An electric analogue of the neuron

An electric analogue model of the neuron is described. The model neuron is composed of the active units which simulate the electric behaviors of the active loci of the membrane of a neuron. The active units include the model axon and the model synapses of six different types (the ordinary, incremental and decremental onse each having the excitatory and the inhibitory types). The properties of the models are described.     

Immunogold electron microscopic demonstration of glutamate and GABA in normal and deafferented cerebellar cortex: correlation between transmitter content and synaptic vesicle size

Selective labeling of mossy fiber terminals and parallel fibers was obtained in rat cerebellar cortex by a glutamate antibody produced and characterized by Hepler et al. The high-resolution electron microscopic immunogold demonstration of this amino acid offered the possibility of determining the size and shape of synaptic vesicles in glutamate-positive mossy endings. Mossy terminals that stained with the glutamate antibody formed two distinct populations, one with spherical synaptic vesicles with an average diameter of 34.0 nm (more than 90% of all mossy fiber endings) and one with pleomorphic and smaller synaptic vesicles which had an average diameter of 28.5 nm. We present experimental evidence that the mossy terminals with large round vesicles are of extracerebellar origin, whereas those with small pleomorphic synaptic vesicles are endings of nucleocortical fibers. The presence of two distinct classes of gamma-aminobutyric acid (GABA)-containing axon terminals within cerebellar glomeruli has also been demonstrated; those originating from the cerebellar nuclei contain large (36.2 nm) synaptic vesicles, whereas the majority of GABA-stained axon terminals that are of local (cortical) origin contain small (29.1 nm) synaptic vesicles. It therefore appears that, at least in the case of glutamate and GABA, morphological characterization of the axon terminals based on the size and shape of synaptic vesicles is not a reliable indicator of their functional nature (i.e., whether they are excitatory or inhibitory); convincing evidence for the identity of the transmitter can be obtained only by electron microscopic immunostaining procedures. Our results also suggest the existence of both inhibitory and excitatory feedback from cerebellar nuclei to cerebellar cortex.     

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.     

Bifurcation properties of the average activity of interconnected neural populations

The relevant scale for the study of the electrical activity of neural networks is a problem of mathematical and biological interest. From a continuous model of the cortex activity we derive a simple model of an interconnected pair of excitatory and inhibitory neural populations that describes the activity of a homogeneous network. Our model depends on three parameters that stand for the scale variability of the network. A bifurcation analysis reveals a great variety of patterns that arise from the interplay of excitatory and inhibitory populations provided by synaptic interactions. We emphasize the differences between the dynamical regimes when considering a moderate and a high inhibitory scale. We discuss the consequences on a propagating activity.     

Calcium dependent plasticity applied to repetitive transcranial magnetic stimulation with a neural field model

The calcium dependent plasticity (CaDP) approach to the modeling of synaptic weight change is applied using a neural field approach to realistic repetitive transcranial magnetic stimulation (rTMS) protocols. A spatially-symmetric nonlinear neural field model consisting of populations of excitatory and inhibitory neurons is used. The plasticity between excitatory cell populations is then evaluated using a CaDP approach that incorporates metaplasticity. The direction and size of the plasticity (potentiation or depression) depends on both the amplitude of stimulation and duration of the protocol. The breaks in the inhibitory theta-burst stimulation protocol are crucial to ensuring that the stimulation bursts are potentiating in nature. Tuning the parameters of a spike-timing dependent plasticity (STDP) window with a Monte Carlo approach to maximize agreement between STDP predictions and the CaDP results reproduces a realistically-shaped window with two regions of depression in agreement with the existing literature. Developing understanding of how TMS interacts with cells at a network level may be important for future investigation.     

