1016/j.brainres.2018.11.021 . OpenUrl CrossRef PubMed 74. ↵ O’Byrne , J. , and Jerbi , K. ( 2022 ). How critical is brain criticality? Trends in Neurosciences 45 , 820 – 837 . doi: 10.1016/j.tins.2022.06.007 . OpenUrl CrossRef 75. ↵ Wang , C. , Li , S. , and Wu , S. ( 2021 ). Analysis of the neuron dynamics in thalamic reticular nucleus by a reduced model . Frontiers in Computational Neuroscience 15 . doi: 10.3389/fncom.2021.670896 . OpenUrl CrossRef 76. ↵ Li , G. , Henriquez , C. S. , and Fröhlich , F. ( 2017 ). Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation . PLoS computational biology 13 , e1005797 . doi: 10.1371/journal.pcbi.1005797 . OpenUrl CrossRef PubMed 77. ↵ Cueni , L. , Canepari , M. , Luján , R. , Emmenegger , Y. , Watanabe , M. , Bond , C. T. , Franken , P. , Adelman , J. P. , and Lüthi , A. ( 2008 ). T-type ca2+ channels, sk2 channels and sercas gate sleep-related oscillations in thalamic dendrites . Nature neuroscience 11 , 683 – 692 . doi: 10.1038/nn.2124 . OpenUrl CrossRef PubMed Web of Science 78. ↵ Vantomme , G. , Osorio-Forero , A. , Lüthi , A. , and Fernandez , L. M. ( 2019 ). Regulation of local sleep by the thalamic reticular nucleus . Frontiers in neuroscience 13 , 576 . doi: 10.3389/fnins.2019.00576 . OpenUrl CrossRef 79. ↵ Fernandez , L. M. , Vantomme , G. , Osorio-Forero , A. , Cardis , R. , Béard , E. , and Lüthi , A. ( 2018 ). Thalamic reticular control of local sleep in mouse sensory cortex . Elife 7 , e39111 . doi: 10.7554/eLife.39111 . OpenUrl CrossRef 80. ↵ Contreras , D. , Curro Dossi , R. , and Steriade , M. ( 1992 ). Bursting and tonic discharges in two classes of reticular thalamic neurons . Journal of neurophysiology 68 , 973 – 977 . doi: 10.1152/jn.1992.68.3.973 . OpenUrl CrossRef PubMed Web of Science 81. ↵ Lee , S.-H. , Govindaiah , G. , and Cox , C. L. ( 2007 ). Heterogeneity of firing properties among rat thalamic reticular nucleus neurons . The Journal of physiology 582 , 195 – 208 . doi: 10.1113/jphysiol.2007.130211 . OpenUrl CrossRef PubMed 82. ↵ Li , Y. , Lopez-Huerta , V. G. , Adiconis , X. , Levandowski , K. , Choi , S. , Simmons , S. K. , Arias-Garcia , M. A. , Guo , B. , Yao , A. Y. , Blosser , T. R. et al. ( 2020 ). Distinct subnetworks of the thalamic reticular nucleus . Nature 583 , 819 – 824 . doi: 10.1038/s41586-020-2475-0 . OpenUrl CrossRef PubMed 83. ↵ Martinez-Garcia , R. I. , Voelcker , B. , Zaltsman , J. B. , Patrick , S. L. , Stevens , T. R. , Connors , B. W. , and Cruikshank , S. J. ( 2020 ). Two dynamically distinct circuits driving inhibition in sensory thalamus . Nature 583 , 813 – 818 . doi: 10.1038/s41586-020-2473-2 . OpenUrl CrossRef PubMed 84. ↵ Haas , J. S. , Zavala , B. , and Landisman , C. E. ( 2011 ). Activity-dependent long-term depression of electrical synapses . Science 334 , 389 – 393 . doi: 10.1126/science.1207502 . OpenUrl Abstract / FREE Full Text 85. ↵ McCormick , D. A. ( 1989 ). Cholinergic and noradrenergic modulation of thalamocortical processing . Trends in neurosciences 12 , 215 – 221 . doi: 10.1016/0166-2236(89)90140-5 . OpenUrl CrossRef PubMed Web of Science 86. ↵ McCormick , D. A. ( 1992 ). Neurotransmitter actions in the thalamus and cerebral cortex and their role in neuromodulation of thalamocortical activity . Progress in neurobiology 39 , 337 – 388 . doi: 10.1016/0301-0082(92)90012-4 . OpenUrl CrossRef PubMed Web of Science 87. ↵ Crunelli , V. , Loőrincz , M. L. , Connelly , W. M. , David , F. , Hughes , S. W. , Lambert , R. C. , Leresche , N. , and Errington , A. C. ( 2018 ). Dual function of thalamic low-vigilance state oscillations: rhythm-regulation and plasticity . Nature Reviews Neuroscience 19 , 107 – 118 . doi: 10.1038/nrn.2018.3 . OpenUrl CrossRef 88. ↵ Krishnan , G. P. , Chauvette , S. , Shamie , I. , Soltani , S. , Timofeev , I. , Cash , S. S. , Halgren , E. , and Bazhenov , M. ( 2016 ). Cellular and neurochemical basis of sleep stages in the thalamocortical network . eLife 5 . doi: 10.7554/eLife.18607 . OpenUrl CrossRef PubMed 89. ↵ Amzica , F. , Núñez , A. , and Steriade , M. ( 1992 ). Delta frequency (1–4 hz) oscillations of perigeniculate thalamic neurons and their modulation by light . Neuroscience 51 , 285 – 294 . doi: 10.1016/0306-4522(92)90318-M . OpenUrl CrossRef PubMed Web of Science 90. ↵ Astori , S. , Wimmer , R. D. , Prosser , H. M. , Corti , C. , Corsi , M. , Liaudet , N. , Volterra , A. , Franken , P. , Adelman , J. P. , and Lüthi , A. ( 2011 ). The cav3.3 calcium channel is the major sleep spindle pacemaker in thalamus . Proceedings of the National Academy of Sciences 108 , 13823 – 13828 . doi: 10.1073/pnas.1105115108 . OpenUrl Abstract / FREE Full Text 91. ↵ Pellegrini , C. , Lecci , S. , Lüthi , A. , and Astori , S. ( 2016 ). Suppression of sleep spindle rhythmogenesis in mice with deletion of cav3.2 and cav3.3 t-type ca2+ channels . Sleep 39 , 875 – 885 . doi: 10.5665/sleep.5654 . OpenUrl CrossRef PubMed 92. ↵ Fogel , S. M. , and Smith , C. T. ( 2011 ). The function of the sleep spindle: A physiological index of intelligence and a mechanism for sleep-dependent memory consolidation . Neu-roscience & Biobehavioral Reviews 35 , 1154 – 1165 . doi: 10.1016/j.neubiorev.2010.12.003 . OpenUrl CrossRef PubMed Web of Science 93. ↵ Bódizs , R. , Kis , T. , Lázár , A. S. , Havran , L. , Rigó , P. , Clemens , Z. , and Halász , P. ( 2005 ). Prediction of general mental ability based on neural oscillation measures of sleep . Journal of Sleep Research 14 . doi: 10.1111/j.1365-2869.2005.00483.x . OpenUrl CrossRef PubMed 94. ↵ Seibt , J. , Timofeev , I. , Carrier , J. , and Peyrache , A. ( 2016 ). Role of spindle oscillations across lifespan in health and disease . Neural Plasticity 2016 . doi: 10.1155/2016/3206190 . OpenUrl CrossRef 95. ↵ Panas , D. , Malinowska , U. , Piotrowski , T. , Żygierewicz , J. , and Suffczyński , P. ( 2013 ). Statistical analysis of sleep spindle occurrences . PLoS One 8 , e59318 . doi: 10.1371/journal.pone.0059318 . OpenUrl CrossRef PubMed 96. Krishnan , G. P. , Rosen , B. Q. , Chen , J.