interactions between core and matrix thalamocortical projections in human sleep spindle...

Interactions between core and matrix thalamocorticalprojections in human sleep spindle synchronization

Maxime Bonjean1,2,*, Tanya Baker1,*, Maxim Bazhenov1,3, Sydney Cash4, Eric Halgren5, andTerrence Sejnowski1,2

1Howard Hughes Medical Institute, The Salk Institute for Biological Studies, La Jolla, CA, USA2Division of Biological Sciences, University of California, San Diego, CA, USA3Department of Cell Biology and Neuroscience, University of California, Riverside, USA4Massachusetts General Hospital and Harvard Medical School, Harvard University, Boston, MA,USA5Department of Neurosciences, University of California, San Diego, USA

AbstractSleep spindles, which are bursts of 11–15 Hz that occur during non-REM sleep, are highlysynchronous across the scalp when measured with EEG, but have low spatial coherence andexhibit low correlation with EEG signals when simultaneously measured with MEG spindles inhumans. We developed a computational model to explore the hypothesis that the spatial coherenceof the EEG spindle is a consequence of diffuse matrix projections of the thalamus to layer 1compared to the focal projections of the core pathway to layer 4 recorded by the MEG. Increasingthe fanout of thalamocortical connectivity in the matrix pathway while keeping the core pathwayfixed led to increased synchrony of the spindle activity in the superficial cortical layers in themodel. In agreement with cortical recordings, the latency for spindles to spread from the core tothe matrix was independent of the thalamocortical fanout but highly dependent on the probabilityof connections between cortical areas.

KeywordsThalamus; thalamocortical; core and matrix; spindle oscillations; sleep

INTRODUCTIONHuman sleep is associated with a profound modification of consciousness and theemergence of distinct sleep oscillations. In the early stages of non-rapid eye movement(NREM) sleep, electroencephalographic (EEG) recordings show characteristic spindleoscillations. These sleep spindles are a hallmark of non-pathological stage 2 NREM sleep inmammals and are thought to play an important role in memory consolidation (Sejnowski andDestexhe, 2000). In humans, sleep spindles consist of waxing-and-waning bursts of fieldpotentials oscillating at 11–15 Hz. These bursts last 0.5–3 seconds and recur every 5–15seconds.

Correspondence should be addressed to: Terrence Sejnowski, PhD, Howard Hughes Medical Institute, The Salk Institute forBiological Studies, La Jolla, CA-92037, Ph: +1 (858)-453-4100, [email protected].*These two authors contributed equally to the work and share the first authorship.

NIH Public AccessAuthor ManuscriptJ Neurosci. Author manuscript; available in PMC 2012 October 11.

Published in final edited form as:J Neurosci. 2012 April 11; 32(15): 5250–5263. doi:10.1523/JNEUROSCI.6141-11.2012.

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Though compelling evidence from decortication in vivo (Morison and Basset, 1945; vonKrosigk et al., 1993) and spindle recordings in thalamic slices (Kim et al., 1995)demonstrate that spindles can be generated by the thalamus without cortical input, theneocortex is required for the long-range synchronization of spindles (Contreras et al., 1996a,1996b; 1997; Destexhe et al., 1998). Previous studies suggest that corticothalamic feedbackprojections to the thalamic reticular nucleus may be primarily responsible for this large-scalecoherence (Destexhe et al., 1998).

Human sleep spindles measured by EEG or magnetoencephalography (MEG) duringsimultaneous EEG/MEG recordings exhibit different synchronization properties: The EEGsignals from different channels have stronger cross-pair coherence than the MEG signal(Dehghani et al., 2010). Although the relative spatial resolution of these modalities is apossible explanation, a more compelling one is that the EEG and MEG signals are generatedfrom different cortical layers. The evidence comes from current source density profiles ofcortical depth electrode recordings of sleep spindles during pre-surgical exploration ofhuman epileptic patients, consistent with spatially coherent spindles generated by uppercortical layers and spatially incoherent spindles e generated in middle cortical layers (Tuanet al., 2010).

To confirm this hypothesis, we have investigated the synchronization properties of spindleoscillations in a biologically plausible computational model using two parallelthalamocortical pathways (core and matrix) – pathways that were suggested from studies inprimates, but whose functional role has remained elusive (Jones 2001; 2002).

This paper reconciles the differences in EEG and MEG recorded during sleep spindles inhumans (Dehghani et al. 2010a,b,c) and in vivo data from anesthetized animals (Zikopouloset al. 2007) and shows that (1) human sleep spindle oscillations are initiated in the specific-projecting thalamocortical core pathway with focal projections to the middle cortical layers,and that (2) the thalamocortical matrix pathway underlies the synchronization of theoscillatory activity through the distributed thalamocortical projections to the upper corticallayers. The activities in thalamocortical core and matrix pathways dominate the MEG andEEG recordings, respectively.

METHODSThough faithful in capturing the most salient features of spindle oscillations, thecomputational models developed thus far have been limited to a unique thalamocorticalpathway (Dextexhe et al., 1994, 1998; Bazhenov et al., 1999, 2000). To adequatelyinvestigate the propagation and synchronization of spindle oscillations, we needed toconstruct a spatially extensive four-layer model, comprising two main distinct butinterconnected thalamocortical pathways based on non-human primate observations (Jones,2002; Zikopoulos and Barbas, 2007): (i) the core pathway, in which thalamic efferentsproject to the middle layers of the cortex (mostly to layers III and IV), and (ii) the matrixpathway, which has thalamic afferents to superficial layers of the cortex (mainly to layer I).The matrix thalamocortical pathway has more diffuse connections than the core, the latterbeing more topologically compact and specific (Jones, 2002; see Fig. 1A). We incorporatedthese specific connectivity and topographic features into our thalamocortical network model.

The thalamic relay (TC) cells and reticular (RE) neurons were based on compartmentmodels with Hodgkin-Huxley kinetics (Hodgkin and Huxley, 1952) used in previous modelsof sleep oscillations (Bazhenov et al., 2002). The cortical model included two-compartmentexcitatory cortical pyramidal (PY) neurons and inhibitory interneurons (IN) with Hodgkin-Huxley kinetics. The TC and RE cells had low-threshold calcium, fast sodium, and

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potassium currents. An h-type and potassium A-currents were also included in the TC modelcells. The PY and IN cells had high-threshold calcium, fast, and persistent sodium, calcium-dependent potassium, and potassium M currents in the dendrites; fast potassium, fastsodium, and persistent sodium currents in the soma. Calcium pumps that extruded calciumwere embedded in all the neurons. The details of the synaptic kinetics and parameters areincluded in the Modeling details below.

