A quantitative theory of gamma synchronization in macaque V1

Quantifying local field potential dynamics with amplitude and frequency stability between ON and OFF medication and stimulation in Parkinson's disease

Neural oscillations are critical to understanding the synchronisation of neural activities and their relevance to neurological disorders. For instance, the amplitude of beta oscillations in the subthalamic nucleus has gained extensive attention, as it has been found to correlate with medication status and the therapeutic effects of continuous deep brain stimulation in people with Parkinson's disease. However, the frequency stability of subthalamic nucleus beta oscillations, which has been suggested to be associated with dopaminergic information in brain states, has not been well explored. Moreover, the administration of medicine can have inverse effects on changes in frequency and amplitude. In this study, we proposed a method based on the stationary wavelet transform to quantify the amplitude and frequency stability of subthalamic nucleus beta oscillations and evaluated the method using simulation and real data for Parkinson's disease patients. The results suggest that the amplitude and frequency stability quantification has enhanced sensitivity in distinguishing pathological conditions in Parkinson's disease patients. Our quantification shows the benefit of combining frequency stability information with amplitude and provides a new potential feedback signal for adaptive deep brain stimulation.

Rodents' visual gamma as a biomarker of pathological neural conditions

Neural gamma oscillations (indicatively 30-100 Hz) are ubiquitous: they are associated with a broad range of functions in multiple cortical areas and across many animal species. Experimental and computational works established gamma rhythms as a global emergent property of neuronal networks generated by the balanced and coordinated interaction of excitation and inhibition. Coherently, gamma activity is strongly influenced by the alterations of synaptic dynamics which are often associated with pathological neural dysfunctions. We argue therefore that these oscillations are an optimal biomarker for probing the mechanism of cortical dysfunctions. Gamma oscillations are also highly sensitive to external stimuli in sensory cortices, especially the primary visual cortex (V1), where the stimulus dependence of gamma oscillations has been thoroughly investigated. Gamma manipulation by visual stimuli tuning is particularly easy in rodents, which have become a standard animal model for investigating the effects of network alterations on gamma oscillations. Overall, gamma in the rodents' visual cortex offers an accessible probe on dysfunctional information processing in pathological conditions. Beyond vision-related dysfunctions, alterations of gamma oscillations in rodents were indeed also reported in neural deficits such as migraine, epilepsy and neurodegenerative or neuropsychiatric conditions such as Alzheimer's, schizophrenia and autism spectrum disorders. Altogether, the connections between visual cortical gamma activity and physio-pathological conditions in rodent models underscore the potential of gamma oscillations as markers of neuronal (dys)functioning.

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay

The analog Hopfield neural network with time delay and random connections has been studied for its similarities in activity to human electroencephalogram and its usefulness in other areas of the applied sciences such as speech recognition, image analysis, and electrocardiogram modeling. Our goal here is to understand the mechanisms that affect the rhythmic activity in the neural network and how the addition of a Gaussian noise contributes to the network behavior. The neural network studied is composed of ten identical neurons. We investigated the excitatory and inhibitory networks with symmetric (square matrix) and asymmetric (triangular matrix) connections. The differential equations that model the network are solved numerically using the stochastic second-order Runge-Kutta method. Without noise, the neural networks with symmetric and asymmetric matrices possessed different synchronization properties: fully connected networks were synchronized both in time and in amplitude, while asymmetric networks were synchronized in time only. Saturation outputs of the excitatory neural networks do not depend on the time delay, whereas saturation oscillation amplitudes of inhibitory networks increase with the time delay until the steady state. The addition of the Gaussian noise is shown to significantly amplify small-amplitude oscillations, dramatically accelerates the rate of amplitude growth to saturation, and changes synchronization properties of the neural network outputs.

Attentional effects on local V1 microcircuits explain selective V1-V4 communication

Selective attention implements preferential routing of attended stimuli, likely through increasing the influence of the respective synaptic inputs on higher-area neurons. As the inputs of competing stimuli converge onto postsynaptic neurons, presynaptic circuits might offer the best target for attentional top-down influences. If those influences enabled presynaptic circuits to selectively entrain postsynaptic neurons, this might explain selective routing. Indeed, when two visual stimuli induce two gamma rhythms in V1, only the gamma induced by the attended stimulus entrains gamma in V4. Here, we modelled induced responses with a Dynamic Causal Model for Cross-Spectral Densities and found that selective entrainment can be explained by attentional modulation of intrinsic V1 connections. Specifically, local inhibition was decreased in the granular input layer and increased in the supragranular output layer of the V1 circuit that processed the attended stimulus. Thus, presynaptic attentional influences and ensuing entrainment were sufficient to mediate selective routing.

Update on Nonhuman Primate Models of Brain Disease and Related Research Tools

The aging of the population is an increasingly serious issue, and many age-related illnesses are on the rise. These illnesses pose a serious threat to the health and safety of elderly individuals and create a serious economic and social burden. Despite substantial research into the pathogenesis of these diseases, their etiology and pathogenesis remain unclear. In recent decades, rodent models have been used in attempts to elucidate these disorders, but such models fail to simulate the full range of symptoms. Nonhuman primates (NHPs) are the most ideal neuroscientific models for studying the human brain and are more functionally similar to humans because of their high genetic similarities and phenotypic characteristics in comparison with humans. Here, we review the literature examining typical NHP brain disease models, focusing on NHP models of common diseases such as dementia, Parkinson's disease, and epilepsy. We also explore the application of electroencephalography (EEG), magnetic resonance imaging (MRI), and optogenetic study methods on NHPs and neural circuits associated with cognitive impairment.

