A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

Heterogeneous firing rate response of mouse layer V pyramidal neurons in the fluctuation-driven regime

KEY POINTS

We recreated in vitro the fluctuation-driven regime observed at the soma during asynchronous network activity in vivo and we studied the firing rate response as a function of the properties of the membrane potential fluctuations. We provide a simple analytical template that captures the firing response of both pyramidal neurons and various theoretical models. We found a strong heterogeneity in the firing rate response of layer V pyramidal neurons: in particular, individual neurons differ not only in their mean excitability level, but also in their sensitivity to fluctuations. Theoretical modelling suggest that this observed heterogeneity might arise from various expression levels of the following biophysical properties: sodium inactivation, density of sodium channels and spike frequency adaptation.

ABSTRACT

Characterizing the input-output properties of neocortical neurons is of crucial importance for understanding the properties emerging at the network level. In the regime of low-rate irregular firing (such as in the awake state), determining those properties for neocortical cells remains, however, both experimentally and theoretically challenging. Here, we studied this problem using a combination of theoretical modelling and in vitro experiments. We first identified, theoretically, three somatic variables that describe the dynamical state at the soma in this fluctuation-driven regime: the mean, standard deviation and time constant of the membrane potential fluctuations. Next, we characterized the firing rate response of individual layer V pyramidal cells in this three-dimensional space by means of perforated-patch recordings and dynamic clamp in the visual cortex of juvenile mice in vitro. We found that individual neurons strongly differ not only in terms of their excitability, but also, and unexpectedly, in their sensitivities to fluctuations. Finally, using theoretical modelling, we attempted to reproduce these results. The model predicts that heterogeneous levels of biophysical properties such as sodium inactivation, sharpness of sodium activation and spike frequency adaptation account for the observed diversity of firing rate responses. Because the firing rate response will determine population rate dynamics during asynchronous neocortical activity, our results show that cortical populations are functionally strongly inhomogeneous in young mouse visual cortex, which should have important consequences on the strategies of cortical computation at early stages of sensory processing.

Application of active electrode compensation to perform continuous voltage-clamp recordings with sharp microelectrodes

OBJECTIVE

Electrophysiological recordings of single neurons in brain tissues are very common in neuroscience. Glass microelectrodes filled with an electrolyte are used to impale the cell membrane in order to record the membrane potential or to inject current. Their high resistance induces a high voltage drop when passing current and it is essential to correct the voltage measurements. In particular, for voltage clamping, the traditional alternatives are two-electrode voltage-clamp technique or discontinuous single electrode voltage-clamp (dSEVC). Nevertheless, it is generally difficult to impale two electrodes in a same neuron and the switching frequency is limited to low frequencies in the case of dSEVC. We present a novel fully computer-implemented alternative to perform continuous voltage-clamp recordings with a single sharp-electrode.

APPROACH

To reach such voltage-clamp recordings, we combine an active electrode compensation algorithm (AEC) with a digital controller (AECVC).

MAIN RESULTS

We applied two types of control-systems: a linear controller (proportional plus integrative controller) and a model-based controller (optimal control). We compared the performance of the two methods to dSEVC using a dynamic model cell and experiments in brain slices.

SIGNIFICANCE

The AECVC method provides an entirely digital method to perform continuous recording and smooth switching between voltage-clamp, current clamp or dynamic-clamp configurations without introducing artifacts.

Prediction of spatiotemporal patterns of neural activity from pairwise correlations

We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and temporal pairwise correlations among neurons. This model is tested on data generated with a Glauber spin-glass system and is shown to correctly predict the occurrence probabilities of spatiotemporal patterns significantly better than Ising models only based on spatial correlations. This increase of predictability was also observed on experimental data recorded in parietal cortex during slow-wave sleep. This approach can also be used to generate surrogates that reproduce the spatial and temporal correlations of a given data set.

Does the 1/f frequency scaling of brain signals reflect self-organized critical states?

Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states in neuronal activity. By analyzing simultaneous recordings of global and neuronal activities, we confirm the 1/f scaling of global variables for selected frequency bands, but show that neuronal activity is not consistent with critical states. We propose a model of 1/f scaling which does not rely on critical states, and which is testable experimentally.

Model of low-pass filtering of local field potentials in brain tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances (approximately 10 microm) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e., at length scales in the order of average interneuronal distances. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarization. Because of the finite velocity of ionic charge movements, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that this situation is analogous to an equivalent RC circuit, or better yet a system of coupled RC circuits. We present a number of numerical simulations of an induced electric field for biologically realistic values of parameters, and show the frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons are the physical origin of frequency filtering properties of LFPs. Experimentally testable predictions are provided allowing us to verify the validity of this model.

An Extended Analytic Expression for the Membrane Potential Distribution of Conductance-Based Synaptic Noise

Synaptically generated subthreshold membrane potential (Vm) fluctuations can be characterized within the framework of stochastic calculus. It is possible to obtain analytic expressions for the steady-state Vm distribution, even in the case of conductance-based synaptic currents. However, as we show here, the analytic expressions obtained may substantially deviate from numerical solutions if the stochastic membrane equations are solved exclusively based on expectation values of differentials of the stochastic variables, hence neglecting the spectral properties of the underlying stochastic processes. We suggest a simple solution that corrects these deviations, leading to extended analytic expressions of the Vm distribution valid for a parameter regime that covers several orders of magnitude around physiologically realistic values. These extended expressions should enable finer characterization of the stochasticity of synaptic currents by analyzing experimentally recorded Vm distributions and may be applicable to other classes of stochastic processes as well.

Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes

Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the sub-threshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by Ornstein-Uhlenbeck processes. We derive and solve the Fokker-Planck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in Hodgkin-Huxley-type models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high-conductance states similar to in vivo conditions. Because the steady-state membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conduct ancesinreal neurons.

Interactions between membrane conductances underlying thalamocortical slow-wave oscillations

Neurons of the central nervous system display a broad spectrum of intrinsic electrophysiological properties that are absent in the traditional "integrate-and-fire" model. A network of neurons with these properties interacting through synaptic receptors with many time scales can produce complex patterns of activity that cannot be intuitively predicted. Computational methods, tightly linked to experimental data, provide insights into the dynamics of neural networks. We review this approach for the case of bursting neurons of the thalamus, with a focus on thalamic and thalamocortical slow-wave oscillations. At the single-cell level, intrinsic bursting or oscillations can be explained by interactions between calcium- and voltage-dependent channels. At the network level, the genesis of oscillations, their initiation, propagation, termination, and large-scale synchrony can be explained by interactions between neurons with a variety of intrinsic cellular properties through different types of synaptic receptors. These interactions can be altered by neuromodulators, which can dramatically shift the large-scale behavior of the network, and can also be disrupted in many ways, resulting in pathological patterns of activity, such as seizures. We suggest a coherent framework that accounts for a large body of experimental data at the ion-channel, single-cell, and network levels. This framework suggests physiological roles for the highly synchronized oscillations of slow-wave sleep.

