Phase-coherence transitions and communication in the gamma range between delay-coupled neuronal populations

Emergence of complex oscillatory dynamics in the neuronal networks with long activity time of inhibitory synapses

The brain displays complex dynamics, including collective oscillations, and extensive research has been conducted to understand their generation. However, our understanding of how biological constraints influence these oscillations is incomplete. This study investigates the essential properties of neuronal networks needed to generate oscillations resembling those in the brain. A simple discrete-time model of interconnected excitable elements is developed, capable of closely resembling the complex oscillations observed in biological neural networks. In the model, synaptic connections remain active for a duration exceeding individual neuron activity. We show that the inhibitory synapses must exhibit longer activity than excitatory synapses to produce a diverse range of the dynamical states, including biologically plausible oscillations. Upon meeting this condition, the transition between different dynamical states can be controlled by external stochastic input to the neurons. The study provides a comprehensive explanation for the emergence of distinct dynamical states in neural networks based on specific parameters.

Phase of neural oscillations as a reference frame for attention-based routing in visual cortex

Selective attention allows the brain to efficiently process the image projected onto the retina, selectively focusing neural processing resources on behaviorally relevant visual information. While previous studies have documented the crucial role of the action potential rate of single neurons in relaying such information, little is known about how the activity of single neurons relative to their neighboring network contributes to the efficient representation of attended stimuli and transmission of this information to downstream areas. Here, we show in the dorsal visual pathway of monkeys (medial superior temporal area) that neurons fire spikes preferentially at a specific phase of the ongoing population beta (∼20 Hz) oscillations of the surrounding local network. This preferred spiking phase shifts towards a later phase when monkeys selectively attend towards (rather than away from) the receptive field of the neuron. This shift of the locking phase is positively correlated with the speed at which animals report a visual change. Furthermore, our computational modeling suggests that neural networks can manipulate the preferred phase of coupling by imposing differential synaptic delays on postsynaptic potentials. This distinction between the locking phase of neurons activated by the spatially attended stimulus vs. that of neurons activated by the unattended stimulus, may enable the neural system to discriminate relevant from irrelevant sensory inputs and consequently filter out distracting stimuli information by aligning the spikes which convey relevant/irrelevant information to distinct phases linked to periods of better/worse perceptual sensitivity for higher cortices. This strategy may be used to reserve the narrow windows of highest perceptual efficacy to the processing of the most behaviorally relevant information, ensuring highly efficient responses to attended sensory events.

Delay-dependent transitions of phase synchronization and coupling symmetry between neurons shaped by spike-timing-dependent plasticity

Synchronization plays a key role in learning and memory by facilitating the communication between neurons promoted by synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity that modifies the strength of synaptic connections between neurons based on the coincidence of pre- and postsynaptic spikes. In this way, STDP simultaneously shapes the neuronal activity and synaptic connectivity in a feedback loop. However, transmission delays due to the physical distance between neurons affect neuronal synchronization and the symmetry of synaptic coupling. To address the question that how transmission delays and STDP can jointly determine the emergent pairwise activity-connectivity patterns, we studied phase synchronization properties and coupling symmetry between two bidirectionally coupled neurons using both phase oscillator and conductance-based neuron models. We show that depending on the range of transmission delays, the activity of the two-neuron motif can achieve an in-phase/anti-phase synchronized state and its connectivity can attain a symmetric/asymmetric coupling regime. The coevolutionary dynamics of the neuronal system and the synaptic weights due to STDP stabilizes the motif in either one of these states by transitions between in-phase/anti-phase synchronization states and symmetric/asymmetric coupling regimes at particular transmission delays. These transitions crucially depend on the phase response curve (PRC) of the neurons, but they are relatively robust to the heterogeneity of transmission delays and potentiation-depression imbalance of the STDP profile.