Temporal characteristics of gamma rhythm constrain properties of noise in an inhibition-stabilized network model

Gamma rhythm refers to oscillatory neural activity between 30 and 80 Hz, induced in visual cortex by stimuli such as iso-luminant hues or gratings. The power and peak frequency of gamma depend on the properties of the stimulus such as size and contrast. Gamma waveform is typically arch-shaped, with narrow troughs and broad peaks, and can be replicated in a self-oscillating Wilson-Cowan (WC) model operating in an appropriate regime. However, oscillations in this model are infinitely long, unlike physiological gamma that occurs in short bursts. Further, unlike the model, gamma is faster after stimulus onset and slows down over time. Here, we first characterized gamma burst duration in local field potential data recorded from two monkeys as they viewed full screen iso-luminant hues. We then added different types of noise in the inputs to the WC model and tested how that affected duration and temporal dynamics of gamma. While the model failed with the often-used Poisson noise, Ornstein-Uhlenbeck noise applied to both the excitatory and the inhibitory populations replicated the duration and slowing of gamma and replicated the shape and stimulus dependencies. Thus, the temporal dynamics of gamma oscillations put constraints on the type and properties of underlying neural noise.

β Band Rhythms Influence Reaction Times

Despite their involvement in many cognitive functions, β oscillations are among the least understood brain rhythms. Reports on whether the functional role of β is primarily inhibitory or excitatory have been contradictory. Our framework attempts to reconcile these findings and proposes that several β rhythms co-exist at different frequencies. β Frequency shifts and their potential influence on behavior have thus far received little attention. In this human magnetoencephalography (MEG) experiment, we asked whether changes in β power or frequency in auditory cortex and motor cortex influence behavior (reaction times) during an auditory sweep discrimination task. We found that in motor cortex, increased β power slowed down responses, while in auditory cortex, increased β frequency slowed down responses. We further characterized β as transient burst events with distinct spectro-temporal profiles influencing reaction times. Finally, we found that increased motor-to-auditory β connectivity also slowed down responses. In sum, β power, frequency, bursting properties, cortical focus, and connectivity profile all influenced behavioral outcomes. Our results imply that the study of β oscillations requires caution as β dynamics are multifaceted phenomena, and that several dynamics must be taken into account to reconcile mixed findings in the literature.

How to entrain a selected neuronal rhythm but not others: open-loop dithered brain stimulation for selective entrainment

Objective.While brain stimulation therapies such as deep brain stimulation for Parkinson's disease (PD) can be effective, they have yet to reach their full potential across neurological disorders. Entraining neuronal rhythms using rhythmic brain stimulation has been suggested as a new therapeutic mechanism to restore neurotypical behaviour in conditions such as chronic pain, depression, and Alzheimer's disease. However, theoretical and experimental evidence indicate that brain stimulation can also entrain neuronal rhythms at sub- and super-harmonics, far from the stimulation frequency. Crucially, these counterintuitive effects could be harmful to patients, for example by triggering debilitating involuntary movements in PD. We therefore seek a principled approach to selectively promote rhythms close to the stimulation frequency, while avoiding potential harmful effects by preventing entrainment at sub- and super-harmonics.Approach.Our open-loop approach to selective entrainment, dithered stimulation, consists in adding white noise to the stimulation period.Main results.We theoretically establish the ability of dithered stimulation to selectively entrain a given brain rhythm, and verify its efficacy in simulations of uncoupled neural oscillators, and networks of coupled neural oscillators. Furthermore, we show that dithered stimulation can be implemented in neurostimulators with limited capabilities by toggling within a finite set of stimulation frequencies.Significance.Likely implementable across a variety of existing brain stimulation devices, dithering-based selective entrainment has potential to enable new brain stimulation therapies, as well as new neuroscientific research exploiting its ability to modulate higher-order entrainment.

Frequency modulation of cortical rhythmicity governs behavioral variability, excitability and synchrony of neurons in the visual cortex

Research in cognitive neuroscience has renewed the idea that brain oscillations are a core organization implicated in fundamental brain functions. Growing evidence reveals that the characteristic features of these oscillations, including power, phase and frequency, are highly non-stationary, fluctuating alongside alternations in sensation, cognition and behavior. However, there is little consensus on the functional implications of the instantaneous frequency variation in cortical excitability and concomitant behavior. Here, we capitalized on intracortical electrophysiology in the macaque monkey's visual area MT performing a visuospatial discrimination task with visual cues. We observed that the instantaneous frequency of the theta-alpha oscillations (4-13 Hz) is modulated among specific neurons whose RFs overlap with the cued stimulus location. Interestingly, we found that such frequency modulation is causally correlated with MT excitability at both scales of individual and ensemble of neurons. Moreover, studying the functional relevance of frequency variations indicated that the average theta-alpha frequencies foreshadow the monkey's reaction time. Our results also revealed that the neural synchronization strength alters with the average frequency shift in theta-alpha oscillations, suggesting frequency modulation is critical for mutually adjusting MTs' rhythms. Overall, our findings propose that theta-alpha frequency variations modulate MT's excitability, regulate mutual neurons' rhythmicity and indicate variability in behavior.

Amplitude and frequency modulation of subthalamic beta oscillations jointly encode the dopaminergic state in Parkinson's disease

Brain states in health and disease are classically defined by the power or the spontaneous amplitude modulation (AM) of neuronal oscillations in specific frequency bands. Conversely, the possible role of the spontaneous frequency modulation (FM) in defining pathophysiological brain states remains unclear. As a paradigmatic example of pathophysiological resting states, here we assessed the spontaneous AM and FM dynamics of subthalamic beta oscillations recorded in patients with Parkinson's disease before and after levodopa administration. Even though AM and FM are mathematically independent, they displayed negatively correlated dynamics. First, AM decreased while FM increased with levodopa. Second, instantaneous amplitude and instantaneous frequency were negatively cross-correlated within dopaminergic states, with FM following AM by approximately one beta cycle. Third, AM and FM changes were also negatively correlated between dopaminergic states. Both the slow component of the FM and the fast component (i.e. the phase slips) increased after levodopa, but they differently contributed to the AM-FM correlations within and between states. Finally, AM and FM provided information about whether the patients were OFF vs. ON levodopa, with partial redundancy and with FM being more informative than AM. AM and FM of spontaneous beta oscillations can thus both separately and jointly encode the dopaminergic state in patients with Parkinson's disease. These results suggest that resting brain states are defined not only by AM dynamics but also, and possibly more prominently, by FM dynamics of neuronal oscillations.

