Non-Gaussian noise optimized spiking activity of Hodgkin–Huxley neurons on random complex networks

In this paper, we numerically study how the NGN's deviation q from Gaussian noise (q = 1) affects the spike coherence and synchronization of 60 coupled Hodgkin–Huxley (HH) neurons driven by a periodic sinusoidal stimulus on random complex networks. It is found that the effect of the deviation depends on the network randomness p (the fraction of random shortcuts): for larger p (p > 0.15), the spiking regularity keeps being improved with increasing q; while, for smaller p (p < 0.15), the spiking regularity can reach the best performance at an optimal intermediate q value, indicating the occurrence of “deviation-optimized spike coherence”. The synchronization becomes enhanced with decreasing q, and the enhancing extent for a random HH neuron network is stronger than for a regular one. These behaviors show that the spike coherence and synchronization of the present HH neurons on random networks can be more strongly enhanced by various other types of external noise than by Gaussian noise, whereby the neuron firings may behave more periodically in time and more synchronously in space. Our results provide the constructive roles of the NGN on the spiking activity of the present system of HH neuron networks.     

Variable neuronal participation in stereotypic motor programs

To what extent are motor networks underlying rhythmic behaviors rigidly hard-wired versus fluid and dynamic entities? Do the members of motor networks change from moment-to-moment or from motor program episode-to-episode? These are questions that can only be addressed in systems where it is possible to monitor the spiking activity of networks of neurons during the production of motor programs. We used large-scale voltage-sensitive dye (VSD) imaging followed by Independent Component Analysis spike-sorting to examine the extent to which the neuronal network underlying the escape swim behavior of Tritonia diomedea is hard-wired versus fluid from a moment-to-moment perspective. We found that while most neurons were dedicated to the swim network, a small but significant proportion of neurons participated in a surprisingly variable manner. These neurons joined the swim motor program late, left early, burst only on some cycles or skipped cycles of the motor program. We confirmed that this variable neuronal participation was not due to effects of the VSD by finding such neurons with intracellular recording in dye-free saline. Further, these neurons markedly varied their level of participation in the network from swim episode-to-episode. The generality of such unreliably bursting neurons was confirmed by their presence in the rhythmic escape networks of two other molluscan species, Tritonia festiva and Aplysia californica. Our observations support a view that neuronal networks, even those underlying rhythmic and stereotyped motor programs, may be more variable in structure than widely appreciated.     

Predicting single spikes and spike patterns with the Hindmarsh–Rose model

Most simple neuron models are only able to model traditional spiking behavior. As physiologists discover and classify different electrical phenotypes, computational neuroscientists become interested in using simple phenomenological models that can exhibit these different types of spiking patterns. The Hindmarsh–Rose model is a three-dimensional relaxation oscillator which can show both spiking and bursting patterns and has a chaotic regime. We test the predictive powers of the Hindmarsh–Rose model on two different test databases. We show that the Hindmarsh–Rose model can predict the spiking response of rat layer 5 neocortical pyramidal neurons on a stochastic input signal with a precision comparable to the best known spiking models. We also show that the Hindmarsh–Rose model can capture qualitatively the electrical footprints in a database of different types of neocortical interneurons. When the model parameters are fit from sub-threshold measurements only, the model still captures well the electrical phenotype, which suggests that the sub-threshold signals contain information about the firing patterns of the different neurons.     

Role of Acetylcholine in the Modulation of Activity of Neocortical Neurons in Awake Animals Performing an Instrumental Conditioned Reflex

We studied modulatory effects of the cholinergic system on the activity of sensorimotor cortex neurons related to realization of an instrumental conditioned placing reflex. Experiments were carried out on awake cats; multibarrel glass microelectrodes were used for extracellular recording of impulse activity of neurons in the sensorimotor cortex and iontophoretic application of synaptically active agents within the recording region. The background and reflex-related activity was recorded in the course of realization of conditioned movements, and then changes of spiking induced by applications of the testing substances were examined. Applications of acetylcholine and carbachol resulted in increases in the intensity of impulse reactions of neocortical neurons evoked by presentation of an acoustic signal and in simultaneous shortening of the response latencies. An agonist of muscarinic receptors, pylocarpine, exerted a similar effect on the evoked activity of sensorimotor cortex neurons. Blockers of muscarinic receptors, atropine and scopolamine, vice versa, sharply suppressed impulse reactions of cortical neurons to afferent stimulation and simultaneously increased latencies of these responses. Applications of an agonist of nicotinic receptors, nicotine, was accompanied by suppression of impulse neuronal responses, an increase in the latency of spike reactions to presentation of a sound signal, and a corresponding increase in the latency of a conditioned motor reaction. In contrast, application of an antagonist of nicotinic receptors, tubocurarine, significantly intensified neuronal spike responses and shortened their latency. The mechanisms underlying the effects of antagonists of membrane muscarinic and nicotinic cholinoreceptors and the role of activation of these receptors in the modulation of activity of pyramidal and non-pyramidal neocortical neurons related to realization of the instrumental motor reflex are discussed.     

