Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10–200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials (_s/T), where T can be determined either from the network or from a single, self-inhibiting neuron. With _s/T > 2, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With _s/T < 1, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.     

Evoked Electrical Activity and Immunocytochemical Peculiarities of Cultured Excitatory and Inhibitory Neurons of the Rat Hippocampus

Experiments were carried out on cultured hippocampal neurons using a patch-clamp technique in the whole-cell configuration. We studied the characteristics of regular series of action potentials (APs), which were generated with a low frequency by inhibitory and excitatory interneurons after their direct stimulation with long-lasting (500 msec) current pulses. Nearly all parameters of the evoked impulse activity (except the frequency of generation and duration of APs) in excitatory and inhibitory neurons were significantly different. According to immunocytochemical analysis, Kv1.2- and Kv4.2-type potassium channels were expressed in the membrane of excitatory neurons (granular cells), and somatostatin was present in all these cells. As to inhibitory interneurons, only a part of such cells (large units) demonstrated immunopositivity with respect to somatostatin. In inhibitory neurons, only Kv1.2-type potassium channels were expressed. Therefore, mechanisms responsible for the ability of hippocampal interneurons to generate impulse activity under conditions of direct stimulation (in our experiments, regular low-frequency series of APs) in inhibitory and excitatory neurons are rather dissimilar. Neirofiziologiya/Neurophysiology, Vol. 37, No. 3, pp. 207–216, May–June, 2005.     

Oscillations and Irregular Emission in Networks of Linear Spiking Neurons

The dynamics of a network of randomly connected inhibitory linear integrate and fire (LIF) neurons (with a floor for the depolarization), in the presence of stochastic external afferent input, is considered in various parameter regimes of the neurons and of the network. Applying a technique recently introduced by Brunel and Hakim, we classify the regimes in which such a network has stable stationary states and in which spike emission rates oscillate. In the vicinity of the bifurcation line, the oscillation frequency and its amplitude are computed and compared with simulations. As for leaky IF neurons, the space of parameters can be compacted into two. Yet despite significant technical differences between the two models, related to both the different dynamics of the depolarization as well as to the different boundary conditions, the qualitative behavior is rather similar. The significance of LIF neurons and of the differences with leaky IF neurons is discussed.     

Inhibitory Postsynaptic Currents Induced by Activation of Interneurons in Cultured Rat Hippocampal Neurons

Using the patch-clamp technique in the whole-cell configuration, we studied the characteristics of a series of action potentials (APs) induced by a 500-msec-long current pulse applied to a pre-synaptic unit, as well as the kinetic characteristics of post-synaptic currents (PSCs) evoked by the APs in a post-synaptic unit, in synaptically connected pairs of cultured hippocampal neurons. Presynaptic inhibitory units were identified as GABA-ergic interneurons; they were divided into two groups according to the size of the soma and the number of processes. The kinetic characteristics of PSCs, which were induced in the post-synaptic neuron by a series of the APs generated in the pre-synaptic cell, demonstrated a certain dependence on the morphological characteristics of these cells. In interneurons with large-sized somata, the kinetics of the currents were more fast, and the reversal potential was close to the equilibrium Cl potential. In interneurons with small-sized somata, currents were slower, and the reversal potential was shifted. We conclude that under conditions of culturing, a pre-synaptic cell not only directly provokes the development of PSC in a post-synaptic neuron and determines the amplitude of this current but also significantly influences the kinetics of this current. Neirofiziologiya/Neurophysiology, Vol. 37, No. 2, pp. 116–123, March–April, 2005.     

Emergent Oscillations in a Realistic Network: The Role of Inhibition and the Effect of the Spatiotemporal Distribution of the Input

We have simulated a network of 10,000 two-compartment cells, spatially distributed on a two-dimensional sheet; 15% of the cells were inhibitory. The input to the network was spatially delimited. Global oscillations frequently were achieved with a simple set of connectivity rules. The inhibitory neurons paced the network, whereas the excitatory neurons amplified the input, permitting oscillations at low-input intensities. Inhibitory neurons were active over a greater area than excitatory ones, forming a ring of inhibition. The oscillation frequency was modulated to some extent by the input intensity, as has been shown experimentally in the striate cortex, but predominantly by the properties of the inhibitory neurons and their connections: the membrane and synaptic time constants and the distribution of delays.In networks that showed oscillations and in those that did not, widely distributed inputs could lead to the specific recruitment of the inhibitory neurons and to near zero activity of the excitatory cells. Hence the spatial distribution of excitatory inputs could provide a means of selectively exciting or inhibiting a target network. Finally, neither the presence of oscillations nor the global spike activity provided any reliable indication of the level of excitatory output from the network.     

Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Effective desynchronization can be exploited as a tool for probing the functional significance of synchronized neural activity underlying perceptual and cognitive processes or as a mild treatment for neurological disorders like Parkinson’s disease. In this article we show that pulse-based desynchronization techniques, originally developed for networks of globally coupled oscillators (Kuramoto model), can be adapted to networks of coupled neurons with dendritic dynamics. Compared to the Kuramoto model, the dendritic dynamics significantly alters the response of the neuron to the stimulation. Under medium stimulation amplitude a bistability of the re- sponse of a single neuron is observed. When stimulated at some initial phases, the neuron displays only modulations of its firing, whereas at other initial phases it stops oscillating entirely. Significant alterations in the duration of stimulation-induced transients are also observed. These transients endure after the end of the stimulation and cause maximal desynchronization to occur not during the stimulation, but with some delay after the stimulation has been turned off. To account for this delayed desynchronization effect, we have designed a new calibration procedure for finding the stimulation parameters that result in optimal desynchronization. We have also developed a new desynchronization technique by low frequency entrainment. The stimulation techniques originally developed for the Kuramoto model, when using the new calibration procedure, can also be applied to networks with dendritic dynamics. However, the mechanism by which desynchronization is achieved is substantially different than for the network of Kuramoto oscillators. In particular, the addition of dendritic dynamics significantly changes the timing of the stimulation required to obtain desynchronization. We propose desynchronization stimulation for experimental analysis of synchronized neural processes and for the therapy of movement disorders.     

