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.     

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of “dynamical relaying” – a mechanism that relies on a specific network motif – has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair – a “resonance pair” – plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.     

Metastability and Inter-Band Frequency Modulation in Networks of Oscillating Spiking Neuron Populations

Groups of neurons firing synchronously are hypothesized to underlie many cognitive functions such as attention, associative learning, memory, and sensory selection. Recent theories suggest that transient periods of synchronization and desynchronization provide a mechanism for dynamically integrating and forming coalitions of functionally related neural areas, and that at these times conditions are optimal for information transfer. Oscillating neural populations display a great amount of spectral complexity, with several rhythms temporally coexisting in different structures and interacting with each other. This paper explores inter-band frequency modulation between neural oscillators using models of quadratic integrate-and-fire neurons and Hodgkin-Huxley neurons. We vary the structural connectivity in a network of neural oscillators, assess the spectral complexity, and correlate the inter-band frequency modulation. We contrast this correlation against measures of metastable coalition entropy and synchrony. Our results show that oscillations in different neural populations modulate each other so as to change frequency, and that the interaction of these fluctuating frequencies in the network as a whole is able to drive different neural populations towards episodes of synchrony. Further to this, we locate an area in the connectivity space in which the system directs itself in this way so as to explore a large repertoire of synchronous coalitions. We suggest that such dynamics facilitate versatile exploration, integration, and communication between functionally related neural areas, and thereby supports sophisticated cognitive processing in the brain.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Attentional modulation of firing rate and synchrony in a model cortical network

The response of a neuron in the visual cortex to stimuli of different contrast placed in its receptive field is commonly characterized using the contrast response curve. When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al., 2000). The neuron will thus be able to respond to weaker stimuli than it responded to without attention. Attention also increases the coherence between neurons responding to the same stimulus (Fries et al., 2001). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. The changes in contrast and attention were modeled as changes in driving current to the network neurons. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values. We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons. Action Editor: David Golomb     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

Changing excitation and inhibition in simulated neural networks: effects on induced bursting behavior

 The development of synchronous bursting in neuronal ensembles represents an important change in network behavior. To determine the influences on development of such synchronous bursting behavior we study the dynamics of small networks of sparsely connected excitatory and inhibitory neurons using numerical simulations. The synchronized bursting activities in networks evoked by background spikes are investigated. Specifically, patterns of bursting activity are examined when the balance between excitation and inhibition on neuronal inputs is varied and the fraction of inhibitory neurons in the network is changed. For quantitative comparison of bursting activities in networks, measures of the degree of synchrony are used. We demonstrate how changes in the strength of excitation on inputs of neurons can be compensated by changes in the strength of inhibition without changing the degree of synchrony in the network. The effects of changing several network parameters on the network activity are analyzed and discussed. These changes may underlie the transition of network activity from normal to potentially pathologic (e.g., epileptic) states. Received: 21 May 2002 / Accepted in revised form: 3 December 2002 / Published online: 7 March 2003 Correspondence to: P. Kudela (e-mail: pkudela@jhmi.edu) Acknowledgements. This research was supported by NIH grant NS 38958.     

How do glutamatergic and GABAergic cells contribute to synchronization in the medial septum?

The medial septum-diagonal band (MSDB) complex is considered as a pacemaker for the hippocampal theta rhythm. Identification of the different cell types, their electro-physiological properties and their possible function in the generation of a synchronized activity in the MSDB is a hot topic. A recent electro-physiological study showed the presence of two antiphasically firing populations of parvalbumin containing GABAergic neurons in the MSDB. Other papers described a network of cluster-firing glutamatergic neurons, which is able to generate synchronized activity in the MSDB. We propose two different computer models for the generation of synchronized population theta oscillation in the MSDB and compare their properties. In the first model GABAergic neurons are intrinsically theta periodic cluster-firing cells; while in the second model GABAergic cells are fast-firing cells and receive periodic input from local glutamatergic neurons simulated as cluster-firing cells. Using computer simulations we show that the GABAergic neurons in both models are capable of generating antiphasic theta periodic population oscillation relying on local, septal mechanisms. In the first model antiphasic theta synchrony could emerge if GABAergic neurons form two populations preferentially innervate each other. In the second model in-phase synchronization of glutamatergic neurons does not require specific network structure, and the network of these cells are able to act as a theta pacemaker for the local fast-firing GABAergic circuit. Our simulations also suggest that neurons being non-cluster-firing in vitro might exhibit clustering properties when connected into a network in vivo. Action Editor: David Golomb     

