Independent Components of Neural Activity Carry Information on Individual Populations

Local field potential (LFP), the low-frequency part of the potential recorded extracellularly in the brain, reflects neural activity at the population level. The interpretation of LFP is complicated because it can mix activity from remote cells, on the order of millimeters from the electrode. To understand better the relation between the recordings and the local activity of cells we used a large-scale network thalamocortical model to compute simultaneous LFP, transmembrane currents, and spiking activity. We used this model to study the information contained in independent components obtained from the reconstructed Current Source Density (CSD), which smooths transmembrane currents, decomposed further with Independent Component Analysis (ICA). We found that the three most robust components matched well the activity of two dominating cell populations: superior pyramidal cells in layer 2/3 (rhythmic spiking) and tufted pyramids from layer 5 (intrinsically bursting). The pyramidal population from layer 2/3 could not be well described as a product of spatial profile and temporal activation, but by a sum of two such products which we recovered in two of the ICA components in our analysis, which correspond to the two first principal components of PCA decomposition of layer 2/3 population activity. At low noise one more cell population could be discerned but it is unlikely that it could be recovered in experiment given typical noise ranges.     

Temporal dynamics of distinct CA1 cell populations during unconscious state induced by ketamine

Ketamine is a widely used dissociative anesthetic which can induce some psychotic-like symptoms and memory deficits in some patients during the post-operative period. To understand its effects on neural population dynamics in the brain, we employed large-scale in vivo ensemble recording techniques to monitor the activity patterns of simultaneously recorded hippocampal CA1 pyramidal cells and various interneurons during several conscious and unconscious states such as awake rest, running, slow wave sleep, and ketamine-induced anesthesia. Our analyses reveal that ketamine induces distinct oscillatory dynamics not only in pyramidal cells but also in at least seven different types of CA1 interneurons including putative basket cells, chandelier cells, bistratified cells, and O-LM cells. These emergent unique oscillatory dynamics may very well reflect the intrinsic temporal relationships within the CA1 circuit. It is conceivable that systematic characterization of network dynamics may eventually lead to better understanding of how ketamine induces unconsciousness and consequently alters the conscious mind.     

Bistable,Irregular Firing and Population Oscillations in a Modular Attractor Memory Network

Attractor neural networks are thought to underlie working memory functions in the cerebral cortex. Several such models have been proposed that successfully reproduce firing properties of neurons recorded from monkeys performing working memory tasks. However, the regular temporal structure of spike trains in these models is often incompatible with experimental data. Here, we show that the in vivo observations of bistable activity with irregular firing at the single cell level can be achieved in a large-scale network model with a modular structure in terms of several connected hypercolumns. Despite high irregularity of individual spike trains, the model shows population oscillations in the beta and gamma band in ground and active states, respectively. Irregular firing typically emerges in a high-conductance regime of balanced excitation and inhibition. Population oscillations can produce such a regime, but in previous models only a non-coding ground state was oscillatory. Due to the modular structure of our network, the oscillatory and irregular firing was maintained also in the active state without fine-tuning. Our model provides a novel mechanistic view of how irregular firing emerges in cortical populations as they go from beta to gamma oscillations during memory retrieval.     

Effect of the topology and delayed interactions in neuronal networks synchronization

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.     

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Global rhythmic activities in hippocampal neural fields and neural coding

Global oscillations of the neural field represent some of the most interesting expressions of the hippocampal activity, being related also to learning and memory. To study oscillatory activities of the CA3 field in theta range, a model of this sub-field of Hippocampus has been formulated. The model describes the firing activity of CA3 neuronal populations within the frame of a kinetic theory of neural systems and it has been used for computer simulations. The results show that the propagation of activities induced in the neural field by hippocampal afferents occurs only in narrow time windows confined by inhibitory barrages, whose time-course follows the theta rhythm. Moreover, during each period of a theta wave, the entire CA3 field bears a firing activity with peculiar space-time patterns, a sort of specific imprint, which can induce effects with similar patterns on brain regions driven by the hippocampal formation. The simulation has also demonstrated the ability of medial septum to influence the global activity of the CA3 pyramidal population through the control of the population of inhibitory interneurons. At last, the possible involvement of global population oscillations in neural coding has been discussed.     