Visual working memory recruits two functionally distinct alpha rhythms in posterior cortex

Oscillatory activity in the human brain is dominated by posterior alpha oscillations (8-14 Hz), which have been shown to be functionally relevant in a wide variety of cognitive tasks. Although posterior alpha oscillations are commonly considered a single oscillator anchored at an individual alpha frequency (IAF; ∼10 Hz), previous work suggests that IAF reflects a spatial mixture of different brain rhythms. In this study, we assess whether Independent Component Analysis (ICA) can disentangle functionally distinct posterior alpha rhythms in the context of visual short-term memory retention. Magnetoencephalography (MEG) was recorded in 33 subjects while performing a visual working memory task. Group analysis at sensor level suggested the existence of a single posterior alpha oscillator that increases in power and decreases in frequency during memory retention. Conversely, single-subject analysis of independent components revealed the existence of two dissociable alpha rhythms: one that increases in power during memory retention (Alpha1) and another one that decreases in power (Alpha2). Alpha1 and Alpha2 rhythms were differentially modulated by the presence of visual distractors (Alpha1 increased in power while Alpha2 decreased) and had an opposite relationship with accuracy (positive for Alpha1 and negative for Alpha2). In addition, Alpha1 rhythms showed a lower peak frequency, a narrower peak width, a greater relative peak amplitude and a more central source than Alpha2 rhythms. Together, our results demonstrate that modulations in posterior alpha oscillations during short-term memory retention reflect the dynamics of at least two distinct brain rhythms with different functions and spatiospectral characteristics.Significance statementAlpha oscillations are the most prominent feature of the human brain's electrical activity, and consist of rhythmic neuronal activity in posterior parts of the cortex. Alpha is usually considered a single brain rhythm that changes in power and frequency to support cognitive operations. We here show that posterior alpha entails at least two dissociable rhythms with distinct functions and characteristics. These findings could solve previous inconsistencies in the literature regarding the direction of task-related alpha power/frequency modulations and their relation to cognitive performance. In addition, the existence of two distinct posterior alpha rhythms could have important consequences for the design of neurostimulation protocols aimed at modulating alpha oscillations and subsequently cognition.

Tuning Neural Synchronization: The Role of Variable Oscillation Frequencies in Neural Circuits

Brain oscillations emerge during sensory and cognitive processes and have been classified into different frequency bands. Yet, even within the same frequency band and between nearby brain locations, the exact frequencies of brain oscillations can differ. These frequency differences (detuning) have been largely ignored and play little role in current functional theories of brain oscillations. This contrasts with the crucial role that detuning plays in synchronization theory, as originally derived in physical systems. Here, we propose that detuning is equally important to understand synchronization in biological systems. Detuning is a critical control parameter in synchronization, which is not only important in shaping phase-locking, but also in establishing preferred phase relations between oscillators. We review recent evidence that frequency differences between brain locations are ubiquitous and essential in shaping temporal neural coordination. With the rise of powerful experimental techniques to probe brain oscillations, the contributions of exact frequency and detuning across neural circuits will become increasingly clear and will play a key part in developing a new understanding of the role of oscillations in brain function.

Spike-Gamma Phase Relationship in the Visual Cortex

Gamma oscillations (30-70 Hz) have been hypothesized to play a role in cortical function. Most of the proposed mechanisms involve rhythmic modulation of neuronal excitability at gamma frequencies, leading to modulation of spike timing relative to the rhythm. I first show that the gamma band could be more privileged than other frequencies in observing spike-field interactions even in the absence of genuine gamma rhythmicity and discuss several biases in spike-gamma phase estimation. I then discuss the expected spike-gamma phase according to several hypotheses. Inconsistent with the phase-coding hypothesis (but not with others), the spike-gamma phase does not change with changes in stimulus intensity or attentional state, with spikes preferentially occurring 2-4 ms before the trough, but with substantial variability. However, this phase relationship is expected even when gamma is a byproduct of excitatory-inhibitory interactions. Given that gamma occurs in short bursts, I argue that the debate over the role of gamma is a matter of semantics. Expected final online publication date for the Annual Review of Vision Science, Volume 8 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Human visual gamma for color stimuli

Strong gamma-band oscillations in primate early visual cortex can be induced by homogeneous color surfaces (Peter et al., 2019; Shirhatti and Ray, 2018). Compared to other hues, particularly strong gamma oscillations have been reported for red stimuli. However, precortical color processing and the resultant strength of input to V1 have often not been fully controlled for. Therefore, stronger responses to red might be due to differences in V1 input strength. We presented stimuli that had equal luminance and cone contrast levels in a color coordinate system based on responses of the lateral geniculate nucleus, the main input source for area V1. With these stimuli, we recorded magnetoencephalography in 30 human participants. We found gamma oscillations in early visual cortex which, contrary to previous reports, did not differ between red and green stimuli of equal L-M cone contrast. Notably, blue stimuli with contrast exclusively on the S-cone axis induced very weak gamma responses, as well as smaller event-related fields and poorer change-detection performance. The strength of human color gamma responses for stimuli on the L-M axis could be well explained by L-M cone contrast and did not show a clear red bias when L-M cone contrast was properly equalized.