Decoupling of interacting neuronal populations by time-shifted stimulation through spike-timing-dependent plasticity

The synaptic organization of the brain is constantly modified by activity-dependent synaptic plasticity. In several neurological disorders, abnormal neuronal activity and pathological synaptic connectivity may significantly impair normal brain function. Reorganization of neuronal circuits by therapeutic stimulation has the potential to restore normal brain dynamics. Increasing evidence suggests that the temporal stimulation pattern crucially determines the long-lasting therapeutic effects of stimulation. Here, we tested whether a specific pattern of brain stimulation can enable the suppression of pathologically strong inter-population synaptic connectivity through spike-timing-dependent plasticity (STDP). More specifically, we tested how introducing a time shift between stimuli delivered to two interacting populations of neurons can effectively decouple them. To that end, we first used a tractable model, i.e., two bidirectionally coupled leaky integrate-and-fire (LIF) neurons, to theoretically analyze the optimal range of stimulation frequency and time shift for decoupling. We then extended our results to two reciprocally connected neuronal populations (modules) where inter-population delayed connections were modified by STDP. As predicted by the theoretical results, appropriately time-shifted stimulation causes a decoupling of the two-module system through STDP, i.e., by unlearning pathologically strong synaptic interactions between the two populations. Based on the overall topology of the connections, the decoupling of the two modules, in turn, causes a desynchronization of the populations that outlasts the cessation of stimulation. Decoupling effects of the time-shifted stimulation can be realized by time-shifted burst stimulation as well as time-shifted continuous simulation. Our results provide insight into the further optimization of a variety of multichannel stimulation protocols aiming at a therapeutic reshaping of diseased brain networks.

From nociception to pain perception, possible implications of astrocytes

Astrocytes are determinants for the functioning of the CNS. They respond to neuronal activity with calcium increases and can in turn modulate synaptic transmission, brain plasticity as well as cognitive processes. Astrocytes display sensory-evoked calcium responses in different brain structures related to the discriminative system of most sensory modalities. In particular, noxious stimulation evoked calcium responses in astrocytes in the spinal cord, the hippocampus, and the somatosensory cortex. However, it is not clear if astrocytes are involved in pain. Pain is a private, personal, and complex experience that warns us about potential tissue damage. It is a perception that is not linearly associated with the amount of tissue damage or nociception; instead, it is constructed with sensory, cognitive, and affective components and depends on our previous experiences. However, it is not fully understood how pain is created from nociception. In this perspective article, we provide an overview of the mechanisms and neuronal networks that underlie the perception of pain. Then we proposed that coherent activity of astrocytes in the spinal cord and pain-related brain areas could be important in binding sensory, affective, and cognitive information on a slower time scale.

Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory proposes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phase-locking and effective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network and communicate effectively. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention.

Oscillations are ubiquitous in the brain and are involved in several cognitive tasks but their role is not completely understood. The Communication Through Coherence theory proposes that background oscillations in the brain regulate the information flow between neural populations. The oscillators that are properly phase-locked so that inputs arrive at the peaks of excitability of the receiving population communicate effectively. In this paper, we study the emerging phase-locking patterns of a network generating PING oscillations under external periodic forcing, simulating the oscillatory input from other neural groups. We identify the conditions for optimal phase-locking and effective communication. Namely, we find that inputs with higher frequency and coherence have an adavantage to entrain the network and we quantify how robust are to distractors. Furthermore, we show how selective attention can be implemented by means of phase locking and we show that pulsatile inputs can switch between attended inputs.

Directed functional and structural connectivity in a large-scale model for the mouse cortex

Inferring the structural connectivity from electrophysiological measurements is a fundamental challenge in systems neuroscience. Directed functional connectivity measures, such as the generalized partial directed coherence (GPDC), provide estimates of the causal influence between areas. However, the relation between causality estimates and structural connectivity is still not clear. We analyzed this problem by evaluating the effectiveness of GPDC to estimate the connectivity of a ground-truth, data-constrained computational model of a large-scale network model of the mouse cortex. The model contains 19 cortical areas composed of spiking neurons, with areas connected by long-range projections with weights obtained from a tract-tracing cortical connectome. We show that GPDC values provide a reasonable estimate of structural connectivity, with an average Pearson correlation over simulations of 0.74. Moreover, even in a typical electrophysiological recording scenario containing five areas, the mean correlation was above 0.6. These results suggest that it may be possible to empirically estimate structural connectivity from functional connectivity even when detailed whole-brain recordings are not achievable.