Running as fast as it can: How spiking dynamics form object groupings in the laminar circuits of visual cortex

How spiking neurons cooperate to control behavioral processes is a fundamental problem in computational neuroscience. Such cooperative dynamics are required during visual perception when spatially distributed image fragments are grouped into emergent boundary contours. Perceptual grouping is a challenge for spiking cells because its properties of collinear facilitation and analog sensitivity occur in response to binary spikes with irregular timing across many interacting cells. Some models have demonstrated spiking dynamics in recurrent laminar neocortical circuits, but not how perceptual grouping occurs. Other models have analyzed the fast speed of certain percepts in terms of a single feedforward sweep of activity, but cannot explain other percepts, such as illusory contours, wherein perceptual ambiguity can take hundreds of milliseconds to resolve by integrating multiple spikes over time. The current model reconciles fast feedforward with slower feedback processing, and binary spikes with analog network-level properties, in a laminar cortical network of spiking cells whose emergent properties quantitatively simulate parametric data from neurophysiological experiments, including the formation of illusory contours; the structure of non-classical visual receptive fields; and self-synchronizing gamma oscillations. These laminar dynamics shed new light on how the brain resolves local informational ambiguities through the use of properly designed nonlinear feedback spiking networks which run as fast as they can, given the amount of uncertainty in the data that they process.     

Bursting dynamics remarkably improve the performance of neural networks on liquid computing

Burst firings are functionally important behaviors displayed by neural circuits, which plays a primary role in reliable transmission of electrical signals for neuronal communication. However, with respect to the computational capability of neural networks, most of relevant studies are based on the spiking dynamics of individual neurons, while burst firing is seldom considered. In this paper, we carry out a comprehensive study to compare the performance of spiking and bursting dynamics on the capability of liquid computing, which is an effective approach for intelligent computation of neural networks. The results show that neural networks with bursting dynamic have much better computational performance than those with spiking dynamics, especially for complex computational tasks. Further analysis demonstrate that the fast firing pattern of bursting dynamics can obviously enhance the efficiency of synaptic integration from pre-neurons both temporally and spatially. This indicates that bursting dynamic can significantly enhance the complexity of network activity, implying its high efficiency in information processing.     

Local cortical circuit model inferred from power-law distributed neuronal avalanches

How cortical neurons process information crucially depends on how their local circuits are organized. Spontaneous synchronous neuronal activity propagating through neocortical slices displays highly diverse, yet repeatable, activity patterns called “neuronal avalanches”. They obey power-law distributions of the event sizes and lifetimes, presumably reflecting the structure of local circuits developed in slice cultures. However, the explicit network structure underlying the power-law statistics remains unclear. Here, we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanche-like spiking activity. We demonstrate a neuronal wiring rule that governs the formation of mutually overlapping cell assemblies during the development of this network. The resultant network comprises a mixture of feedforward chains and recurrent circuits, in which neuronal avalanches are stable if the former structure is predominant. Interestingly, the recurrent synaptic connections formed by this wiring rule limit the number of cell assemblies embeddable in a neuron pool of given size. We investigate how the resultant power laws depend on the details of the cell-assembly formation as well as on the inhibitory feedback. Our model suggests that local cortical circuits may have a more complex topological design than has previously been thought. Competing financial interests: The authors declare that they have no competing financial interests. Action Editor: Peter Latham     

Possible role of GABAergic depolarization in neocortical neurons in generating hyperexcitatory behaviors during emergence from sevoflurane anesthesia in the rat