Spontaneous variability in gamma dynamics described by a damped harmonic oscillator driven by noise

Circuits of excitatory and inhibitory neurons generate gamma-rhythmic activity (30-80 Hz). Gamma-cycles show spontaneous variability in amplitude and duration. To investigate the mechanisms underlying this variability, we recorded local-field-potentials (LFPs) and spikes from awake macaque V1. We developed a noise-robust method to detect gamma-cycle amplitudes and durations, which showed a weak but positive correlation. This correlation, and the joint amplitude-duration distribution, is well reproduced by a noise-driven damped harmonic oscillator. This model accurately fits LFP power-spectra, is equivalent to a linear, noise-driven E-I circuit, and recapitulates two additional features of gamma: (1) Amplitude-duration correlations decrease with oscillation strength; (2) amplitudes and durations exhibit strong and weak autocorrelations, respectively, depending on oscillation strength. Finally, longer gamma-cycles are associated with stronger spike-synchrony, but lower spike-rates in both (putative) excitatory and inhibitory neurons. In sum, V1 gamma-dynamics are well described by the simplest possible model of gamma: A damped harmonic oscillator driven by noise.

Mutual information resonances in delay-coupled limit cycle and quasi-cycle brain rhythms

We elucidate how coupling delays and noise impact phase and mutual information relationships between two stochastic brain rhythms. This impact depends on the dynamical regime of each PING-based rhythm, as well as on network heterogeneity and coupling asymmetry. The number of peaks at positive and negative time lags in the delayed mutual information between the two bi-directionally communicating rhythms defines our measure of flexibility of information sharing and reflects the number of ways in which the two networks can alternately lead one another. We identify two distinct mechanisms for the appearance of qualitatively similar flexible information sharing. The flexibility in the quasi-cycle regime arises from the coupling delay-induced bimodality of the phase difference distribution, and the related bimodal mutual information. It persists in the presence of asymmetric coupling and heterogeneity but is limited to two routes of information sharing. The second mechanism in noisy limit cycle regime is not induced by the delay. However, delay-coupling and heterogeneity enable communication routes at multiple time lags. Noise disrupts the shared compromise frequency, allowing the expression of individual network frequencies which leads to a slow beating pattern. Simulations of an envelope-phase description for delay-coupled quasi-cycles yield qualitatively similar properties as for the full system. Near the bifurcation from in-phase to out-of-phase behaviour, a single preferred phase difference can coexist with two information sharing routes; further, the phase laggard can be the mutual information leader, or vice versa. Overall, the coupling delay endows a two-rhythm system with an array of lead-lag relationships and mutual information resonances that exist in spite of the noise and across the Hopf bifurcation. These beg to be mapped out experimentally with the help of our predictions.

Predictive coding of natural images by V1 firing rates and rhythmic synchronization

Predictive coding is an important candidate theory of self-supervised learning in the brain. Its central idea is that sensory responses result from comparisons between bottom-up inputs and contextual predictions, a process in which rates and synchronization may play distinct roles. We recorded from awake macaque V1 and developed a technique to quantify stimulus predictability for natural images based on self-supervised, generative neural networks. We find that neuronal firing rates were mainly modulated by the contextual predictability of higher-order image features, which correlated strongly with human perceptual similarity judgments. By contrast, V1 gamma (γ)-synchronization increased monotonically with the contextual predictability of low-level image features and emerged exclusively for larger stimuli. Consequently, γ-synchronization was induced by natural images that are highly compressible and low-dimensional. Natural stimuli with low predictability induced prominent, late-onset beta (β)-synchronization, likely reflecting cortical feedback. Our findings reveal distinct roles of synchronization and firing rates in the predictive coding of natural images.

•

Predictability in natural images quantified with self-supervised neural networks

•

V1 firing rates decrease with predictability of high- not low-level image features

•

γ-synchronization increases with predictability of low-level image features

•

Late-onset β-synchronization for natural scenes with low predictability

A mechanism for inter-areal coherence through communication based on connectivity and oscillatory power

Inter-areal coherence between field potentials is a widespread phenomenon in cortex. Coherence has been hypothesized to reflect phase-synchronization between oscillators and flexibly gate communication according to behavioral and cognitive demands. We reveal an alternative mechanism where coherence is not the cause but the consequence of communication and naturally emerges because spiking activity in a sending area causes post-synaptic potentials both in the same and in other areas. Consequently, coherence depends in a lawful manner on power and phase-locking in the sender and connectivity. Changes in oscillatory power explained prominent changes in fronto-parietal and LGN-V1 coherence across behavioral conditions. Optogenetic experiments and excitatory-inhibitory network simulations identified afferent synaptic inputs rather than spiking entrainment as the principal determinant of coherence. These findings suggest that unique spectral profiles of different brain areas automatically give rise to large-scale coherence patterns that follow anatomical connectivity and continuously reconfigure as a function of behavior and cognition.

Stimulus-specific plasticity of macaque V1 spike rates and gamma

When a visual stimulus is repeated, average neuronal responses typically decrease, yet they might maintain or even increase their impact through increased synchronization. Previous work has found that many repetitions of a grating lead to increasing gamma-band synchronization. Here, we show in awake macaque area V1 that both repetition-related reductions in firing rate and increases in gamma are specific to the repeated stimulus. These effects show some persistence on the timescale of minutes. Gamma increases are specific to the presented stimulus location. Further, repetition effects on gamma and on firing rates generalize to images of natural objects. These findings support the notion that gamma-band synchronization subserves the adaptive processing of repeated stimulus encounters.

