Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays

Design of coupling for synchronization in time-delayed systems

We report a design of delay coupling for targeting desired synchronization in delay dynamical systems. We target synchronization, antisynchronization, lag-and antilag-synchronization, amplitude death (or oscillation death), and generalized synchronization in mismatched oscillators. A scaling of the size of an attractor is made possible in different synchronization regimes. We realize a type of mixed synchronization where synchronization and antisynchronization coexist in different pairs of state variables of the coupled system. We establish the stability condition of synchronization using the Krasovskii-Lyapunov function theory and the Hurwitz matrix criterion. We present numerical examples using the Mackey-Glass system and a delay Rössler system.

Perceptual retouch theory derived modeling of interactions in the processing of successive visual objects for consciousness: two-stage synchronization of neuronal oscillators

We introduce a new version of the perceptual retouch model. This model was used for explaining properties of temporal interaction of successive objects in reaching conscious representation. The new model incorporates two interactive binding operations - binding features for objects and binding the bound feature-objects with a large scale oscillatory system that corresponds to perceptual consciousness. Here, the typical result of masking experiments - second object advantage in conscious perception - is achieved by applying the effects of a common synchronizing oscillator with a delay. This delayed modulation of each of the feature-binding first-order oscillators that represent emerging and decaying neural activities of each of the objects guarantees that the oscillating synchrony of the feature-neurons of the following object is higher than the synchrony of the feature-neurons of the first presented object. Thus we model the fact that the following object dominates the preceding object in conscious perception. We also show the capacity of the model to simulate illusory misbinding of features from different objects. The third qualitative effect, the relative release of the first object from backward masking is achieved by priming the non-specific oscillatory modulation ahead in time.

When Long-Range Zero-Lag Synchronization is Feasible in Cortical Networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Developmental changes of BOLD signal correlations with global human EEG power and synchronization during working memory

In humans, theta band (5–7 Hz) power typically increases when performing cognitively demanding working memory (WM) tasks, and simultaneous EEG-fMRI recordings have revealed an inverse relationship between theta power and the BOLD (blood oxygen level dependent) signal in the default mode network during WM. However, synchronization also plays a fundamental role in cognitive processing, and the level of theta and higher frequency band synchronization is modulated during WM. Yet, little is known about the link between BOLD, EEG power, and EEG synchronization during WM, and how these measures develop with human brain maturation or relate to behavioral changes. We examined EEG-BOLD signal correlations from 18 young adults and 15 school-aged children for age-dependent effects during a load-modulated Sternberg WM task. Frontal load (in-)dependent EEG theta power was significantly enhanced in children compared to adults, while adults showed stronger fMRI load effects. Children demonstrated a stronger negative correlation between global theta power and the BOLD signal in the default mode network relative to adults. Therefore, we conclude that theta power mediates the suppression of a task-irrelevant network. We further conclude that children suppress this network even more than adults, probably from an increased level of task-preparedness to compensate for not fully mature cognitive functions, reflected in lower response accuracy and increased reaction time. In contrast to power, correlations between instantaneous theta global field synchronization and the BOLD signal were exclusively positive in both age groups but only significant in adults in the frontal-parietal and posterior cingulate cortices. Furthermore, theta synchronization was weaker in children and was –in contrast to EEG power– positively correlated with response accuracy in both age groups. In summary we conclude that theta EEG-BOLD signal correlations differ between spectral power and synchronization and that these opposite correlations with different distributions undergo similar and significant neuronal developments with brain maturation.

Mechanisms of gamma oscillations

Gamma rhythms are commonly observed in many brain regions during both waking and sleep states, yet their functions and mechanisms remain a matter of debate. Here we review the cellular and synaptic mechanisms underlying gamma oscillations and outline empirical questions and controversial conceptual issues. Our main points are as follows: First, gamma-band rhythmogenesis is inextricably tied to perisomatic inhibition. Second, gamma oscillations are short-lived and typically emerge from the coordinated interaction of excitation and inhibition, which can be detected as local field potentials. Third, gamma rhythm typically concurs with irregular firing of single neurons, and the network frequency of gamma oscillations varies extensively depending on the underlying mechanism. To document gamma oscillations, efforts should be made to distinguish them from mere increases of gamma-band power and/or increased spiking activity. Fourth, the magnitude of gamma oscillation is modulated by slower rhythms. Such cross-frequency coupling may serve to couple active patches of cortical circuits. Because of their ubiquitous nature and strong correlation with the "operational modes" of local circuits, gamma oscillations continue to provide important clues about neuronal population dynamics in health and disease.