Hyperexcitatory behaviors occurring after sevoflurane anesthesia are of serious clinical concern, but the underlying mechanism is unknown. These behaviors may result from the potentiation by sevoflurane of GABAergic depolarization/excitation in neocortical neurons, cells implicated in the genesis of consciousness and arousal. The current study sought to provide evidence for this hypothesis with rats, the neocortical neurons of which are known to respond to GABA (γ-aminobutyric acid) with depolarization/excitation at early stages of development (i.e., until the second postnatal week) and with hyperpolarization/inhibition during adulthood. Employing behavioral tests and electrophysiological recordings in neocortical slice preparations, we found: (1) sevoflurane produced PAHBs (post-anesthetic hyperexcitatory behaviors) in postnatal day (P)1–15 rats, whereas it failed to elicit PAHBs in P16 or older rats; (2) GABAergic PSPs (postsynaptic potentials) were depolarizing/excitatory in the neocortical neurons of P5 and P10 rats, whereas mostly hyperpolarizing/inhibitory in the cells of adult rats; (3) at P14–15, <50% of rats had PAHBs and, in general, the cells of the animals with PAHBs exhibited strongly depolarizing GABAergic PSPs, whereas those without PAHBs showed hyperpolarizing or weakly depolarizing GABAergic PSPs; (4) bumetanide [inhibitor of the Cl⁻ importer NKCC (Na⁺–K⁺–2Cl⁻ cotransporter)] treatment at P5 suppressed PAHBs and depolarizing GABAergic responses; and (5) sevoflurane at 1% (i.e., concentration <1 minimum alveolar concentration) potentiated depolarizing GABAergic PSPs in the neurons of P5 and P10 rats and of P14–15 animals with PAHBs, evoking action potentials in ≥50% of these cells. On the basis of these results, we conclude that sevoflurane may produce PAHBs by potentiating GABAergic depolarization/excitation in neocortical neurons.     

Fast inference of interactions in assemblies of stochastic integrate-and-fire neurons from spike recordings

We present two Bayesian procedures to infer the interactions and external currents in an assembly of stochastic integrate-and-fire neurons from the recording of their spiking activity. The first procedure is based on the exact calculation of the most likely time courses of the neuron membrane potentials conditioned by the recorded spikes, and is exact for a vanishing noise variance and for an instantaneous synaptic integration. The second procedure takes into account the presence of fluctuations around the most likely time courses of the potentials, and can deal with moderate noise levels. The running time of both procedures is proportional to the number S of spikes multiplied by the squared number N of neurons. The algorithms are validated on synthetic data generated by networks with known couplings and currents. We also reanalyze previously published recordings of the activity of the salamander retina (including from 32 to 40 neurons, and from 65,000 to 170,000 spikes). We study the dependence of the inferred interactions on the membrane leaking time; the differences and similarities with the classical cross-correlation analysis are discussed.     

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411–425, 1988; Sherman and Rinzel, Biophys J 59:547–559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire neurons (Medvedev, Neural Comput 21 (11):3057–3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska, The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity (Fiedler, Czech Math J 23(98):298–305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models.     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.     

Probabilistic inference in general graphical models through sampling in stochastic networks of spiking neurons

An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows ("explaining away") and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

Do Brain Networks Evolve by Maximizing Their Information Flow Capacity?

We propose a working hypothesis supported by numerical simulations that brain networks evolve based on the principle of the maximization of their internal information flow capacity. We find that synchronous behavior and capacity of information flow of the evolved networks reproduce well the same behaviors observed in the brain dynamical networks of Caenorhabditis elegans and humans, networks of Hindmarsh-Rose neurons with graphs given by these brain networks. We make a strong case to verify our hypothesis by showing that the neural networks with the closest graph distance to the brain networks of Caenorhabditis elegans and humans are the Hindmarsh-Rose neural networks evolved with coupling strengths that maximize information flow capacity. Surprisingly, we find that global neural synchronization levels decrease during brain evolution, reflecting on an underlying global no Hebbian-like evolution process, which is driven by no Hebbian-like learning behaviors for some of the clusters during evolution, and Hebbian-like learning rules for clusters where neurons increase their synchronization.     

Distinct intracellular signaling mediates C‐MET regulation of dendritic growth and synaptogenesis

Hepatocyte growth factor (HGF) activation of the MET receptor tyrosine kinase influences multiple neurodevelopmental processes. Evidence from human imaging and mouse models shows that, in the forebrain, disruptions in MET signaling alter circuit formation and function. One likely means of modulation is by controlling neuron maturation. Here, we examined the signaling mechanisms through which MET exerts developmental effects in the neocortex. In situ hybridization revealed that hgf is located near MET‐expressing neurons, including deep neocortical layers and periventricular zones. Western blot analyses of neocortical crude membranes demonstrated that HGF‐induced MET autophosphorylation peaks during synaptogenesis, with a striking reduction in activation between P14 and P17 just before pruning. In vitro analysis of postnatal neocortical neurons assessed the roles of intracellular signaling following MET activation. There is rapid, HGF‐induced phosphorylation of MET, ERK1/2, and Akt that is accompanied by two major morphological changes: increases in total dendritic growth and synapse density. Selective inhibition of each signaling pathway altered only one of the two distinct events. MAPK/ERK pathway inhibition significantly reduced the HGF‐induced increase in dendritic length, but had no effect on synapse density. In contrast, inhibition of the PI3K/Akt pathway reduced HGF‐induced increases in synapse density, with no effect on dendritic length. The data reveal a key role for MET activation during the period of neocortical neuron growth and synaptogenesis, with distinct biological outcomes mediated via discrete MET‐linked intracellular signaling pathways in the same neurons. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 76: 1160–1181, 2016     

