Modeling positive Granger causality and negative phase lag between cortical areas

Feedforward and feedback influences through distinct frequency bands between two spiking-neuron networks

Several studies on brain signals suggested that bottom-up and top-down influences are exerted through distinct frequency bands among visual cortical areas. It was recently shown that theta and gamma rhythms subserve feedforward, whereas the feedback influence is dominated by the alpha-beta rhythm in primates. A few theoretical models for reproducing these effects have been proposed so far. Here we show that a simple but biophysically plausible two-network motif composed of spiking-neuron models and chemical synapses can exhibit feedforward and feedback influences through distinct frequency bands. Different from previous studies, this kind of model allows us to study directed influences not only at the population level, by using a proxy for the local field potential, but also at the cellular level, by using the neuronal spiking series.

Functional Interactions between Entorhinal Cortical Pathways Modulate Theta Activity in the Hippocampus

Simple Summary

The activity in the hippocampus is characterized by a strong oscillation at theta frequency that organizes the neuronal firing. We have recently shown that different theta oscillations are present in the hippocampus, opening the possibility to multiple interactions between theta rhythms. In this work, we analyzed the functional connectivity between theta generators during the exploration of a known environment with or without a novel stimulus. The directionality of the interactions was determined using tools based on Granger causality and transfer entropy. We found significant interactions between activity components originated in CA3 and in layers II and III of the entorhinal cortex. During exploration with a novel stimulus, the connectivity from the entorhinal cortex layer II increased, while the influence of CA3 decreased. These results suggest that the entorhinal cortex layer II may drive theta interactions and synchronization in the hippocampus during novelty exploration.

Abstract

Theta oscillations organize neuronal firing in the hippocampus during context exploration and memory formation. Recently, we have shown that multiple theta rhythms coexist in the hippocampus, reflecting the activity in their afferent regions in CA3 (Schaffer collaterals) and the entorhinal cortex layers II (EC-II, perforant pathway) and III (EC-III, temporoammonic pathway). Frequency and phase coupling between theta rhythms were modulated by the behavioral state, with synchronized theta rhythmicity preferentially occurring in tasks involving memory updating. However, information transmission between theta generators was not investigated. Here, we used source separation techniques to disentangle the current generators recorded in the hippocampus of rats exploring a known environment with or without a novel stimulus. We applied analytical tools based on Granger causality and transfer entropy to investigate linear and non-linear directed interactions, respectively, between the theta activities. Exploration in the novelty condition was associated with increased theta power in the generators with EC origin. We found a significant directed interaction from the Schaffer input over the EC-III input in CA1, and a bidirectional interaction between the inputs in the hippocampus originating in the EC, likely reflecting the connection between layers II and III. During novelty exploration, the influence of the EC-II over the EC-III generator increased, while the Schaffer influence decreased. These results associate the increase in hippocampal theta activity and synchrony during novelty exploration with an increase in the directed functional connectivity from EC-II to EC-III.

Anticipated synchronization in human EEG data: Unidirectional causality with negative phase lag

Understanding the functional connectivity of the brain has become a major goal of neuroscience. In many situations the relative phase difference, together with coherence patterns, has been employed to infer the direction of the information flow. However, it has been recently shown in local field potential data from monkeys the existence of a synchronized regime in which unidirectionally coupled areas can present both positive and negative phase differences. During the counterintuitive regime, called anticipated synchronization (AS), the phase difference does not reflect the causality. Here we investigate coherence and causality at the alpha frequency band (f∼10 Hz) between pairs of electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show that human EEG signals can exhibit anticipated synchronization, which is characterized by a unidirectional influence from an electrode A to an electrode B, but the electrode B leads the electrode A in time. To the best of our knowledge, this is the first verification of AS in EEG signals and in the human brain. The usual delayed synchronization (DS) regime is also present between many pairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B and a positive phase difference between A and B which indicates that the electrode A leads the electrode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: the pairs of electrodes can present in-phase, antiphase, or out-of-phase synchronization with a similar distribution of positive and negative phase differences.

Transmission delays and frequency detuning can regulate information flow between brain regions

Brain networks exhibit very variable and dynamical functional connectivity and flexible configurations of information exchange despite their overall fixed structure. Brain oscillations are hypothesized to underlie time-dependent functional connectivity by periodically changing the excitability of neural populations. In this paper, we investigate the role of the connection delay and the detuning between the natural frequencies of neural populations in the transmission of signals. Based on numerical simulations and analytical arguments, we show that the amount of information transfer between two oscillating neural populations could be determined by their connection delay and the mismatch in their oscillation frequencies. Our results highlight the role of the collective phase response curve of the oscillating neural populations for the efficacy of signal transmission and the quality of the information transfer in brain networks.