Increased phase synchronization during continuous face integration measured simultaneously with EEG and fMRI

OBJECTIVE

Gamma zero-lag phase synchronization has been measured in the animal brain during visual binding. Human scalp EEG studies used a phase locking factor (trial-to-trial phase-shift consistency) or gamma amplitude to measure binding but did not analyze common-phase signals so far. This study introduces a method to identify networks oscillating with near zero-lag phase synchronization in human subjects.

METHODS

We presented unpredictably moving face parts (NOFACE) which - during some periods - produced a complete schematic face (FACE). The amount of zero-lag phase synchronization was measured using global field synchronization (GFS). GFS provides global information on the amount of instantaneous coincidences in specific frequencies throughout the brain.

RESULTS

Gamma GFS was increased during the FACE condition. To localize the underlying areas, we correlated gamma GFS with simultaneously recorded BOLD responses. Positive correlates comprised the bilateral middle fusiform gyrus and the left precuneus.

CONCLUSIONS

These areas may form a network of areas transiently synchronized during face integration, including face-specific as well as binding-specific regions and regions for visual processing in general.

SIGNIFICANCE

Thus, the amount of zero-lag phase synchronization between remote regions of the human visual system can be measured with simultaneously acquired EEG/fMRI.

Enhancing synchrony in chaotic oscillators by dynamic relaying

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of the Lorenz system, in the Rössler system in the absence of coupling delay, and in the Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in the electronic circuit of Rössler oscillators.

Effect of duration of synaptic activity on spike rate of a Hodgkin-Huxley neuron with delayed feedback

A recurrent loop consisting of a single Hodgkin-Huxley neuron influenced by a chemical excitatory delayed synaptic feedback is considered. We show that the behavior of the system depends on the duration of the activity of the synapse, which is determined by the activation and deactivation time constants of the synapse. For the fast synapses, those for which the effect of the synaptic activity is small compared to the period of firing, depending on the delay time, spiking with single and multiple interspike intervals is possible and the average firing rate can be smaller or larger than that of the open loop neuron. For slow synapses for which the synaptic time constants are of order of the period of the firing, the self-excitation increases the firing rate for all values of the delay time. We also show that for a chain consisting of few similar oscillators, if the synapses are chosen from different time constants, the system will follow the dynamics imposed by the fastest element, which is the oscillator that receives excitations via a slow synapse. The generalization of the results to other types of relaxation oscillators is discussed and the results are compared to those of the loops with inhibitory synapses as well as with gap junctions.

Spectral fingerprints of large-scale neuronal interactions

Cognition results from interactions among functionally specialized but widely distributed brain regions; however, neuroscience has so far largely focused on characterizing the function of individual brain regions and neurons therein. Here we discuss recent studies that have instead investigated the interactions between brain regions during cognitive processes by assessing correlations between neuronal oscillations in different regions of the primate cerebral cortex. These studies have opened a new window onto the large-scale circuit mechanisms underlying sensorimotor decision-making and top-down attention. We propose that frequency-specific neuronal correlations in large-scale cortical networks may be 'fingerprints' of canonical neuronal computations underlying cognitive processes.

Short conduction delays cause inhibition rather than excitation to favor synchrony in hybrid neuronal networks of the entorhinal cortex

How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity.