Differential effects of GABA on three muscles innervated by a common inhibitory axon ofOcypode

Summary The effect of GABA (-aminobutyric acid) on three muscles innervated by the common inhibitory axon in the walking leg of the crabOcypode cursor, was studied. The muscles differ in the percentage of fibres responding to GABA by membrane resistance decrease, and in the magnitude of the response (Table 1). In addition to the postsynaptic effect (on muscle fibre membrane) of GABA, a presynaptic effect (on excitatory terminals) was observed in one muscle, resulting in more effective inhibition of excitatory potentials. The presynaptic effect sustained as long as GABA was present, while the postsynaptic effect underwent desensitization (Fig. 2). The data demonstrate differential inhibition of distinct functional units innervated by a common axon. The channeling of inhibitory information results from spatial organization of innervation, differing in location (pre-or postsynaptic) and density.This investigation was supported by grant AZ11 1955 for Stiftung Volkswagenwerk.     

Stability and structural constraints of random brain networks with excitatory and inhibitory neural populations

The stability of brain networks with randomly connected excitatory and inhibitory neural populations is investigated using a simplified physiological model of brain electrical activity. Neural populations are randomly assigned to be excitatory or inhibitory and the stability of a brain network is determined by the spectrum of the network’s matrix of connection strengths. The probability that a network is stable is determined from its spectral density which is numerically determined and is approximated by a spectral distribution recently derived by Rajan and Abbott. The probability that a brain network is stable is maximum when the total connection strength into a population is approximately zero and is shown to depend on the arrangement of the excitatory and inhibitory connections and the parameters of the network. The maximum excitatory and inhibitory input into a structure allowed by stability occurs when the net input equals zero and, in contrast to networks with randomly distributed excitatory and inhibitory connections, substantially increases as the number of connections increases. Networks with the largest excitatory and inhibitory input allowed by stability have multiple marginally stable modes, are highly responsive and adaptable to external stimuli, have the same total input into each structure with minimal variance in the excitatory and inhibitory connection strengths, and have a wide range of flexible, adaptable, and complex behavior.     

Differences in synaptic output between excitatory and inhibitory motoneurons in a crayfish muscle

A pair of antagonistic motoneurons, one excitatory and one inhibitory, innervates the distal accessory flexor muscle in the walking limb of the crayfish Procambarus clarkii. The number and size of synapses formed by these two axons on the muscle fibers (neuromuscular synapses) and on each other (axo-axonal synapses) were estimated using thin-section electron microscopy. Although profiles of nerve terminals of the two axons occur in roughly equal proportions, the frequency of occurrence of neuromuscular synapses differed markedly: 73% were excitatory and 27% were inhibitory. However, inhibitory synapses were 4–5 times larger than excitatory ones, and consequently, the total contact areas devoted to neuromuscular synapses were similar for both axons. Axo-axonal synapses were predominantly from the inhibitory axon to the excitatory axon (86%), and a few were from the excitatory axon to the inhibitory axon (14%). The role of the inhibitory axo-axonal synapse is presynaptic inhibition, but that of the excitatory axo-axonal synapse is not known. The differences in size of neuromuscular synapses between the two axons may reflect intrinsic determinants of the neuron, while the similarity in total synaptic area may reflect retrograde influences from the muscle for regulating synapse number.     

Mesoscopic Segregation of Excitation and Inhibition in a Brain Network Model

Neurons in the brain are known to operate under a careful balance of excitation and inhibition, which maintains neural microcircuits within the proper operational range. How this balance is played out at the mesoscopic level of neuronal populations is, however, less clear. In order to address this issue, here we use a coupled neural mass model to study computationally the dynamics of a network of cortical macrocolumns operating in a partially synchronized, irregular regime. The topology of the network is heterogeneous, with a few of the nodes acting as connector hubs while the rest are relatively poorly connected. Our results show that in this type of mesoscopic network excitation and inhibition spontaneously segregate, with some columns acting mainly in an excitatory manner while some others have predominantly an inhibitory effect on their neighbors. We characterize the conditions under which this segregation arises, and relate the character of the different columns with their topological role within the network. In particular, we show that the connector hubs are preferentially inhibitory, the more so the larger the node''s connectivity. These results suggest a potential mesoscale organization of the excitation-inhibition balance in brain networks.     