Neuronal heterogeneity modulates phase synchronization between unidirectionally coupled populations with excitation-inhibition balance

Several experiments and models have highlighted the importance of neuronal heterogeneity in brain dynamics and function. However, how such a cell-to-cell diversity can affect cortical computation, synchronization, and neuronal communication is still under debate. Previous studies have focused on the effect of neuronal heterogeneity in one neuronal population. Here we are specifically interested in the effect of neuronal variability on the phase relations between two populations, which can be related to different cortical communication hypotheses. It has been recently shown that two spiking neuron populations unidirectionally connected in a sender-receiver configuration can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag. This phenomenon has been reported in electrophysiological data of nonhuman primates and human EEG during a visual discrimination cognitive task. In experiments, the unidirectional coupling could be accessed by Granger causality and can be accompanied by either positive or negative phase difference between cortical areas. Here we propose a model of two coupled populations in which the neuronal heterogeneity can determine the dynamical relation between the sender and the receiver and can reproduce phase relations reported in experiments. Depending on the distribution of parameters characterizing the neuronal firing patterns, the system can exhibit both AS and the usual delayed synchronization regime (DS, with positive phase) as well as a zero-lag synchronization regime and phase bistability between AS and DS. Furthermore, we show that our network can present diversity in their phase relations maintaining the excitation-inhibition balance.

Event-related network changes unfold the dynamics of cortical integration during face processing

Face perception arises from a collective activation of brain regions in the occipital, parietal and temporal cortices. Despite the wide acknowledgment that these regions act in an intertwined network, the network behavior itself is poorly understood. Here we present a study in which time-varying connectivity estimated from EEG activity elicited by facial expressions presentation was characterized using graph-theoretical measures of node centrality and global network topology. Results revealed that face perception results from a dynamic reshaping of the network architecture, characterized by the emergence of hubs located in the occipital and temporal regions of the scalp. The importance of these nodes can be observed from the early stages of visual processing and reaches a climax in the same time-window in which the face-sensitive N170 is observed. Furthermore, using Granger causality, we found that the time-evolving centrality of these nodes is associated with ERP amplitude, providing a direct link between the network state and local neural response. Additionally, investigating global network topology by means of small-worldness and modularity, we found that face processing requires a functional network with a strong small-world organization that maximizes integration, at the cost of segregated subdivisions. Interestingly, we found that this architecture is not static, but instead, it is implemented by the network from stimulus onset to ~200 ms. Altogether, this study reveals the event-related changes underlying face processing at the network level, suggesting that a distributed processing mechanism operates through dynamically weighting the contribution of the cortical regions involved.

Phase bistability between anticipated and delayed synchronization in neuronal populations

Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag, if the receiver also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (with positive phase lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase locking to a bistable regime and eventually to a phase drift. We suggest that our spiking neuronal populations model could be potentially useful to study phase bistability in cortical regions related to bistable perception.

Exploring the Phase-Locking Mechanisms Yielding Delayed and Anticipated Synchronization in Neuronal Circuits

Synchronization is one of the brain mechanisms allowing the coordination of neuronal activity required in many cognitive tasks. Anticipated Synchronization (AS) is a specific type of out-of-phase synchronization that occurs when two systems are unidirectionally coupled and, consequently, the information is transmitted from the sender to the receiver, but the receiver leads the sender in time. It has been shown that the primate cortex could operate in a regime of AS as part of normal neurocognitive function. However it is still unclear what is the mechanism that gives rise to anticipated synchronization in neuronal motifs. Here, we investigate the synchronization properties of cortical motifs on multiple scales and show that the internal dynamics of the receiver, which is related to its free running frequency in the uncoupled situation, is the main ingredient for AS to occur. For biologically plausible parameters, including excitation/inhibition balance, we found that the phase difference between the sender and the receiver decreases when the free running frequency of the receiver increases. As a consequence, the system switches from the usual delayed synchronization (DS) regime to an AS regime. We show that at three different scales, neuronal microcircuits, spiking neuronal populations and neural mass models, both the inhibitory loop and the external current acting on the receiver mediate the DS-AS transition for the sender-receiver configuration by changing the free running frequency of the receiver. Therefore, we propose that a faster internal dynamics of the receiver system is the main mechanism underlying anticipated synchronization in brain circuits.