-Y. , Muller , L. , Sejnowski , T. J. , Cash , S. S. , Halgren , E. , and Bazhenov , M. ( 2018 ). Thalamocortical and intracortical laminar connectivity determines sleep spindle properties . PLoS Computational Biology 14 , e1006171 . doi: 10.1371/journal.pcbi.1006171 . OpenUrl CrossRef 97. ↵ Peyrache , A. ( 2020 ). In humans, sleep spindles are generated by local thalamic pacemakers . The Journal of physiology 598 , 2041 – 2042 . doi: 10.1113/JP280042 . OpenUrl CrossRef 98. ↵ Kohmann , D. , Lüttjohann , A. , Seidenbecher , T. , Coulon , P. , and Pape , H.-C. ( 2016 ). Shortterm depression of gap junctional coupling in reticular thalamic neurons of absence epileptic rats . The Journal of Physiology 594 . doi: 10.1113/JP272682 . OpenUrl CrossRef 99. ↵ Coulon , P. , and Landisman , C. E. ( 2017 ). The potential role of gap junctional plasticity in the regulation of state . Neuron 93 , 1275 – 1295 . doi: 10.1016/j.neuron.2017.02.041 . OpenUrl CrossRef PubMed 100. ↵ Haas , J. S. , Zavala , B. , and Landisman , C. E. ( 2011 ). Activity-dependent long-term depression of electrical synapses . Science 334 , 389 – 393 . doi: 10.1126/science.1207505 . OpenUrl Abstract / FREE Full Text 101. ↵ Haas , J. S. , and Landisman , C. E. ( 2012 ). Bursts modify electrical synaptic strength . Brain research 1487 , 140 – 149 . doi: 10.1016/j.brainres.2012.09.043 . OpenUrl CrossRef PubMed 102. ↵ Clemente-Perez , A. , Makinson , S. R. , Higashikubo , B. , Brovarney , S. , Cho , F. S. , Urry , A. , Holden , S. S. , Wimer , M. , Dávid , C. , Fenno , L. E. et al. ( 2017 ). Distinct thalamic reticular cell types differentially modulate normal and pathological cortical rhythms . Cell reports 19 , 2130 – 2142 . doi: 10.1016/j.celrep.2017.05.034 . OpenUrl CrossRef 103. ↵ Vaughn , M. J. , Laswick , Z. , Wang , H. , and Haas , J. S. ( 2024 ). Functionally distinct circuits are linked by heterocellular electrical synapses in the thalamic reticular nucleus . eneuro 11 . doi: 10.1523/ENEURO.0216-23.2023 . OpenUrl CrossRef 104. ↵ Peng , C.-K. , Havlin , S. , Stanley , H. E. , and Goldberger , A. L. ( 1995 ). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series . Chaos 5 , 82 – 87 . doi: 10.1063/1.166141 . OpenUrl CrossRef PubMed Web of Science 105. ↵ Fuentealba , P. , Crochet , S. , Timofeev , I. , Bazhenov , M. , Sejnowski , T. J. , and Steriade , M. ( 2004 ). Experimental evidence and modeling studies support a synchronizing role for electrical coupling in the cat thalamic reticular neurons in vivo . European Journal of Neuroscience 20 , 111 – 119 . doi: 10.1111/j.1460-9568.2004.03468.x . OpenUrl CrossRef PubMed Web of Science 106. ↵ Spreafico , R. , Battaglia , G. , and Frassoni , C. ( 1991 ). The reticular thalamic nucleus (rtn) of the rat: cytoarchitectural, golgi, immunocytochemical, and horseradish peroxidase study . Journal of comparative neurology 304 , 478 – 490 . doi: 10.1002/cne.903040310 . OpenUrl CrossRef PubMed Web of Science 107. ↵ Cox , C. L. , Huguenard , J. R. , and Prince , D. A. ( 1996 ). Heterogeneous axonal arborizations of rat thalamic reticular neurons in the ventrobasal nucleus . Journal of Comparative Neurology 366 , 416 – 430 . doi: 10.1002/(SICI)1096-9861(19960318)366:33.0.CO;2-6 . OpenUrl CrossRef PubMed Web of Science 108. ↵ Cox , C. L. , Huguenard , J. R. , and