Network structureA schematic of the model thalamocortical network geometry is shown in Figure 1B. Ourmodel incorporated two populations of TC cells: matrix TC neurons forming diffuseprojections to matrix PY cortical neurons with cell bodies in layer V, and core TC neuronsforming specific, focused projections to the core PY neurons with cell bodies in layer VI.The apical dendrites of all PY cells extended to supragranular layers. The termination ofmatrix TC neurons was in cortical layer I and those of core TC neurons in cortical layer IV.We have not explicitly modeled supragranular cortical neurons; instead we focused on thecontacts made by matrix thalamic projections to the apical dendrites of the layer Vpyramidal cells. This simplification allowed varying easily the main anatomical features ofthe matrix and core subsystems, such as radius of thalamocortical projections that was in thefocus of our study. Also incorporated were matrix and core RE neurons interconnected withmatrix and core PY and TC neurons respectively. Each cortical layer included a layerspecific population of inhibitory interneurons (IN) also receiving thalamocortical inputsfrom the respective thalamic areas. The thalamocortical model was structured as a one-dimensional six-layer array of cells: (i) a four-layered cortex of matrix PY, matrix IN, corePY, and core IN cells, and (ii) a two-layered thalamus of TC and RE cells, core and matrixbeing equally divided (see Fig, 1C). Core and matrix pathways were connected at thethalamic and cortical levels: (i) along one of the boundaries in the thalamus (TC and RElayers) and (ii) additional “long-range” cortical connections between the matrix and corepathways were made between their respective PY layers, with a 2% probability (p = 0.02)corticocortical connection. We further tested effect of increasing probability up to p=0.25.This choice of long-range intracortical probability was largely determined by the averagesize of the presynaptic population; probability p=0.02 corresponded to only few (0–1) long-range connections, probability p=0.25 corresponded to about 7 long-range connection for anaverage footprint of 30 neurons. Within thalamus, interactions between core and matrixsubsystems were provided through thalamic reticular neurons. Specifically, we tested effectof the varying overlap between reticular neurons of two subsystems on the development andsynchronization of spindles.

We performed one-dimensional multi-layer simulations consisting of 200 PY neurons and50 IN neurons per cortical core and matrix networks, and 50 TC neurons and 50 RE neuronsin each of the thalamic core and matrix networks, totaling 700 cells. The widths of thefanout of the thalamocortical and corticothalamic projections of the matrix were initiallyfocal and equal to those of the core fanout widths. In subsequent simulations, matrix fanoutswere progressively widened while keeping the corresponding focal connections in the coresystem constant (see Fig. 1B–C, dashed lines). The maximal values of synaptic connectivityradiuses were determined by the network size; to avoid limitations of “all-to-all”connectivity, we limited connectivity by 50 cells in any direction so the system would beable to display complex spatiotemporal dynamics (e.g., propagating waves). The totalsynaptic strength per cell was scaled accordingly to maintain constant the overall synapticstrength of a given pathway. The maximal conductances for individual synapses were themaximal conductance per synaptic release scaled by the number of synapses. Theseconnectivity properties are summarized in Table 1 and visualized in Figure 1C. The matrixPY cells were also slightly more hyperpolarized than the core PY cells (by adjusting the

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potassium leak conductance: gKL = 0.0025 mS/cm2 for core PY cells and 0.003 mS/cm2 formatrix PY cells; see Modeling details below). Otherwise, all parameters in the twosubsystems were modeled identically.

Most simulations were initiated by a brief external stimulus to 5 cells at the edge of the coreRE layer modeled by AMPA synapses that had a maximal conductance of 20 μS, butspindle sequences also occurred spontaneously within the network.

To quantify the synchrony in the system, we used an all-to-all, zero-time-lag cross-correlation of the estimated local field potential (LFP) during the spindle activity. Themeasure of the synchrony in the cortical activity, R, was found by taking the weighted sumof the dot products of all possible pairs of LFP spindle activity time courses within a corticallayer. This metric is related to the Schreiber reliability measure (Schreiber et al., 2003):

(1)

where N is the number of LFP points in the population and s⃗i is the time course of the LFPat location i. Eq. 1 captures the similarity of the LFP spindle activity across a cortical layer.

The LFP was estimated using the axial current between dendritic and somatic compartmentsof the cortical cells by an approximate dipole measure. For each subsystem, the LFP at acortical location i, s ⃗i, was computed by the following equation:

(2)

where the sum is taken over all excitatory cortical neurons within the subsystem, Iaxial is theaxial current from the dendritic compartment (source) to the soma compartment (sink) forthe model cortical pyramidal cells, and rd and rs are the distances from the dendrite andsoma, respectively, to the location of the LFP measurement (see Fig. 2.) This equationapproximately reduces to a dipole field as described in (Nunez and Srinivasan, 2006, see Eq.5.7; modulo a scaling factor) when rd, rs ≫ 1. The distance between the dendrite and thesoma (from layer I to layer V in the matrix and from layer II to layer VI in core) wasassumed to be 2 mm. The distance between cortical cells was estimated to be 100 μm basedon the assumption that the synaptic footprint (equal to twice the fanout plus 1), within whichthere were approximately 10 cells, was approximately 1 mm. The LFP signal was bandpass-filtered between 5–20 Hz to extract spindle activity.

Modeling detailsIntrinsic currents: Thalamus—TC and RE cells were modeled as single compartmentcells with voltage- and calcium-dependent currents described by Hodgkin-Huxley kinetics:

(1)

where Cm = 1 μF/cm2 is the membrane capacitance, gL is the leakage conductance (gL =0.01 mS/cm2 for TC cells and gL = 0.05 mS/cm2 for RE cells), and EL is the reversalpotential (EL = −70 mV for TC cells and EL = −77 mV for RE cells.) Iint is the sum of activeintrinsic currents (Ijint), and Isyn is the sum of synaptic currents (Ijsyn). The area of a TC cellwas STC = 2.9 · 10−4 cm2, and SRE = 1.43 · 10−4 cm2 for an RE cell. Both TC and RE cellsincluded a fast sodium current, INa, a fast potassium current, IK (Traub and Miles, 1991), a

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low-threshold Ca2+ current, IT (Huguenard and Prince, 1991, for RE cells; Huguenard andMcCormick, 1992, for TC cells) and a potassium leak current, IKL, where IKL = gKL(V −EKL), with EKL = −95mV. TC cells also included a hyperpolarization-activated cationcurrent, Ih (McCormick and Pape, 1990; Destexhe et al., 1996). A potassium A-current isalso included in the TC cell compartment. The expressions for voltage- and Ca2+-dependenttransition rates for all currents are given in Bazhenov et al. (1998). The maximalconductances were gK = 10 mS/cm2, gNa = 90 mS/cm2, gT = 2.2 mS/cm2, gh = 0.017 mS/cm2, gCa = 2.7 mS/cm2 gKL = 0.0142 mS/cm2 for TC cells, and gK = 10 mS/cm2, gNa = 100mS/cm2, gT = 2.3 mS/cm2, gCa = 2.3 mS/cm2 and gKL = 0.005 mS/cm2 for RE cells.