Wiener–Granger Causality Theory Supported by a Genetic Algorithm to Characterize Natural Scenery

Image recognition and classification have been widely used for research in computer vision systems. This paper aims to implement a new strategy called Wiener-Granger Causality theory for classifying natural scenery images. This strategy is based on self-content images extracted using a Content-Based Image Retrieval (CBIR) methodology (to obtain different texture features); later, a Genetic Algorithm (GA) is implemented to select the most relevant natural elements from the images which share similar causality patterns. The proposed method is comprised of a sequential feature extraction stage, a time series conformation task, a causality estimation phase, causality feature selection throughout the GA implementation (using the classification process into the fitness function). A classification stage was implemented and 700 images of natural scenery were used for validating the results. Tested in the distribution system implementation, the technical efficiency of the developed system is 100% and 96% for resubstitution and cross-validation methodologies, respectively. This proposal could help with recognizing natural scenarios in the navigation of an autonomous car or possibly a drone, being an important element in the safety of autonomous vehicles navigation.

Inhibitory autapse mediates anticipated synchronization between coupled neurons

Two identical autonomous dynamical systems unidirectionally coupled in a sender-receiver configuration can exhibit anticipated synchronization (AS) if the receiver neuron also receives a delayed negative self-feedback. Recently, AS was shown to occur in a three-neuron motif with standard chemical synapses where the delayed inhibition was provided by an interneuron. Here, we show that a two-neuron model in the presence of an inhibitory autapse, which is a massive self-innervation present in the cortical architecture, may present AS. The GABAergic autapse regulates the internal dynamics of the receiver neuron and acts as the negative delayed self-feedback required by dynamical systems in order to exhibit AS. In this biologically plausible scenario, a smooth transition from the usual delayed synchronization (DS) to AS typically occurs when the inhibitory conductance is increased. The phenomenon is shown to be robust when model parameters are varied within a physiological range. For extremely large values of the inhibitory autapse the system undergoes to a phase-drift regime in which the receiver is faster than the sender. Furthermore, we show that the inhibitory autapse promotes a faster internal dynamics of the free-running Receiver when the two neurons are uncoupled, which could be the mechanism underlying anticipated synchronization and the DS-AS transition.

Evaluation of connectivity estimates using spiking neuronal network models

The flow of information between different regions of the cortex is fundamental for brain function. Researchers use causality detection techniques, such as Granger causality, to infer connectivity among brain areas from time series. Generalized partial directed coherence (GPDC) is a frequency domain linear method based on vector autoregressive model, which has been applied in electroencephalography, local field potential, and blood oxygenation level-dependent signals. Despite its widespread usage, previous attempts to validate GPDC use oversimplified simulated data, which do not reflect the nonlinearities and network couplings present in biological signals. In this work, we evaluated the GPDC performance when applied to simulated LFP signals, i.e., generated from networks of spiking neuronal models. We created three models, each containing five interacting networks, and evaluated whether the GPDC method could accurately detect network couplings. When using a stronger coupling, we showed that GPDC correctly detects all existing connections from simulated LFP signals in the three models, without false positives. Varying the coupling strength between networks, by changing the number of connections or synaptic strengths, and adding noise in the times series, altered the receiver operating characteristic (ROC) curve, ranging from perfect to chance level retrieval. We also showed that GPDC values correlated with coupling strength, indicating that GPDC values can provide useful information regarding coupling strength. These results reinforce that GPDC can be used to detect causality relationships over neural signals.

Anticipation via canards in excitable systems

Neurons can anticipate incoming signals by exploiting a physiological mechanism that is not well understood. This article offers a novel explanation on how a receiver neuron can predict the sender's dynamics in a unidirectionally-coupled configuration, in which both sender and receiver follow the evolution of a multi-scale excitable system. We present a novel theoretical viewpoint based on a mathematical object, called canard, to explain anticipation in excitable systems. We provide a numerical approach, which allows to determine the transient effects of canards. To demonstrate the general validity of canard-mediated anticipation in the context of excitable systems, we illustrate our framework in two examples, a multi-scale radio-wave circuit (the van der Pol model) that inspired a caricature neuronal model (the FitzHugh-Nagumo model) and a biophysical neuronal model (a 2-dimensional reduction of the Hodgkin-Huxley model), where canards act as messengers to the senders' prediction. We also propose an experimental paradigm that would enable experimental neuroscientists to validate our predictions. We conclude with an outlook to possible fascinating research avenues to further unfold the mechanisms underpinning anticipation. We envisage that our approach can be employed by a wider class of excitable systems with appropriate theoretical extensions.