We analyzed the relationship between structural and directed functional connectivity by evaluating the effectiveness of generalized partial directed coherence (GPDC) to estimate the connectivity of a ground-truth, data-constrained computational model of a large-scale network model of the mouse cortex. We show that GPDC values provide a reasonable estimate of structural connectivity even in a typical electrophysiological recording scenario containing few areas. These results suggest that it may be possible to empirically estimate structural connectivity from functional connectivity even when detailed whole-brain recordings are not achievable.

Sex differences in neuronal systems function and behaviour: beyond a single diagnosis in autism spectrum disorders

Autism spectrum disorder (ASD) is a complex neurodevelopmental disorder that is associated with functional brain alterations that underlie the expression of behaviour. Males are diagnosed up to four times more than females, and sex differences have been identified in memory, cognitive flexibility, verbal fluency, and social communication. Unfortunately, there exists a lack of information on the sex-dependent mechanisms of ASD, as well as biological markers to distinguish sex-specific symptoms in ASD. This can often result in a standardized diagnosis for individuals across the spectrum, despite significant differences in the various ASD subtypes. Alterations in neuronal connectivity and oscillatory activity, such as is observed in ASD, are highly coupled to behavioural states. Yet, despite the well-identified sexual dimorphisms that exist in ASD, these functional patterns have rarely been analyzed in the context of sex differences or symptomology. This review summarizes alterations in neuronal oscillatory function in ASD, discusses the age, region, symptom and sex-specific differences that are currently observed across the spectrum, and potential targets for regulating neuronal oscillatory activity in ASD. The need to identify sex-specific biomarkers, in order to facilitate specific diagnostic criteria and allow for more targeted therapeutic approaches for ASD will also be discussed.

The Antidepressant-Like and Analgesic Effects of Kratom Alkaloids are accompanied by Changes in Low Frequency Oscillations but not ΔFosB Accumulation

Mitragyna speciosa (“kratom”), employed as a traditional medicine to improve mood and relieve pain, has shown increased use in Europe and North America. Here, the dose-dependent effects of a purified alkaloid kratom extract on neuronal oscillatory systems function, analgesia, and antidepressant-like behaviour were evaluated and kratom-induced changes in ΔFosB expression determined. Male rats were administered a low or high dose of kratom (containing 0.5 or 1 mg/kg of mitragynine, respectively) for seven days. Acute or repeated low dose kratom suppressed ventral tegmental area (VTA) theta oscillatory power whereas acute or repeated high dose kratom increased delta power, and reduced theta power, in the nucleus accumbens (NAc), prefrontal cortex (PFC), cingulate cortex (Cg) and VTA. The repeated administration of low dose kratom additionally elevated delta power in PFC, decreased theta power in NAc and PFC, and suppressed beta and low gamma power in Cg. Suppressed high gamma power in NAc and PFC was seen selectively following repeated high dose kratom. Both doses of kratom elevated NAc-PFC, VTA-NAc, and VTA-Cg coherence. Low dose kratom had antidepressant-like properties whereas both doses produced analgesia. No kratom-induced changes in ΔFosB expression were evident. These results support a role for kratom as having both antidepressant and analgesic properties that are accompanied by specific changes in neuronal circuit function. However, the absence of drug-induced changes in ΔFosB expression suggest that the drug may circumvent this cellular signaling pathway, a pathway known for its significant role in addiction.