Global and local synchrony of coupled neurons in small-world networks

Synchronous firing of neurons is thought to play important functional roles such as feature binding and switching of cognitive states. Although synchronization has mainly been investigated so far using model neurons with simple connection topology, real neural networks have more complex structures. Here we examine the behavior of pulse-coupled leaky integrate-and-fire neurons with various network structures. We first show that the dispersion of the number of connections for neurons influences dynamical behavior even if other major topological statistics are kept fixed. The rewiring probability parameter representing the randomness of networks bridges two spatially opposite frameworks: precise local synchrony and rough global synchrony. Finally, cooperation of the global connections and the local clustering property, which is prominent in small-world networks, inforces synchrony of distant neuronal groups receiving coherent inputs.Acknowledgments. We thank M. Watanabe, Y. Tsubo, and\linebreak C. van Leeuwen for helpful discussions. This work is partially supported by the Japan Society for the Promotion of Science and by the Advanced and Innovational Research program in Life Sciences and a Grant-in-Aid no. 15016023 on priority areas (C) Advanced Brain Science Project from the Ministry of Education, Culture, Sports, Science, and Technology, the Japanese Government.     

Synchrony with shunting inhibition in a feedforward inhibitory network

Recent experiments have shown that GABA_A receptor mediated inhibition in adult hippocampus is shunting rather than hyperpolarizing. Simulation studies of realistic interneuron networks with strong shunting inhibition have been demonstrated to exhibit robust gamma band (20–80 Hz) synchrony in the presence of heterogeneity in the intrinsic firing rates of individual neurons in the network. In order to begin to understand how shunting can contribute to network synchrony in the presence of heterogeneity, we develop a general theoretical framework using spike time response curves (STRC’s) to study patterns of synchrony in a simple network of two unidirectionally coupled interneurons (UCI network) interacting through a shunting synapse in the presence of heterogeneity. We derive an approximate discrete map to analyze the dynamics of synchronous states in the UCI network by taking into account the nonlinear contributions of the higher order STRC terms. We show how the approximate discrete map can be used to successfully predict the domain of synchronous 1:1 phase locked state in the UCI network. The discrete map also allows us to determine the conditions under which the two interneurons can exhibit in-phase synchrony. We conclude by demonstrating how the information from the study of the discrete map for the dynamics of the UCI network can give us valuable insight into the degree of synchrony in a larger feed-forward network of heterogeneous interneurons.     

The necessity of connection structures in neural models of variable binding

In his review of neural binding problems, Feldman (Cogn Neurodyn 7:1–11, 2013) addressed two types of models as solutions of (novel) variable binding. The one type uses labels such as phase synchrony of activation. The other (‘connectivity based’) type uses dedicated connections structures to achieve novel variable binding. Feldman argued that label (synchrony) based models are the only possible candidates to handle novel variable binding, whereas connectivity based models lack the flexibility required for that. We argue and illustrate that Feldman’s analysis is incorrect. Contrary to his conclusion, connectivity based models are the only viable candidates for models of novel variable binding because they are the only type of models that can produce behavior. We will show that the label (synchrony) based models analyzed by Feldman are in fact examples of connectivity based models. Feldman’s analysis that novel variable binding can be achieved without existing connection structures seems to result from analyzing the binding problem in a wrong frame of reference, in particular in an outside instead of the required inside frame of reference. Connectivity based models can be models of novel variable binding when they possess a connection structure that resembles a small-world network, as found in the brain. We will illustrate binding with this type of model with episode binding and the binding of words, including novel words, in sentence structures.     

