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.     

Recurrent circuitry dynamically shapes the activation of piriform cortex

In the piriform cortex, individual odorants activate a unique ensemble of neurons that are distributed without discernable spatial order. Piriform neurons receive convergent excitatory inputs from random collections of olfactory bulb glomeruli. Pyramidal cells also make extensive recurrent connections with other excitatory and inhibitory neurons. We introduced channelrhodopsin into the piriform cortex to characterize these intrinsic circuits and to examine their contribution to activity driven by afferent bulbar inputs. We demonstrated that individual pyramidal cells are sparsely interconnected by thousands of excitatory synaptic connections that extend, largely undiminished, across the piriform cortex, forming a large excitatory network that can dominate the bulbar input. Pyramidal cells also activate inhibitory interneurons that mediate strong, local feedback inhibition that scales with excitation. This recurrent network can enhance or suppress bulbar input, depending on whether the input arrives before or after the cortex is activated. This circuitry may shape the ensembles of piriform cells that encode odorant identity.     

Inhibitory Control of Linear and Supralinear Dendritic Excitation in CA1 Pyramidal Neurons

The transformation of dendritic excitatory synaptic inputs to axonal action potential output is the fundamental computation performed by all principal neurons. We show that in the hippocampus this transformation is potently controlled by recurrent inhibitory microcircuits. However, excitatory input on highly excitable dendritic branches could resist inhibitory?control by generating strong dendritic spikes and?trigger precisely timed action potential output. Furthermore, we show that inhibition-sensitive branches can be transformed into inhibition-resistant, strongly spiking branches by intrinsic plasticity of branch excitability. In addition, we demonstrate that the inhibitory control of spatially defined dendritic excitation is strongly regulated by network activity patterns. Our findings suggest that dendritic spikes may serve to transform correlated branch input into reliable and temporally precise output even in the presence of inhibition.     

Regulation of rhythm genesis by volume-limited,astroglia-like signals in neural networks

Rhythmic activity of the brain often depends on synchronized spiking of interneuronal networks interacting with principal neurons. The quest for physiological mechanisms regulating network synchronization has therefore been firmly focused on synaptic circuits. However, it has recently emerged that synaptic efficacy could be influenced by astrocytes that release signalling molecules into their macroscopic vicinity. To understand how this volume-limited synaptic regulation can affect oscillations in neural populations, here we explore an established artificial neural network mimicking hippocampal basket cells receiving inputs from pyramidal cells. We find that network oscillation frequencies and average cell firing rates are resilient to changes in excitatory input even when such changes occur in a significant proportion of participating interneurons, be they randomly distributed or clustered in space. The astroglia-like, volume-limited regulation of excitatory synaptic input appears to better preserve network synchronization (compared with a similar action evenly spread across the network) while leading to a structural segmentation of the network into cell subgroups with distinct firing patterns. These observations provide us with some previously unknown insights into the basic principles of neural network control by astroglia.     

Membrane properties and the balance between excitation and inhibition control gamma-frequency oscillations arising from feedback inhibition

Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30-80 Hz gamma rhythm in which network oscillations arise through 'stochastic synchrony' capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

Glutamate-Bound NMDARs Arising from In Vivo-like Network Activity Extend Spatio-temporal Integration in a L5 Cortical Pyramidal Cell Model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.     

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.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.     

A neural network model of reliably optimized spike transmission

We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.     

Activity-dependent matching of excitatory and inhibitory inputs during refinement of visual receptive fields

The receptive field (RF) of single visual neurons undergoes progressive refinement during development. It remains largely unknown how the excitatory and inhibitory inputs on single developing neurons are refined in a coordinated manner to allow the formation of functionally correct circuits. Using whole-cell voltage-clamp recording from Xenopus tectal neurons, we found that RFs determined by excitatory and inhibitory inputs in more mature tectal neurons are spatially matched, with each spot stimulus evoking balanced synaptic excitation and inhibition. This emerges during development through a gradual reduction in the RF size and a transition from disparate to matched topography of excitatory and inhibitory inputs to the tectal neurons. Altering normal spiking activity of tectal neurons by either blocking or elevating GABA(A) receptor activity significantly impeded the developmental reduction and topographic matching of RFs. Thus, appropriate inhibitory activity is essential for the coordinated refinement of excitatory and inhibitory connections.     