A delayed-feedback filter with negative group delay

A filter with delay-induced negative group delay is presented. The filter consists of multiple time-delayed feedback terms, which lead to a negative group delay for frequencies in the baseband. It can be used for the real-time prediction of band-limited signals. The filter is universal as it does not rely on a specific model of the signal. Specifically, as long as the signal to be predicted is band-limited with a known cutoff frequency, the filter predicts the signal in real time up to a prediction horizon that depends on the cutoff frequency. How signal prediction arises from the negative group delay of the filter is worked out in detail. Its properties, including stability, are derived analytically and demonstrated by numerical simulations. For chaotic systems, the filter is predictive during phases of high predictability.

Estimating the impact of structural directionality: How reliable are undirected connectomes?

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

Top-down beta oscillatory signaling conveys behavioral context in early visual cortex

Top-down modulation of sensory processing is a critical neural mechanism subserving numerous important cognitive roles, one of which may be to inform lower-order sensory systems of the current ‘task at hand’ by conveying behavioral context to these systems. Accumulating evidence indicates that top-down cortical influences are carried by directed interareal synchronization of oscillatory neuronal populations, with recent results pointing to beta-frequency oscillations as particularly important for top-down processing. However, it remains to be determined if top-down beta-frequency oscillations indeed convey behavioral context. We measured spectral Granger Causality (sGC) using local field potentials recorded from microelectrodes chronically implanted in visual areas V1/V2, V4, and TEO of two rhesus macaque monkeys, and applied multivariate pattern analysis to the spatial patterns of top-down sGC. We decoded behavioral context by discriminating patterns of top-down (V4/TEO-to-V1/V2) beta-peak sGC for two different task rules governing correct responses to identical visual stimuli. The results indicate that top-down directed influences are carried to visual cortex by beta oscillations, and differentiate task demands even before visual stimulus processing. They suggest that top-down beta-frequency oscillatory processes coordinate processing of sensory information by conveying global knowledge states to early levels of the sensory cortical hierarchy independently of bottom-up stimulus-driven processing.

Anticipated and zero-lag synchronization in motifs of delay-coupled systems

Anticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators.

Diversity of functional connectivity patterns is reduced in propofol-induced unconsciousness

INTRODUCTION

Recent evidence suggests that the conscious brain is characterized by a diverse repertoire of functional connectivity patterns while the anesthetized brain shows stereotyped activity. However, classical time-averaged methods of connectivity dismiss dynamic and temporal characteristics of functional configurations. Here we demonstrate a new approach which characterizes time-varying patterns of functional connectivity at the subsecond time scale.

METHODS

We introduce phase-lag entropy (PLE), a measure of the diversity of temporal patterns in the phase relationships between two signals. The proposed measure was applied to multichannel electroencephalogram (EEG), which were recorded from two distinct experimental settings: (1) propofol was administrated at a constant infusion rate for 60 min (n = 96); (2) administration of propofol by a target effect-site concentration-controlled infusion with simultaneous assessment of the level of consciousness (n = 10).

RESULTS

From the first dataset, two substantial changes of the phase relationship during anesthesia was found: (1) the dynamics of the phase relationship between frontal channels became progressively less diverse and more stereotyped during unconsciousness, quantified as a reduction in PLE; and (2) the reduction in PLE was consistent across subjects. Furthermore, PLE provided better performance in the classification of states of consciousness than did phase-lag index, a classical time-averaged connectivity method. From the second dataset, PLE showed the highest agreement with the level of consciousness, compared to existing anesthetic depth indicators.

CONCLUSIONS

This study suggests that a scarcity of functional configurations is closely associated with anesthetically induced unconsciousness, and shows promise as a basis for a new consciousness monitoring system during general anesthesia. Hum Brain Mapp 38:4980-4995, 2017. © 2017 Wiley Periodicals, Inc.

Predicting the Existence and Stability of Phase-Locked Mode in Neural Networks Using Generalized Phase-Resetting Curve

We used the phase-resetting method to study a biologically relevant three-neuron network in which one neuron receives multiple inputs per cycle. For this purpose, we first generalized the concept of phase resetting to accommodate multiple inputs per cycle. We explicitly showed how analytical conditions for the existence and the stability of phase-locked modes are derived. In particular, we solved newly derived recursive maps using as an example a biologically relevant driving-driven neural network with a dynamic feedback loop. We applied the generalized phase-resetting definition to predict the relative-phase and the stability of a phase-locked mode in open loop setup. We also compared the predicted phase-locked mode against numerical simulations of the fully connected network.