Prince , D. A. ( 1997 ). Nucleus reticularis neurons mediate diverse inhibitory effects in thalamus . Proceedings of the National Academy of Sciences 94 , 8854 – 8859 . doi: 10.1073/pnas.94.16.8854 . OpenUrl Abstract / FREE Full Text 109. ↵ Penny , G. , Conley , M. , Schmechel , D. , and Diamond , I. ( 1984 ). The distribution of glutamic acid decarboxylase immunoreactivity in the diencephalon of the opossum and rabbit . Journal of Comparative Neurology 228 , 38 – 56 . doi: 10.1002/cne.902280104 . OpenUrl CrossRef PubMed Web of Science 110. ↵ Houser , C. R. , Vaughn , J. E. , Barber , R. P. , and Roberts , E. ( 1980 ). Gaba neurons are the major cell type of the nucleus reticularis thalami . Brain research 200 , 341 – 354 . doi: 10.1016/0006-8993(80)90969-5 . OpenUrl CrossRef PubMed Web of Science 111. ↵ Wells , M. F. , Wimmer , R. D. , Schmitt , L. I. , Feng , G. , and Halassa , M. M. ( 2016 ). Thalamic reticular impairment underlies attention deficit in ptchd1 y/mice . Nature 532 , 58 – 63 . doi: 10.1038/nature17427 . OpenUrl CrossRef PubMed 112. ↵ Landisman , C. E. , and Connors , B. W. ( 2005 ). Long-term modulation of electrical synapses in the mammalian thalamus . Science 310 , 1809 – 1813 . doi: 10.1126/science.1118266 . OpenUrl Abstract / FREE Full Text 113. ↵ Wang , Z. , Neely , R. , and Landisman , C. E. ( 2015 ). Activation of group i and group ii metabotropic glutamate receptors causes ltd and ltp of electrical synapses in the rat thalamic reticular nucleus . The Journal of Neuroscience 35 , 7616 – 7625 . doi: 10.1523/JNEUROSCI.0717-15.2015 . OpenUrl Abstract / FREE Full Text 114. ↵ Ayoub , A. , Aumann , D. , Hörschelmann , A. , Kouchekmanesch , A. , Paul , P. , Born , J. , and Marshall , L. ( 2013 ). Differential effects on fast and slow spindle activity, and the sleep slow oscillation in humans with carbamazepine and flunarizine to antagonize voltage-dependent na+ and ca2+ channel activity . Sleep 36 , 905 – 911 . doi: 10.5665/sleep.2720 . OpenUrl CrossRef PubMed Web of Science 115. ↵ Crick , F. ( 1984 ). Function of the thalamic reticular complex: the searchlight hypothesis . Proceedings of the National Academy of Sciences 81 , 4586 – 4590 . doi: 10.1073/pnas.81.14.4586 . OpenUrl Abstract / FREE Full Text 116. McAlonan , K. , Cavanaugh , J. , and Wurtz , R. H. ( 2008 ). Guarding the gateway to cortex with attention in visual thalamus . Nature 456 , 391 – 394 . doi: 10.1038/nature07382 . OpenUrl CrossRef PubMed Web of Science 117. Wimmer , R. D. , Schmitt , L. I. , Davidson , T. J. , Nakajima , M. , Deisseroth , K. , and Halassa , M. M. ( 2015 ). Thalamic control of sensory selection in divided attention . Nature 526 , 705 – 709 . doi: 10.1038/nature15398 . OpenUrl CrossRef PubMed 118. ↵ Nakajima , M. , Schmitt , L. I. , and Halassa , M. M. ( 2019 ). Prefrontal cortex regulates sensory filtering through a basal ganglia-to-thalamus pathway . Neuron 103 , 445 – 458 . doi: 10.1016/j.neuron.2019.05.026 . OpenUrl CrossRef PubMed 119. ↵ Lewis , L. D. , Voigts , J. , Flores , F. J. , Schmitt , L. I. , Wilson , M. A. , Halassa , M. M. , and Brown , E. N. ( 2015 ). Thalamic reticular nucleus induces fast and local modulation of arousal state . eLife 4 , e08760 . doi: 10.7554/eLife.08760 . OpenUrl CrossRef PubMed 120. ↵ Shew , W. L. , and Plenz , D. ( 2013 ). The functional benefits of criticality in the cortex . The Neuroscientist 19 , 88 – 100 . doi: 10.1177/1073858412445488 . OpenUrl CrossRef 121. ↵ Morison , R. S. , and Bassett , D. L. ( 1945 ). Electrical activity of the thalamus and basal ganglia in decorticate cats . Journal of Nervous and Mental Disease 104 , 452 . doi: 10.1097/00005053-194511000-00002 . OpenUrl CrossRef 122. ↵ Timofeev , I. , and Steriade , M. ( 1996 ). Low-frequency rhythms in the thalamus of intactcortex and decorticated cats . Journal of neurophysiology 76 , 4152 – 4168 . doi: 10.1152/jn.1996.76.6.4152 . OpenUrl CrossRef PubMed Web of Science 123. ↵ Dehghani , N. , Cash , S. S. , Chen , C. C. , Hagler , D. J. , Huang , M. , Dale , A. M. , and Halgren , E. ( 2010 ). Divergent cortical generators of meg and eeg during human sleep spindles suggested by distributed source modeling . PLoS ONE 5 . doi: 10.1371/journal.pone.0011429 . OpenUrl CrossRef PubMed 124. ↵ Bonjean , M. , Baker , T. , Bazhenov , M. , Cash , S. , Halgren , E. , and Sejnowski , T. ( 2012 ). Interactions between core and matrix thalamocortical projections in human sleep spindle synchronization . Journal of Neuroscience 32 , 5250 – 5263 . doi: 10.1523/JNEUROSCI.6141-11.2012 . OpenUrl Abstract / FREE Full Text 125. ↵ Piantoni , G. , Halgren , E. , and Cash , S. S. ( 2016 ). The contribution of thalamocortical core and matrix pathways to sleep spindles . Neural Plasticity 2016 . doi: 10.1155/2016/3024342 . OpenUrl CrossRef PubMed 126. ↵ Niethard , N. , Ngo , H.-V. V. , Ehrlich , I. , and Born , J. ( 2018 ). Cortical circuit activity underlying sleep slow oscillations and spindles . Proceedings of the National Academy of Sciences 115 , E9220 – E9229 . doi: 10.1073/pnas.1805517115 . OpenUrl Abstract / FREE Full Text 127. ↵ Krishnan , G. P. , Rosen , B. Q. , Chen , J.-Y. , Muller , L. E. , Sejnowski , T. J. , Cash , S. S. , Halgren , E. , and Bazhenov , M. ( 2018 ). Thalamocortical and intracortical laminar connectivity determines sleep spindle properties . PLoS Computational Biology 14 . doi: 10.1371/journal.pcbi.1005928 . OpenUrl CrossRef 128. ↵ Li , G. , Henriquez , C. S. , and Fröhlich , F. ( 2017 ). Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation . PLoS Computational Biology 13 . doi: 10.1371/journal.pcbi.1005797 . OpenUrl CrossRef PubMed 129. ↵ Bazhenov , M. , Timofeev , I. , Steriade , M. , and Sejnowski , T. J. ( 2002 ). Model of thalamocortical slow-wave sleep oscillations and transitions to activated states . Journal of Neuroscience 22 , 8691 – 8704 . doi: 10.1523/JNEUROSCI.22-19-08691.2002 . OpenUrl Abstract / FREE Full Text 130. ↵ Yazdanbakhsh , A. , Barbas , H. , and Zikopoulos , B. ( 2023 ). Sleep spindles in primates: Modeling the effects of distinct laminar thalamocortical connectivity in core, matrix, and reticular thalamic circuits . Network Neuroscience 7 , 743 – 768 . 