A novel network of multipolar bursting interneurons generates theta frequency oscillations in neocortex

GABAergic interneurons can phase the output of principal cells, giving rise to oscillatory activity in different frequency bands. Here we describe a new subtype of GABAergic interneuron, the multipolar bursting (MB) cell in the mouse neocortex. MB cells are parvalbumin positive but differ from fast-spiking multipolar (FS) cells in their morphological, neurochemical, and physiological properties. MB cells are reciprocally connected with layer 2/3 pyramidal cells and are coupled with each other by chemical and electrical synapses. MB cells innervate FS cells but not vice versa. MB to MB cell as well as MB to pyramidal cell synapses exhibit paired-pulse facilitation. Carbachol selectively induced synchronized theta frequency oscillations in MB cells. Synchrony required both gap junction coupling and GABAergic chemical transmission, but not excitatory glutamatergic input. Hence, MB cells form a distinct inhibitory network, which upon cholinergic drive can generate rhythmic and synchronous theta frequency activity, providing temporal coordination of pyramidal cell output.     

Steady-state and limit cycle activity of mass of neurons forming simple feedback loops (I): lumped circuit model

The neurons in the mammalian olfactory bulb sustain two types of synaptic feedback. The periglomerular cells excite each other and form a positive feedback loop. The mitral-tufted cells are excited by periglomerular neurons, and they excite granule cells and are inhibited by them. The last two neural populations form a negative feedback loop. This work contains mathematical proofs for the existence of steady state unvarying activity in periglomerular neurons, and of steady state oscillatory activity of mitral-tufted and granule cells, which is manifested in the EEG. The following predictions are made. 1) The level of mean ongoing pulse activity of the periglomerular population is determined by peripheral sensory and centrifugal input. 2) The interaction of mitral and granule populations determines a limit cycle detectable in the EEG. 3) The frequency of the limit cycle is determined by periglomerular and centrifugal input. 4) The steady and oscillatory pulse rates are stable, and if they are perturbed, they return to the levels preceding perturbation.     

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.     

Hippocampal rhythm generation: Gamma-related theta-frequency resonance in CA3 interneurons

 During different behavioral states different population activities are present in the hippocampal formation. These activities are not independent: sharp waves often occur together with high-frequency ripples, and gamma-frequency activity is usually superimposed on theta oscillations. There is both experimental and theoretical evidence supporting the notion that gamma oscillation is generated intrahippocampally, but there is no generally accepted view about the origin of theta waves. Precise timing of population bursts of pyramidal cells may be due to a synchronized external drive. Membrane potential oscillations recorded in the septum are unlikely to fulfill this purpose because they are not coherent enough. We investigated the prospects of an intrahippocampal mechanism supplying pyramidal cells with theta frequency periodic inhibition, by studying a model of a network of hippocampal inhibitory interneurons. As shown previously, interneurons are capable of generating synchronized gamma-frequency action potential oscillations. Exciting the neurons by periodic current injection, the system could either be entrained in an oscillation with the frequency of the inducing current or exhibit in-phase periodic changes at the frequency of single cell (and network) activity. Simulations that used spatially inhomogeneous stimulus currents showed anti-phase frequency changes across cells, which resulted in a periodic decrease in the synchrony of the network. As this periodic change in synchrony occurred in the theta frequency range, our network should be able to exhibit the theta-frequency weakening of inhibition of pyramidal cells, thus offering a possible mechanism for intrahippocampal theta generation. Received: 23 February 2000 / Accepted in revised form: 30 June 2000     

Neural organization of the locomotive oscillator

We study the relation of neural development, organization, and activity to behavior. We provide a model of the locomotive oscillator, a neural system supplying alternating stimulation to extensor and flexor muscles creating an oscillatory motion. We propose a protocol by which this neural system starting from unstructured, unconnected neural populations develops structure and function. The protocol is studied by both computer simulation and mathematical analysis. Our main results are 1 The locomotive oscillator self-organizes and maintains its organization, assuming certain properties of the neural populations. 2 Imperfections disturbing the functional adequacy of the neural populations may lead to the deterioration and disappearance of the oscillatory behavior. 3 The locomotive oscillator may fail to organize if the development is not staged in time.     