Information Transmission in Delay-Coupled Neuronal Circuits in the Presence of a Relay Population

Synchronization between neuronal populations is hypothesized to play a crucial role in the communication between brain networks. The binding of features, or the association of computations occurring in spatially segregated areas, is supposed to take place when a stable synchronization between cortical areas occurs. While a direct cortico-cortical connection typically fails to support this mechanism, the participation of a third area, a relay element, mediating in the communication was proposed to overcome this limitation. Among the different structures that could play the role of coordination during the binding process, the thalamus is the best placed region to carry out this task. In this paper we study how information flows in a canonical motif that mimics a cortico-thalamo-cortical circuit composed by three mutually coupled neuronal populations (also called the V-motif). Through extensive numerical simulations, we found that the amount of information transferred between the oscillating neuronal populations is determined by the delay in their connections and the mismatch in their oscillation frequencies (detuning). While the transmission from a cortical population is mostly restricted to positive detuning, transmission from the relay (thalamic) population to the cortical populations is robust for a broad range of detuning values, including negative values, while permitting feedback communication from the cortex at high frequencies, thus supporting robust bottom up and top down interaction. In this case, a strong feedback transmission between the cortex to thalamus supports the possibility of robust bottom-up and top-down interactions in this motif. Interestingly, adding a cortico-cortical bidirectional connection to the V-motif (C-motif) expands the dynamics of the system with distinct operation modes. While overall transmission efficiency is decreased, new communication channels establish cortico-thalamo-cortical association loops. Switching between operation modes depends on the synaptic strength of the cortico-cortical connections. Our results support a role of the transthalamic V-motif in the binding of spatially segregated cortical computations, and suggest an important regulatory role of the direct cortico-cortical connection.

FNS allows efficient event-driven spiking neural network simulations based on a neuron model supporting spike latency

Neural modelling tools are increasingly employed to describe, explain, and predict the human brain's behavior. Among them, spiking neural networks (SNNs) make possible the simulation of neural activity at the level of single neurons, but their use is often threatened by the resources needed in terms of processing capabilities and memory. Emerging applications where a low energy burden is required (e.g. implanted neuroprostheses) motivate the exploration of new strategies able to capture the relevant principles of neuronal dynamics in reduced and efficient models. The recent Leaky Integrate-and-Fire with Latency (LIFL) spiking neuron model shows some realistic neuronal features and efficiency at the same time, a combination of characteristics that may result appealing for SNN-based brain modelling. In this paper we introduce FNS, the first LIFL-based SNN framework, which combines spiking/synaptic modelling with the event-driven approach, allowing us to define heterogeneous neuron groups and multi-scale connectivity, with delayed connections and plastic synapses. FNS allows multi-thread, precise simulations, integrating a novel parallelization strategy and a mechanism of periodic dumping. We evaluate the performance of FNS in terms of simulation time and used memory, and compare it with those obtained with neuronal models having a similar neurocomputational profile, implemented in NEST, showing that FNS performs better in both scenarios. FNS can be advantageously used to explore the interaction within and between populations of spiking neurons, even for long time-scales and with a limited hardware configuration.

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.

Synchronization of Independent Neural Ensembles in Human EEG during Choice Tasks

During behavioral experiments, humans placed in a situation of having to choose between a more valuable but risky reward and a less valuable but guaranteed reward make their decisions in accordance with external situational factors and individual characteristics, such as inclination to risk or caution. In such situations, humans can be divided into “risk-inclined” and “risk-averse” (or “cautious”) subjects. In this work, characteristics of EEG rhythms, such as phase–phase relationships and time lags between rhythms, were studied in pairs of alpha–beta and theta–beta rhythms. Phase difference can also be expressed as a time lag. It has been suggested that statistically significant time lags between rhythms are due to the combined neural activity of anatomically separate, independent (in activation/inhibition processes) ensembles. The extents of synchronicity between rhythms were compared as percentages between risk-inclined and risk-averse subjects. The results showed that synchronicity in response to stimuli was more often observed in pairs of alpha–beta rhythms of risk-averse subjects compared with risk-inclined subjects during the choice of a more valuable but less probable reward. In addition, significant differences in the percentage ratio of alpha and beta rhythms were revealed between (i) cases of synchronization without long time lags and (ii) cases with long time lags between rhythms (from 0.08 to 0.1 s).

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.

Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits

Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated in routing information. While multiple cellular mechanisms influence the network oscillatory dynamics and structure the macroscopic firing motifs, one of the key questions is to identify the biophysical neuronal and synaptic properties that permit such motifs to arise. A second important issue is how the different neural activity coherence states determine the communication between the neural circuits. Here we analyse the emergence of phase-locking within bidirectionally delayed-coupled spiking circuits in which global gamma band oscillations arise from synaptic coupling among largely excitable neurons. We consider both the interneuronal (ING) and the pyramidal-interneuronal (PING) population gamma rhythms and the inter coupling targeting the pyramidal or the inhibitory neurons. Using a mean-field approach together with an exact reduction method, we reduce each spiking network to a low dimensional nonlinear system and derive the macroscopic phase resetting-curves (mPRCs) that determine how the phase of the global oscillation responds to incoming perturbations. This is made possible by the use of the quadratic integrate-and-fire model together with a Lorentzian distribution of the bias current. Depending on the type of gamma (PING vs. ING), we show that incoming excitatory inputs can either speed up the macroscopic oscillation (phase advance; type I PRC) or induce both a phase advance and a delay (type II PRC). From there we determine the structure of macroscopic coherence states (phase-locking) of two weakly synaptically-coupled networks. To do so we derive a phase equation for the coupled system which links the synaptic mechanisms to the coherence states of the system. We show that a synaptic transmission delay is a necessary condition for symmetry breaking, i.e. a non-symmetric phase lag between the macroscopic oscillations. This potentially provides an explanation to the experimentally observed variety of gamma phase-locking modes. Our analysis further shows that symmetry-broken coherence states can lead to a preferred direction of signal transfer between the oscillatory networks where this directionality also depends on the timing of the signal. Hence we suggest a causal theory for oscillatory modulation of functional connectivity between cortical circuits.

Large scale brain oscillations emerge from synaptic interactions within neuronal circuits. Over the past years, such macroscopic rhythms have been suggested to play a crucial role in routing the flow of information across cortical regions, resulting in a functional connectome. The underlying mechanism is cortical oscillations that bind together following a well-known motif called phase-locking. While there is significant experimental support for multiple phase-locking modes in the brain, it is still unclear what is the underlying mechanism that permits macroscopic rhythms to phase lock. In the present paper we take up with this issue, and to show that, one can study the emergent macroscopic phase-locking within the mathematical framework of weakly coupled oscillators. We find that under synaptic delays, fully symmetrically coupled networks can display symmetry-broken states of activity, where one network starts to lead in phase the second (also sometimes known as stuttering states). When we analyse how incoming transient signals affect the coupled system, we find that in the symmetry-broken state, the effect depends strongly on which network is targeted (the leader or the follower) as well as the timing of the input. Hence we show how the dynamics of the emergent phase-locked activity imposes a functional directionality on how signals are processed. We thus offer clarification on the synaptic and circuit properties responsible for the emergence of multiple phase-locking patterns and provide support for its functional implication in information transfer.

Phase Difference between Model Cortical Areas Determines Level of Information Transfer

Communication between cortical sites is mediated by long-range synaptic connections. However, these connections are relatively static, while everyday cognitive tasks demand a fast and flexible routing of information in the brain. Synchronization of activity between distant cortical sites has been proposed as the mechanism underlying such a dynamic communication structure. Here, we study how oscillatory activity affects the excitability and input-output relation of local cortical circuits and how it alters the transmission of information between cortical circuits. To this end, we develop model circuits showing fast oscillations by the PING mechanism, of which the oscillatory characteristics can be altered. We identify conditions for synchronization between two brain circuits and show that the level of intercircuit coherence and the phase difference is set by the frequency difference between the intrinsic oscillations. We show that the susceptibility of the circuits to inputs, i.e., the degree of change in circuit output following input pulses, is not uniform throughout the oscillation period and that both firing rate, frequency and power are differentially modulated by inputs arriving at different phases. As a result, an appropriate phase difference between the circuits is critical for the susceptibility windows of the circuits in the network to align and for information to be efficiently transferred. We demonstrate that changes in synchrony and phase difference can be used to set up or abolish information transfer in a network of cortical circuits.