Alterations in a cross-hemispheric circuit associates with novelty discrimination deficits in mouse models of neurodegeneration

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Prolonged Decay of Evoked Inhibitory Postsynaptic Currents in Hippocampal Neurons Is Not Shaped by Asynchronous Release

During evoked release, several quanta of neurotransmitter are synchronously released in several GABA-ergic synapses. Assuming that not more than one vesicle is released at each release site, the decay of miniature and evoked IPSC (mIPSC and eIPSC, respectively) should coincide. In this study, we found that in a considerable part of the cultured hippocampal neurons eIPSC decayed more slowly than mIPSC did. We investigated the mechanisms underlying this difference using conventional electrophysiological approaches, deconvolution, simulations, and nonstationary noise analysis. Our results indicate that asynchronous release of synaptic vesicles cannot explain the prolonged decay of the GABA-ergic IPSC. We suggest that some interaction between the quanta at the pre- and/or post-synaptic level should result in a slower decay of the eIPSC in comparison with that of mIPSC.     

Synchronization of neuronal assemblies in reciprocally connected cortical areas

Summary To investigate scene segmentation in the visual system we present a model of two reciprocally connected visual areas comprising spiking neurons. The peripheral area P is modeled similar to the primary visual cortex, while the central area C is modeled as an associative memory representing stimulus objects according to Hebbian learning. Without feedback from area C, spikes corresponding to stimulus representations in P are synchronized only locally (slow state). Feedback from C can induce fast oscillations and an increase of synchronization ranges (fast state). Presenting a superposition of several stimulus objects, scene segmentation happens on a time scale of hundreds of milliseconds by alternating epochs of the slow and fast state, where neurons representing the same object are simultaneously in the fast state. We relate our simulation results to various phenomena observed in neurophysiological experiments, such as stimulus-dependent synchronization of fast oscillations, synchronization on different time scales, ongoing activity, and attention-dependent neural activity.     

Variety of types of cortical interneurons

A most important component of the mammalian neocortex is the system of inhibitory interneurons. It is composed of cellular elements, which differ from each other in morphological, electrophysiological, and genetical features; these cells form a complex system of synaptic connections with glutamatergic cells and with each other. Some regularities that characterize the variety of types of cortical interneurons are discussed in our study. Neirofiziologiya/Neurophysiology, Vol. 39, No. 3, pp. 260–269, May–June, 2007.     

Hippocampal Ripple Coordinates Retrosplenial Inhibitory Neurons during Slow-Wave Sleep

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Hippocampal GABAergic Interneurons: A Physiological Perspective

Oscillations within and across neuronal systems are believed to serve various complex functions, such as perception, cognition, movement initiation, plasticity and memory. GABAergic interneurons and their inhibitory synapses play a major role in these oscillatory patterns. Networks of inhibitory interneurons impose a coordinated oscillatory context for the content carried by networks of principal cells. This hypothesis implies that GABAergic neuronal supernetworks may cooperatively entrain large populations of pyramidal cells throughout the forebrain. Experiments on hippocampal interneurons are reviewed and possible solutions for some of these complex functions are illustrated.     

Novel Bursting Patterns Emerging from Model Inhibitory Networks with Synaptic Depression

Studies show that short-term synaptic plasticity plays important roles in neural coding and the normal operation of the synapse. Basket cells in the hippocampus demonstrate this plasticity in the form of synaptic depression, and recent in vivo work indicates that basket cell activities contribute significantly to hippocampal output associated with different behavioural states. Thus it is essential to understand the generation and synchronization of patterns produced by basket cell networks with depression. We study two-cell model inhibitory networks with depression and obtain alternating bursting patterns and synchronous activity occurring between bursts. We describe mechanisms for how these patterns emerge by performing several simulations in the plane of different depression time constants, tauD. Such patterns might contribute significantly to various population activities observed in the hippocampus.     

Gamma frequency activation of inhibitory neurons in the acute phase after stroke attenuates vascular and behavioral dysfunction

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Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons

Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.     

Two-Cell to N-Cell Heterogeneous,Inhibitory Networks: Precise Linking of Multistable and Coherent Properties

Inhibitory networks are now recognized as being the controllers of several brain rhythms. However, experimental work with inhibitory cells is technically difficult not only because of their smaller percentage of the neuronal population, but also because of their diverse properties. As such, inhibitory network models with tight links to the experimental data are needed to understand their contributions to population rhythms. However, mathematical analyses of network models with more than two cells is challenging when the cellular models involve biophysical details. We use bifurcation analyses and simulations to show that two-cell analyses can quantitatively predict N-cell (N = 20, 50, 100) network dynamics for heterogeneous, inhibitory networks. Interestingly, multistable states in the two-cell system are manifest as different and distinct coherent network patterns in the N-cell networks for the same parameter sets.