Low-threshold Ca2+ current, IT, and hyperpolarization-activated cation current, Ih playparticularly important role in spindles (Destexhe et al., 1996; Bazhenov et al. 2002). Themodel used in this study for computing Ih follows a single-variable kinetic scheme proposedby Destexhe et al. (1996), modified after a version introduced previously in Destexhe et al.(1993). The present model assumes that the voltage dependence and conductance isinfluenced by Ca2+ to a regulating factor, P, which itself binds to the open form of thechannel and blocks its transition to the closed form. The dependence of the amplitude of Ihwith the intracellular Ca2+ concentration is captured by the parameter k. All parameters usedin the computation of Ih were taken from previously published papers (Destexhe et al., 1996;Bazhenov et al. 2002) and were kept constant throughout the simulations. Therefore, theinfluence of Ih on spindle oscillations in our model was in all aspect comparable to previousobservations both in computational models and in vitro experiments (see Bal andMcCormick, 1996; Luthi and McCormick, 1998). In vitro characterization of spindlesrevealed a slowly decaying after-depolarization (ADP), which is strongly pronounced inthalamocortical cells.

Intrinsic currents: cortex—Each PY and IN cortical neuron was modeled by twocompartments coupled by a somato-dendritic resistance of R=10 MΩ. The ionic currentsfollowed Hodgkin-Huxley kinetics (Mainen and Sejnowski, 1996) with the addition of apersistent sodium current, INa(p), in the PY cells to increase bursting propensity. The firingpattern depends on the coupling conductance between the axosomatic and dendriticcompartments (g = 1/R) and the parameter ρ, which is the ratio of the surface area of thedendritic compartment to the somatic compartment (Mainen and Sejnowksi, 1996). The areaof the soma was Ssoma = 1.0 · 10−6 cm2 for the axosomatic compartment and Sdend = ρSsomafor the dendritic compartment. For the cortical pyramidal (PY) cells, ρ = 165 to matchintrinsic bursting responses observed in the majority of pyramidal cells in cortical slabs, andρ = 50 for interneurons (IN) to obtain fast spiking firing patterns.

The membrane potentials of PY and IN cells were governed by the equations:

(2)

where Cm is the membrane capacitance and gL is the leakage conductance of the dendriticcompartment, EL is the reversal potential (EL = −70 mV for IN, and −68mV for PY cells),VD and VS are the membrane potentials of the dendritic and axosomatic compartments, ID

intand IS

int are the sums of active intrinsic currents in dendritic and axosomatic compartments,Isyn is a sum of synaptic currents, and g is the conductance between dendritic andaxosomatic compartments. To increase simulation speed, the axosomatic compartment hadno capacitance as already described in a previous study (Bazhenov et al., 2002) Thecapacitance of the dendritic compartment was Cm = 0.075 μF/cm2.

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Both IN and PY cells included fast Na+ channels, INa, of a high density in the axosomaticcompartment and of a low density in the dendritic compartment. A fast delayed rectifierpotassium K+ current, IK, was present in the axosomatic compartment. A slow voltage-dependent non-inactivating K+ current, IKm, a slow Ca2+-dependent K+ current, IKCa, ahigh-threshold Ca2+ current, IHVA, and a potassium leak current, IKL, where IKL = gKL(V −EKL), EKL = −95mV, were included in the dendritic compartment. A persistent sodiumcurrent, INa(p), was included in the axosomatic and dendritic compartments of the PY cells(Alzheimer et al., 1993; Kay et al., 1998) The voltage- and Ca2+-dependent transition ratesfor all currents followed kinetics given in Timofeev et al. (2000). The maximalconductances were gNa = 3000 mS/cm2 (2500 mS/cm2 for IN), gK = 200 mS/cm2, gNa(p) =15 mS/cm2 for axosomatic compartments, and, gL = 0.033 mS/cm2 (0.06 mS/cm2 for PYcells), gKL =0–0.0025 mS/cm2 (0.0025 for core PY cells and 0.003 for matrix PY cells),gHVA = 0.01 mS/cm2, gNa = 0.8 mS/cm2, gKCa = 0.3 mS/cm2, gKm = 0.01 mS/cm2 (0.02mS/cm2 for PY cells), and gNa(p) = 3.5 mS/cm2 for dendritic compartment.

Synaptic currents—All synaptic currents were calculated according to

(3)

where gsyn is the maximal conductance, Esyn is the reversal potential, and [O](t) is thefraction of open channels. For AMPA and NMDA receptors Esyn = 0 mV, for GABAAreceptors Esyn = −70 mV in the RE and PY cells and −80 mV for the TC cells (Ulrich andHuguenard, 1997) and for the GABAB receptors Esyn = −95 mV.

The maximal conductance was multiplied by a depression variable, E ≤ 1 representing theamount of available “synaptic resources.” E was non-unitary for the GABAA intercorticalconnections and the thalamo-cortical AMPA connections in order to describe short-termdepression for these connections (Bazhenov et al., 2002.) A simple phenomenological modelwas used:E = 1 − (1− Ei(1 − U))e−(t−ti)/τ where U is the fraction of resources used per actionpotential, τ = 700 ms is the time constant of recovery of the synaptic resources, Ei is thevalue of E immediately before the ith event and (t − ti) is the time after the ith event. For INGABAA synaptic conductance U = 0.07, and for TC thalamocortical AMPA synapticconductance U = 0.073.

The GABAA, NMDA and AMPA synaptic currents were modeled by first-order activationschemes (Destexhe et al., 1994; Golomb and Amitai, 1997) For the NMDA receptors, thedependence on post-synaptic voltage was 1/(1 + exp(−(Vpost −Vth)/σ)) where Vth = −25 mVand σ = 12.5 mV (Traub et al., 1991; Destexhe et al., 1994; Golomb and Amitai, 1997) Ahigher order reaction scheme that took into account the G-protein activated K+ channelsmodeled the GABAB receptors (Bazhenov et al., 2002). The equations for all synapticcurrents are given in Bazhenov et al. (1998) and Timofeev et al. (2000). The maximalconductances per synaptic release were gAMPA(PY-PY) = 150 μS, gNMDA(PY-PY) = 10 μS,gAMPA(PY-IN) = 50 μS, gNMDA(PY-IN) = 8 μS, gAMPA(PY-TC) = 25 μS, gAMPA(PY-RE) = 50μS, gGABAA(IN-PY) = 50 μS, gAMPA(TC-PY) = 100 μS, gAMPA(TC-RE) = 4.00 μS,gGABAA(RE-TC) = 30 μS, gGABAB(RE-TC) = 80 μS, gGABAA(RE-RE) = 175 μS.

The maximal conductances for individual synapses were the maximal conductance persynaptic release scaled by the number of synapses. The exception to this was for thesynapses onto edge neurons in the TC and RE layers where they were scaled by the numberof synapses as in the center of the layers, as well as for connections between the core andmatrix PY layers in which they were scaled by the number of synapses within a connectivityfootprint.

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Computational methods—All simulations described in the paper were performed usinga forth-order Runge-Kutta integration method. The time step was 0.02 ms. Source C++ codewas compiled on a Linux server using GCC compiler.