The discharge variability of neocortical neurons during high-conductance states

In vivo recordings have shown that the discharge of cortical neurons is often highly variable and can have statistics similar to a Poisson process with a coefficient of variation around unity. To investigate the determinants of this high variability, we analyzed the spontaneous discharge of Hodgkin-Huxley type models of cortical neurons, in which in vivo-like synaptic background activity was modeled by random release events at excitatory and inhibitory synapses. By using compartmental models with active dendrites, or single compartment models with fluctuating conductances and fluctuating currents, we found that a high discharge variability was always paralleled with a high-conductance state, while some active and passive cellular properties had only a minor impact. Furthermore, a balance between excitation and inhibition was not a necessary condition for high discharge variability. We conclude that the fluctuating high-conductance state caused by the ongoing activity in the cortical network in vivo may be viewed as a natural determinant of the highly variable discharges of these neurons.

Variability of quantal synaptic currents in thalamocortical neurons

Broad amplitude variability and skewed distributions are characteristic features of quantal synaptic currents (minis) at central synapses. The relative contributions of the various underlying sources are still debated. Through computational models of thalamocortical neurons, we separated intra- from extra-synaptic sources. Our simulations indicate that the external factors of local input resistance and dendritic filtering generate equally small amounts of negatively skewed synaptic variability. The ability of these two factors to reduce positive skew increased as their contribution to variability increased, which in control trials for morphological, biophysical, and experimental parameters never exceeded 10% of the range. With these dendritic factors ruled out, we tested multiple release models, which led to distributions with clearly non-physiological multiple peaks. We conclude that intra-synaptic organization is the primary determinant of synaptic variability in thalamocortical neurons and, due to extra-synaptic mechanisms, is more potent than the data suggested. Thalamortical neurons, especially in rodents, constitute a remarkably favorable system for molecular genetic studies of synaptic variability and its functional consequence.

Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity

In vivo, in vitro and computational studies were used to investigate the impact of the synaptic background activity observed in neocortical neurons in vivo. We simulated background activity in vitro using two stochastic Ornstein-Uhlenbeck processes describing glutamatergic and GABAergic synaptic conductances, which were injected into a cell in real time using the dynamic clamp technique. With parameters chosen to mimic in vivo conditions, layer 5 rat prefrontal cortex cells recorded in vitro were depolarized by about 15 mV, their membrane fluctuated with a S.D. of about 4 mV, their input resistances decreased five-fold, their spontaneous firing had a high coefficient of variation and an average firing rate of about 5-10 Hz. Brief changes in the variance of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic conductance fluctuations induced time-locked spiking without significantly changing the average membrane potential of the cell. These transients mimicked increases in the correlation of excitatory inputs. Background activity was highly effective in modulating the firing-rate/current curve of the cell: the variance of the simulated gamma-aminobutyric acid (GABA) and AMPA conductances individually set the input/output gain, the mean excitatory and inhibitory conductances set the working point, and the mean inhibitory conductance controlled the input resistance. An average ratio of inhibitory to excitatory mean conductances close to 4 was optimal in generating membrane potential fluctuations with high coefficients of variation. We conclude that background synaptic activity can dynamically modulate the input/output properties of individual neocortical neurons in vivo.

Do neocortical pyramidal neurons display stochastic resonance?

Neocortical pyramidal neurons in vivo are subject to an intense synaptic background activity that has a significant impact on various electrophysiological properties and dendritic integration. Using detailed biophysical models of a morphologically reconstructed neocortical pyramidal neuron, in which synaptic background activity was simulated according to recent measurements in cat parietal cortex in vivo, we show that the responsiveness of the cell to additional periodic subthreshold stimuli can be significantly enhanced through mechanisms similar to stochastic resonance. We compare several paradigms leading to stochastic resonance-like behavior, such as varying the strength or the correlation in the background activity. A new type of resonance-like behavior was obtained when the correlation was varied, in which case the responsiveness is sensitive to the statistics rather than the strength of the noise. We suggest that this type of resonance may be relevant to information processing in the cerebral cortex.

Correlation detection and resonance in neural systems with distributed noise sources

We investigated the resonance behavior in model neurons receiving a large number of random synaptic inputs, whose distributed nature permits one to introduce correlations between them and investigate its effect on cellular responsiveness. A change in the strength of this background led to enhanced responsiveness, consistent with stochastic resonance. Altering the correlation revealed a type of resonance behavior in which the neuron is sensitive to statistical properties rather than the strength of the noise. Remarkably, the neuron could detect weak correlations among the distributed inputs within millisecond time scales.

Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons

To investigate the basis of the fluctuating activity present in neocortical neurons in vivo, we have combined computational models with whole-cell recordings using the dynamic-clamp technique. A simplified 'point-conductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic random-walk processes. An advantage of this approach is that all the model parameters can be determined from voltage-clamp experiments. We show that the point-conductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivo-like activity, we injected this point-conductance model into a single-compartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of high-amplitude membrane potential fluctuations, a low-input resistance and irregular spontaneous firing activity. In addition, the point-conductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and GABAergic conductances varying stochastically.

Why do we sleep?

Slow-wave sleep consists in slowly recurring waves that are associated with a large-scale spatio-temporal synchrony across neocortex. These slow-wave complexes alternate with brief episodes of fast oscillations, similar to the sustained fast oscillations that occur during the wake state. We propose that alternating fast and slow waves consolidate information acquired previously during wakefulness. Slow-wave sleep would thus begin with spindle oscillations that open molecular gates to plasticity, then proceed by iteratively 'recalling' and 'storing' information primed in neural assemblies. This scenario provides a biophysical mechanism consistent with the growing evidence that sleep serves to consolidate memories.

Nonlinear thermodynamic models of voltage-dependent currents

Hodgkin and Huxley provided the first quantitative description of voltage-dependent currents and adjusted their model to experimental data using empirical functions of voltage. A physically plausible formalism was proposed later by assuming that transition rates depend exponentially on a free-energy barrier, by analogy with the theory of reaction rates. It was also assumed that the free energy depends linearly on voltage. This thermodynamic formalism can accurately describe many processes, but the resulting time constants can be arbitrarily fast, which may also lead to aberrant behavior. We considered here a physically plausible solution to this problem by including nonlinear effects of the electrical field on the free energy. We show that including effects such as mechanical constraints, inherent to the structure of the ion channel protein, leads to more accurate thermodynamic models. These models can account for voltage-dependent transitions that are rate-limited in a given voltage range, without invoking additional states. We illustrate their applicability to fit experimental data by considering the case of the T-type calcium current in thalamic neurons.