Recurrent dynamics in the cerebral cortex: Integration of sensory evidence with stored knowledge

Current concepts of sensory processing in the cerebral cortex emphasize serial extraction and recombination of features in hierarchically structured feed-forward networks in order to capture the relations among the components of perceptual objects. These concepts are implemented in convolutional deep learning networks and have been validated by the astounding similarities between the functional properties of artificial systems and their natural counterparts. However, cortical architectures also display an abundance of recurrent coupling within and between the layers of the processing hierarchy. This massive recurrence gives rise to highly complex dynamics whose putative function is poorly understood. Here a concept is proposed that assigns specific functions to the dynamics of cortical networks and combines, in a unifying approach, the respective advantages of recurrent and feed-forward processing. It is proposed that the priors about regularities of the world are stored in the weight distributions of feed-forward and recurrent connections and that the high-dimensional, dynamic space provided by recurrent interactions is exploited for computations. These comprise the ultrafast matching of sensory evidence with the priors covertly represented in the correlation structure of spontaneous activity and the context-dependent grouping of feature constellations characterizing natural objects. The concept posits that information is encoded not only in the discharge frequency of neurons but also in the precise timing relations among the discharges. Results of experiments designed to test the predictions derived from this concept support the hypothesis that cerebral cortex exploits the high-dimensional recurrent dynamics for computations serving predictive coding.

Mechanisms of Flexible Information Sharing through Noisy Oscillations

Simple Summary

To properly interact with our environment, the brain must be able to identify external stimuli, process them, and make the right decisions all in a short time. This may involve several brain regions interacting together by sharing information birectionally via rhythmic activity. Such flexibility requires the functional connectivity between the areas to be dynamic, and a key question is the relevant parameter and operating regimes that make this possible in spite of fixed structural connectivity. Working towards this goal, we consider two coupled brain regions, each of which exhibits a noisy rhythm, a commonly observed type of neural activity. Such rhythms can be induced by the stochasticity in the neural circuitry, or be autonomously generated through nonlinearities and not necessitating noise. For these two types of rhythms, we computed the amount of information shared between the brain areas and the preferred direction(s) of sharing. We found that without the coupling delay, the flexibility needed by the brain to perform cognitive tasks requires the rhythms to be autogenerated rather than noise-induced. This is the case even with asymmetry or heterogeneity. This suggests that the importance of the dynamical regime has to be taken into account when modeling interacting neural rhythms from an information theoretical point of view.

Abstract

Brain areas must be able to interact and share information in a time-varying, dynamic manner on a fast timescale. Such flexibility in information sharing has been linked to the synchronization of rhythm phases between areas. One definition of flexibility is the number of local maxima in the delayed mutual information curve between two connected areas. However, the precise relationship between phase synchronization and information sharing is not clear, nor is the flexibility in the face of the fixed structural connectivity and noise. Here, we consider two coupled oscillatory excitatory-inhibitory networks connected through zero-delay excitatory connections, each of which mimics a rhythmic brain area. We numerically compute phase-locking and delayed mutual information between the phases of excitatory local field potential (LFPs) of the two networks, which measures the shared information and its direction. The flexibility in information sharing is shown to depend on the dynamical origin of oscillations, and its properties in different regimes are found to persist in the presence of asymmetry in the connectivity as well as system heterogeneity. For coupled noise-induced rhythms (quasi-cycles), phase synchronization is robust even in the presence of asymmetry and heterogeneity. However, they do not show flexibility, in contrast to noise-perturbed rhythms (noisy limit cycles), which are shown here to exhibit two local information maxima, i.e., flexibility. For quasi-cycles, phase difference and information measures for the envelope-phase dynamics obtained from previous analytical work using the Stochastic Averaging Method (SAM) are found to be in good qualitative agreement with those obtained from the original dynamics. The relation between phase synchronization and communication patterns is not trivial, particularly in the noisy limit cycle regime. There, complex patterns of information sharing can be observed for a single value of the phase difference. The mechanisms reported here can be extended to I-I networks since their phase synchronizations are similar. Our results set the stage for investigating information sharing between several connected noisy rhythms in neural and other complex biological networks.

Cortical Synchrony as a Mechanism of Collinear Facilitation and Suppression in Early Visual Cortex

Stimulus-induced oscillations and synchrony among neuronal populations in visual cortex are well-established phenomena. Their functional role in cognition are, however, not well-understood. Recent studies have suggested that neural synchrony may underlie perceptual grouping as stimulus-frequency relationships and stimulus-dependent lateral connectivity profiles can determine the success or failure of synchronization among neuronal groups encoding different stimulus elements. We suggest that the same mechanism accounts for collinear facilitation and suppression effects where the detectability of a target Gabor stimulus is improved or diminished by the presence of collinear flanking Gabor stimuli. We propose a model of oscillators which represent three neuronal populations in visual cortex with distinct receptive fields reflecting the target and two flankers, respectively, and whose connectivity is determined by the collinearity of the presented Gabor stimuli. Our model simulations confirm that neuronal synchrony can indeed explain known collinear facilitation and suppression effects for attended and unattended stimuli.

Monkey V1 epidural field potentials provide detailed information about stimulus location, size, shape, and color

Brain signal recordings with epidural microarrays constitute a low-invasive approach for recording distributed neuronal signals. Epidural field potentials (EFPs) may serve as a safe and highly beneficial signal source for a variety of research questions arising from both basic and applied neuroscience. A wider use of these signals, however, is constrained by a lack of data on their specific information content. Here, we make use of the high spatial resolution and the columnar organization of macaque primary visual cortex (V1) to investigate whether and to what extent EFP signals preserve information about various visual stimulus features. Two monkeys were presented with different feature combinations of location, size, shape, and color, yielding a total of 375 stimulus conditions. Visual features were chosen to access different spatial levels of functional organization. We found that, besides being highly specific for locational information, EFPs were significantly modulated by small differences in size, shape, and color, allowing for high stimulus classification rates even at the single-trial level. The results support the notion that EFPs constitute a low-invasive, highly beneficial signal source for longer-term recordings for medical and basic research by showing that they convey detailed and reliable information about constituent features of activating stimuli.