RESULTSHuman spindles have divergent EEG and MEG synchronization properties

Typical simultaneous EEG and MEG recordings of sleep spindles obtained from six normalhuman subjects during stage 2 of non-pathological non-REM sleep are displayed in Figure3. The high density EEG confirmed widespread synchrony across the scalp during spindles(Fig. 3A) whereas MEG was highly variable across the head (Fig. 3B) with widely varyingphase and amplitude in different sensors. Furthermore, the simultaneously recorded EEGand MEG signals had low coherence and little discernable relationship with each other (Fig.3C). Spindles were generated somewhat independently in different cortical areas (Fig. 3D).Overall, the average coherence between pairs of MEG gradiometers was only ~0.3 duringspindles, in contrast to the coherence value of ~0.7 for EEG sensor pairs. The variability ofspindles across MEG sensors suggested that the signal may be formed by multiple partiallyindependent cortical generators, in contrast to the EEG, which may instead be dominated bya weak but widespread spindle generator.

When simultaneously recorded by MEG and EEG, the spindle onset in the MEG precededthe EEG activity by 1–2 cycles (Dehghani et al., 2010). The current sinks and sourcesgenerating spindles (identified with linear microelectrode arrays) were either in middlelayers when spindles were focal in the overlying subdural grid, or in superficial layers whenspindles were coherent in the grid (Tuan et al., 2010).

Spindle oscillations are reproduced in a thalamocortical network model using twosegregated pathways

Previous models have reproduced regular spindle oscillations using a simplified, singlethalamocortical pathway with a unique layer for each cell type (see for instance Bazhenov etal., 2002; Destexhe et al., 1998). To faithfully address the role of matrix and corethalamocortical pathways, we reproduced spindle oscillations in a spatially extensive four-layer model comprising two main distinct but interconnected thalamocortical networksbased on primate literature (Jones, 2001; 2002; Zikopoulos and Barbas, 2007; see Methodsfor details). Each pathway initially followed the parameters and topology of thethalamocortical model proposed in an earlier model (Bazhenov et al., 2002); however, wesubsequently allowed the fanout of thalamocortical projections to be up to five times widerin matrix vs. core pathways. As in previous models, the spindle oscillations were maintainedby interactions between thalamocortical (TC) and reticular (RE) neurons. Sequences ofspindle oscillations alternated with localized patterns of spike-burst activity propagatinginside the RE network. New sequences of spindle oscillations were initiated by input fromthe RE nucleus onto the TC cells upon removal of Ih-mediated depolarization. RE activationwas either mediated by intrinsic activity of the RE nucleus (as in Bazhenov et al. (2000), orby spontaneous cortical activity (as in Destexhe et al. (1998)).

An example of the typical neuronal activity for simulated spindle oscillations using theentire thalamocortical network with both interconnected core and matrix pathways is shownin Figure 4 (left column: core pathway; right column: matrix pathway). Some of the mostsalient properties of spindles known from animal data (Steriade and Llinas, 1988) werereproduced in this simulated activity, such as the waxing-and-waning of the membranepotential and the sub-harmonic firing (~ 5 Hz) observed in individual TC cells.

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A single spindle sequence was usually observed during the 10-second simulation, althoughmultiple spontaneous spindles recurred for longer simulations. Once the sequence initiatedin the core pathway, it spread to the matrix pathway within about 700 ms (see Fig. 4A,dotted vertical bars). Both local field potentials (LFPs) and neuronal firing were dominatedby ~10 Hz oscillatory rhythms lasting on average 2.9 ± 0.45 seconds during the subsequentautonomously organized spindle discharge – values within physiological range (Steriade andMcCarley, 2005). The local field potentials (LFPs) of the underlying activity for both coreand matrix were characterized by a typical waxing-and-waning envelope (Fig. 4A, toptraces), as did the membrane potentials for the cellular activity of TC cells during reboundspike-bursts (Fig. 4A, second to fourth traces; IN not displayed).

The population dynamics of each subsystem confirmed that the site of initiation of spindlesoccurred in the core and preceded by a few hundreds of milliseconds the occurrence ofspontaneous spindles in the matrix subsystem (Fig. 4B). Although the initiation and the firstcycle of oscillation were qualitatively similar in the two distinct pathways, the spatialpropagation of the spindle sequence was more synchronous in the matrix than in the core(Fig. 4B) – a fundamental property of these pathways as shown later. In each network, thespindle oscillation started from one edge of the layer and propagated to the opposite edge ata velocity close to 2.5 mm/s (Fig. 4B). The termination of the spindle sequence was alsowell defined temporally in the matrix pathway, as opposed to the core where the oscillationwaned asynchronously – suggesting that the spread and strength of corticothalamic feedbackinfluences spindle termination (Bonjean et al., 2011).

This data suggests that the focused corticothalamic projections of the core pathway facilitatespindle initiation, while the diffuse connections that characterize the matrix pathway areconducive to creating synchronization. We investigate below the impact of the breadth ofthalamocortical connectivity in the synchronization properties of spindles.

Matrix and core pathways exhibited different degrees of synchrony during spindlegeneration

The breadth of connectivity in the core and matrix was investigated by carrying outsimulations in which the matrix thalamocortical and corticothalamic connections becameincreasingly diffuse whereas connections in the core pathway remained focal (see Methods).The two pathways only differed in their respective connectivity profiles and otherwiseshared the same properties. Although the core thalamic cell afferents terminate with largeboutons and the matrix projections terminate in a dense matrix of small boutons (Zikopoulosand Barbas 2007) –structural characteristics that are useful for anatomically differentiatingthe two pathways – these features were not included in the model.

When the profiles of the matrix and core connections (i.e. TC →{PY,IN} and PY→{TC,RE} connections) were identical (Fig. 5A, upper subpanel). the characteristics ofspindle activity were similar in both networks (Fig. 5A, lower subpanel). After beinginitiated in the core, the spindle propagated to the matrix by a latency of about 700 ms. Thedegree of synchrony in the two pathways during a spindle sequence was indistinguishable(Fig. 5A). Similarly, the termination of the sequence could not be qualitatively distinguishedbetween the core and matrix.

We next analyzed and quantified how the fanout of thalamocortical connections affected thedegree of synchrony during spindle generation within the core and matrix pathways. Whenthe fanout of the thalamocortical (TC →{PY;IN}) and corticothalamic (PY→{TC;RE})matrix connections significantly increased while maintaining constant focal coreconnectivity (Fig. 5B, upper subpanel), the cortical spindle activity appeared moresynchronous in the matrix compared to the spindle activity in the core (Fig. 5B, lower

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subpanel). As before, the spindles were initiated in the core and propagated to the matrixwith a delay. A striking difference between the degree of synchrony in the two networks wasobserved in such circumstances. Whereas the core network population activity wasqualitatively identical as in Fig. 5A, the matrix network population had a significantly higherdegree of synchrony, with nearly simultaneous cortical firing within the whole layer on eachburst cycle. These synchrony differences were quantified by the Schreiber measure (see textbelow).

Sample LFP traces from three different virtual recording sites of the matrix network weresimulated for both focal (Fig. 5C(a)) and diffuse fanouts (Fig. 5C(b)). The three virtual siteswere respectively located at the top, center, and bottom of the matrix layer, and equallyseparated from each other (cf. Fig. 5A, lower subpanel, horizontal arrows). In agreementwith the spatio-temporal plots, the three LFPs recorded from a single cortical layer wereincommensurate when the fanout was focal and topographically limited (Fig. 5C(a)).Conversely, the LFP traces were better phase-locked and showed very similar spindleduration when the cortical layer had a diffuse fanout (Fig. 5C(b)).