Cortical feedback controls the frequency and synchrony of oscillations in the visual thalamus

Thalamic circuits have an intrinsic capacity to generate state-dependent oscillations of different frequency and degrees of synchrony, but little is known of how synchronized oscillation is controlled in the intact brain or what function it may serve. The influence of cortical feedback was examined using slice preparations of the visual thalamus and computational models. Cortical feedback was mimicked by stimulating corticothalamic axons, triggered by the activity of relay neurons. This artificially coupled network had the capacity to self-organize and to generate qualitatively different rhythmical activities according to the strength of corticothalamic feedback stimuli. Weak feedback (one to three shocks at 100-150 Hz) phase-locked the spontaneous spindle oscillations (6-10 Hz) in geniculate and perigeniculate nuclei. However, strong feedback (four to eight shocks at 100-150 Hz) led to a more synchronized oscillation, slower in frequency (2-4 Hz) and dependent on GABA(B) receptors. This increase in synchrony was essentially attributable to a redistribution of the timing of action potential generation in lateral geniculate nucleus cells, resulting in an increased output of relay cells toward the cortex. Corticothalamic feedback is thus capable of inducing highly synchronous slow oscillations in physiologically intact thalamic circuits. This modulation may have implications for a better understanding of the descending control of thalamic nuclei by the cortex, and the genesis of pathological rhythmical activity, such as absence seizures.

Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons

Neocortical pyramidal neurons in vivo are subject to an intense synaptic background activity but little is known of how this activity affects cellular responsiveness and what function it may serve. These issues were examined in morphologically reconstructed neocortical pyramidal neurons in which synaptic background activity was simulated based on recent measurements in cat parietal cortex. We show that background activity can be decomposed into two components: a tonically active conductance and voltage fluctuations. Previous studies have mostly focused on the conductance effect, revealing that background activity is responsible for a decrease in responsiveness, which imposes severe conditions of coincidence of inputs necessary to discharge the cell. It is shown here, in contrast, that responsiveness is enhanced if voltage fluctuations are taken into account; in this case the model can produce responses to inputs that would normally be subthreshold. This effect is analyzed by dissecting and comparing the different components of background activity, as well as by evaluating the contribution of parameters such as the dendritic morphology, the distribution of leak currents, the value of axial resistivity, the densities of voltage-dependent currents, and the release parameters underlying background activity. Interestingly, the model's optimal responsiveness was obtained when voltage fluctuations were of the same order as those measured intracellularly in vivo. Possible consequences were also investigated at the population level, where the presence of background activity allowed networks of pyramidal neurons to instantaneously detect inputs that are small compared with the classical detection threshold. These results suggest, at the single-cell level, that the presence of voltage fluctuations has a determining influence on cellular responsiveness and that these should be taken into account in models of background activity. At the network level, we predict that background activity provides the necessary drive for detecting events that would normally be undetectable. Experiments are suggested to explore this possible functional role for background activity.

Modelling corticothalamic feedback and the gating of the thalamus by the cerebral cortex

Morphological studies have shown that excitatory synapses from the cortex constitute the major source of synapses in the thalamus. However, the effect of these corticothalamic synapses on the function of the thalamus is not well understood because thalamic neurones have complex intrinsic firing properties and interact through multiple types of synaptic receptors. Here we investigate these complex interactions using computational models. We show first, using models of reconstructed thalamic relay neurones, that the effect of corticothalamic synapses on relay cells can be similar to that of afferent synapses, in amplitude, kinetics and timing, although these synapses are located in different regions of the dendrites. This suggests that cortical EPSPs may complement (or predict) the afferent information. Second, using models of reconstructed thalamic reticular neurones, we show that high densities of the low-threshold Ca2+ current in dendrites can give these cells an exquisite sensitivity to cortical EPSPs, but only if their dendrites are hyperpolarized. This property has consequences at the level of thalamic circuits, where corticothalamic EPSPs evoke bursts in reticular neurones and recruit relay cells predominantly through feedforward inhibition. On the other hand, with depolarized dendrites, thalamic reticular neurones do not generate bursts and the cortical influence on relay cells is mostly excitatory. Models therefore suggest that the cortical influence can either promote or antagonize the relay of information, depending on the state of the dendrites of reticular neurones. The control of these dendrites may therefore be a determinant of attentional mechanisms. We also review the effect of corticothalamic feedback at the network level, and show how the cortical control over the thalamus is essential in co-ordinating widespread, coherent oscillations. We suggest mechanisms by which different modes of corticothalamic interaction would allow oscillations of very different spatiotemporal coherence to coexist in the thalamocortical system.

Dual intracellular recordings and computational models of slow inhibitory postsynaptic potentials in rat neocortical and hippocampal slices