10.1162/netn_a_00311. doi: 10.1162/netn_a_00311 . arXiv: https://direct.mit.edu/netn/article-pdf/7/2/743/2118366/netna00311.pd OpenUrl CrossRef 131. ↵ Bazhenov , M. , Timofeev , I. , Steriade , M. , and Sejnowski , T. J. ( 1998 ). Cellular and network models for intrathalamic augmenting responses during 10-hz stimulation . Journal of Neurophysiology 79 , 2730 – 2748 . doi: 10.1152/jn.1998.79.5.2730 . OpenUrl CrossRef PubMed Web of Science 132. ↵ Wang , C. , Zhang , T. , Chen , X. , He , S. , Li , S. , and Wu , S. ( 2023 ). Brainpy, a flexible, integrative, efficient, and extensible framework for general-purpose brain dynamics programming . eLife 12 , e86365 . 10.7554/eLife.86365. doi: 10.7554/eLife.86365 . OpenUrl CrossRef 133. ↵ Wang , C. , Zhang , T. , He , S. , Gong , Y. , Gu , H. , Li , S. , and Wu , S. ( 2023 ). A differentiable brain simulator bridging brain simulation and brain-inspired computing . arXiv preprint arxiv: 2311.05106 . https://arxiv.org/abs/2311.05106 . 134. ↵ Gramfort , A. , Luessi , M. , Larson , E. , Engemann , D. A. , Strohmeier , D. , Brodbeck , C. , Goj , R. , Jas , M. , Brooks , T. , Parkkonen , L. , and Hämäläinen , M. S. ( 2013 ). MEG and EEG data analysis with MNE-Python . Frontiers in Neuroscience 7 , 1 – 13 . doi: 10.3389/fnins.2013.00267 . OpenUrl CrossRef 135. ↵ Mazzoni , A. , Panzeri , S. , Logothetis , N. K. , and Brunel , N. ( 2008 ). Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons . PLOS Computational Biology 4 , 1 – 20 . 10.1371/journal.pcbi.1000239. doi: 10.1371/journal.pcbi.1000239 . OpenUrl CrossRef 136. ↵ Lindén , H. , Tetzlaff , T. , Potjans , T. , Pettersen , K. , Grün , S. , Diesmann , M. , and Einevoll , G. ( 2011 ). Modeling the spatial reach of the lfp . Neuron 72 , 859 – 872 . https://www.sciencedirect.com/science/article/pii/S0896627311010051 . doi: 10.1016/j.neuron.2011.11.006 . OpenUrl CrossRef PubMed Web of Science 137. ↵ Lacourse , K. , Delfrate , J. , Beaudry , J. , Peppard , P. , and Warby , S. C. ( 2019 ). A sleep spindle detection algorithm that emulates human expert spindle scoring . Journal of neuroscience methods 316 , 3 – 11 . doi: 10.1016/j.jneumeth.2018.09.018 . OpenUrl CrossRef 138. ↵ Vallat , R. , and Walker , M. P. ( 2021 ). An open-source, high-performance tool for automated sleep staging . Elife 10 , e70092 . doi: 10.7554/eLife.70092 . OpenUrl CrossRef 139. ↵ Beggs , J. M. , and Plenz , D. ( 2003 ). Neuronal avalanches in neocortical circuits . The Journal of Neuroscience 23 , 11167 – 11177 . doi: 10.1523/JNEUROSCI.23-35-11167.2003 . OpenUrl Abstract / FREE Full Text 140. ↵ Yu , S. , Klaus , A. , Yang , H. , and Plenz , D. ( 2014 ). Scale-invariant neuronal avalanche dynamics and the cut-off in size distributions . PLoS ONE 9 . doi: 10.1371/journal.pone.0099744 . OpenUrl CrossRef PubMed 141. ↵ Alstott , J. , Bullmore , E. T. , and Plenz , D. ( 2013 ). powerlaw: A python package for analysis of heavy-tailed distributions . PLoS ONE 9 . doi: 10.1371/journal.pone.0085777 . OpenUrl CrossRef PubMed 142. ↵ Clauset , A. , Shalizi , C. R. , and Newman , M. E. J. ( 2007 ). Power-law distributions in empirical data . SIAM Rev . 