Individual oscillators, such as pendulum-based clocks and fireflies, can spontaneously organize into a coherent, synchronized entity with a common frequency. Neurons can oscillate under some circumstances, and can synchronize their firing both within and across brain regions. Synchronized assemblies of neurons are thought to underlie cognitive functions such as recognition, recall, perception and attention. Pathological synchrony can lead to epilepsy, tremor and other dynamical diseases, and synchronization is altered in most mental disorders. Biological neurons synchronize despite conduction delays, heterogeneous circuit composition, and noise. In biological experiments, we built simple networks in which two living neurons could interact via a computer in real time. The computer precisely controlled the nature of the connectivity and the length of the communication delays. We characterized the synchronization tendencies of individual, isolated oscillators by measuring how much a single input delivered by the computer transiently shortened or lengthened the cycle period of the oscillation. We then used this information to correctly predict the strong dependence of the coordination pattern of the firing of the component neurons on the length of the communication delays. Upon this foundation, we can begin to build a theory of the basic principles of synchronization in more complex brain circuits.

Statistical physics approach to dendritic computation: the excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

Organization of Anti-Phase Synchronization Pattern in Neural Networks: What are the Key Factors?

Anti-phase oscillation has been widely observed in cortical neural network. Elucidating the mechanism underlying the organization of anti-phase pattern is of significance for better understanding more complicated pattern formations in brain networks. In dynamical systems theory, the organization of anti-phase oscillation pattern has usually been considered to relate to time delay in coupling. This is consistent to conduction delays in real neural networks in the brain due to finite propagation velocity of action potentials. However, other structural factors in cortical neural network, such as modular organization (connection density) and the coupling types (excitatory or inhibitory), could also play an important role. In this work, we investigate the anti-phase oscillation pattern organized on a two-module network of either neuronal cell model or neural mass model, and analyze the impact of the conduction delay times, the connection densities, and coupling types. Our results show that delay times and coupling types can play key roles in this organization. The connection densities may have an influence on the stability if an anti-phase pattern exists due to the other factors. Furthermore, we show that anti-phase synchronization of slow oscillations can be achieved with small delay times if there is interaction between slow and fast oscillations. These results are significant for further understanding more realistic spatiotemporal dynamics of cortico-cortical communications.

Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons

We show that a ring of unidirectionally delay-coupled spiking neurons may possess a multitude of stable spiking patterns and provide a constructive algorithm for generating a desired spiking pattern. More specifically, for a given time-periodic pattern, in which each neuron fires once within the pattern period at a predefined time moment, we provide the coupling delays and/or coupling strengths leading to this particular pattern. The considered homogeneous networks demonstrate a great multistability of various travelling time- and space-periodic waves which can propagate either along the direction of coupling or in opposite direction. Such a multistability significantly enhances the variability of possible spatio-temporal patterns and potentially increases the coding capability of oscillatory neuronal loops. We illustrate our results using FitzHugh-Nagumo neurons interacting via excitatory chemical synapses as well as limit-cycle oscillators.

Frequency-dependent functional connectivity within resting-state networks: an atlas-based MEG beamformer solution

The brain consists of functional units with more-or-less specific information processing capabilities, yet cognitive functions require the co-ordinated activity of these spatially separated units. Magnetoencephalography (MEG) has the temporal resolution to capture these frequency-dependent interactions, although, due to volume conduction and field spread, spurious estimates may be obtained when functional connectivity is estimated on the basis of the extra-cranial recordings directly. Connectivity estimates on the basis of reconstructed sources may similarly be affected by biases introduced by the source reconstruction approach.

Here we propose an analysis framework to reliably determine functional connectivity that is based around two main ideas: (i) functional connectivity is computed for a set of atlas-based ROIs in anatomical space that covers almost the entire brain, aiding the interpretation of MEG functional connectivity/network studies, as well as the comparison with other modalities; (ii) volume conduction and similar bias effects are removed by using a functional connectivity estimator that is insensitive to these effects, namely the Phase Lag Index (PLI).

Our analysis approach was applied to eyes-closed resting-state MEG data for thirteen healthy participants. We first demonstrate that functional connectivity estimates based on phase coherence, even at the source-level, are biased due to the effects of volume conduction and field spread. In contrast, functional connectivity estimates based on PLI are not affected by these biases. We then looked at mean PLI, or weighted degree, over areas and subjects and found significant mean connectivity in three (alpha, beta, gamma) of the five (including theta and delta) classical frequency bands tested. These frequency-band dependent patterns of resting-state functional connectivity were distinctive; with the alpha and beta band connectivity confined to posterior and sensorimotor areas respectively, and with a generally more dispersed pattern for the gamma band. Generally, these patterns corresponded closely to patterns of relative source power, suggesting that the most active brain regions are also the ones that are most-densely connected.