Feedforward architectures driven by inhibitory interactions

Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward networks, activity is exclusively driven by excitatory neurons and the wiring patterns between them, while inhibitory neurons play only a stabilizing role for the network dynamics. Motivated by recent experimental discoveries of hippocampal circuitry, cortical circuitry, and the diversity of inhibitory neurons throughout the brain, here we illustrate that one can construct such networks even if the connectivity between the excitatory units in the system remains random. This is achieved by endowing inhibitory nodes with a more active role in the network. Our findings demonstrate that apparent feedforward activity can be caused by a much broader network-architectural basis than often assumed.     

Analytical results on a Wilson-Cowan neuronal network modified model

Wilson-Cowan model is employed in studies concerning neuronal networks. This model consists of two nonlinear differential equations that represent the interaction between excitatory and inhibitory populations of neurons. The mutual influence of these populations is described through a sigmoidal function, which is usually chosen as the hyperbolic tangent or the logistic curve. Both choices make difficult theoretical analyses. Here we choose another sigmoidal function and analytically obtain the set of parameter values for which an asymptotically stable limit cycle exists. This result is potentially useful to analytical and numerical works on the binding problem, which is the problem of creating a coherent representation of objects from the oscillatory activity of spatially separated cortical columns.     

Allotransplanted nerves regenerate inhibitory synapses on a crayfish muscle: Possible postsynaptic specification

Donor nerves of different origins, when transplanted onto a previously denervated adult crayfish abdominal superficial flexor muscle (SFM), regenerate excitatory synaptic connections. Here we report that an inhibitory axon in these nerves also regenerates synaptic connections based on observation of nerve terminals with irregular to elliptically shaped synaptic vesicles characteristic of the inhibitory axon in aldehyde fixed tissue. Inhibitory terminals were found at reinnervated sites in all 12 allotransplanted-SFMs, underscoring the fact that the inhibitory axon regenerates just as reliably as the excitatory axons. At sites with degenerating nerve terminals and at sparsely reinnervated sites, we observe densely stained membranes, reminiscent of postsynaptic membranes, but occurring as paired, opposing membranes, extending between extracellular channels of the subsynaptic reticulum. These structures are not found at richly innervated sites in allotransplanted SFMs, in control SFMs, or at several other crustacean muscles. Although their identity is unknown, they are likely to be remnant postsynaptic membranes that become paired with collapse of degenerated nerve terminals of excitatory and inhibitory axons. Because these two axons have uniquely different receptor channels and intramembrane structure, their remnant postsynaptic membranes may therefore attract regenerating nerve terminals to form synaptic contacts selectively by excitatory or inhibitory axons, resulting in postsynaptic specification.     

A Realistic Neural Mass Model of the Cortex with Laminar-Specific Connections and Synaptic Plasticity – Evaluation with Auditory Habituation

In this work we propose a biologically realistic local cortical circuit model (LCCM), based on neural masses, that incorporates important aspects of the functional organization of the brain that have not been covered by previous models: (1) activity dependent plasticity of excitatory synaptic couplings via depleting and recycling of neurotransmitters and (2) realistic inter-laminar dynamics via laminar-specific distribution of and connections between neural populations. The potential of the LCCM was demonstrated by accounting for the process of auditory habituation. The model parameters were specified using Bayesian inference. It was found that: (1) besides the major serial excitatory information pathway (layer 4 to layer 2/3 to layer 5/6), there exists a parallel “short-cut” pathway (layer 4 to layer 5/6), (2) the excitatory signal flow from the pyramidal cells to the inhibitory interneurons seems to be more intra-laminar while, in contrast, the inhibitory signal flow from inhibitory interneurons to the pyramidal cells seems to be both intra- and inter-laminar, and (3) the habituation rates of the connections are unsymmetrical: forward connections (from layer 4 to layer 2/3) are more strongly habituated than backward connections (from Layer 5/6 to layer 4). Our evaluation demonstrates that the novel features of the LCCM are of crucial importance for mechanistic explanations of brain function. The incorporation of these features into a mass model makes them applicable to modeling based on macroscopic data (like EEG or MEG), which are usually available in human experiments. Our LCCM is therefore a valuable building block for future realistic models of human cognitive function.     