Excitatory actions of GABA in the cortex

Little is known about how GABAergic inputs interact with excitatory inputs under conditions that maintain physiological concentrations of intracellular anions. Using extracellular and gramicidin perforated-patch recording, we show that somatic and dendritic GABA responses in mature cortical pyramidal neurons are depolarizing from rest and can facilitate action potential generation when combined with proximal excitatory input. Dendritic GABA responses were excitatory regardless of timing, whereas somatic GABA responses were inhibitory when coincident with excitatory input but excitatory at earlier times. These excitatory actions of GABA occur even though the GABA reversal potential is below action potential threshold and largely uniform across the somato-dendritic axis, and arise when GABAergic inputs are temporally or spatially isolated from concurrent excitation. Our findings demonstrate that under certain circumstances GABA will have an excitatory role in synaptic integration in the cortex.     

Interrelated modification of excitatory and inhibitory synaptic connections in the olivary-cerebellar neuronal network

The model of simultaneous interrelated modification in the efficacy of synaptic inputs to different neurons of the olivary-cerebellar network is developed. The model is based on the following features of the network: simultaneous activation of the input layer (granule) cells and the output layer (deep cerebellar nuclei) cells by mossy fibers; simultaneous activation of Purkinje cells and cerebellar cells of the input and output layers by climbing fibers and their collaterals; the existence of local feedback excitatory, inhibitory, and disinhibitory circuits. The rise (decrease) of posttetanic Ca2+ concentration in reference to the level produced by previous stimulation causes the decrease (increase) in cGMP-dependent protein kinase G activity, and increase (decrease) inprotein phosphatase 1 activity. Subsequent dephosphorylation (phosphorylation) of ionotropic receptors results in simultaneous LTD (LTP) of the excitatory input together with the LTP (LTD) of the inhibitory input to the same neuron. The character of interrelated modifications of synapses at different cerebellar levels strongly depends on the olivary cell activity. In the presence (absence) of the signal from the inferior olive LTD (LTP) of the output cerebellar signal can be induced.     

Does inhibition balance excitation in neocortex?

The distribution of inhibitory and excitatory synapses on neocortical neurons is at odds with a simple view that cortical functioning can persist by maintaining a balance between inhibitory and excitatory drives. Pyramidal cells can potentially be shut down by very powerful proximal inhibitory synapses, despite these accounting for perhaps less than 1% of their total number of synaptic inputs. Interneurons in contrast are dominated by excitatory inputs. These may be powerful enough to effect an apparent depolarizing block at the soma. In this extreme case though, models suggest that action potentials are generated down the axon, and the cells behave like integrate-and-fire neurons. We discuss possible network implications of these modelling studies.     

A Continuous Attractor Network Model Without Recurrent Excitation: Maintenance and Integration in the Head Direction Cell System

Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of selective external inputs, and to accurately update this variable on the basis of angular velocity inputs. The network is composed of one excitatory population and two inhibitory populations, with inter-connections between populations but no connections within the neurons of a same population. In particular, there are no excitatory-to-excitatory connections. Angular velocity signals are represented as inputs in one inhibitory population (clockwise turns) or the other (counterclockwise turns). The system is studied using a combination of analytical and numerical methods. Analysis of a simplified model composed of threshold-linear neurons gives the conditions on the connectivity for (i) the emergence of the spatially selective profile, (ii) reliable integration of angular velocity inputs, and (iii) the range of angular velocities that can be accurately integrated by the model. Numerical simulations allow us to study the proposed scenario in a large network of spiking neurons and compare their dynamics with that of head direction cells recorded in the rat limbic system. In particular, we show that the directional representation encoded by the attractor network can be rapidly updated by external cues, consistent with the very short update latencies observed experimentally by Zugaro et al. (2003) in thalamic head direction cells.     