Our results reveal for the first time, using an analysis framework that enables the reliable characterisation of resting-state dynamics in the human brain, how resting-state networks of functionally connected regions vary in a frequency-dependent manner across the cortex.

Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators

Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.

Loss of coherence in dynamical networks: spatial chaos and chimera states

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatiotemporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback

The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.

Phase clustering in complex networks of delay-coupled oscillators

We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example, the Caenorhabditis elegans or the autonomous systems connectivity.

Effect of the topology and delayed interactions in neuronal networks synchronization

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.

Structural and functional networks in complex systems with delay

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in a system of diffusively delay-coupled elements in complex networks. We solve exactly the resulting equations in motifs (directed structures of three nodes) and in directed networks. The mean-field solution for directed uncorrelated networks shows that the clusterization of the activity is dominated by the in-degree of the nodes, and that the locking frequency decreases with increasing average degree. We find that the exponent of a power law degree distribution of the structural topology γ is related to the exponent of the associated functional network as α=(2-γ)(-1) for γ<2.

Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers

We study the synchronization properties of the delay dynamics of two identical semiconductor lasers coupled through a semitransparent mirror. Via an analytical and numerical approach, we investigate the influence of asymmetries, in particular mismatches of self- and cross-coupling strength and differences in self- and cross-coupling delay. We show that the former mismatch affects the stability of the zero-lag state but not the dynamics within the synchronization manifold, while the latter mismatch does not affect the quality of synchronization but alters the dynamics significantly. Our results are extended to different unidirectional coupling schemes. This is highly relevant for communication schemes utilizing chaotic dynamics. Finally, the influence of nonlinear gain saturation on the dynamics and stability of synchronization is discussed.

Role of delay for the symmetry in the dynamics of networks

The symmetry in a network of oscillators determines the spatiotemporal patterns of activity that can emerge. We study how a delay in the coupling affects symmetry-breaking and -restoring bifurcations. We are able to draw general conclusions in the limit of long delays. For one class of networks we derive a criterion that predicts that delays have a symmetrizing effect. Moreover, we demonstrate that for any network admitting a steady-state solution, a long delay can solely advance the first bifurcation point as compared to the instantaneous-coupling regime.

Weight-conserving characterization of complex functional brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Important functional network measures include measures of modularity (measures of the goodness with which a network is optimally partitioned into functional subgroups) and measures of centrality (measures of the functional influence of individual brain regions). Characterizations of functional networks are increasing in popularity, but are associated with several important methodological problems. These problems include the inability to characterize densely connected and weighted functional networks, the neglect of degenerate topologically distinct high-modularity partitions of these networks, and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties. In this study we describe a set of methods to overcome these problems. Specifically, we generalize measures of modularity and centrality to fully connected and weighted complex networks, describe the detection of degenerate high-modularity partitions of these networks, and introduce a weighted-connectivity null model of these networks. We illustrate our methods by demonstrating degenerate high-modularity partitions and strong correlations between two complementary measures of centrality in resting-state functional magnetic resonance imaging (MRI) networks from the 1000 Functional Connectomes Project, an open-access repository of resting-state functional MRI datasets. Our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects.

Cerebellar motor learning versus cerebellar motor timing: the climbing fibre story

Theories concerning the role of the climbing fibre system in motor learning, as opposed to those addressing the olivocerebellar system in the organization of motor timing, are briefly contrasted. The electrophysiological basis for the motor timing hypothesis in relation to the olivocerebellar system is treated in detail.

