State transitions through inhibitory interneurons in a cortical network model

Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.     

Effects of phase on homeostatic spike rates

Recent experimental results by Talathi et al. (Neurosci Lett 455:145–149, 2009) showed a divergence in the spike rates of two types of population spike events, representing the putative activity of the excitatory and inhibitory neurons in the CA1 area of an animal model for temporal lobe epilepsy. The divergence in the spike rate was accompanied by a shift in the phase of oscillations between these spike rates leading to a spontaneous epileptic seizure. In this study, we propose a model of homeostatic synaptic plasticity which assumes that the target spike rate of populations of excitatory and inhibitory neurons in the brain is a function of the phase difference between the excitatory and inhibitory spike rates. With this model of homeostatic synaptic plasticity, we are able to simulate the spike rate dynamics seen experimentally by Talathi et al. in a large network of interacting excitatory and inhibitory neurons using two different spiking neuron models. A drift analysis of the spike rates resulting from the homeostatic synaptic plasticity update rule allowed us to determine the type of synapse that may be primarily involved in the spike rate imbalance in the experimental observation by Talathi et al. We find excitatory neurons, particularly those in which the excitatory neuron is presynaptic, have the most influence in producing the diverging spike rates and causing the spike rates to be anti-phase. Our analysis suggests that the excitatory neuronal population, more specifically the excitatory to excitatory synaptic connections, could be implicated in a methodology designed to control epileptic seizures.     

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.     

Gap junctions promote synchronous activities in a network of inhibitory interneurons

By using a single compartment biophysical model of a fast spiking interneuron the synchronization properties of a pair of cells, coupled by electrical and inhibitory synapses, are investigated. The inhibitory and excitatory synaptic couplings are modeled in order to reproduce the experimental time course of the corresponding currents. It is shown that increasing the conductance value of the electrical synapses enhances the synchronization between the spike trains of the two cells. Moreover, increasing either the decay time constant of the inhibitory current or the firing frequency of the cells favours the emergence of synchronous discharges.     

Synchronization without oscillatory neurons

Experimental results suggest that neurons in the cortex synchronize their action potentials on the millisecond time scale. More importantly this binding expresses functional relationships between the neurons. A model of neuronal interactions is proposed in which simultaneous discharges of neurons develop through specialized synaptic circuits. As an important prerequisite for this synchronization it is demonstrated that SynFire chains, generating different levels of excitation, propagate their activity waves at distinct velocities. Two chains were coupled by excitatory synapses and their activity was initiated at different times. Due to synaptic interactions, activity in the earlier-initiated chain accelerates propagation in the other chain until the two activity waves are synchronized. Compared with several neural network models with oscillatory units, physiologically more plausible neurons are simulated. It is still under debate whether neurons in the cortex show oscillatory dischargesper se. In particular, a high rate of noise relative to very weak synaptic gains cannot impair our results in the neural network simulations.     

Spike suppression in a local cortical circuit induced by transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) noninvasively interferes with human cortical function, and is widely used as an effective technique for probing causal links between neural activity and cognitive function. However, the physiological mechanisms underlying TMS-induced effects on neural activity remain unclear. We examined the mechanism by which TMS disrupts neural activity in a local circuit in early visual cortex using a computational model consisting of conductance-based spiking neurons with excitatory and inhibitory synaptic connections. We found that single-pulse TMS suppressed spiking activity in a local circuit model, disrupting the population response. Spike suppression was observed when TMS was applied to the local circuit within a limited time window after the local circuit received sensory afferent input, as observed in experiments investigating suppression of visual perception with TMS targeting early visual cortex. Quantitative analyses revealed that the magnitude of suppression was significantly larger for synaptically-connected neurons than for isolated individual neurons, suggesting that intracortical inhibitory synaptic coupling also plays an important role in TMS-induced suppression. A conventional local circuit model of early visual cortex explained only the early period of visual suppression observed in experiments. However, models either involving strong recurrent excitatory synaptic connections or sustained excitatory input were able to reproduce the late period of visual suppression. These results suggest that TMS targeting early visual cortex disrupts functionally distinct neural signals, possibly corresponding to feedforward and recurrent information processing, by imposing inhibitory effects through intracortical inhibitory synaptic connections.     