Transition between Functional Regimes in an Integrate-And-Fire Network Model of the Thalamus

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 − 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

Stimulus-dependent synchronization in delayed-coupled neuronal networks

Time delay is a general feature of all interactions. Although the effects of delayed interaction are often neglected when the intrinsic dynamics is much slower than the coupling delay, they can be crucial otherwise. We show that delayed coupled neuronal networks support transitions between synchronous and asynchronous states when the level of input to the network changes. The level of input determines the oscillation period of neurons and hence whether time-delayed connections are synchronizing or desynchronizing. We find that synchronizing connections lead to synchronous dynamics, whereas desynchronizing connections lead to out-of-phase oscillations in network motifs and to frustrated states with asynchronous dynamics in large networks. Since the impact of a neuronal network to downstream neurons increases when spikes are synchronous, networks with delayed connections can serve as gatekeeper layers mediating the firing transfer to other regions. This mechanism can regulate the opening and closing of communicating channels between cortical layers on demand.

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.

Areas V1 and V2 show microsaccade-related 3-4-Hz covariation in gamma power and frequency

Neuronal gamma-band synchronization (25-80 Hz) in visual cortex appears sustained and stable during prolonged visual stimulation when investigated with conventional averages across trials. However, recent studies in macaque visual cortex have used single-trial analyses to show that both power and frequency of gamma oscillations exhibit substantial moment-by-moment variation. This has raised the question of whether these apparently random variations might limit the functional role of gamma-band synchronization for neural processing. Here, we studied the moment-by-moment variation in gamma oscillation power and frequency, as well as inter-areal gamma synchronization, by simultaneously recording local field potentials in V1 and V2 of two macaque monkeys. We additionally analyzed electrocorticographic V1 data from a third monkey. Our analyses confirm that gamma-band synchronization is not stationary and sustained but undergoes moment-by-moment variations in power and frequency. However, those variations are neither random and nor a possible obstacle to neural communication. Instead, the gamma power and frequency variations are highly structured, shared between areas and shaped by a microsaccade-related 3-4-Hz theta rhythm. Our findings provide experimental support for the suggestion that cross-frequency coupling might structure and facilitate the information flow between brain regions.

Synchronization-based computation through networks of coupled oscillators

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.

Parametric variation of gamma frequency and power with luminance contrast: A comparative study of human MEG and monkey LFP and spike responses

Gamma oscillations contribute significantly to the manner in which neural activity is bound into functional assemblies. The mechanisms that underlie the human gamma response, however, are poorly understood. Previous computational models of gamma rely heavily on the results of invasive recordings in animals, and it is difficult to assess whether these models hold in humans. Computational models of gamma predict specific changes in gamma spectral response with increased excitatory drive. Hence, differences and commonalities between spikes, LFPs and MEG in the spectral responses to changes in excitatory drive can lead to a refinement of existing gamma models. We compared gamma spectral responses to varying contrasts in a monkey dataset acquired previously (Roberts et al., 2013) with spectral responses to similar contrast variations in a new human MEG dataset. We found parametric frequency shifts with increasing contrast in human MEG at the single-subject and the single-trial level, analogous to those observed in the monkey. Additionally, we observed parametric modulations of spectral asymmetry, consistent across spikes, LFP and MEG. However, while gamma power scaled linearly with contrast in MEG, it saturated at high contrasts in both the LFP and spiking data. Thus, while gamma frequency changes to varying contrasts were comparable across spikes, LFP and MEG, gamma power changes were not. This indicates that gamma frequency may be a more stable parameter across scales of measurements and species than gamma power. The comparative approach undertaken here represents a fruitful path towards a better understanding of gamma oscillations in the human brain.

Input-dependent frequency modulation of cortical gamma oscillations shapes spatial synchronization and enables phase coding

Fine-scale temporal organization of cortical activity in the gamma range (∼25-80Hz) may play a significant role in information processing, for example by neural grouping ('binding') and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.