Synchronicity, instant messaging, and performance among financial traders

Successful animal systems often manage risk through synchronous behavior that spontaneously arises without leadership. In critical human systems facing risk, such as financial markets or military operations, our understanding of the benefits associated with synchronicity is nascent but promising. Building on previous work illuminating commonalities between ecological and human systems, we compare the activity patterns of individual financial traders with the simultaneous activity of other traders--an individual and spontaneous characteristic we call synchronous trading. Additionally, we examine the association of synchronous trading with individual performance and communication patterns. Analyzing empirical data on day traders' second-to-second trading and instant messaging, we find that the higher the traders' synchronous trading is, the less likely they are to lose money at the end of the day. We also find that the daily instant messaging patterns of traders are closely associated with their level of synchronous trading. This result suggests that synchronicity and vanguard technology may help traders cope with risky decisions in complex systems and may furnish unique prospects for achieving collective and individual goals.

Theta band zero-lag long-range cortical synchronization via hippocampal dynamical relaying

Growing evidence suggests that synchronization among distributed neuronal networks underlie functional integration in the brain. Neural synchronization is typically revealed by a consistent phase delay between neural responses generated in two separated sources. But the influence of a third neuronal assembly in that synchrony pattern remains largely unexplored. We investigate here the potential role of the hippocampus in determining cortico-cortical theta synchronization in different behavioral states during motor quiescent and while animals actively explore the environment. To achieve this goal, the two states were modeled with a recurrent network involving the hippocampus, as a relay element, and two distant neocortical sites. We found that cortico-cortical neural coupling accompanied higher hippocampal theta oscillations in both behavioral states, although the highest level of synchronization between cortical regions emerged during motor exploration. Local field potentials recorded from the same brain regions qualitatively confirm these findings in the two behavioral states. These results suggest that zero-lag long-range cortico-cortical synchronization is likely mediated by hippocampal theta oscillations in lower mammals as a function of cognitive demands and motor acts.

The role of phase synchronization in memory processes

In recent years, studies ranging from single-unit recordings in animals to electroencephalography and magnetoencephalography studies in humans have demonstrated the pivotal role of phase synchronization in memory processes. Phase synchronization - here referring to the synchronization of oscillatory phases between different brain regions - supports both working memory and long-term memory and acts by facilitating neural communication and by promoting neural plasticity. There is evidence that processes underlying working and long-term memory might interact in the medial temporal lobe. We propose that this is accomplished by neural operations involving phase-phase and phase-amplitude synchronization. A deeper understanding of how phase synchronization supports the flexibility of and interaction between memory systems may yield new insights into the functions of phase synchronization in general.

It's about Time

The purpose of this review/opinion paper is to argue that human cognitive neuroscience has focused too little attention on how the brain may use time and time-based coding schemes to represent, process, and transfer information within and across brain regions. Instead, the majority of cognitive neuroscience studies rest on the assumption of functional localization. Although the functional localization approach has brought us a long way toward a basic characterization of brain functional organization, there are methodological and theoretical limitations of this approach. Further advances in our understanding of neurocognitive function may come from examining how the brain performs computations and forms transient functional neural networks using the rich multi-dimensional information available in time. This approach rests on the assumption that information is coded precisely in time but distributed in space; therefore, measures of rapid neuroelectrophysiological dynamics may provide insights into brain function that cannot be revealed using localization-based approaches and assumptions. Space is not an irrelevant dimension for brain organization; rather, a more complete understanding of how brain dynamics lead to behavior dynamics must incorporate how the brain uses time-based coding and processing schemes.

Crowd synchrony and quorum sensing in delay-coupled lasers

Crowd synchrony and quorum sensing arise when a large number of dynamical elements communicate with each other via a common information pool. Previous evidence has shown that this type of coupling leads to synchronization, when coupling is instantaneous and the number of coupled elements is large enough. Here we consider a situation in which the transmission of information between the system components and the coupling pool is not instantaneous. To that end, we model a system of semiconductor lasers optically coupled to a central laser with a delay. Our results show that, even though the lasers are nonidentical due to their distinct optical frequencies, zero-lag synchronization arises. By changing a system parameter, we can switch between two different types of synchronization transition. The dependence of the transition with respect to the delay-coupling parameters is studied.

Amplitude and phase effects on the synchronization of delay-coupled oscillators

We consider the behavior of Stuart-Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding self-feedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behavior.