Control of computational dynamics of coupled integrate-and-fire neurons

 Generation and control of different dynamical modes of computational processes in a net of interconnected integrate-and-fire neurons are demonstrated. A net architecture resembling a generic cortical structure is formed from pairs of excitatory and inhibitory units with excitatory connections between and inhibitory connections within pairs. Integrate-and-fire model neurons derived from detailed conductance-based models of neocortical pyramidal cells and fast-spiking interneurons are employed for the excitatory and inhibitory units, respectively. Firing-rate adaptation is incorporated into the excitatory units based on the regulation of the slow afterhyperpolarization phase of action potentials by intracellular calcium ions. Saturation of synaptic conductances is implemented for the interconnections between units. It is shown that neuronal adaptation of the excitatory units can generate richer net dynamics than relaxation to fixed-point attractors in a pattern space. At strong adaptivity, i.e. when the neuronal excitability is strongly influenced by the preceding activity, complex dynamics of either aperiodic or limit-cycle character are generated in both the pattern space and the phase space of all dynamical variables. This regime corresponds to an exploratory mode of the system, in which the pattern space can be searched. At weak adaptivity, the dynamics are governed by fixed-point attractors in the pattern space, and this corresponds to a mode for retrieval of a particular pattern. In the brain, neuronal adaptivity can be regulated by various neuromodulators. The results are in accordance with those recently obtained by means of more abstract models formulated in terms of mean firing rates. The increased realism makes the present model reveal more detailed mechanisms and strengthens the relevance of the conclusions to biological systems. The simplicity and realism of the coupled integrate-and-fire neurons make the present model useful for studies of systems in which the temporal aspects of neural coding are important. Received: 8 December 1995 / Accepted in revised form: 23 January 1997     

Computer simulation of shared input among projection neurons in the dorsal cochlear nucleus

Computer simulations of a network model of an isofrequency patch of the dorsal cochlear nucleus (DCN) were run to explore possible mechanisms for the level-dependent features observed in the cross-correlograms of pairs of type IV units in the cat and nominal type IV units in the gerbil DCN. The computer model is based on the conceptual model (of a cat) that suggests two sources of shared input to DCN's projection neurons (type IV units): excitatory input from auditory nerves and inhibitory input from interneurons (type II units). Use of tonal stimuli is thought to cause competition between these sources resulting in the decorrelation of type IV unit activities at low levels. In the model, P-cells (projection neurons), representing type IV units, receive inhibitory input from I-cells (interneurons), representing type II units. Both sets of model neurons receive a simulated excitatory auditory nerve (AN) input from same-CF AN fibers, where the AN input is modeled as a dead-time modified Poisson process whose intensity is given by a computationally tractable discharge rate versus sound pressure level function. Subthreshold behavior of each model neuron is governed by a set of normalized state equations. The computer model has previously been shown to reproduce the major response properties of both type IV and type II units (e.g., rate-level curves and peri-stimulus time histograms) and the level-dependence of the functional type II-type IV inhibitory interaction. This model is adapted for the gerbil by simulating a reduced population of I-cells. Simulations were carried out for several auditory nerve input levels, and cross-correlograms were computed from the activities of pairs of P-cells for a complete (cat model) and reduced (gerbil model) population of I-cells. The resultant correlograms show central mounds (CMs), indicative of either shared excitatory or inhibitory input, for both spontaneous and tone-evoked driven activities. Similar to experimental results, CM amplitudes are a non-monotonic function of level and CM widths decrease as a function of level. These results are consistent with the hypothesis that shared excitatory input correlates the spontaneous activities of type IV units and shared inhibitory input correlates their driven activities. The results also suggest that the decorrelation of the activities of type IV units can result from a reduced effectiveness of the AN input as a function of increasing level. Thus, competition between the excitatory and inhibitory inputs is not required.     

