Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.     

Spiking regularity in a noisy small-world neuronal network

The regularity of spiking oscillations is studied in the networks with different topological structures. The network is composed of coupled Fitz-Hugh-Nagumo neurons driven by colored noise. The investigation illustrates that the spike train in both the regular and the Watts-Strogatz small-world neuronal networks can show the best regularity at a moderate noise intensity, indicating the existence of coherence resonance. Moreover, the temporal coherence of the spike train in the small-world network is superior to that in a regular network due to the increase of the randomness of the network topology. Besides the noise intensity, the spiking regularity can be optimized by tuning the randomness of the network topological structure or by tuning the correlation time of the colored noise. In particular, under the cooperation of the small-world topology and the correlation time, the spike train with good regularity could sustain a large magnitude of the local noise.     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Unsupervised learning and recall of temporal sequences: an application to robotics

This paper describes an unsupervised neural network model for learning and recall of temporal patterns. The model comprises two groups of synaptic weights, named competitive feedforward and Hebbian feedback, which are responsible for encoding the static and temporal features of the sequence respectively. Three additional mechanisms allow the network to deal with complex sequences: context units, a neuron commitment equation, and redundancy in the representation of sequence states. The proposed network encodes a set of robot trajectories which may contain states in common, and retrieves them accurately in the correct order. Further tests evaluate the fault-tolerance and noise sensitivity of the proposed model.     

Collective behavior of large-scale neural networks with GPU acceleration

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.     

Ornstein-Uhlenbeck model neuron revisited

 The temporal patterns of action potentials fired by a two-point stochastic neuron model were investigated. In this model the membrane potential of the dendritic compartment follows the Orstein-Uhlenbeck process and is not affected by the spiking activity. The axonal compartment, corresponding to the spike initiation site, is described by a simplified RC circuit. Estimators of the mean and variance of the input, based on a sampling of the axonal membrane potential, were derived and applied to simulated data. The dependencies of the mean firing frequency and of the coefficient of variation and serial correlation of interspike intervals on the mean and variance of the input were also studied by computer simulation in both 1- and 2-point models. The main property distinguishing the 2-point model from the classical 1-point model is its ability to produce clusters of short (or long) intervals between spikes under conditions of constant stimulation, as often observed in real neurons. It is shown that the nearly linear frequency response of the neuron, starting with subthreshold values of the input, is accounted for by the variability of the input (noise), which indicates that noise can play a positive role in nervous systems. The linear response frequency with respect to noise of the models suggests that the neuron can function as a noise encoder. Received: 2 April 1993/Accepted in revised form: 15 September 1994     

Oscillations and oscillatory behavior in small neural circuits

In order to determine the dynamical properties of central pattern generators (CPGs), we have examined the lobster stomatogastric ganglion using the tools of nonlinear dynamics. The lobster pyloric and gastric mill central pattern generators can be analyzed at both the cellular and network levels because they are small, i.e., contain only 25 neurons between them and each neuron and synapse are repeatedly identifiable from animal to animal. We discuss how the biophysical properties of each neuron and synapse in the two circuits act cooperatively to generate two different patterns of sequential activity, how these patterns are altered by neuromodulators and perturbed by noise and sensory inputs. Finally, we show how simplified Hindmarsh–Rose models can be made into analog electronic neurons that mimic the lobster neurons and in addition be incorporated into artificial CPGs with robotic applications.     

Population synchrony in small-world networks

Network topography ranges from regular graphs (linkage between nearest neighbours only) via small-world graphs (some random connections between nodes) to completely random graphs. Small-world linkage is seen as a revolutionary architecture for a wide range of social, physical and biological networks, and has been shown to increase synchrony between oscillating subunits. We study small-world topographies in a novel context: dispersal linkage between spatially structured populations across a range of population models. Regular dispersal between population patches interacting with density-dependent renewal provides one ecological explanation for the large-scale synchrony seen in the temporal fluctuations of many species, for example, lynx populations in North America, voles in Fennoscandia and grouse in the UK. Introducing a small-world dispersal kernel leads to a clear reduction in synchrony with both increasing dispersal rate and small-world dispersal probability across a variety of biological scenarios. Synchrony is also reduced when populations are affected by globally correlated noise. We discuss ecological implications of small-world dispersal in the frame of spatial synchrony in population fluctuations.     