Optical neuron using polarisation switching in a 1550nm-VCSEL

We report a new approach to mimic basic functionalities of a neuron using a 1550 nm Vertical Cavity Surface Emitting Laser (VCSEL) which is based on the polarisation switching (PS) that can be induced in these devices when subject to polarised optical injection. Positive and negative all-optical threshold operations are demonstrated experimentally using external optical injection into the two orthogonal polarizations of the fundamental transverse mode. The polarisation of the light emitted by the device is used to determine the state of the VCSEL-Neuron, active (orthogonal) or inactive (parallel). This approach forms a new way to reproduce optically the response of a neuron to an excitatory and an inhibitory stimulus.

A new look at gamma? High- (>60 Hz) γ-band activity in cortical networks: function, mechanisms and impairment

γ-band oscillations are thought to play a crucial role in information processing in cortical networks. In addition to oscillatory activity between 30 and 60 Hz, current evidence from electro- and magnetoencephalography (EEG/MEG) and local-field potentials (LFPs) has consistently shown oscillations >60 Hz (high γ-band) whose function and generating mechanisms are unclear. In the present paper, we summarize data that highlights the importance of high γ-band activity for cortical computations through establishing correlations between the modulation of oscillations in the 60-200 Hz frequency and specific cognitive functions. Moreover, we will suggest that high γ-band activity is impaired in neuropsychiatric disorders, such as schizophrenia and epilepsy. In the final part of the paper, we will review physiological mechanisms underlying the generation of high γ-band oscillations and discuss the functional implications of low vs. high γ-band activity patterns in cortical networks.

Patterned Activity within the Local Cortical Architecture

The cerebral cortex is a vastly complex structure consisting of multiple distinct populations of neurons residing in functionally specialized cortical compartments. A fundamental goal in systems neuroscience is to understand the interactions among cortical neurons and their relationship to behavior. It is hypothesized that dynamic activity patterns, such as oscillations in global neuronal activity, could span large, heterogeneous populations of cortical neurons in such a manner as to bind together the activity of otherwise disparate cortical networks. Little is known about the mechanisms by which such global oscillatory patterns entrain cortical networks, or the contribution of such activity patterns to cortical function. An important step toward elucidating the role of such patterned activity in cortical information processing is understanding these interactions at the local circuit level. Here, we highlight recent findings that provide insight into how dynamic activity patterns affect specific neuronal populations and circuits.

Maturation of "neocortex isole" in vivo in mice

How much neocortical development depends on connections remains elusive. Here, we show that Celsr3|Dlx mutant mice have no extrinsic neocortical connections yet survive to postnatal day 20, acquire a basic behavioral repertoire, and display spontaneous hyperactivity, with abnormal light/dark activity cycling. Except for hallmarks related to thalamic input, such as barrels in somatosensory cortex, cortical arealization and laminar maturation proceeded normally. However, the tangential extension of the mature cortex was diminished, with radial thickness less severely affected. Deep layer neurons were reduced in number, and their apical and basal dendritic arbors were blunted, with reduced synapse density. Interneurons reached the cortex, and their density was comparable with wild type. The excitability of mutant pyramidal neurons, measured in vitro in patch-clamp experiments in acute slices, was decreased. However, their firing activity in vivo was quite similar to the wild type, except for the presence of rapid firing exhaustion in some mutant neurons. Local field potential and electrocorticogram showed similar range of oscillations, albeit with higher frequency peaks and reduced left-right synchrony in the mutant. Thus, "protomap" formation, namely cortical lamination and arealization, proceed normally in absence of extrinsic connections, but survival of projection neurons and acquisition of mature morphological and some electrophysiological features depend on the establishment of normal cortical-subcortical relationships.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Zero lag synchronization of chaotic systems with time delayed couplings

Zero-lag synchronization (ZLS) between chaotic units, which do not have self-feedback or a relay unit connecting them, is experimentally demonstrated for two mutually coupled chaotic semiconductor lasers. The mechanism is based on two mutual coupling delay times with certain allowed integer ratios, whereas for a single mutual delay time ZLS cannot be achieved. This mechanism is also found numerically for mutually coupled chaotic maps where its stability is analyzed using the Schur-Cohn theorem for the roots of polynomials. The symmetry of the polynomials allows only specific integer ratios for ZLS. In addition, we present a general argument for ZLS when several mutual coupling delay times are present.