We quantified the degree of synchrony of the cortical LFPs using the Schreiber reliabilitymeasure R as a metric (Schreiber et al., 2003, see Methods). We varied the thalamocorticaland the corticothalamic fanouts of the matrix, while the connectivity profile of the coreremained focal and constant (cf. Fig. 1B–C, dashed lines). In so doing, we observed that thesynchrony value increased as a function of the fanout width of the thalamocorticalconnectivity in the matrix pathway. Indeed, synchronous activity in the superficial corticallayers became more prevalent as the fanout of the projections broadened (from the matrixpathway). The red (resp. blue) dots denote the degree of synchrony value for the matrix(resp. core) pathway with error bars for the standard deviation (n = 10 simulations). Whenboth the core and matrix footprints were focal and equal to 11 (i.e. each TC cell projected to11 PY cells), the two pathways had the same measure of synchrony (~0.21). As the matrixfootprint increased from 11 to 101, the degree of synchrony R for this pathway reached 0.34(ANOVA, F = 51, df = 19, p < 10−5) – a 62% increase compared to the initial value (Fig.5D, red dots). In contrast, the cortical core synchrony was unaffected by a change in thematrix fanout (Fig. 5D, blue dots).

Impact of feedforward versus feedback and probability of intercortical connectionsBoth feedforward thalamocortical and feedback corticothalamic projections may affect thedegree of synchrony observed in the core and matrix networks. To unravel the specific roleof each projection type, we performed simulations varying the fanout of one projection ofthe matrix while keeping the fanout of the other pathway focal (see Model, Fig. 2B–C, blackdashed lines). As before, the core network had constant focal connectivity for allsimulations. The diffuse feedforward thalamocortical connections of the matrix wereprimarily responsible for producing more synchronous spindles in the matrix cortical layersthan in the core and, accordingly, the degree of synchrony in the spindle activity wassignificantly higher in the matrix than in the core (Fig. 6A(i), ANOVA, F = 58, df = 19,p<10−6). In contrast, increasing only the footprint size of the feedback connections from thecortex to the thalamus in the matrix system did not significantly affect the synchrony ofspindle activity (Fig. 6A(ii), ANOVA, F = 1.42, df = 19, p > 0.1).

We also examined how the interconnectivity density between the core and matrix corticallayers affected the degree of synchrony (see Model, Fig. 2B–C, gray dashed lines). Wemaintained the footprint for cortical connections between layers the same as that ofconnections within a given cortical layer; however, each intercortical connection betweenthe matrix and core cortical layers was made with probability p within the footprint. Thedefault probability in previous simulations was p = 0.02. Varying the probability of

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connectivity from p = 0 to p = 0.5, we saw no significant influence on the degree ofsynchrony of the core and matrix pathways (Fig. 6B). That observation held whether thematrix footprint was focal (Fig. 6B(a)) or diffuse (Fig. 6B(b)), with the core footprintremaining constant (TC→PY = 11) throughout. From this, we can conclude that the onlymajor architectural parameter that significantly affected the synchrony measure was thespread of the feedforward thalamocortical footprint whereas neither the cortical feedbackprojections to the thalamus nor the corticocortical connectivity significantly impactedspindle synchrony.

Impact of the intrathamic connections on spindle synchronizationThough the core and matrix pathways have been clearly identified, the extent of reticulo-reticular connections between these two pathways yet remained unknown. In our initialmodel, we used with a limited connectivity profile between the core and matrix reticularnuclei. Here, we wanted to assess the impact of a progressive overlap between the tworeticular layers on the spindle synchrony. We found that, as the degree of RE-RE overlapincreased up to 50 cells per layer, so did the synchrony degree for both core and matrixpathways (Fig. 6C).

We also tested the hypothesis of a lesion at the reticular level, thereby isolating core andmatrix reticular nuclei from each other. In this case we found that, though the spindle werestill initiated and sustained in the core, the thalamic lesion prevented the matrix from beingrecruited in the spindle oscillatory activity. A progressive increase in the density of inter-cortical connections did not succeed in recruiting the matrix, confirming that reticularneurons – which can be recruited by cortical cells – are critical in the initiation of spindleoscillation.

Latency and duration of spindles in the core and matrix systemsFinally, we addressed the impact of corticocortical connectivity on the latency of spindleinitiation between the core and the matrix, as well as the duration of spindle sequences inboth networks. To ensure similar initial states for different simulations, the initial spindlewas always initiated by external stimulation to the core.

Surprisingly, the breadth of connections in the core and matrix did not reliably affect thelatency of spindle initiation between these two thalamocortical pathways, as shown by theabsence of significant difference in the spindle latency when the fanout diffusiveness in thematrix was varied under fixed intercortical connectivity probability (Fig. 7A, p = 0.02).However, the degree of interconnection alone between the core and matrix greatly impactedthe spindle latency between these pathways (Fig. 7B). As the probability p of intercorticalconnections increased, the propagation delay between the two pathways decreased underfixed thalamocortical footprints (Fig. 7B). For example, the spindle initiation latency was817 ms for a low cortical interconnection probability (p = 0.02) but decreased to 150 ms forhigher probability values (p = 0.3) under constant thalamocortical footprints, as illustratedby membrane potential traces in Figs. 7C(a) and 7C(b), respectively.

The duration of spindle sequences in the core and matrix was quantitatively comparablewhen the footprints in both networks were equal and focal (Fig. 8A). But increasing thecorticocortical probability between the two pathways slightly increased the spindle durationfrom an average of 2.9 seconds in both networks for p = 0.02 to 3.3 (resp. 3.6) seconds inthe core (resp. matrix) for p = 0.5 (Fig. 8A).

The same assessment for the influence of interconnection probability on spindle durationwas performed under a more diffuse footprint for the matrix pathway (TC→PY = 83), whilethe core remained constant and focal (TC→PY = 11). Under these different conditions, we

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similarly found no statistically significant differences in the average spindle sequenceduration between the two thalamocortical pathways (2.9 s for p = 0.02; 3.2 s (core) and 3.9 s(matrix) for p = 0.5, n.s., see Fig. 8B).

Taken together, these results indicate that, on the one hand, the breadth of connections(matrix fanout) neither statistically influence the average spindle latency between core andmatrix nor the average spindle sequence duration – at odds with its role in spindlesynchronization as shown earlier and in line with the literature (Contreras et al., 1996; 1997;Destexhe et al., 1998). On the other hand, though the cortical interconnection probabilityplayed no significant role in spindle synchrony, it was, however, the key factor to constrainspindle initiation latency between core and matrix.