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron

Based on the FitzHugh–Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.     

Graph theoretical model of a sensorimotor connectome in zebrafish

Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.     

Effects of Poisson noise in a IF model with STDP and spontaneous replay of periodic spatiotemporal patterns,in absence of cue stimulation

We consider a network of leaky integrate and fire neurons, whose learning mechanism is based on the Spike-Timing-Dependent Plasticity. The spontaneous temporal dynamic of the system is studied, including its storage and replay properties, when a Poissonian noise is added to the post-synaptic potential of the units. The temporal patterns stored in the network are periodic spatiotemporal patterns of spikes. We observe that, even in absence of a cue stimulation, the spontaneous dynamics induced by the noise is a sort of intermittent replay of the patterns stored in the connectivity and a phase transition between a replay and non-replay regime exists at a critical value of the spiking threshold. We characterize this transition by measuring the order parameter and its fluctuations.     

Nonmonotonic noise tuning of BOLD fMRI signal to natural images in the visual cortex of the anesthetized monkey

BACKGROUND: The perceptual ability of humans and monkeys to identify objects in the presence of noise varies systematically and monotonically as a function of how much noise is introduced to the visual display. That is, it becomes more and more difficult to identify an object with increasing noise. Here we examine whether the blood oxygen level-dependent functional magnetic resonance imaging (BOLD fMRI) signal in anesthetized monkeys also shows such monotonic tuning. We employed parametric stimulus sets containing natural images and noise patterns matched for spatial frequency and intensity as well as intermediate images generated by interpolation between natural images and noise patterns. Anesthetized monkeys provide us with the unique opportunity to examine visual processing largely in the absence of top-down cognitive modulations and can thus provide an important baseline against which work with awake monkeys and humans can be compared. RESULTS: We measured BOLD activity in occipital visual cortical areas as natural images and noise patterns, as well as intermediate interpolated patterns at three interpolation levels (25%, 50%, and 75%) were presented to anesthetized monkeys in a block paradigm. We observed reliable visual activity in occipital visual areas including V1, V2, V3, V3A, and V4 as well as the fundus and anterior bank of the superior temporal sulcus (STS). Natural images consistently elicited higher BOLD levels than noise patterns. For intermediate images, however, we did not observe monotonic tuning. Instead, we observed a characteristic V-shaped noise-tuning function in primary and extrastriate visual areas. BOLD signals initially decreased as noise was added to the stimulus but then increased again as the pure noise pattern was approached. We present a simple model based on the number of activated neurons and the strength of activation per neuron that can account for these results. CONCLUSIONS: We show that, for our parametric stimulus set, BOLD activity varied nonmonotonically as a function of how much noise was added to the visual stimuli, unlike the perceptual ability of humans and monkeys to identify such stimuli. This raises important caveats for interpreting fMRI data and demonstrates the importance of assessing not only which neural populations are activated by contrasting conditions during an fMRI study, but also the strength of this activation. This becomes particularly important when using the BOLD signal to make inferences about the relationship between neural activity and behavior.     

Olfactory coding in the insect brain: molecular receptive ranges, spatial and temporal coding

Odor information is coded in the insect brain in a sequence of steps, ranging from the receptor cells, via the neural network in the antennal lobe, to higher order brain centers, among which the mushroom bodies and the lateral horn are the most prominent. Across all of these processing steps, coding logic is combinatorial, in the sense that information is represented as patterns of activity across a population of neurons, rather than in individual neurons. Because different neurons are located in different places, such a coding logic is often termed spatial, and can be visualized with optical imaging techniques. We employ in vivo calcium imaging in order to record odor‐evoked activity patterns in olfactory receptor neurons, different populations of local neurons in the antennal lobes, projection neurons linking antennal lobes to the mushroom bodies, and the intrinsic cells of the mushroom bodies themselves, the Kenyon cells. These studies confirm the combinatorial nature of coding at all of these stages. However, the transmission of odor‐evoked activity patterns from projection neuron dendrites via their axon terminals onto Kenyon cells is accompanied by a progressive sparsening of the population code. Activity patterns also show characteristic temporal properties. While a part of the temporal response properties reflect the physical sequence of odor filaments, another part is generated by local neuron networks. In honeybees, γ‐aminobutyric acid (GABA)‐ergic and histaminergic neurons both contribute inhibitory networks to the antennal lobe. Interestingly, temporal properties differ markedly in different brain areas. In particular, in the antennal lobe odor‐evoked activity develops over slow time courses, while responses in Kenyon cells are phasic and transient. The termination of an odor stimulus is reflected by a decrease in activity within most glomeruli of the antennal lobe and an off‐response in some glomeruli, while in the mushroom bodies about half of the odor‐activated Kenyon cells also exhibit off‐responses.     