Broadband chaos generated by an optoelectronic oscillator

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Cooperation and competition among frontal eye field neurons during visual target selection

The role of spike rate versus timing codes in visual target selection is unclear. We simultaneously recorded activity from multiple frontal eye field neurons and asked whether they interacted to select targets from distractors during visual search. When both neurons in a pair selected the target and had overlapping receptive fields (RFs), they cooperated more than when one or neither neuron in the pair selected the target, measured by positive spike timing correlations using joint peristimulus time histogram analysis. The amount of cooperation depended on the location of the search target: it was higher when the target was inside both neurons' RFs than when it was inside one RF but not the other, or outside both RFs. Elevated spike timing coincidences occurred at the time of attentional selection of the target as measured by average modulation of discharge rates. We observed competition among neurons with spatially non-overlapping RFs, measured by negative spike timing correlations. Thus, we provide evidence for dynamic and task-dependent cooperation and competition among frontal eye field neurons during visual target selection.

Controlling synchrony by delay coupling in networks: from in-phase to splay and cluster states

We study synchronization in delay-coupled oscillator networks using a master stability function approach. Within a generic model of Stuart-Landau oscillators (normal form of supercritical or subcritical Hopf bifurcation), we derive analytical stability conditions and demonstrate that by tuning the coupling phase one can easily control the stability of synchronous periodic states. We propose the coupling phase as a crucial control parameter to switch between in-phase synchronization or desynchronization for general network topologies or between in-phase, cluster, or splay states in unidirectional rings. Our results are robust even for slightly nonidentical elements of the network.

Can structure predict function in the human brain?

Over the past decade, scientific interest in the properties of large-scale spontaneous neural dynamics has intensified. Concurrently, novel technologies have been developed for characterizing the connective anatomy of intra-regional circuits and inter-regional fiber pathways. It will soon be possible to build computational models that incorporate these newly detailed structural network measurements to make predictions of neural dynamics at multiple scales. Here, we review the practicality and the value of these efforts, while at the same time considering in which cases and to what extent structure does determine neural function. Studies of the healthy brain, of neural development, and of pathology all yield examples of direct correspondences between structural linkage and dynamical correlation. Theoretical arguments further support the notion that brain network topology and spatial embedding should strongly influence network dynamics. Although future models will need to be tested more quantitatively and against a wider range of empirical neurodynamic features, our present large-scale models can already predict the macroscopic pattern of dynamic correlation across the brain. We conclude that as neuroscience grapples with datasets of increasing completeness and complexity, and attempts to relate the structural and functional architectures discovered at different neural scales, the value of computational modeling will continue to grow.

Dynamic control for synchronization of separated cortical areas through thalamic relay

Binding of features and information which are processed at different cortical areas is generally supposed to be achieved by synchrony despite the non-negligible delays between these areas. In this work we study the dynamics and synchronization properties of a simplified model of the thalamocortical circuit where different cortical areas are interconnected with a certain delay, that is longer than the internal time scale of the neurons. Using this simple model we find that the thalamus could serve as a central subcortical area that is able to generate zero-lag synchrony between distant cortical areas by means of dynamical relaying (Vicente et al., 2008). Our results show that the model circuit is able to generate fast oscillations in frequency ranges of the beta and gamma bands triggered by an external input to the thalamus formed by independent Poisson trains. We propose a control mechanism to turn "On" and "Off" the synchronization between cortical areas as a function of the relative rate of the external input fed into dorsal and ventral thalamic neuronal populations. The current results emphasize the hypothesis that the thalamus could control the dynamics of the thalamocortical functional networks enabling two separated cortical areas to be either synchronized (at zero-lag) or unsynchronized. This control may happen at a fast time scale, in agreement with experimental data, and without any need of plasticity or adaptation mechanisms which typically require longer time scales.