51 , 661 – 703 . doi: 10.1137/070710111 . OpenUrl CrossRef 143. ↵ Steriade , M. , Domich , L. , and Oakson , G. ( 1986 ). Reticularis thalami neurons revisited: activity changes during shifts in states of vigilance . Journal of Neuroscience 6 , 68 – 81 . doi: 10.1523/JNEUROSCI.06-01-00068.1986 . OpenUrl Abstract / FREE Full Text 144. Huguenard , J. , and Prince , D. ( 1992 ). A novel t-type current underlies prolonged ca (2+)-dependent burst firing in gabaergic neurons of rat thalamic reticular nucleus . Journal of Neuroscience 12 , 3804 – 3817 . doi: 10.1523/JNEUROSCI.12-10-03804.1992 . OpenUrl Abstract / FREE Full Text 145. Bal , T. , and McCORMICK , D. A. ( 1993 ). Mechanisms of oscillatory activity in guinea-pig nucleus reticularis thalami in vitro: a mammalian pacemaker . The Journal of Physiology 468 , 669 – 691 . doi: 10.1113/jphysiol.1993.sp019789 . OpenUrl CrossRef PubMed Web of Science 146. ↵ Llinás , R. R. , and Steriade , M. ( 2006 ). Bursting of thalamic neurons and states of vigilance . Journal of neurophysiology 95 , 3297 – 3308 . doi: 10.1152/jn.00166.2006 . OpenUrl CrossRef PubMed Web of Science 147. ↵ Steriade , M. , McCormick , D. A. , and Sejnowski , T. J. ( 1993 ). Thalamocortical oscillations in the sleeping and aroused brain . Science 262 , 679 – 685 . doi: 10.1126/science.8235588 . OpenUrl Abstract / FREE Full Text 148. Fuentealba , P. , Timofeev , I. , and Steriade , M. ( 2004 ). Prolonged hyperpolarizing potentials precede spindle oscillations in the thalamic reticular nucleus . Proceedings of the National Academy of Sciences of the United States of America 101 , 9816 – 9821 . doi: 10.1073/pnas.0402504101 . OpenUrl Abstract / FREE Full Text View the discussion thread. Back to top Previous Next Posted September 06, 2024. Download PDF Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. 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Share Spindle Oscillations Emerge at the Critical State of Electrically Coupled Networks in the Thalamic Reticular Nucleus Shangyang Li , Chaoming Wang , Si Wu bioRxiv 2023.12.31.573769; doi: https://doi.org/10.1101/2023.12.31.573769 Share This Article: Copy Citation Tools Spindle Oscillations Emerge at the Critical State of Electrically Coupled Networks in the Thalamic Reticular Nucleus Shangyang Li , Chaoming Wang , Si Wu bioRxiv 2023.12.31.573769; doi: https://doi.org/10.1101/2023.12.31.573769 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Neuroscience Subject Areas All Articles Animal Behavior and Cognition (7644) Biochemistry (17728) Bioengineering (13916) Bioinformatics (42037) Biophysics (21489) Cancer Biology (18637) Cell Biology (25553) Clinical Trials (138) Developmental Biology (13401) Ecology (19941) Epidemiology (2067) Evolutionary Biology (24367) Genetics (15622) Genomics (22547) Immunology (17764) Microbiology (40475) Molecular Biology (17208) Neuroscience (88747) Paleontology (667) Pathology (2842) Pharmacology and Toxicology (4834) Physiology (7659) Plant Biology (15175) Scientific Communication and Education (2047) Synthetic Biology (4304) Systems Biology (9835) Zoology (2272)