Analysis of Chaotic Resonance in Izhikevich Neuron Model

In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.     

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.     

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.     

Temporal population code of concurrent vocal signals in the auditory midbrain

Unique patterns of spike activity across neuron populations have been implicated in the coding of complex sensory stimuli. Delineating the patterns of neural activity in response to varying stimulus parameters and their relationships to the tuning characteristics of individual neurons is essential to ascertaining the nature of population coding within the brain. Here, we address these points in the midbrain coding of concurrent vocal signals of a sound-producing fish, the plainfin midshipman. Midshipman produce multiharmonic vocalizations which frequently overlap to produce beats. We used multivariate statistical analysis from single-unit recordings across multiple animals to assess the presence of a temporal population code. Our results show that distinct patterns of temporal activity emerge among midbrain neurons in response to concurrent signals that vary in their difference frequency. These patterns can serve to code beat difference frequencies. The patterns directly result from the differential temporal coding of difference frequency by individual neurons. Difference frequency encoding, based on temporal patterns of activity, could permit the segregation of concurrent vocal signals on time scales shorter than codes requiring averaging. Given the ubiquity across vertebrates of auditory midbrain tuning to the temporal structure of acoustic signals, a similar temporal population code is likely present in other species.     

Rhythm-induced spike-timing patterns characterized by 1D firing maps

We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected with a constant current to induce a steady firing rate and then a modest rhythm was added which altered the spike times and their corresponding phases relative to the rhythm. For both experiment and theory the relationship between consecutive spike phases is characterized by a probability distribution with peaks concentrated near a one-dimensional firing map. As is well-known, stable fixed points of this map correspond to the neuron phase-locking to the rhythm. We show that the interaction between noise and sufficiently steep maps can also cause a new kind of spike-time organization, in which consecutive spike time pairs organize into discrete clusters, with transitions between these clusters proceeding in a fixed sequence. This structure is not just a vestige of the noise-free dynamics. This slow dynamics and temporal organization in the relationship between consecutive spike phases is not evident in either the neuron’s voltage traces or single phase or interspike interval histograms. Furthermore, the consecutive spike relationship is also evident in consecutive ISIs, and hence this ordering can be observed without detailed knowledge of the rhythm (e.g. without concurrent LFP recordings).     

Temperature dependence of temporal resolution in an insect nervous system

The vast majority of animals are poikilotherms, and thus face the problem that the temperature of their nervous systems rather smoothly follows the temperature changes imposed by their environment. Since basic properties of nerve cells, e.g., the time constants of ion channels, strongly depend on temperature, a temperature shift likely affects the processing of the temporal structure of sensory stimuli. This can be critical in acoustic communication systems in which time patterns of signals are decisive for recognition by the receiver. We investigated the temperature dependence of the responses of locust auditory receptors and interneurons by varying the temperature of the experimental animals during intracellular recordings. The resolution of fast amplitude modulations of acoustic signals was determined in a gap detection paradigm. In auditory receptors and local (second order) interneurons, temporal resolution was improved at higher temperatures. This gain could be attributed to a higher precision of spike timing. In a third-order neuron, a rise in temperature affected the interactions of inhibition and excitation in a complex manner, also resulting in a better resolution of gaps in the millisecond range.     

Analysis of protein surface patterns by pocket similarity network

In this work, in order to reveal protein surface patterns in a systems biology framework, we analyze the similarity among the surface cavities by investigating the features of the pocket similarity network such as the community structure, the small-world property, the scale-free characteristic, and the hubs.