Neural field model of seizure-like activity in isolated cortex

Epileptiform discharges on an isolated cortex are explored using neural field theory. A neural field model of the isolated cortex is used that consists of three neural populations, excitatory, inhibitory, and excitatory bursting. Mechanisms by which an isolated cortex gives rise to seizure-like waveforms thought to underly pathological EEG waveforms on the deafferented cortex are explored. It is shown that the model reproduces similar time series and oscillatory frequencies for paroxysmal discharges when compared with physiological recordings both during acute and chronic deafferentation states. Furthermore, within our model ictal activity arises from perturbations to steady-states very close to the dynamical system’s instability boundary; hence, these are distinct from corticothalamic seizures observed in the model for the intact brain which involved limit-cycle dynamics. The results are applied to experiments in deafferented cats.     

Neurotransmitter and Neuromodulator Activity in the Gustatory Zone of the Nucleus Tractus Solitarius

The rostral nucleus of the solitary tract (rNST) is the firstcentral relay in the gustatory pathway. While previous investigationshave provided a wealth of information on the pattern of centralterminations of gustatory afferent fibers, the morphology ofsynaptic connections of rNST neurons and responses of secondorder neurons to taste stimuli applied to the tongue, littleis known regarding the neurophysiological characteristics ofsynaptic transmission in rNST. We have used an in vitro brainslice preparation of the rNST to study the intrinsic biophysicalproperties, neuropharmacology and synaptic responses of rNSTneurons. These experiments have revealed that rNST neurons respondto the excitatory amino acid neurotransmitter glutamate, aswell as the inhibitory amino acid neurotransmitter     

Mechanisms of seizure propagation in a cortical model

We consider a mathematical model of mesoscopic human cortical ictal electrical activity. We compare the model results with ictal electrocortical data recorded from three human subjects and show how the two agree. We determine that, in the model system, seizures result from increased connectivity between excitatory and inhibitory cell populations, or from decreased connectivity within either excitatory or inhibitory cell populations. We compare the model results with the disinhibition and 4-AP models of epilepsy and suggest how the model may guide the development of new anticonvulsant therapies.     

Role of astrocytes in the maintenance and modulation of glutamatergic and GABAergic neurotransmission

The functional activity in the brain is primarily composed of an interplay between excitation and inhibition. In any given region the output is based upon a complex processing of incoming signals that require both excitatory and inhibitory units. Moreover, these units must be regulated and balanced such that an integrated and finely tuned response is generated. In each of these units or synapses the activity depends on biosynthesis, release, receptor interaction, and inactivation of the neurotransmitter in question; thus, it is easily understood that each of these processes needs to be highly regulated and controlled. It is interesting to note that in case of the most prevailing neurotransmitters, glutamate and GABA, which mediate excitation and inhibition, respectively, the inactivation process is primarily maintained by highly efficient, high-affinity transport systems capable of maintaining transmembrane concentration gradients of these amino acids of 10⁴–10⁵-fold. The demonstration of the presence of transporters for glutamate and GABA in both neuronal and astrocytic elements naturally raises the question of the functional importance of the astrocytes in the regulation of the level of the neurotransmitters in the synaptic cleft and hence for the activity of excitatory and inhibitory neurotransmission. Obviously, this discussion has important implications for the understanding of the role of astrocytes in disease states in which imbalances between excitation and inhibition are a triggering factor, for example, epilepsy and neurodegeneration.     

Flowers and weeds: cell-type specific pruning in the developing visual thalamus

In the first weeks of vertebrate postnatal life, neural networks in the visual thalamus undergo activity-dependent refinement thought to be important for the development of functional vision. This process involves pruning of synaptic connections between retinal ganglion cells and excitatory thalamic neurons that relay signals on to visual areas of the cortex. A recent report in Neural Development shows that this does not occur in inhibitory neurons, questioning our current understanding of the development of mature neural circuits. See research article: http://www.neuraldevelopment.com/content/8/1/24