Emergence of preferred firing sequences in large spiking neural networks during simulated neuronal development

Two main processes concurrently refine the nervous system over the course of development: cell death and selective synaptic pruning. We simulated large spiking neural networks (100 x 100 neurons "at birth") characterized by an early developmental phase with cell death due to excessive firing rate, followed by the onset of spike timing dependent synaptic plasticity (STDP), driven by spatiotemporal patterns of stimulation. The cell death affected the inhibitory units more than the excitatory units during the early developmental phase. The network activity showed the appearance of recurrent spatiotemporal firing patterns along the STDP phase, thus suggesting the emergence of cell assemblies from the initially randomly connected networks. Some of these patterns were detected throughout the simulation despite the activity-driven network modifications while others disappeared.     

Oscillations in Large-Scale Cortical Networks: Map-Based Model

We develop a new computationally efficient approach for the analysis of complex large-scale neurobiological networks. Its key element is the use of a new phenomenological model of a neuron capable of replicating important spike pattern characteristics and designed in the form of a system of difference equations (a map). We developed a set of map-based models that replicate spiking activity of cortical fast spiking, regular spiking and intrinsically bursting neurons. Interconnected with synaptic currents these model neurons demonstrated responses very similar to those found with Hodgkin-Huxley models and in experiments. We illustrate the efficacy of this approach in simulations of one- and two-dimensional cortical network models consisting of regular spiking neurons and fast spiking interneurons to model sleep and activated states of the thalamocortical system. Our study suggests that map-based models can be widely used for large-scale simulations and that such models are especially useful for tasks where the modeling of specific firing patterns of different cell classes is important.     

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Mechanism of activation of human c-KIT kinase by internal tandem duplications of the juxtamembrane domain and point mutations at aspartic acid 816

The patients suffering from acidosis usually sign psychological deficits. The cerebral dysfunction is reportedly caused by an acid-induced functional impairment of GABAergic neurons; however, the role of pyramidal neurons in this process remains unclear. By using electrophysiological method and changing extracellular pH, we investigated the influence of acidic environment on pyramidal neurons in the cortical slices, such as their ability of firing spikes and response to synaptic inputs. A low pH of artificial cerebral spinal fluid elevates the responses of pyramidal neurons to excitatory synaptic inputs and their ability of encoding digital spikes, as well as reduces the signal transmission at GABAergic synapses. The elevated ability of neuronal spiking is associated with the decreases of refractory periods and threshold potentials. Therefore, acidosis deteriorates brain functions through making the activities between cortical pyramidal neurons and GABAergic neurons imbalanced toward the overexcitation of neural networks, a process similar to neural excitotoxicity.     

A network of spiking neurons that can represent interval timing: mean field analysis

Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.     

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.     

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.     

Travelling waves and EEG patterns during epileptic seizure: analysis with an integrate-and-fire neural network

Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50 x 50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio-temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low-amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level.     

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.     

Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters

Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.     

Propagation and synchronization of reverberatory bursts in developing cultured networks

Developing networks of neural systems can exhibit spontaneous, synchronous activities called neural bursts, which can be important in the organization of functional neural circuits. Before the network matures, the activity level of a burst can reverberate in repeated rise-and-falls in periods of hundreds of milliseconds following an initial wave-like propagation of spiking activity, while the burst itself lasts for seconds. To investigate the spatiotemporal structure of the reverberatory bursts, we culture dissociated, rat cortical neurons on a high-density multi-electrode array to record the dynamics of neural activity over the growth and maturation of the network. We find the synchrony of the spiking significantly reduced following the initial wave and the activities become broadly distributed spatially. The synchrony recovers as the system reverberates until the end of the burst. Using a propagation model we infer the spreading speed of the spiking activity, which increases as the culture ages. We perform computer simulations of the system using a physiological model of spiking networks in two spatial dimensions and find the parameters that reproduce the observed resynchronization of spiking in the bursts. An analysis of the simulated dynamics suggests that the depletion of synaptic resources causes the resynchronization. The spatial propagation dynamics of the simulations match well with observations over the course of a burst and point to an interplay of the synaptic efficacy and the noisy neural self-activation in producing the morphology of the bursts.     

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.