Dual intracellular recordings in slices of adult rat neocortex and hippocampus investigated slow, putative GABA(B) receptor-mediated inhibitory postsynaptic potentials. In most pairs tested in which the interneuron elicited a fast inhibitory postsynaptic potential in the pyramid, this GABA(A) receptor mediated inhibitory postsynaptic potential was entirely blocked by bicuculline or picrotoxin (3:3 in neocortex, 6:8 in CA1, all CA1 basket cells), even when high-frequency presynaptic spike trains were elicited. However, in three of 85 neocortical paired recordings involving an interneuron, although no discernible response was elicited by single presynaptic interneuronal spikes, a long latency (> or =20 ms) inhibitory postsynaptic potential was elicited by a train of > or =3 spikes at frequencies > or =50-100 Hz. This slow inhibitory postsynaptic potential was insensitive to bicuculline (one pair tested). In neocortex, slow inhibitory postsynaptic potential duration reached a maximum of 200 ms even with prolonged presynaptic spike trains. In contrast, summing fast, GABA(A) inhibitory postsynaptic potentials, elicited by spike trains, lasted as long as the train. Between four and 10 presynaptic spikes, mean peak slow inhibitory postsynaptic potential amplitude increased sharply to 0.38, 2.6 and 2.9 mV, respectively, in the three neocortical pairs (membrane potential -60 to -65 mV). Thereafter increases in spike number had little additional effect on amplitude. In two of eight pairs in CA1, one involving a presynaptic basket cell and the other a putative bistratified interneuron, the fast inhibitory postsynaptic potential was blocked by bicuculline revealing a slow inhibitory postsynaptic potential that was greatly reduced by 100 microM CGP 35348 (basket cell pair). The sensitivity of this slow inhibitory postsynaptic potential to spike number was similar to that of neocortical 'pure' slow inhibitory postsynaptic potentials, but was of longer duration, its plateau phase outlasting 200 ms spike trains and its maximum duration exceeding 400 ms. Computational models of GABA release, diffusion and uptake suggested that extracellular accumulation of GABA cannot alone account for the non-linear relationship between spike number and inhibitory postsynaptic potential amplitude. However, cooperativity in the kinetics of GABA(B) transduction mechanisms provided non-linear relations similar to experimental data. Different kinetic models were considered for how G-proteins activate K+ channels, including allosteric models. For all models, the best fit to experimental data was obtained with four G-protein binding sites on the K+ channels, consistent with a tetrameric structure for the K+ channels associated with GABA(B) receptors. Thus some inhibitory connections in neocortex and hippocampus appear mediated solely by fast GABA(A) receptors, while others appear mediated solely by slow, non-ionotropic, possibly GABA(B) receptors. In addition, some inhibitory postsynaptic potentials arising in proximal portions of CA1 pyramidal cells are mediated by both GABA(A) and GABA(B) receptors. Our data indicate that the GABA released by a single interneuron can saturate the GABA(B) receptor mechanism(s) accessible to it and that 'spillover' to extrasynaptic sites need not necessarily be proposed to explain these slow inhibitory postsynaptic potential properties.

Cortically-induced coherence of a thalamic-generated oscillation

Oscillatory patterns in neocortical electrical activity show various degrees of large-scale synchrony depending on experimental conditions, but the exact mechanisms underlying these variations of coherence are not known. Analysis of multisite local field potentials revealed that the coherence of spindle oscillations varied during different states. During natural sleep, the coherence was remarkably high over cortical distances of several millimeters, but could be disrupted by artificial cortical depression, similar to the effect of barbiturates. Possible mechanisms for these variations of coherence were investigated by computational models of interacting cortical and thalamic neurons, including their intrinsic firing patterns and various synaptic receptors present in the circuitry. The model indicates that modulation of the excitability of the cortex can affect spatiotemporal coherence with no change in the thalamus. The highest level of coherence was obtained by enhancing the excitability of cortical pyramidal cells, simulating the action of neuromodulators such as acetylcholine and noradrenaline. The underlying mechanism was due to cortex-thalamus-cortex loops in which a more excitable cortical network generated a more powerful and coherent feedback onto the thalamus, resulting in highly coherent oscillations, similar to the properties measured during natural sleep. In conclusion, these experiments and models are compatible with a powerful role for the cortex in triggering and synchronizing oscillations generated in the thalamus, through corticothalamic feedback projections. The model suggests that intracortical mechanisms may be responsible for synchronizing oscillations over cortical distances of several millimeters through cortex-thalamus-cortex loops, thus providing a possible cellular mechanism to explain the genesis of large-scale coherent oscillations in the thalamocortical system.

Can GABAA conductances explain the fast oscillation frequency of absence seizures in rodents?

Rodent models of absence epilepsy generate spike-and-wave oscillations at relatively fast frequency (5-10 Hz) compared with humans ( approximately 3 Hz). Possible mechanisms for these oscillations were investigated by computational models that included the complex intrinsic firing properties of thalamic and cortical neurons, as well as the multiple types of synaptic receptors mediating their interactions. The model indicates that oscillations with spike-and-wave field potentials can be generated by thalamocortical circuits. The frequency of these oscillations critically depended on GABAergic conductances in thalamic relay cells, ranging from 2-4 Hz for strong GABAB conductances to 5-10 Hz when GABAA conductances were dominant. This model therefore suggests that thalamocortical circuits can generate two types of spike-and-wave oscillations, whose frequency is determined by the receptor type mediating inhibition in thalamic relay cells. Experiments are proposed to test this mechanism.

Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states

The electroencephalogram displays various oscillation patterns during wake and sleep states, but their spatiotemporal distribution is not completely known. Local field potentials (LFPs) and multiunits were recorded simultaneously in the cerebral cortex (areas 5-7) of naturally sleeping and awake cats. Slow-wave sleep (SWS) was characterized by oscillations in the slow (<1 Hz) and delta (1-4 Hz) frequency range. The high-amplitude slow-wave complexes consisted in a positivity of depth LFP, associated with neuronal silence, followed by a sharp LFP negativity, correlated with an increase of firing. This pattern was of remarkable spatiotemporal coherence, because silences and increased firing occurred simultaneously in units recorded within a 7 mm distance in the cortex. During wake and rapid-eye-movement (REM) sleep, single units fired tonically, whereas LFPs displayed low-amplitude fast activities with increased power in fast frequencies (15-75 Hz). In contrast with the widespread synchronization during SWS, fast oscillations during REM and wake periods were synchronized only within neighboring electrodes and small time windows (100-500 msec). This local synchrony occurred in an apparent irregular manner, both spatially and temporally. Brief periods (<1 sec) of fast oscillations were also present during SWS in between slow-wave complexes. During these brief periods, the spatial and temporal coherence, as well as the relation between units and LFPs, was identical to that of fast oscillations of wake or REM sleep. These results show that natural SWS in cats is characterized by slow-wave complexes, synchronized over large cortical territories, interleaved with brief periods of fast oscillations, characterized by local synchrony, and of characteristics similar to that of the sustained fast oscillations of activated states.

Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo

During wakefulness, neocortical neurons are subjected to an intense synaptic bombardment. To assess the consequences of this background activity for the integrative properties of pyramidal neurons, we constrained biophysical models with in vivo intracellular data obtained in anesthetized cats during periods of intense network activity similar to that observed in the waking state. In pyramidal cells of the parietal cortex (area 5-7), synaptic activity was responsible for an approximately fivefold decrease in input resistance (Rin), a more depolarized membrane potential (Vm), and a marked increase in the amplitude of Vm fluctuations, as determined by comparing the same cells before and after microperfusion of tetrodotoxin (TTX). The model was constrained by measurements of Rin, by the average value and standard deviation of the Vm measured from epochs of intense synaptic activity recorded with KAc or KCl-filled pipettes as well as the values measured in the same cells after TTX. To reproduce all experimental results, the simulated synaptic activity had to be of relatively high frequency (1-5 Hz) at excitatory and inhibitory synapses. In addition, synaptic inputs had to be significantly correlated (correlation coefficient approximately 0.1) to reproduce the amplitude of Vm fluctuations recorded experimentally. The presence of voltage-dependent K+ currents, estimated from current-voltage relations after TTX, affected these parameters by <10%. The model predicts that the conductance due to synaptic activity is 7-30 times larger than the somatic leak conductance to be consistent with the approximately fivefold change in Rin. The impact of this massive increase in conductance on dendritic attenuation was investigated for passive neurons and neurons with voltage-dependent Na+/K+ currents in soma and dendrites. In passive neurons, correlated synaptic bombardment had a major influence on dendritic attenuation. The electrotonic attenuation of simulated synaptic inputs was enhanced greatly in the presence of synaptic bombardment, with distal synapses having minimal effects at the soma. Similarly, in the presence of dendritic voltage-dependent currents, the convergence of hundreds of synaptic inputs was required to evoke action potentials reliably. In this case, however, dendritic voltage-dependent currents minimized the variability due to input location, with distal apical synapses being as effective as synapses on basal dendrites. In conclusion, this combination of intracellular and computational data suggests that, during low-amplitude fast electroencephalographic activity, neocortical neurons are bombarded continuously by correlated synaptic inputs at high frequency, which significantly affect their integrative properties. A series of predictions are suggested to test this model.

Spike-and-wave oscillations based on the properties of GABAB receptors

Neocortical and thalamic neurons are involved in the genesis of generalized spike-and-wave (SW) epileptic seizures. The cellular mechanism of SW involves complex interactions between intrinsic neuronal firing properties and multiple types of synaptic receptors, but because of the complexity of these interactions the exact details of this mechanism are unclear. In this paper these types of interactions were investigated by using biophysical models of thalamic and cortical neurons. It is shown first that, because of the particular activation properties of GABAB receptor-mediated responses, simulated field potentials can display SW waveforms if cortical pyramidal cells and interneurons generate prolonged discharges in synchrony, without any other assumptions. Here the "spike" component coincided with the synchronous firing, whereas the "wave" component was generated mostly by slow GABAB-mediated K+ currents. Second, the model suggests that intact thalamic circuits can be forced into a approximately 3 Hz oscillatory mode by corticothalamic feedback. Here again, this property was attributable to the characteristics of GABAB-mediated inhibition. Third, in the thalamocortical system this property can lead to generalized approximately 3 Hz oscillations with SW field potentials. The oscillation consisted of a synchronous prolonged firing in all cell types, interleaved with a approximately 300 msec period of neuronal silence, similar to experimental observations during SW seizures. This model suggests that SW oscillations can arise from thalamocortical loops in which the corticothalamic feedback indirectly evokes GABAB-mediated inhibition in the thalamus. This mechanism is shown to be consistent with a number of different experimental models, and experiments are suggested to test its consistency.

Dendritic low-threshold calcium currents in thalamic relay cells

The low-threshold calcium current (IT) underlies burst generation in thalamocortical (TC) relay cells and plays a central role in the genesis of synchronized oscillations by thalamic circuits. Here we have combined in vitro recordings and computational modeling techniques to investigate the consequences of dendritically located IT in TC cells. Simulations of a reconstructed TC cell were compared with the recordings obtained in the same cell to constrain the values of its passive parameters. T-current densities in soma and proximal dendrites were then estimated by matching the model to voltage-clamp recordings obtained in dissociated TC cells, which lack most of the dendrites. The distal dendritic T-current density was constrained by recordings in intact TC cells, which show 5-14 times larger peak T-current amplitudes compared with dissociated cells. Comparison of the model with the recordings of the same cell constrained further the T-current density in dendrites, which had to be 4.5-7.6 times higher than in the soma to reproduce all experimental results. Similar conclusions were reached using a simplified three-compartment model. Functionally, the model shows that the same amount of T-channels can lead to different bursting behaviors if they are exclusively somatic or distributed throughout the dendrites. In conclusion, this combination of models and experiments shows that dendritic T-currents are necessary to reproduce low-threshold calcium electrogenesis in TC cells. Dendritic T-current may also have significant functional consequences, such as an efficient modulation of thalamic burst discharges by corticothalamic feedback.

Inhibitory control of somatodendritic interactions underlying action potentials in neocortical pyramidal neurons in vivo: an intracellular and computational study

The effect of synaptic inputs on somatodendritic interactions during action potentials was investigated, in the cat, using in vivo intracellular recording and computational models of neocortical pyramidal cells. An array of 10 microelectrodes, each ending at a different cortical depth, was used to preferentially evoke synaptic inputs to different somatodendritic regions. Relative to action potentials evoked by current injection, spikes elicited by cortical microstimuli were reduced in amplitude and duration, with stimuli delivered at proximal (somatic) and distal (dendritic) levels evoking the largest and smallest decrements, respectively. When the inhibitory postsynaptic potential reversal was shifted to around -50 mV by recording with KCl pipettes, synaptically-evoked spikes were significantly less reduced than with potassium acetate or cesium acetate pipettes, suggesting that spike decrements are not only due to a shunt, but also to voltage-dependent effects. Computational models of neocortical pyramidal cells were built based on available data on the distribution of active currents and synaptic inputs in the soma and dendrites. The distribution of synapses activated by extracellular stimulation was estimated by matching the model to experimental recordings of postsynaptic potentials evoked at different depths. The model successfully reproduced the progressive spike amplitude reduction as a function of stimulation depth, as well as the effects of chloride and cesium. The model revealed that somatic spikes contain an important contribution from proximal dendritic sodium currents up to approximately 100 microm and approximately 300 microm from the soma under control and cesium conditions, respectively. Proximal inhibitory postsynaptic potentials can present this dendritic participation thus reducing the spike amplitude at the soma. The model suggests that the somatic spike amplitude and shape can be used as a "window" to infer the electrical participation of proximal dendrites. Thus, our results suggest that inhibitory postsynaptic potentials can control the participation of proximal dendrites in somatic sodium spikes.

Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons In vivo

The frequency of spontaneous synaptic events in vitro is probably lower than in vivo because of the reduced synaptic connectivity present in cortical slices and the lower temperature used during in vitro experiments. Because this reduction in background synaptic activity could modify the integrative properties of cortical neurons, we compared the impact of spontaneous synaptic events on the resting properties of intracellularly recorded pyramidal neurons in vivo and in vitro by blocking synaptic transmission with tetrodotoxin (TTX). The amount of synaptic activity was much lower in brain slices (at 34 degrees C), as the standard deviation of the intracellular signal was 10-17 times lower in vitro than in vivo. Input resistances (Rins) measured in vivo during relatively quiescent epochs ("control Rins") could be reduced by up to 70% during periods of intense spontaneous activity. Further, the control Rins were increased by approximately 30-70% after TTX application in vivo, approaching in vitro values. In contrast, TTX produced negligible Rin changes in vitro (approximately 4%). These results indicate that, compared with the in vitro situation, the background synaptic activity present in intact networks dramatically reduces the electrical compactness of cortical neurons and modifies their integrative properties. The impact of the spontaneous synaptic bombardment should be taken into account when extrapolating in vitro findings to the intact brain.

Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells

Early studies have shown that spindle oscillations are generated in the thalamus and are synchronized over wide cortical territories. More recent experiments have shown that this large-scale synchrony depends on the integrity of corticothalamic feedback. Previously proposed mechanisms emphasized exclusively intrathalamic mechanisms to generate the synchrony of these oscillations. In the present paper, we propose a cellular mechanism in which the synchrony is dependent of a mutual interaction between cortex and thalamus. This cellular mechanism is tested by computational models consisting of pyramidal cells, interneurons, thalamic reticular (RE) and thalamocortical (TC) relay cells, on the basis of voltage-clamp data on intrinsic currents and synaptic receptors present in the circuitry. The model suggests that corticothalamic feedback must operate on the thalamus mainly through excitation of GABAergic RE neurons, therefore recruiting relay cells essentially through inhibition and rebound. We provide experimental evidence for such dominant inhibition in the lateral posterior nucleus. In these conditions, the model shows that cortical discharges optimally evoked thalamic oscillations. This feature is essential to the present cellular mechanism and is also consistently observed experimentally. The model further shows that, with this type of corticothalamic feedback, cortical discharges recruited large areas of the thalamus because of the divergent cortex-to-RE and RE-to-TC axonal projections. Consequently, the thalamocortical network generated patterns of oscillations and synchrony similar to in vivo recordings. The model also emphasizes the important role of the modulation of the Ih current by calcium in TC cells. This property conferred a relative refractoriness to the entire network, a feature also observed experimentally, as we show here. Further, the same property accounted for various spatiotemporal features of oscillations, such as systematic propagation after low-intensity cortical stimulation, local oscillations, and more generally, a high variability in the patterns of spontaneous oscillations, similar to in vivo recordings. We propose that the large-scale synchrony of spindle oscillations in vivo is the result of thalamocortical interactions in which the corticothalamic feedback acts predominantly through the RE nucleus. Several predictions are suggested to test the validity of this model.

Intracellular and computational characterization of the intracortical inhibitory control of synchronized thalamic inputs in vivo

We investigated the presence and role of local inhibitory cortical control over synchronized thalamic inputs during spindle oscillations (7-14 Hz) by combining intracellular recordings of pyramidal cells in barbiturate-anesthetized cats and computational models. The recordings showed that 1) similar excitatory postsynaptic potential (EPSP)/inhibitory postsynaptic potential (IPSP) sequences occurred either during spindles or following thalamic stimulation; 2) reversed IPSPs with chloride-filled pipettes transformed spindle-related EPSP/IPSP sequences into robust bursts with spike inactivation, resembling paroxysmal depolarizing shifts during seizures; and 3) dual simultaneous impalements showed that inhibition associated with synchronized thalamic inputs is local. Computational models were based on reconstructed pyramidal cells constrained by recordings from the same cells. These models showed that the transformation of EPSP/IPSP sequences into fully developed spike bursts critically needs a relatively high density of inhibitory currents in the soma and proximal dendrites. In addition, models predict significant Ca2+ transients in dendrites due to synchronized thalamic inputs. We conclude that synchronized thalamic inputs are subject to strong inhibitory control within the cortex and propose that 1) local impairment of inhibition contributes to the transformation of spindles into spike-wave-type discharges, and 2) spindle-related inputs trigger Ca2+ events in cortical dendrites that may subserve plasticity phenomena during sleep.

Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures

In vivo intracellular recording from cat thalamus and cortex was performed during spontaneous spike-wave seizures characterized by synchronously firing cortical neurons correlated with the electroencephalogram. During these seizures, thalamic reticular (RE) neurons discharged with long spike bursts riding on a depolarization, whereas thalamocortical (TC) neurons were either entrained into the seizures (40%) or were quiescent (60%). During quiescence, TC neurons showed phasic inhibitory postsynaptic potentials (IPSPs) that coincided with paroxysmal depolarizing shifts in the simultaneously recorded cortical neuron. Computer simulations of a reciprocally connected TC-RE pair showed two major modes of TC-RE interaction. In one mode, a mutual oscillation involved direct TC neuron excitation of the RE neuron leading to a burst that fed back an IPSP into the TC neuron, producing a low-threshold spike. In the other, quiescent mode, the TC neuron was subject to stronger coalescing IPSPs. Simulated cortical stimulation could trigger a transition between the two modes. This transition could go in either direction and was dependent on the precise timing of the input. The transition did not always follow the stimulation immediately. A larger, multicolumnar simulation was set up to assess the role of the TC-RE pair in the context of extensive divergence and convergence. The amount of TC neuron spiking generally correlated with the strength of total inhibitory input, but large variations in the amount of spiking could be seen. Evidence for mutual oscillation could be demonstrated by comparing TC neuron firing with that in reciprocally connected RE neurons. An additional mechanism for TC neuron quiescence was assessed with the use of a cooperative model of gamma-aminobutyric acid-B (GABA(B))-mediated responses. With this model, RE neurons receiving repeated strong excitatory input produced TC neuron quiescence due to burst-duration-associated augmentation of GABA(B) current. We predict the existence of spatial inhomogeneity in apparently generalized spike-wave seizures, involving a center-surround pattern. In the center, intense cortical and RE neuron activity would be associated with TC neuron quiescence. In the surround, less intense hyperpolarization of TC neurons would allow low-threshold spikes to occur. This surround, an "epileptic penumbra," would be the forefront of the expanding epileptic wave during the process of initial seizure generalization. Therapeutically, we would then predict that agents that reduce TC neuron activity would have a greater effect on seizure onset than on ongoing spike-wave seizures or other thalamic oscillations.