Cortical gamma-band resonance preferentially transmits coherent input

Synchronization has been implicated in neuronal communication, but causal evidence remains indirect. We use optogenetics to generate depolarizing currents in pyramidal neurons of the cat visual cortex, emulating excitatory synaptic inputs under precise temporal control, while measuring spike output. The cortex transforms constant excitation into strong gamma-band synchronization, revealing the well-known cortical resonance. Increasing excitation with ramps increases the strength and frequency of synchronization. Slow, symmetric excitation profiles reveal hysteresis of power and frequency. White-noise input sequences enable causal analysis of network transmission, establishing that the cortical gamma-band resonance preferentially transmits coherent input components. Models composed of recurrently coupled excitatory and inhibitory units uncover a crucial role of feedback inhibition and suggest that hysteresis can arise through spike-frequency adaptation. The presented approach provides a powerful means to investigate the resonance properties of local circuits and probe how these properties transform input and shape transmission.

Rhythmic synchronization has been implicated in neuronal communication, yet causal evidence has remained scarce. Lewis et al. optogenetically stimulate the visual cortex to emulate synaptic input while recording spike output. Cortex resonates at the gamma band (30–90 Hz) and preferentially transmits input that is coherent to the ongoing gamma-band rhythm.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

The Generation and Modulation of Distinct Gamma Oscillations with Local, Horizontal, and Feedback Connections in the Primary Visual Cortex: A Model Study on Large-Scale Networks

Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in information processing. Studies have shown that the response property of GAMMA is related to neural interaction through local recurrent connections (RC), feed-forward (FF), and feedback (FB) connections. However, the relationship between GAMMA and long-range horizontal connections (HC) in the brain remains unclear. Here, we aimed to understand this question in a large-scale network model for the primary visual cortex (V1). We created a computational model composed of multiple excitatory and inhibitory units with biologically plausible connectivity patterns for RC, FF, FB, and HC in V1; then, we quantitated GAMMA in network models at different strength levels of HC and other connection types. Surprisingly, we found that HC and FB, the two types of large-scale connections, play very different roles in generating and modulating GAMMA. While both FB and HC modulate a fast gamma oscillation (around 50-60 Hz) generated by FF and RC, HC generates a new GAMMA oscillating around 30 Hz, whose power and peak frequency can also be modulated by FB. Furthermore, response properties of the two GAMMAs in a network with both HC and FB are different in a way that is highly consistent with a recent experimental finding for distinct GAMMAs in macaque V1. The results suggest that distinct GAMMAs are signatures for neural connections in different spatial scales and they might be related to different functions for information integration. Our study, for the first time, pinpoints the underlying circuits for distinct GAMMAs in a mechanistic model for macaque V1, which might provide a new framework to study multiple gamma oscillations in other cortical regions.

Dynamic Modulation of Cortical Excitability during Visual Active Sensing

Visual physiology is traditionally investigated by presenting stimuli with gaze held constant. However, during active viewing of a scene, information is actively acquired using systematic patterns of fixations and saccades. Prior studies suggest that during such active viewing, both nonretinal, saccade-related signals and “extra-classical” receptive field inputs modulate visual processing. This study used a set of active viewing tasks that allowed us to compare visual responses with and without direct foveal input, thus isolating the contextual eye movement-related influences. Studying nonhuman primates, we find strong contextual modulation in primary visual cortex (V1): excitability and response amplification immediately after fixation onset, transiting to suppression leading up to the next saccade. Time-frequency decomposition suggests that this amplification and suppression cycle stems from a phase reset of ongoing neuronal oscillatory activity. The impact of saccade-related contextual modulation on stimulus processing makes active visual sensing fundamentally different from the more passive processes investigated in traditional paradigms.

By isolating contextual eye movement-related influences during active vision, Barczak et al. show that eye movements affect excitability in V1 such that responses are amplified immediately after fixation onset and suppressed as the next saccade approaches. This amplification and suppression cycle stems from a phase reset of ambient oscillatory activity in V1.

Determinants of Brain Rhythm Burst Statistics

Brain rhythms recorded in vivo, such as gamma oscillations, are notoriously variable both in amplitude and frequency. They are characterized by transient epochs of higher amplitude known as bursts. It has been suggested that, despite their short-life and random occurrence, bursts in gamma and other rhythms can efficiently contribute to working memory or communication tasks. Abnormalities in bursts have also been associated with e.g. motor and psychiatric disorders. It is thus crucial to understand how single cell and connectivity parameters influence burst statistics and the corresponding brain states. To address this problem, we consider a generic stochastic recurrent network of Pyramidal Interneuron Network Gamma (PING) type. Using the stochastic averaging method, we derive dynamics for the phase and envelope of the amplitude process, and find that they depend on only two meta-parameters that combine all the model parameters. This allows us to identify an optimal parameter regime of healthy variability with similar statistics to those seen in vivo; in this regime, oscillations and bursts are supported by synaptic noise. The probability density for the rhythm’s envelope as well as the mean burst duration are then derived using first passage time analysis. Our analysis enables us to link burst attributes, such as duration and frequency content, to system parameters. Our general approach can be extended to different frequency bands, network topologies and extra populations. It provides the much needed insight into the biophysical determinants of rhythm burst statistics, and into what needs to be changed to correct rhythms with pathological statistics.