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Computing with neural synchrony

Neurons communicate primarily with spikes, but most theories of neural computation are based on firing rates. Yet, many experimental observations suggest that the temporal coordination of spikes plays a role in sensory processing. Among potential spike-based codes, synchrony appears as a good candidate because neural firing and plasticity are sensitive to fine input correlations. However, it is unclear what role synchrony may play in neural computation, and what functional advantage it may provide. With a theoretical approach, I show that the computational interest of neural synchrony appears when neurons have heterogeneous properties. In this context, the relationship between stimuli and neural synchrony is captured by the concept of synchrony receptive field, the set of stimuli which induce synchronous responses in a group of neurons. In a heterogeneous neural population, it appears that synchrony patterns represent structure or sensory invariants in stimuli, which can then be detected by postsynaptic neurons. The required neural circuitry can spontaneously emerge with spike-timing-dependent plasticity. Using examples in different sensory modalities, I show that this allows simple neural circuits to extract relevant information from realistic sensory stimuli, for example to identify a fluctuating odor in the presence of distractors. This theory of synchrony-based computation shows that relative spike timing may indeed have computational relevance, and suggests new types of neural network models for sensory processing with appealing computational properties.     

Minimal size of cell assemblies coordinated by gamma oscillations

In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25-100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.     

A spiking neuron model for synchronous flashing of fireflies

Certain species of fireflies show a group behavior of synchronous flashing. Their synchronized and rhythmic flashing has received much attention among many researchers, and there has been a study of biological models for their entrainment of flashing. The synchronous behavior of fireflies resembles the firing synchrony of integrate-and-fire neurons with excitatory or inhibitory connections. This paper shows an analysis of spiking neurons specialized for a firefly flashing model, and provides simulation results of multiple neurons with various transmission delays and coupling strengths. It also explains flashing patterns of some firefly species and examines the synchrony conditions depending on transmission delays and coupling strengths.     

Synconset Waves and Chains: Spiking Onsets in Synchronous Populations Predict and Are Predicted by Network Structure

Synfire waves are propagating spike packets in synfire chains, which are feedforward chains embedded in random networks. Although synfire waves have proved to be effective quantification for network activity with clear relations to network structure, their utilities are largely limited to feedforward networks with low background activity. To overcome these shortcomings, we describe a novel generalisation of synfire waves, and define ‘synconset wave’ as a cascade of first spikes within a synchronisation event. Synconset waves would occur in ‘synconset chains’, which are feedforward chains embedded in possibly heavily recurrent networks with heavy background activity. We probed the utility of synconset waves using simulation of single compartment neuron network models with biophysically realistic conductances, and demonstrated that the spread of synconset waves directly follows from the network connectivity matrix and is modulated by top-down inputs and the resultant oscillations. Such synconset profiles lend intuitive insights into network organisation in terms of connection probabilities between various network regions rather than an adjacency matrix. To test this intuition, we develop a Bayesian likelihood function that quantifies the probability that an observed synfire wave was caused by a given network. Further, we demonstrate it''s utility in the inverse problem of identifying the network that caused a given synfire wave. This method was effective even in highly subsampled networks where only a small subset of neurons were accessible, thus showing it''s utility in experimental estimation of connectomes in real neuronal-networks. Together, we propose synconset chains/waves as an effective framework for understanding the impact of network structure on function, and as a step towards developing physiology-driven network identification methods. Finally, as synconset chains extend the utilities of synfire chains to arbitrary networks, we suggest utilities of our framework to several aspects of network physiology including cell assemblies, population codes, and oscillatory synchrony.     

Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) with asymmetric learning windows is commonly found in the brain and useful for a variety of spike-based computations such as input filtering and associative memory. A natural consequence of STDP is establishment of causality in the sense that a neuron learns to fire with a lag after specific presynaptic neurons have fired. The effect of STDP on synchrony is elusive because spike synchrony implies unitary spike events of different neurons rather than a causal delayed relationship between neurons. We explore how synchrony can be facilitated by STDP in oscillator networks with a pacemaker. We show that STDP with asymmetric learning windows leads to self-organization of feedforward networks starting from the pacemaker. As a result, STDP drastically facilitates frequency synchrony. Even though differences in spike times are lessened as a result of synaptic plasticity, the finite time lag remains so that perfect spike synchrony is not realized. In contrast to traditional mechanisms of large-scale synchrony based on mutual interaction of coupled neurons, the route to synchrony discovered here is enslavement of downstream neurons by upstream ones. Facilitation of such feedforward synchrony does not occur for STDP with symmetric learning windows. Action Editor: Wulfram Gerstner     

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.     

Two types of independent bursting mechanisms in inspiratory neurons: an integrative model

The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca²⁺, respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca²⁺ oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.