Theta phase precession emerges from a hybrid computational model of a CA3 place cell

The origins and functional significance of theta phase precession in the hippocampus remain obscure, in part, because of the difficulty of reproducing hippocampal place cell firing in experimental settings where the biophysical underpinnings can be examined in detail. The present study concerns a neurobiologically based computational model of the emergence of theta phase precession in which the responses of a single model CA3 pyramidal cell are examined in the context of stimulation by realistic afferent spike trains including those of place cells in entorhinal cortex, dentate gyrus, and other CA3 pyramidal cells. Spike-timing dependent plasticity in the model CA3 pyramidal cell leads to a spatially correlated associational synaptic drive that subsequently creates a spatially asymmetric expansion of the model cell’s place field. Following an initial training period, theta phase precession can be seen in the firing patterns of the model CA3 pyramidal cell. Through selective manipulations of the model it is possible to decompose theta phase precession in CA3 into the separate contributing factors of inheritance from upstream afferents in the dentate gyrus and entorhinal cortex, the interaction of synaptically controlled increasing afferent drive with phasic inhibition, and the theta phase difference between dentate gyrus granule cell and CA3 pyramidal cell activity. In the context of a single CA3 pyramidal cell, the model shows that each of these factors plays a role in theta phase precession within CA3 and suggests that no one single factor offers a complete explanation of the phenomenon. The model also shows parallels between theta phase encoding and pattern completion within the CA3 autoassociative network. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A Canonical Circuit for Generating Phase-Amplitude Coupling

‘Phase amplitude coupling’ (PAC) in oscillatory neural activity describes a phenomenon whereby the amplitude of higher frequency activity is modulated by the phase of lower frequency activity. Such coupled oscillatory activity – also referred to as ‘cross-frequency coupling’ or ‘nested rhythms’ – has been shown to occur in a number of brain regions and at behaviorally relevant time points during cognitive tasks; this suggests functional relevance, but the circuit mechanisms of PAC generation remain unclear. In this paper we present a model of a canonical circuit for generating PAC activity, showing how interconnected excitatory and inhibitory neural populations can be periodically shifted in to and out of oscillatory firing patterns by afferent drive, hence generating higher frequency oscillations phase-locked to a lower frequency, oscillating input signal. Since many brain regions contain mutually connected excitatory-inhibitory populations receiving oscillatory input, the simplicity of the mechanism generating PAC in such networks may explain the ubiquity of PAC across diverse neural systems and behaviors. Analytic treatment of this circuit as a nonlinear dynamical system demonstrates how connection strengths and inputs to the populations can be varied in order to change the extent and nature of PAC activity, importantly which phase of the lower frequency rhythm the higher frequency activity is locked to. Consequently, this model can inform attempts to associate distinct types of PAC with different network topologies and physiologies in real data.     

Short-Term Synaptic Plasticity Orchestrates the Response of Pyramidal Cells and Interneurons to Population Bursts

The synaptic drive from neuronal populations varies considerably over short time scales. Such changes in the pre-synaptic rate trigger many temporal processes absent under steady-state conditions. This paper examines the differential impact of pyramidal cell population bursts on post-synaptic pyramidal cells receiving depressing synapses, and on a class of interneuron that receives facilitating synapses. In experiment a significant shift of the order of one hundred milliseconds is seen between the response of these two cell classes to the same population burst. It is demonstrated here that such a temporal differentiation of the response can be explained by the synaptic and membrane properties without recourse to elaborate cortical wiring schemes. Experimental data is first used to construct models of the two types of dynamic synaptic response. A population-based approach is then followed to examine analytically the temporal synaptic filtering effects of the population burst for the two post-synaptic targets. The peak-to-peak delays seen in experiment can be captured by the model for experimentally realistic parameter ranges. It is further shown that the temporal separation of the response is communicated in the outgoing action potentials of the two post-synaptic cells: pyramidal cells fire at the beginning of the burst and the class of interneuron receiving facilitating synapses fires at the end of the burst. The functional role of such delays in the temporal organisation of activity in the cortical microcircuit is discussed.     