Human visual cortical gamma reflects natural image structure

Many studies have reported visual cortical gamma-band activity related to stimulus processing and cognition. Most respective studies used artificial stimuli, and the few studies that used natural stimuli disagree. Electrocorticographic (ECoG) recordings from awake macaque areas V1 and V4 found gamma to be abundant during free viewing of natural images. In contrast, a study using ECoG recordings from V1 of human patients reported that many natural images induce no gamma and concluded that it is not necessary for seeing. To reconcile these apparently disparate findings, we reanalyzed those same human ECoG data recorded during presentation of natural images. We find that the strength of gamma is positively correlated with different image-computable metrics of image structure. This holds independently of the precise metric used to quantify gamma. In fact, an average of previously used gamma metrics reflects image structure most robustly. Gamma was sufficiently diagnostic of image structure to differentiate between any possible pair of images with >70% accuracy. Thus, while gamma might be weak for some natural images, the graded strength of gamma reflects the graded degree of image structure, and thereby conveys functionally relevant stimulus properties.

Tracking Transient Changes in the Neural Frequency Architecture: Harmonic Relationships between Theta and Alpha Peaks Facilitate Cognitive Performance

The synchronization between neural oscillations at different frequencies has been proposed as a core mechanism for the coordination and integration of neural systems at different spatiotemporal scales. Because neural oscillations of different frequencies can only fully synchronize when their "peak" frequencies form harmonic relationships (e.g., f ₂ = f ₁/2), the present study explored whether the transient occurrence of harmonic cross-frequency relationship between task-relevant rhythms underlies efficient cognitive processing. Continuous EEG recordings (51 human participants; 14 males) were obtained during an arithmetic task, rest and breath focus. In two separate experiments, we consistently show that the proportion of epochs displaying a 2:1 harmonic relationship between alpha (8-14 Hz) and theta (4-8 Hz) peak frequencies (i.e., alpha_peak ≈ 10.6 Hz; theta_peak ≈ 5.3 Hz), was significantly higher when cognitive demands increased. In addition, a higher incidence of 2:1 harmonic cross-frequency relationships was significantly associated with increased alpha-theta phase synchrony and improved arithmetic task performance, thereby underlining the functional relevance of this cross-frequency configuration. Notably, opposite dynamics were identified for a specific range of "nonharmonic" alpha-theta cross-frequency relationships (i.e., alpha_peak/theta_peak = 1.1-1.6), which showed a higher incidence during rest compared with the arithmetic task. The observation that alpha and theta rhythms shifted into harmonic versus nonharmonic cross-frequency relationships depending on (cognitive) task demands is in line with the notion that the neural frequency architecture entails optimal frequency arrangements to facilitate cross-frequency "coupling" and "decoupling".SIGNIFICANCE STATEMENT Neural activity is known to oscillate within discrete frequency bands and the interplay between these brain rhythms is hypothesized to underlie cognitive functions. A recent theory posits that shifts in the peak frequencies of oscillatory rhythms form the principal mechanism by which cross-frequency coupling and decoupling is implemented in the brain. In line with this notion, we show that the occurrence of a cross-frequency arrangement that mathematically enables coupling between alpha and theta rhythms is more prominent during active cognitive processing (compared with rest and non-cognitively demanding tasks) and is associated with improved cognitive performance. Together, our results open new vistas for future research on cross-frequency dynamics in the brain and their functional role in cognitive processing.

Dynamic Computation in Visual Thalamocortical Networks

Contemporary neurodynamical frameworks, such as coordination dynamics and winnerless competition, posit that the brain approximates symbolic computation by transitioning between metastable attractive states. This article integrates these accounts with electrophysiological data suggesting that coherent, nested oscillations facilitate information representation and transmission in thalamocortical networks. We review the relationship between criticality, metastability, and representational capacity, outline existing methods for detecting metastable oscillatory patterns in neural time series data, and evaluate plausible spatiotemporal coding schemes based on phase alignment. We then survey the circuitry and the mechanisms underlying the generation of coordinated alpha and gamma rhythms in the primate visual system, with particular emphasis on the pulvinar and its role in biasing visual attention and awareness. To conclude the review, we begin to integrate this perspective with longstanding theories of consciousness and cognition.

Detection of Multiway Gamma Coordination Reveals How Frequency Mixing Shapes Neural Dynamics

A principle of communication technology, frequency mixing, describes how novel oscillations are generated when rhythmic inputs converge on a nonlinearly activating target. As expected given that neurons are nonlinear integrators, it was demonstrated that neuronal networks exhibit mixing in response to imposed oscillations of known frequencies. However, determining when mixing occurs in spontaneous conditions, where weaker or more variable rhythms prevail, has remained impractical. Here, we show that, by exploiting the predicted phase (rather than frequency) relationships between oscillations, the contributions of mixing can be readily identified, even in small samples of noisy data. Assessment of extracellular data using this approach revealed that frequency mixing is widely expressed in a state- and region-dependent manner and that oscillations emerging from mixing entrain unit activity. Frequency mixing is thus intrinsic to the structure of neural activity and contributes importantly to neural dynamics.

Gamma Synchronization between V1 and V4 Improves Behavioral Performance

Behavior is often driven by visual stimuli, relying on feedforward communication from lower to higher visual areas. Effective communication depends on enhanced interareal coherence, but it remains unclear whether this coherence occurs at an optimal phase relation that actually improves stimulus transmission to behavioral report. We recorded local field potentials from V1 and V4 of macaques performing an attention task during which they reported changes in the attended stimulus. V1-V4 gamma synchronization immediately preceding the stimulus change partly predicted subsequent reaction times (RTs). RTs slowed systematically as trial-by-trial interareal gamma phase relations deviated from the phase relation at which V1 and V4 synchronized on average. V1-V4 gamma phase relations accounted for RT differences of 13-31 ms. Effects were specific to the attended stimulus and not explained by local power or phase. Thus, interareal gamma synchronization occurs at the optimal phase relation for transmission of sensory inputs to motor responses.