DISCUSSIONThis study was motivated by recent findings that human spindles simultaneously recordedby EEG and MEG sensors have strikingly different characteristics (Dehghani et al.,2010a,b,c). Here, we have explored a mechanism to explain the spatiotemporal propertiesand synchronization differences found in human spindle oscillations. Implementing acomputational model incorporating the known anatomical properties of two separatethalamocortical networks (“core” and “matrix”) found in non-human primates (Jones, 2001),we have shown that the difference between core and matrix pathways in the fanout ofthalamocortical projections best explains the discrepancies in spindle synchronizationbetween scalp EEG and MEG recordings.

Specifically, we have shown that while the spindle activity was initiated in the corepathway, the matrix pathway contributed to the widespread spindle synchronization acrossthe network. Surprisingly, we found that the spread of corticothalamic connections, unlikethalamocortical ones, had little significance on spindle coherence. Finally, we found that thelatency of spindle propagation between the core and the matrix pathways was constrained bythe probability of corticocortical connections between the two systems.

Synchrony divergence between EEG and MEGIn simultaneous EEG/MEG recordings, spindle activity was sometimes detected in one ofthe modalities only (Hughes et al., 1976; Manshanden et al., 2002; Nakasato et al., 1990;Yoshida et al., 1996, Dehghani et al., 2010b). Recently, Dehghani et al. (2010) reported thatthe MEG signal was asynchronous and varied strongly in amplitude and phase acrosslocations and across spindles, unlike the simultaneously recorded EEG signal, which wasspatially and temporally highly coherent across the scalp and across spindles. Overall, theaverage coherence between pairs of MEG gradiometers was only ~0.3 during spindles, incontrast to the coherence value of ~0.7 for EEG sensor pairs. Moreover, many spindleepochs were visible in MEG but not in EEG (Dehghani et al., 2010). When they did appearin both modalities, the MEG spindle led the EEG spindle by about 190 ms on average(Dehghani et al., 2010).

The variability of spindles across MEG sensors may reflect multiple, partially independentcortical generators, whereas EEG recordings may instead be dominated by a weak butwidespread unique spindle generator. These empirical observations led to the hypothesis thatMEG and EEG primarily record spindles from different thalamocortical pathways,specifically the core and matrix pathways, respectively. This interpretation suggests thatspindles occur first in the core pathway, and then quickly spread to the matrix pathway,which contributes to the widespread synchronization of spindles across the cortical network– interpretation that was observed and confirmed in the present study.

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The volume conduction effects that smear EEG signals, relative to MEG signals, mayexplain the differences in global versus focal coherence during spindle activity. In otherwords, the lead fields associated with EEG are smoother and more distributed than those ofMEG. As a consequence, focal synchrony will appear to be more globally coherent oversensors. However, this is not a sufficient explanation for the synchrony differences betweenEEG and MEG because 1) intracranial recordings acquired at the same time as non-invasiveelectromagnetic measures suggest that EEG and MEG signals are generated in differentcortical layers. It is this fact that motivates the current study, in which we propose that bothlocal and global synchrony could co-exist and that EEG is selectively sensitive to globalsynchrony, and 2) the existence of the relatively large phase delays between MEG electrodesin vivo that commonly exceed the period of spindle oscillations (see, e.g., Fig. 3) suggeststhat the averaging of the MEG signal over the larger volume would only lead to the loss ofperiodicity.

Core mediates multiple focal generators while matrix mediates large-scale synchronyPrevious models of spindle oscillations did not consider the differences between core andmatrix thalamocortical pathways. Our model is the first to incorporate these twothalamocortical networks and to investigate the impact of their topological differences onspindle activity. Specifically, our model captures the distinct thalamocortical projectionsbetween the core and the matrix pathways found in non-human primates (Jones, 2001).Relay cells from the core project to a highly restricted target domain, typically terminatingwith large boutons in layer IV, which transmit focal sensory information via ionotropicreceptors (Zikopoulos and Barbas, 2007). In contrast, relay cells from the matrix projectvery diffusely, often to multiple cortical areas and terminate in a dense matrix of smallboutons in layer I, associated with the slow modulatory NMDA and metabotropictransmission (Rubio-Garrido et al., 2009).

Although some of the differences in glutamate receptors and synaptic morphology betweenmatrix and core were not included in the model, its architecture critically incorporated theessential differences between the focal thalamocortical connections in the core and the morediffuse and widespread connectivity of the matrix. This difference of thalamocortical fanoutwas in itself sufficient to explain the synchrony mismatch between the core and matrixpathways.

Our results can explain the discrepancies outlined above between EEG and MEG recordings.The cortical anatomy combined with the biophysics of signal propagation (i.e. the so-called‘forward solution’) predicts MEG sensors to be more sensitive to focal activity and EEGsensors to distributed sources (Dehghani et al., 2010c). Using models incorporating thesubcranial cerebrospinal fluid, the calculated leadfields – that is, the cortical areas projectingto each sensor – were about 25 times larger for referential EEG sensors than for MEGgradiometers (Irimia et al., personal communication). Furthermore, when a distributedcurrent generator was active, less than 30% of the referential EEG signal was cancelledunlike up to 90% for the MEG gradiometer. We can conclude that the EEG is therefore morebiased toward diffusely synchronous spindle generators – as produced by the cortical matrixpathway – whereas the MEG is more likely to pick up the activity from focal asynchronousspindle generators – as produced by the cortical core pathway.

Asynchronous activation of various core thalamocortical domains may be visible in thevarying location, frequency, and synchrony of MEG spindles. The local generation ofspindles could be found in many cortical locations including ventrolateral frontal andtemporal areas, such as in the left middle frontal gyrus, left inferior frontal sulcus, leftmiddle temporal gyrus, left cingulate sulcus, right inferior frontal gyrus, right superiorfrontal gyrus, right precentral sulcus, and right middle temporal gyrus (Tuan et al., 2010).

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Synchronization of focal thalamocortical domains by the matrix pathway into coherentdischarge may be visible in EEG spindles (Dehghani et al., 2010b,c). We gained additionalinsight as to the differential role of the two thalamocortical networks via laminar recordingsduring spindle oscillations. Current source density (CSD) analysis of multielectrode depthrecordings during spindles obtained in 5 subjects recorded during natural stage 2 sleepsuggested that spindle generation involved multiple systems. CSD profiles showed twopatterns of laminar spindle activity (Tuan et al., 2010). The first pattern was generated bywidely separated source/sink current pairs in deep and superficial layers and the secondpattern was generated by adjacent source/sink pairs in the middle layers. The first pattern ofspindle activity, consistent with an input from the matrix cells in the thalamus, had lowspatial coherence whereas the second, consistent with input from the core thalamocorticalprojections, had high spatial coherence (Cash S. and Halgren E., unpublished observations).From this we can draw a conclusion on the different roles for the matrix and the corethalamocortical pathways.

Interactions between the core and matrix networksIn our model, spindle activity, which initiated in the core, was transmitted to the matrix witha delay that was inversely proportional to the density of corticocortical connections betweenthe two networks. This transfer of spontaneous activity from the core to the matrix couldlead to the large-scale synchronization of multiple, focal, scattered spindle generators. It wasshown recently that sleep spindles are predominantly local and occur separately in specificregions, mostly confined to local circuits (Nir et al., 2011; see also Fig. 3D). Our results, inline with this study, suggest that the local, distributed core pathways underlie local spindles,whereas global spindle activity is a result of the synchronization by the matrix pathway.