Central organization of common inhibitory motoneurons in the locust: role of afferent signals from leg mechanoreceptors

Intracellular recordings of mesothoracic common inhibitory neurons (CI₁, CI₂ and CI₃) were made while tactile hairs of the middle legs of locusts (Locusta migratoria) were mechanically stimulated. Generally the three common inhibitory neurons were excited by stimulation of tactile hairs on the ventral and dorsal surface of femur and tibia. The response pattern of all three CI neurons was similar suggesting that they work as a functional unit. Touching hairs on the dorsal surface of tibia and tarsus in some cases led to inhibition of CIs. The connection between sensory cells of tactile hairs and common inhibitory neurons is polysynaptic.To identify interneurons which mediate afferent signals, simultaneous intracellular recordings from CIs and interneurons were made. Different spiking interneurons were identified which made excitatory or inhibitory monosynaptic connections with CIs. Interneurons with inhibitory input to CIs belonged to the ventral midline group of spiking local interneurons. Behavioral and electrophysiological results indicate that reflex movements of the leg are accompanied by activity of CI neurons. Further it appears that CI activity is inhibited when reflex movements of the leg are actively suppressed by the animal.Abbreviations CI common inhibitor - IN interneuron - LY Lucifer Yellow     

Realignment of signal processing within a sensory brainstem nucleus as brain temperature declines in the Syrian hamster, a hibernating species

Crucial for survival, the central nervous system must reliably process sensory information over all stages of a hibernation bout to ensure homeostatic regulation is maintained and well-matched to dramatically altered behavioral states. Comparing neural responses in the nucleus tractus solitarius of rats and euthermic Syrian hamsters, we tested the hypothesis that hamster neurons have adaptations sustaining signal processing while conserving energy. Using patch-clamp techniques, we classified second-order neurons in the nucleus as rapid-onset or delayed-onset spiking phenotypes based on their spiking onset to a depolarizing pulse (following a −80 mV prepulse). As temperature decreased from 33 to 15°C, the excitability of all neurons decreased. However, hamster rapid-onset spiking neurons had the highest spiking response and shortest action potential width at every temperature, while hamster delayed-onset spiking neurons had the most negative resting membrane potential. The frequency of spontaneous excitatory postsynaptic currents in both phenotypes decreased as temperature decreased, yet the amplitudes of tractus solitarius stimulation-evoked currents were greater in hamsters than in rats regardless of phenotype and temperature. Changes were significant (P < 0.05), supporting our hypothesis by showing that, as temperature falls, rapid-onset neurons contribute more to signal processing but less to energy conservation than do delayed-onset neurons.     

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin–Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks. Action Editor: Barry J. Richmond     

M-channels modulate the intrinsic excitability and synaptic responses of layer 2/3 pyramidal neurons in auditory cortex

Neurons in the auditory cortex are believed to utilize temporal patterns of neural activity to accurately process auditory information but the intrinsic neuronal mechanism underlying the control of auditory neural activity is not known. The slowly activating, persistent K⁺ channel, also called M-channel that belongs to the Kv7 family, is already known to be important in regulating subthreshold neural excitability and synaptic summation in neocortical and hippocampal pyramidal neurons. However, its functional role in the primary auditory cortex (A1) has never been characterized. In this study, we investigated the roles of M-channels on neuronal excitability, short-term plasticity, and synaptic summation of A1 layer 2/3 regular spiking pyramidal neurons with whole-cell current-clamp recordings in vitro. We found that blocking M-channels with a selective M-channel blocker, XE991, significantly increased neural excitability of A1 layer 2/3 pyramidal neurons. Furthermore, M-channels controled synaptic responses of intralaminar-evoked excitatory postsynaptic potentials (EPSPs); XE991 significantly increased EPSP amplitude, decreased the rate of short-term depression, and increased the synaptic summation. These results suggest that M-channels are involved in controlling spike output patterns and synaptic responses of A1 layer 2/3 pyramidal neurons, which would have important implications in auditory information processing.     

Bifurcations of large networks of two-dimensional integrate and fire neurons

Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045–1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.