Anticipated synchronization in neuronal circuits unveiled by a phase-response-curve analysis

Anticipated synchronization (AS) is a counterintuitive behavior that has been observed in several systems. When AS occurs in a sender-receiver configuration, the latter can predict the future dynamics of the former for certain parameter values. In particular, in neuroscience AS was proposed to explain the apparent discrepancy between information flow and time lag in the cortical activity recorded in monkeys. Despite its success, a clear understanding of the mechanisms yielding AS in neuronal circuits is still missing. Here we use the well-known phase-response-curve (PRC) approach to study the prototypical sender-receiver-interneuron neuronal motif. Our aim is to better understand how the transitions between delayed to anticipated synchronization and anticipated synchronization to phase-drift regimes occur. We construct a map based on the PRC method to predict the phase-locking regimes and their stability. We find that a PRC function of two variables, accounting simultaneously for the inputs from sender and interneuron into the receiver, is essential to reproduce the numerical results obtained using a Hodgkin-Huxley model for the neurons. On the contrary, the typical approximation that considers a sum of two independent single-variable PRCs fails for intermediate to high values of the inhibitory coupling strength of the interneuron. In particular, it loses the delayed-synchronization to anticipated-synchronization transition.

On the role of the entorhinal cortex in the effective connectivity of the hippocampal formation

Inferring effective connectivity from neurophysiological data is a challenging task. In particular, only a finite (and usually small) number of sites are simultaneously recorded, while the response of one of these sites can be influenced by other sites that are not being recorded. In the hippocampal formation, for instance, the connections between areas CA1-CA3, the dentate gyrus (DG), and the entorhinal cortex (EC) are well established. However, little is known about the relations within the EC layers, which might strongly affect the resulting effective connectivity estimations. In this work, we build excitatory/inhibitory neuronal populations representing the four areas CA1, CA3, the DG, and the EC and fix their connectivities. We model the EC by three layers (LII, LIII, and LV) and assume any possible connection between them. Our results, based on Granger Causality (GC) and Partial Transfer Entropy (PTE) measurements, reveal that the estimation of effective connectivity in the hippocampus strongly depends on the connectivities between EC layers. Moreover, we find, for certain EC configurations, very different results when comparing GC and PTE measurements. We further demonstrate that causal links can be robustly inferred regardless of the excitatory or inhibitory nature of the connection, adding complexity to their interpretation. Overall, our work highlights the importance of a careful analysis of the connectivity methods to prevent unrealistic conclusions when only partial information about the experimental system is available, as usually happens in brain networks. Our results suggest that the combination of causality measures with neuronal modeling based on precise neuroanatomical tracing may provide a powerful framework to disambiguate causal interactions in the brain.

A generalized phase resetting method for phase-locked modes prediction

We derived analytically and checked numerically a set of novel conditions for the existence and the stability of phase-locked modes in a biologically relevant master-slave neural network with a dynamic feedback loop. Since neural oscillators even in the three-neuron network investigated here receive multiple inputs per cycle, we generalized the concept of phase resetting to accommodate multiple inputs per cycle. We proved that the phase resetting produced by two or more stimuli per cycle can be recursively computed from the traditional, single stimulus, phase resetting. We applied the newly derived generalized phase resetting definition to predicting the relative phase and the stability of a phase-locked mode that was experimentally observed in this type of master-slave network with a dynamic loop network.

The epidemic spreading model and the direction of information flow in brain networks

The interplay between structural connections and emerging information flow in the human brain remains an open research problem. A recent study observed global patterns of directional information flow in empirical data using the measure of transfer entropy. For higher frequency bands, the overall direction of information flow was from posterior to anterior regions whereas an anterior-to-posterior pattern was observed in lower frequency bands. In this study, we applied a simple Susceptible-Infected-Susceptible (SIS) epidemic spreading model on the human connectome with the aim to reveal the topological properties of the structural network that give rise to these global patterns. We found that direct structural connections induced higher transfer entropy between two brain regions and that transfer entropy decreased with increasing distance between nodes (in terms of hops in the structural network). Applying the SIS model, we were able to confirm the empirically observed opposite information flow patterns and posterior hubs in the structural network seem to play a dominant role in the network dynamics. For small time scales, when these hubs acted as strong receivers of information, the global pattern of information flow was in the posterior-to-anterior direction and in the opposite direction when they were strong senders. Our analysis suggests that these global patterns of directional information flow are the result of an unequal spatial distribution of the structural degree between posterior and anterior regions and their directions seem to be linked to different time scales of the spreading process.