Efficient determination of synchronization domains from observations of asynchronous dynamics

We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized.

Characterization of network structure in stereoEEG data using consensus-based partial coherence

Coherence is a widely used measure to determine the frequency-resolved functional connectivity between pairs of recording sites, but this measure is confounded by shared inputs to the pair. To remove shared inputs, the 'partial coherence' can be computed by conditioning the spectral matrices of the pair on all other recorded channels, which involves the calculation of a matrix (pseudo-) inverse. It has so far remained a challenge to use the time-resolved partial coherence to analyze intracranial recordings with a large number of recording sites. For instance, calculating the partial coherence using a pseudoinverse method produces a high number of false positives when it is applied to a large number of channels. To address this challenge, we developed a new method that randomly aggregated channels into a smaller number of effective channels on which the calculation of partial coherence was based. We obtained a 'consensus' partial coherence (cPCOH) by repeating this approach for several random aggregations of channels (permutations) and only accepting those activations in time and frequency with a high enough consensus. Using model data we show that the cPCOH method effectively filters out the effect of shared inputs and performs substantially better than the pseudo-inverse. We successfully applied the cPCOH procedure to human stereotactic EEG data and demonstrated three key advantages of this method relative to alternative procedures. First, it reduces the number of false positives relative to the pseudo-inverse method. Second, it allows for titration of the amount of false positives relative to the false negatives by adjusting the consensus threshold, thus allowing the data-analyst to prioritize one over the other to meet specific analysis demands. Third, it substantially reduced the number of identified interactions compared to coherence, providing a sparser network of connections from which clear spatial patterns emerged. These patterns can serve as a starting point of further analyses that provide insight into network dynamics during cognitive processes. These advantages likely generalize to other modalities in which shared inputs introduce confounds, such as electroencephalography (EEG) and magneto-encephalography (MEG).

Microsaccade-rhythmic modulation of neural synchronization and coding within and across cortical areas V1 and V2

Primates sample their visual environment actively through saccades and microsaccades (MSs). Saccadic eye movements not only modulate neural spike rates but might also affect temporal correlations (synchrony) among neurons. Neural synchrony plays a role in neural coding and modulates information transfer between cortical areas. The question arises of how eye movements shape neural synchrony within and across cortical areas and how it affects visual processing. Through local field recordings in macaque early visual cortex while monitoring eye position and through neural network simulations, we find 2 distinct synchrony regimes in early visual cortex that are embedded in a 3- to 4-Hz MS-related rhythm during visual fixation. In the period shortly after an MS (“transient period”), synchrony was high within and between cortical areas. In the subsequent period (“sustained period”), overall synchrony dropped and became selective to stimulus properties. Only mutually connected neurons with similar stimulus responses exhibited sustained narrow-band gamma synchrony (25–80 Hz), both within and across cortical areas. Recordings in macaque V1 and V2 matched the model predictions. Furthermore, our modeling provides predictions on how (micro)saccade-modulated gamma synchrony in V1 shapes V2 receptive fields (RFs). We suggest that the rhythmic alternation between synchronization regimes represents a basic repeating sampling strategy of the visual system.

During visual exploration, we continuously move our eyes in a quick, coordinated manner several times a second to scan our environment. These movements are called saccades. Even while we fixate on a visual object, we unconsciously execute small saccades that are termed microsaccades (MSs). Despite MSs being relatively small, they are suggested to be critical to maintain and support accurate perception during visual fixation. Here, we studied in macaques the influence of MSs on the synchronization of neural rhythms—which are important to regulate information flow in the brain—in areas of the cerebral cortex that are important for early processing of visual information, and we complemented the analysis with computational modeling. We found that synchronization properties shortly after an MS were distinct from synchronization in the later phase. Specifically, we found an early and spectrally broadband synchronization within and between visual cortices that was broadly tuned over the cortical space and stimulus properties. This was followed by narrow-band synchronization in the gamma range (25–80 Hz) that was spatially and stimulus specific. This suggests that the manner in which information is transmitted and integrated between early visual cortices depends on the timing relative to MSs. We illustrate this in a computational model showing that the receptive field (RF) of neurons in the secondary visual cortex are expected to be different depending on MS timing. Our results highlight the significance of MS timing for understanding cortical dynamics and suggest that the regulation of synchronization might be one mechanism by which MSs support visual perception.

Neuronal oscillations: unavoidable and useful?

Neuronal systems have a high propensity to engage in oscillatory activity because both the properties of individual neurons and canonical circuit motifs favour rhythmic activity. In addition, coupled oscillators can engage in a large variety of dynamical regimes, ranging from synchronization with different phase offsets to chaotic behaviour. Which regime prevails depends on differences between preferred oscillation frequencies, coupling strength and coupling delays. The ability of delay coupled oscillator networks to generate a rich repertoire of temporally structured activation sequences is exploited by central pattern generator networks for the control of movements. However, it is less clear whether temporal patterning of neuronal discharges also plays a role in cognitive processes. Here, it will be argued that the temporal patterning of neuronal discharges emerging from delay coupled oscillator networks plays a pivotal role in all instances in which selective relations have to be established between the responses of distributed assemblies of neurons. Examples are the dynamic formation of functional networks, the selective routing of activity in densely interconnected networks, the attention-dependent selection of sensory signals, the fast and context-dependent binding of responses for further joint processing in pattern recognition and the formation of associations by learning. Special consideration is given to arguments that challenge a functional role of oscillations and synchrony in cognition because of the volatile nature of these phenomena and recent evidence will be reviewed suggesting that this volatility is functionally advantageous.