A computer model of generation of the motor cortex neuron processes seen in the course of execution of instrumental movement

A computer model of neuronal processes in the motor cortex column is presented. The model is consisted of two pyramidal cell layers with two groups of inhibitory interneurons, selectively controlling pyramidal cell soma and dendrite, in each. Active Na, Ca and K conductances are included in the model of a single neuron. Horizontal excitatory connections between pyramidal cells in the upper layer are largely of NMDA-receptor type, that in the lower layer--of non-NMDA-type. All inhibitory synapses are of GABA(A)-type. The model reproduces the main phenomenon observed in the motor cortex during the execution of conditioned movements. Consequent to an early excitation the upper layer pyramidal cells generate a late NMDA-dependent reflexive response to afferent conditional stimulation, which as in a real case is diminished by GABA(A)-type synaptic inhibition and afferent stimulus strength increase. The characteristic inverse relation between the late response manifestation and the stimulus strength observed in the real cortex can be reproduced in the model only if NMDA-glutamate receptors were preferentially localized in the terminals of pyramidal cell backward collaterals, not in the terminals of the afferent fibers on pyramidal neurons. The intended component of motor cortex neuronal activity is generated in NMDA-independent manner by the pyramidal cells of lower layer. The slow time coarse of intended component as compared with short duration of AMPA epsp's is due to a consecutive relay-race--like activation of pyramidal neurons with different dendrit-to-soma ratio.     

Density dependent neurodynamics

The dynamics of a neural network depends on density parameters at (at least) two different levels: the subcellular density of ion channels in single neurons, and the density of cells and synapses at a network level. For the Frankenhaeuser-Huxley (FH) neural model, the density of sodium (Na) and potassium (K) channels determines the behaviour of a single neuron when exposed to an external stimulus. The features of the onset of single neuron oscillations vary qualitatively among different regions in the channel density plane. At a network level, the density of neurons is reflected in the global connectivity. We study the relation between the two density levels in a network of oscillatory FH neurons, by qualitatively distinguishing between three regions, where the mean network activity is (1) spiking, (2) oscillating with enveloped frequencies, and (3) bursting, respectively. We demonstrate that the global activity can be shifted between regions by changing either the density of ion channels at the subcellular level, or the connectivity at the network level, suggesting that different underlying mechanisms can explain similar global phenomena. Finally, we model a possible effect of anaesthesia by blocking specific inhibitory ion channels.     

Physiological and pathological oscillatory networks in the human motor system.

Human brain functions are heavily contingent on neural interactions both at the single neuron and the neural population or system level. Accumulating evidence from neurophysiological studies strongly suggests that coupling of oscillatory neural activity provides an important mechanism to establish neural interactions. With the availability of whole-head magnetoencephalography (MEG) macroscopic oscillatory activity can be measured non-invasively from the human brain with high temporal and spatial resolution. To localise, quantify and map oscillatory activity and interactions onto individual brain anatomy we have developed the 'dynamic imaging of coherent sources' (DICS) method which allows to identify and analyse cerebral oscillatory networks from MEG recordings. Using this approach we have characterized physiological and pathological oscillatory networks in the human sensorimotor system. Coherent 8 Hz oscillations emerge from a cerebello-thalamo-premotor-motor cortical network and exert an 8 Hz oscillatory drive on the spinal motor neurons which can be observed as a physiological tremulousness of the movement termed movement discontinuities. This network represents the neurophysiological substrate of a discrete mode of motor control. In parkinsonian resting tremor we have identified an extensive cerebral network consisting of primary motor and lateral premotor cortex, supplementary motor cortex, thalamus/basal ganglia, posterior parietal cortex and secondary somatosensory cortex, which are entrained in the tremor or twice the tremor rhythm. This low frequency entrapment of motor areas likely plays an important role in the pathophysiology of parkinsonian motor symptoms. Finally, studies on patients with postural tremor in hepatic encephalopathy revealed that this type of tremor results from a pathologically slow thalamocortical and cortico-muscular coupling during isometric hold tasks. In conclusion, the analysis of oscillatory cerebral networks provides new insights into physiological mechanisms of motor control and pathophysiological mechanisms of tremor disorders.     

An isomorphic mapping hypothesis of the grid representation

We introduce a grid cell microcircuit hypothesis. We propose the ‘grid in the world’ (evident in grid cell discharges) is generated by a ‘grid in the cortex’. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.     

A cortical attractor network with Martinotti cells driven by facilitating synapses

The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an attractor state and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the attractor state. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.