A model of the mechanisms of formation of unit activity

Dependence of the temporal structure of the spike discharge of a neuron in a weakly interacting network on the characteristics of excitatory and inhibitory input flows and on cell parameters was analyzed by a mathematical model. The intensity of communication between individual neurons corresponded to the intensity of synaptic communication between real spinal neurons. The temporal course of trace and accommodation processes in the model was similar to that of these processes in real spinal neurons. Connection of inhibitory inputs and an increase in the intensity of their influences were shown to be equivalent to a decrease in the intensity of excitatory input flows. Changes in cell parameters had a significant effect on the spike discharge only in the case of weak input influences (the ratio of the amplitude of the combined ESP evoked by the input spike train to the threshold value of membrane potential at rest was about 1.2:1.0 to 1.4:1.0). An increase in the input flow intensity led to considerable reorganization of the firing pattern: Mean values of interspike intervals and their fluctuations were reduced, histograms of interspike intervals became more symmetrical, and periodic waves appeared on the autocorrelation histograms. It is concluded on the basis of these results and of data in the literature that the main factor determining reorganization of the temporal structure of unit activity in a network of weakly interacting cells is the intensity of the input flow.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 199–207, March–April, 1980.     

An improved neural-network model for the neural integrator of the oculomotor system: More realistic neuron behavior

The discharge rates of premotor, brain-stem neurons that create eye movements modulate in relation to eye velocity yet firing rates of extraocular motoneurons contain both eye-position and eyevelocity signals. The eye-position signal is derived from the eye-velocity command by means of a neural network which functioins as a temporal integrator. We have previously proposed a network of lateral-inhibitory neurons that is capable of performing the required integration. That analysis centered on the temporal aspects of the signal processing for a limited class of idealized inputs. All of its cells were identical and carried only the integrated signal. Recordings in the brain stem, however, show that neurons in the region of the neural integrator have a variety of background firing rates, all carry some eye-velocity signal as well as the eye-position signal, and carry the former with different strengths depending on the type of eye movement being made. It was necessary to see if the proposed model could be modified to make its neurons more realistic.By modifying the spatial distribution of afferents to the network, we demonstrate that the same basic model functions properly in spite of afferents with nonuniform background firing rates. To introduce the eye-velocity signal a double-layer network, consisting of inhibitory and excitatory cells, was necessary. By presenting the velocity input to only local regions of this network it was shown that all cells in the network still carried the integrated signal and that its cells could carry different eye-velocity signals for different types of eye movements. Thus, this model stimulates quantitatively and qualitatively, the behavior of neurons seen in the region of the neural integrator.     

Dependency analysis of frequency and strength of gamma oscillations on input difference between excitatory and inhibitory neurons

It has been found that gamma oscillations and the oscillation frequencies are regulated by the properties of external stimuli in many biology experimental researches. To unveil the underlying mechanism, firstly, we reproduced the experimental observations in an excitatory/inhibitory (E/I) neuronal network that the oscillation became stronger and moved to a higher frequency band (gamma band) with the increasing of the input difference between E/I neurons. Secondly, we found that gamma oscillation was induced by the unbalance between positive and negative synaptic currents, which was caused by the input difference between E/I neurons. When this input difference became greater, there would be a stronger gamma oscillation (i.e., a higher peak power in the power spectrum of the population activity of neurons). Further investigation revealed that the frequency dependency of gamma oscillation on the input difference between E/I neurons could be explained by the well-known mechanisms of inter-neuron-gamma (ING) and pyramidal-interneuron-gamma (PING). Finally, we derived mathematical analysis to verify the mechanism of frequency regulations and the results were consistent with the simulation results. The results of this paper provide a possible mechanism for the external stimuli-regulated gamma oscillations.