Spindle oscillations during cortical spreading depression in naturally sleeping cats

Spindling activity characterizes the EEG of animals and humans in the early stages of resting sleep. Spindles are defined as waxing and waning rhythmic waves at 7-14 Hz that recur periodically every 3-10 s. Spindling originates in the thalamus, but a role for the cerebral cortex in triggering and synchronizing thalamic spindles was shown by stimulation of the contralateral cortex avoiding antidromic activation of thalamocortical axons and by diminished coherency of thalamic spindles after hemidecortication. Spontaneous spindles under barbiturate anesthesia are waxing and waning but under ketamine-xylazine anesthesia or when evoked by strong stimuli spindle waves are almost exclusively waning, i.e. they start with maximum amplitude and then decrease progressively. Waxing and waning of spindles has been ascribed to progressive entrainment of units into the oscillation followed by a progressive desynchronization. Therefore, exclusively waning spindles would be produced by an initial high synchrony in the corticothalamic network. Such a situation is observable upon strong stimulation or, spontaneously, when spindles are paced by the slow cortical oscillation and preceded by a strong corticothalamic drive. We have conducted experiments in naturally sleeping cats to verify the occurrence of two patterns of spindle oscillations and to test the role of the cortex in synchronizing and shaping spindles. We have found that indeed two types of spindles (waxing and waning or mostly waning) occur in naturally sleeping animals. We also demonstrate that during cortical spreading depression spindles are less synchronous and only of the waxing and waning type. As cortical activity recovers, waning spindles reappear and are preceded by electroencephalogram deflections which are related to corticothalamic depolarizing inputs. Our results strongly support the hypothesis of the role of the cerebral cortex in shaping and synchronizing thalamically generated spindles.

Conductance-based integrate-and-fire models

A conductance-based model of Na+ and K+ currents underlying action potential generation is introduced by simplifying the quantitative model of Hodgkin and Huxley (HH). If the time course of rate constants can be approximated by a pulse, HH equations can be solved analytically. Pulse-based (PB) models generate action potentials very similar to the HH model but are computationally faster. Unlike the classical integrate-and-fire (IAF) approach, they take into account the changes of conductances during and after the spike, which have a determinant influence in shaping neuronal responses. Similarities and differences among PB, IAF, and HH models are illustrated for three cases: high-frequency repetitive firing, spike timing following random synaptic inputs, and network behavior in the presence of intrinsic currents.

Spatiotemporal patterns of spindle oscillations in cortex and thalamus

Spindle oscillations (7-14 Hz) appear in the thalamus and cortex during early stages of sleep. They are generated by the combination of intrinsic properties and connectivity patterns of thalamic neurons and distributed to cortical territories by thalamocortical axons. The corticothalamic feedback is a major factor in producing coherent spatiotemporal maps of spindle oscillations in widespread thalamic territories. Here we have investigated the spatiotemporal patterns of spontaneously occurring and evoked spindles by means of multisite field potential and unit recordings in intact cortex and decorticated animals. We show that (1) spontaneous spindle oscillations are synchronized over large cortical areas during natural sleep and barbiturate anesthesia; (2) under barbiturate anesthesia, the cortical coherence is not disrupted by transection of intracortical synaptic linkages; (3) in intact cortex animals, spontaneously occurring barbiturate spindle sequences occur nearly simultaneously over widespread thalamic territories; (4) in the absence of cortex, the spontaneous spindle oscillations throughout the thalamus are less organized, but the local coherence (within 2-4 mm) is still maintained; and (5) spindling propagation is observed in intact cortex animals only when elicited by low intensity cortical stimulation, applied shortly before the initiation of a spontaneous spindle sequence; propagation velocities are between 1 and 3 mm/sec, measured in the anteroposterior axis of the thalamus; increasing the intensity of cortical stimulation triggers spindle oscillations, which start simultaneously in all leads. We propose that, in vivo, the coherence of spontaneous spindle oscillations in corticothalamic networks is attributable to the combined action of continuous background corticothalamic input initiating spindle sequences in several thalamic sites at the same time and divergent corticothalamic and intrathalamic connectivity.

Control of spatiotemporal coherence of a thalamic oscillation by corticothalamic feedback

The mammalian thalamus is the gateway to the cortex for most sensory modalities. Nearly all thalamic nuclei also receive massive feedback projections from the cortical region to which they project. In this study, the spatiotemporal properties of synchronized thalamic spindle oscillations (7 to 14 hertz) were investigated in barbiturate-anesthetized cats, before and after removal of the cortex. After complete ipsilateral decortication, the long-range synchronization of thalamic spindles in the intact cortex hemisphere changed into disorganized patterns with low spatiotemporal coherence. Local thalamic synchrony was still present, as demonstrated by dual intracellular recordings from nearby neurons. In the cortex, synchrony was insensitive to the disruption of horizontal intracortical connections. These results indicate that the global coherence of thalamic oscillations is determined by corticothalamic projections.

Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices

1. A network model of thalamocortical (TC) and thalamic reticular (RE) neurons was developed based on electrophysiological measurements in ferret thalamic slices. Single-compartment TC and RE cells included voltage- and calcium-sensitive currents described by Hodgkin-Huxley type of kinetics. Synaptic currents were modeled by kinetic models of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA), gamma-aminobutyric acid-A (GABAA) and GABAB receptors. 2. The model reproduced successfully the characteristics of spindle and slow bicuculline-induced oscillations observed in vitro. The characteristics of these two types of oscillations depended on both the intrinsic properties of TC and RE cells and their pattern of interconnectivity. 3. The oscillations were organized by the reciprocal recruitment between TC and RE cells, due to their manual connectivity and bursting properties. TC cells elicited AMPA-mediated excitatory postsynaptic potentials (EPSPs) in RE cells, whereas RE cells elicited a mixture of GABAA and GABAB inhibitory postsynaptic potentials (IPSPs) in TC cells. Because of the presence of a T current, sufficiently strong EPSPs could elicit a burst in RE cells, and TC cells could generate a rebound burst following GABAergic IPSPs. Under these conditions, interaction between the TC and RE cells produced sustained oscillations. 4. In the absence of spontaneous oscillation in any cell, the TC-RE network remained quiescent. Spindle oscillations with a frequency of 9-11 Hz could be initiated by stimulation of either TC or RE neurons. A few spontaneously oscillating TC neurons recruited the entire network model into a "waxing-and waning" oscillation. These "initiator" cells could be an extremely small proportion of TC cells. 5. In intracellular recordings, TC cells display a reduced ability for burst firing after a sequence of bursts. The "waning" phase of spindles was reproduced in the network model by assuming an activity-dependent upregulation of Ih operating via a calcium-binding protein in TC cells, as shown previously in a two-cell model. 6. Following the global suppression of GABAA inhibition, the disinhibited RE cells produced prolonged burst discharges that elicited strong GABAB-mediated currents in TC cells. The enhancement of slow IPSPs in TC cells was also due to cooperativity in the activation of GABAB-mediated current. These slow IPSPs recruited TC and RE cells into slower waxing-and-waning oscillations (3-4 HZ) that were even more highly synchronized. 7. Local axonal arborization of the TC to RE and RE to TC projections allowed oscillations to propagate through the network. An oscillation starting at a single focus induced a propagating wavefront as more cells were recruited progressively. The waning of the oscillation also propagated due to upregulation of Ih in TC cells, leading to waves of spindle activity as observed in experiments. 8. The spatiotemporal properties of propagating waves in the model were highly dependent on the intrinsic properties of TC cells. The spatial pattern of spiking activity was markedly different for spindles compared with bicuculline-induced oscillations and depended on the rebound burst behavior of TC cells. The upregulation of Ih produced a refractory period so that colliding spindle waves merged into a single oscillation and extinguished. Finally, reducing the Ih conductance led to sustained oscillations. 9. Two key properties of cells in the thalamic network may account for the initiation, propagation, and termination of spindle oscillations, the activity-dependent upregulation of Ih in TC cells, and the localized axonal projections between TC and RE cells. In addition, the model predicts that a nonlinear stimulus dependency of GABAB responses accounts for the genesis of prolonged synchronized discharges following block of GABAA receptors.