The delay in the spread of activity from one system to another explains the loose linkagebetween MEG and EEG spindles observed experimentally. Our model shows thatintercortical connectivity between the matrix and core can tune the value of this delay. Thepropagation latency in the model that best matched the experimental results (MEG leadsEEG by ~190 ms, cf. Dehghani et al., 2010d) was obtained with an intercortical connectionprobability between the core and the matrix of about ~0.25.

In our study, although the involvement of the thalamocortical circuitry was required forsynchronization, varying the range of corticothalamic feedback did not significantlyinfluence the synchrony when the fanout of feedforward (thalamocortical) connections wassmall. This predicts that in the brain only the fanout of the feedforward thalamocortical andnot the corticothalamic feedback affects spindle synchronization. One possible explanationis that corticothalamic feedback onto the population of inhibitory reticular thalamic neuronsreduces the synchronizing effects of corticothalamic input through lateral inhibitoryinteractions among the reticular thalamic neurons.

The modeling results support a mechanism whereby the spread of spindle discharges fromthe core to matrix occurs by intercortical coupling, as well as through thalamocortical loops,but without the involvement of interthalamic synchronizing mechanisms. In the model, thecorticocortical connectivity had little impact on the spindle coherence within core andmatrix, in agreement with Contreras et al. (1996). In contrast, the probability ofcorticocortical connections between these two pathways did influence the latency andduration of spindle sequences.

The ultimate test of our hypothesis would be a selective inactivation of neurons in thethalamus where the cells in the matrix and core systems are somewhat segregated. Ourmodel predicts that the core cells would engage in spindles rather independently of eachother and with spotty cortical synchronization, whereas the matrix cells would tend to

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engage synchronously in spindles, synchronously with each other and across the corticalareas. Therefore, inactivation of the core (resp. matrix) thalamic populations should decrease(resp. increase) the appearance of spindles in deep vs. superficial cortical layers and affectthe overall level of spindle synchronization. The techniques for such manipulations currentlybecome available (e.g., optogenetic stimulation), however these experiments are onlyfeasible in rodents and we currently have no data to evaluate the spatiotemporal propertiesof spindles across cortical layers in such settings. The other prediction is that the corepattern spindles with current sinks and sources concentrated in middle cortical layers wouldtend to be focal and asynchronous whereas the matrix, generated in superficial corticallayers, would tend to be synchronous and widespread. In other words, the prediction is thatthere would be a correlation between the cortical layer generating the spindle and the degreeof synchrony it exhibits with other cortical areas. These recordings are possible in humansusing depth electrodes and could provide a valuable test of our model.

ConclusionThe thalamocortical model herein described explains the empirical results fromsimultaneous EEG and MEG recordings and supports the working hypothesis that moresynchronous, spatially coherent spindle activity is generated in the matrix pathway due tothe broad and widespread thalamocortical projections pertaining to this network. In contrast,spindle activities in the core pathway are less spatially coherent because the thalamicprojections are more focal. Surprisingly, the corticothalamic feedback projections areineffective in supporting greater spindle synchrony. Although core spindles are largelyindependent across the cortical surface, functionally related cortical columns may besynchronized by the matrix even if they are not adjacent. Synchronization between distantcolumns arises mainly because the thalamocortical feedforward projections of the matrixpathway are widespread. This study reconciles the discrepancies observed in simultaneousMEG/EEG recordings of human spindle and proposes a principle mechanism based onanatomical observations from the primate. This sheds new light onto the differentmechanisms of thalamocortical and corticothalamic projections underlying local and globalspindles.

AcknowledgmentsThis study was supported by the National Institutes of Health, NIH-NIBIB (Grant 1R01EB009282-01, to T.S.,E.H., M.Ba., and M.Bo.), the Crick-Jacobs Center for Theoretical Neurobiology and the Swartz Foundation (T.B.),the Howard Hughes Medical Institute, Salk Institute for Biological Studies (T.S. and M.Bo.), Jolla, CA, USA andDivision of Biological Sciences, UCSD, La Jolla, CA, USA (T.S. and M. Bo.), NIH-NINDS (Grant1R01NS060870-01 to M.Ba.).

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Figure 1. Model topology(A) The thalamocortical system with the distribution of matrix cells (red) and core cells(blue) indicated in a frontal section through the middle of a macaque monkey thalamus. Thecore thalamic projections are topographically ordered to the middle layers of a singlecortical field. The matrix thalamic projections collectively project diffusely to the superficiallayers of dispersed cortical fields. Modified from Jones (2001).(Abbreviations: CL, central lateral nucleus; CM, centre médian nucleus; HI, lateralhabenular nuclei; Hm, medial habenular nuclei; LD, lateral dorsal nucleus; LGN, lateralgeniculate nucleus; LP, lateral posterior nucleus; MD, mediodorsal nucleus; OT, optic tract;P, color-code retinal ganglion cells; Pla, anterior pulvinar nucleus; PP, peripeduncularnucleus; R, reticular nucleus; s, s laminae; SNr, substantia nigra, pars reticulata; VMb, basalventral medial nucleus; VPI, ventral posterior inferior nucleus; VPM, ventral posteriormedial nucleus.(B) Schematic diagram showing the topology of the thalamocortical computational model,where both the matrix and core systems are depicted. The network connectivity shows theprojections between the thalamus and the cortex (bottom and top, respectively) and betweenthe core and matrix networks (left and right sides, respectively). Excitatory (inhibitory)connections are indicated by solid (empty) circles at the end of a directed path (representedby the arrows). The black dotted lines indicate the projections in the matrix network whosefanout is a variable parameter for the purpose of this study. The gray dotted lines indicatethe corticocortical connections between the matrix and core systems whose connectivityfanout is fixed at 5 but whose probability p of each connection existing varied from 0 to50% (default value of 2%).(C) Schematic connectivity showing the structure of the core and matrix thalamocorticalnetworks distributed into four interconnected layers. Each cell is represented by a dot and

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the area to which it projects is depicted as a shaded area for a representative cell.Intrathalamic connections were topographic with a divergence (fanout) of 4 cells. For theseconnections only, the cells at the boundary between the thalamic core and matrix networksare neighboring cells (indicated by the gray arrows.) Thalamocortical and corticothalamicprojections in the matrix pathway (black dashed lines) were made more expansive than inthe core pathway. The fanout values for all connections are summarized in Table 1.Connections between the core and matrix PY layers (gray dashed lines) are topographic witha fanout of 5 with a low probability (2% for simulations in which this value was not varied.)

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Figure 2. Local field potential (LFP)Schematic of the contribution of pyramidal neuron j to the local field potential calculated atlocation i. Arrows indicate the flow of current through ionic channels, the axial current,Iaxial, between the dendritic (cylindrical) and somatic (spherical) compartments, and theresulting dipole current in the extracellular space (dashed lines.) The distances from thedendritic and somatic compartments to the location of the LFP calculation point i are rd andrs, respectively.