Inhibitory loop robustly induces anticipated synchronization in neuronal microcircuits

We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamic inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and the external noise controls the phase relations between the neurons in a counterintuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the inhibitory feedback. In this nonusual regime, called anticipated synchronization (AS), the phase of the postsynaptic neuron is advanced with respect to that of the presynaptic neuron. We also show that the AS regime survives even in the presence of unbalanced bidirectional excitatory coupling. Moreover, for the symmetric mutually coupled situation, the neuron that is subject to the inhibitory loop leads in phase.

The Leaky Integrator with Recurrent Inhibition as a Predictor

The leaky integrator, the basis for many neuronal models, possesses a negative group delay when a time-delayed recurrent inhibition is added to it. By means of this delay, the leaky integrator becomes a predictor for some frequency components of the input signal. The prediction properties are derived analytically, and an application to a local field potential is provided.

Renormalized time scale for anticipating and lagging synchronization

Anticipating synchronization has been recently proposed as a mechanism of interaction in dynamical systems which are able to bring about predictions of future states of a driver system. We suggest that an interesting insight into anticipating synchronization can be obtained by the renormalization of the time scale in the driven system. Our approach directly links the feedback delay of the driven system with the renormalized time scale of the driven system, identifying the main component in the anticipating synchronization paradigm and suggesting an alternative method to generate anticipating and lagging synchronization.

Diversity improves performance in excitable networks

As few real systems comprise indistinguishable units, diversity is a hallmark of nature. Diversity among interacting units shapes properties of collective behavior such as synchronization and information transmission. However, the benefits of diversity on information processing at the edge of a phase transition, ordinarily assumed to emerge from identical elements, remain largely unexplored. Analyzing a general model of excitable systems with heterogeneous excitability, we find that diversity can greatly enhance optimal performance (by two orders of magnitude) when distinguishing incoming inputs. Heterogeneous systems possess a subset of specialized elements whose capability greatly exceeds that of the nonspecialized elements. We also find that diversity can yield multiple percolation, with performance optimized at tricriticality. Our results are robust in specific and more realistic neuronal systems comprising a combination of excitatory and inhibitory units, and indicate that diversity-induced amplification can be harnessed by neuronal systems for evaluating stimulus intensities.

Signal prediction by anticipatory relaxation dynamics

Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here, a parsimonious prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequency-dependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input-output system with negative group delay. It is characterized, including its prediction horizon, by its analytically given frequency response function.

A symbolic information approach to determine anticipated and delayed synchronization in neuronal circuit models

The phenomenon of synchronization between two or more areas of the brain coupled asymmetrically is a relevant issue for understanding mechanisms and functions within the cerebral cortex. Anticipated synchronization (AS) refers to the situation in which the receiver system synchronizes to the future dynamics of the sender system while the intuitively expected delayed synchronization (DS) represents exactly the opposite case. AS and DS are investigated in the context of causal information formalism. More specifically, we use a multi-scale symbolic information-theory approach for discriminating the time delay displayed between two areas of the brain when they exchange information.

Self-Organized Near-Zero-Lag Synchronization Induced by Spike-Timing Dependent Plasticity in Cortical Populations

Several cognitive tasks related to learning and memory exhibit synchronization of macroscopic cortical areas together with synaptic plasticity at neuronal level. Therefore, there is a growing effort among computational neuroscientists to understand the underlying mechanisms relating synchrony and plasticity in the brain. Here we numerically study the interplay between spike-timing dependent plasticity (STDP) and anticipated synchronization (AS). AS emerges when a dominant flux of information from one area to another is accompanied by a negative time lag (or phase). This means that the receiver region pulses before the sender does. In this paper we study the interplay between different synchronization regimes and STDP at the level of three-neuron microcircuits as well as cortical populations. We show that STDP can promote auto-organized zero-lag synchronization in unidirectionally coupled neuronal populations. We also find synchronization regimes with negative phase difference (AS) that are stable against plasticity. Finally, we show that the interplay between negative phase difference and STDP provides limited synaptic weight distribution without the need of imposing artificial boundaries.

Anticipated synchronization in coupled complex Ginzburg-Landau systems

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.