Control of slow oscillations in the thalamocortical neuron: a computer model

We investigated computer models of a single thalamocortical neuron to assess the interaction of intrinsic voltage-sensitive channels and cortical synaptic input in producing the range of oscillation frequencies observed in these cells in vivo. A morphologically detailed model with Hodgkin-Huxley-like ion channels demonstrated that intrinsic properties would be sufficient to readily produce 3 to 6 Hz oscillations. Hyperpolarization of the model cell reduced its oscillation frequency monotonically whether through current injection or modulation of a potassium conductance, simulating the response to a neuromodulatory input. We performed detailed analysis of highly reduced models to determine the mechanism of this frequency control. The interburst interval was controlled by two different mechanisms depending on whether or not the pacemaker current, IH, was present. In the absence of IH, depolarization during the interburst interval occurred at the same rate with different current injections. The voltage difference from the nadir to threshold for the low-threshold calcium current, IT, determined the interburst interval. In contrast, with IH present, the rate of depolarization depended on injected current. With the full model, simulated repetitive cortical synaptic input entrained oscillations up to approximately double the natural frequency. Cortical input readily produced phase resetting as well. Our findings suggest that neither ascending brainstem control altering underlying hyperpolarization, nor descending drive by repetitive cortical inputs, would alone be sufficient to produce the range of oscillation frequencies seen in thalamocortical neurons. Instead, intrinsic neuronal mechanisms would dominate for generating the delta range (0.5-4 Hz) oscillations seen during slow wave sleep, whereas synaptic interactions with cortex and the thalamic reticular nucleus would be required for faster oscillations in the frequency range of spindling (7-14 Hz).

In vivo, in vitro, and computational analysis of dendritic calcium currents in thalamic reticular neurons

Thalamic reticular (RE) neurons are involved in the genesis of synchronized thalamocortical oscillations, which depend in part on their complex bursting properties. We have investigated the intrinsic properties of RE cells using computational models based on morphological and electrophysiological data. Simulations of a reconstructed RE cells were compared directly with recordings from the same cell to obtain precise values for the passive parameters. In a first series of experiments, the low-threshold calcium current (I(Ts)) was studied via voltage clamp in acutely dissociated RE cells that lack most of their dendrites. Simulations based on a cell with truncated dendrites and Hodgkin-Huxley kinetics reproduced these recordings with a relatively low density of I(Ts). In a second series of experiments, voltage-clamp recordings obtained in intact RE cells in slices showed a higher amplitude and slower kinetics of I(Ts). These properties could be reproduced from the reconstructed cell model assuming higher densities of I(Ts) in distal dendrites. In a third series of experiments, current-clamp recordings were obtained on RE cells in vivo. The marked differences with in vitro recordings could be reconciled by simulating synaptic bombardment in the dendrites of RE cells, but only if they contained high distal densities of I(Ts). In addition, simpler models with as few as three compartments could reproduce the same behavior assuming dendritic I(Ts). These models and experiments show how intrinsic bursting properties of RE cells, as recorded in vivo and in vitro, may be explained by dendritic calcium currents.

G protein activation kinetics and spillover of gamma-aminobutyric acid may account for differences between inhibitory responses in the hippocampus and thalamus

We have developed a model of gamma-aminobutyric acid (GABA)ergic synaptic transmission mediated by GABAA and GABAB receptors, including cooperativity in the guanine nucleotide binding protein (G protein) cascade mediating the activation of K+ channels by GABAB receptors. If the binding of several G proteins is needed to activate the K+ channels, then only a prolonged activation of GABAB receptors evoked detectable currents. This could occur if strong stimuli evoked release in adjacent terminals and the spillover resulted in prolonged activation of the receptors, leading to inhibitory responses similar to those observed in hippocampal slices. The same model also reproduced thalamic GABAB responses to high-frequency bursts of stimuli. In this case, prolonged activation of the receptors was due to high-frequency release conditions. This model provides insights into the function of GABAB receptors in normal and epileptic discharges.

Modeling the control of reticular thalamic oscillations by neuromodulators

Compartmental models of thalamic reticular (RE) neurons were investigated based on current-clamp and voltage-clamp data. Spontaneous oscillations in the model arise from the interaction between inhibitory synaptic currents and the rebound burst of RE cells. These oscillations critically depend on the level of the resting membrane potential. A network of RE neurons can be switched between silent and sustained oscillatory behavior by modulating a leak potassium current through neuromodulatory synapses. These results suggest that neuromodulators, such as noradrenaline, serotonin and glutamate, can exert a decisive control over the oscillatory activity of systems of RE cells. The model may explain why the isolated RE nucleus oscillates spontaneously in vivo but not in vitro.

Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism

Markov kinetic models were used to synthesize a complete description of synaptic transmission, including opening of voltage-dependent channels in the presynaptic terminal, release of neurotransmitter, gating of postsynaptic receptors, and activation of second-messenger systems. These kinetic schemes provide a more general framework for modeling ion channels than the Hodgkin-Huxley formalism, supporting a continuous spectrum of descriptions ranging from the very simple and computationally efficient to the highly complex and biophysically precise. Examples are given of simple kinetic schemes based on fits to experimental data that capture the essential properties of voltage-gated, synaptic and neuromodulatory currents. The Markov formalism allows the dynamics of ionic currents to be considered naturally in the larger context of biochemical signal transduction. This framework can facilitate the integration of a wide range of experimental data and promote consistent theoretical analysis of neural mechanisms from molecular interactions to network computations.