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Figure 3. Spindle recordings with EEG versus MEG sensors(A) Referential EEG waveforms from 60 scalp channels during a single spindle(superimposed) in healthy subjects (n = xx) during natural sleep (1) and shown with voltagecolor coded (2). EEG appears highly synchronous across the scalp.(B) MEG spindle recorded by 204 gradiometers at the same time as (A) in the same healthyhuman subjects. MEG appears highly variable and asynchronous across the scalp. The EEGpeaks, marked with vertical lines, show no regular relationship with MEG peak activity. Thearrows mark the peaks of a particular MEG channel that initially precedes and later followsthe EEG peaks.(C) Superposition of two of the largest amplitude EEG and MEG waveforms during a singlespindle (1) further shows that EEG and MEG have variable relationships during spindles.The instantaneous phase lag, found via the Hilbert transform, varies considerably (2)Modified from Dehghani et al. (2010a).(D) Spindles generated simultaneously in multiple regions of the cortex show variable phaserelationships and relative amplitudes. In each of the five spindles recorded in patientsunderlying pre-surgical epileptic mapping, six depth sites with locally generated spindles(colored traces) and one scalp site (Fz, black trace) are superimposed. Different corticalgenerators are relatively larger in different spindles or portions of spindles (coloredasterisks). Local generation was assured by choosing transcortical bipolar depth recordings(e.g. with one lead in white matter and one in CSF), with spindles that were larger andpolarity inverted from adjacent leads.(E) Participation by different cortical areas varies across spindles. Power from 7 to 14 Hzwas calculated for moving 0.5s epochs, and each channel was normalized to its peak

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amplitude in the 60s epoch. Although most but not necessarily all cortical locationsparticipate in the larger spindles (^), the relative amplitudes of different locations variesacross spindles (*), and there are times where spindles are being generated in many corticallocations in both hemispheres but are not recorded at the scalp (v). Plastic screw guides wereused so the scalp EEG remained insulated from the brain by the skull, as in controls.

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Figure 4. Canonical spindles(A) Top: Local field potentials (LFP) in the cortical domains of the core and matrixnetworks during a 10-second simulation of spindle activity. Bottom: Voltage traces ofindividual neurons (cortical pyramidal [PY], thalamocortical [TC], and reticular [RE]) ineach layer of core and matrix networks (blue and red traces, respectively). The time ofspindle initiation in the core system is indicated by the vertical arrows.(B) Space-time plot representing the activity of the whole model for 10 seconds, showingthe pattern of wave propagation within core and matrix networks. Individual membranepotential activity from (A) corresponds to the cell in the middle of each respective layer (cell#50 of PY, TC, and RE) of (B). The value of the membrane potential for each neuron iscoded by the false color scale. The time of spindle initiation in the core network is indicatedby the arrows. (Results are shown for the case with matrix TC→PY fanout = 40 while thecore TC→PY fanout is 5).

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Figure 5. Spindle synchronization measure(A) Top: Schematic diagram illustrating the connection profile used for the core and matrixnetworks. Situation of equal and focal fanout for both pathways. Lower: Space-time plots ofcortical core and matrix pathways using the connection profile in (A, top) during a 7-secondsimulation of spindle activity.(B) Top: Schematic diagram illustrating the connection profile used for the core and matrixnetworks. Situation of focal fanout for the core pathway only. The matrix fanout is nowdiffuse. Lower: Space-time plots of cortical core and matrix pathways using the connectionprofile in (A, top) during a 7-second simulation of spindle activity.(C) LFP traces for cortical neurons in the matrix pathway under the connectivity profilesused in (A) and (B). The three virtual recording sites are indicated by the horizontal arrowsin the panels above.(D) Quantification of the degree of synchrony of cortical activity in both core (blue dots)and matrix (red dots) as a function of different thalamocortical and corticothalamicfootprints in the matrix pathway (footprints in the core are kept identical). (Each dotrepresents the average of 10 simulations ± standard deviation. Letters (a) and (b) correspondto the LFPs represented in (C(a)) and (C(d)), respectively).

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Figure 6. Roles of increased connectivity between different neuronal populations in cortico-cortical synchrony of spindle discharges(A) Impact of feedforward versus feedback footprints in the matrix pathway. (a) Evolutionof the degree of synchrony R as a function of the feedforward thalamocortical connections.(b) Evolution of the degree of synchrony R as a function of the feedback thalamocorticalconnections. (Core connections remained focal for both panels).(B) Impact of the probability of corticocortical connections between core and matrixnetworks. (a) Both core and matrix networks have an equal focal fanout. (b) Core fanout wasfocal whereas matrix fanout was more diffuse.(C) Impact of the overlap between the two reticular layers (core and matrix) on the spindlesynchrony.

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Figure 7. Connectivity factors affecting the delay from spindle onset in the core versus matrixsystems(A) Latency of spindle propagation between core and matrix networks as a function of thematrix thalamocortical fanout (core fanout kept constant).(B) Latency of spindle propagation between core and matrix networks as a function of theprobability p of corticocortical connections between the two networks (core and matrixfanout kept constant).(C) Example of individual voltage traces for pyramidal cells in the core and matrix pathwayillustrating the latency of spindle propagation between the two pathways. (a) For p = 0.02(cf. vertical arrow (a) in (B)). (b) For p = 0.3 (cf. vertical arrow (b) in (B)).

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Figure 8. Spindle Duration as a function of connectivity between and within systemsAverage spindle duration of a spindle sequence in both core (blue dots) and matrix (red dots)networks. (Each dot represents mean value ± standard deviation.)(A) With both core and matrix fanouts equal and focal.(B) With focal core fanout and diffuse matrix fanout.

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Tabl

e 1

Con

nect

ivity

pro

pert

ies.

Top

row

s: F

anou

ts u

sed

for

conn

ectio

ns in

the

mat

rix

and

core

thal

amoc

ortic

al n

etw

ork

mod

el. M

ultip

le n

umbe

rs w

ithin

a s

ingl

ece

ll re

pres

ent p

aram

eter

cha

nges

with

incr

ease

d fa

nout

. Bot

tom

row

: syn

aptic

cur

rent

s of

net

wor

k co

nnec

tivity

.

PY→

TC

PY→

RE

TC→

PY

TC→

INP

Y→

PY

PY→

ININ

→P

YR

E→

RE

TC→

RE

RE→

TC

Mat

rix

path

way

fan

out

5, 9

, 13,

17,2

1,25

5, 9

, 13,

17,2

1,25

5,14

,23,

32,

41,5

01,

3, 5

, 7, 9

, 11

51

54

44

Cor

e pa

thw

ay f

anou

t5

55

15

15

44

4

Syna

ptic

cur

rent

AM

PAA

MPA

AM

PAA

MPA

AM

PA, N

MD

AA

MPA

, NM

DA

GA

BA

AG

AB

AA

AM

PAG

AB

AA

, GA

BA

B


interactions between core and matrix thalamocortical projections in human sleep spindle...

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