Phase-lags in large scale brain synchronization: Methodological considerations and in-silico analysis

Phase-Dependent Response to Electrical Stimulation of Cortical Networks during Recurrent Epileptiform Short Discharge Generation In Vitro

The closed-loop control of pathological brain activity is a challenging task. In this study, we investigated the sensitivity of continuous epileptiform short discharge generation to electrical stimulation applied at different phases between the discharges using an in vitro 4-AP-based model of epilepsy in rat hippocampal slices. As a measure of stimulation effectiveness, we introduced a sensitivity function, which we then measured in experiments and analyzed with different biophysical and abstract mathematical models, namely, (i) the two-order subsystem of our previous Epileptor-2 model, describing short discharge generation governed by synaptic resource dynamics; (ii) a similar model governed by shunting conductance dynamics (Epileptor-2B); (iii) the stochastic leaky integrate-and-fire (LIF)-like model applied for the network; (iv) the LIF model with potassium M-channels (LIF+KM), belonging to Class II of excitability; and (v) the Epileptor-2B model with after-spike depolarization. A semi-analytic method was proposed for calculating the interspike interval (ISI) distribution and the sensitivity function in LIF and LIF+KM models, which provided parametric analysis. Sensitivity was found to increase with phase for all models except the last one. The Epileptor-2B model is favored over other models for subthreshold oscillations in the presence of large noise, based on the comparison of ISI statistics and sensitivity functions with experimental data. This study also emphasizes the stochastic nature of epileptiform discharge generation and the greater effectiveness of closed-loop stimulation in later phases of ISIs.

Human connectome topology directs cortical traveling waves and shapes frequency gradients

Traveling waves and neural oscillation frequency gradients are pervasive in the human cortex. While the direction of traveling waves has been linked to brain function and dysfunction, the factors that determine this direction remain elusive. We hypothesized that structural connectivity instrength gradients - defined as the gradually varying sum of incoming connection strengths across the cortex - could shape both traveling wave direction and frequency gradients. We confirm the presence of instrength gradients in the human connectome across diverse cohorts and parcellations. Using a cortical network model, we demonstrate how these instrength gradients direct traveling waves and shape frequency gradients. Our model fits resting-state MEG functional connectivity best in a regime where instrength-directed traveling waves and frequency gradients emerge. We further show how structural subnetworks of the human connectome generate opposing wave directions and frequency gradients observed in the alpha and beta bands. Our findings suggest that structural connectivity instrength gradients affect both traveling wave direction and frequency gradients.

Rhythmicity of neuronal oscillations delineates their cortical and spectral architecture

Neuronal oscillations are commonly analyzed with power spectral methods that quantify signal amplitude, but not rhythmicity or 'oscillatoriness' per se. Here we introduce a new approach, the phase-autocorrelation function (pACF), for the direct quantification of rhythmicity. We applied pACF to human intracerebral stereoelectroencephalography (SEEG) and magnetoencephalography (MEG) data and uncovered a spectrally and anatomically fine-grained cortical architecture in the rhythmicity of single- and multi-frequency neuronal oscillations. Evidencing the functional significance of rhythmicity, we found it to be a prerequisite for long-range synchronization in resting-state networks and to be dynamically modulated during event-related processing. We also extended the pACF approach to measure 'burstiness' of oscillatory processes and characterized regions with stable and bursty oscillations. These findings show that rhythmicity is double-dissociable from amplitude and constitutes a functionally relevant and dynamic characteristic of neuronal oscillations.

A phase-shifting anterior-posterior network organizes global phase relations

Prior research has identified a variety of task-dependent networks that form through inter-regional phase-locking of oscillatory activity that are neural correlates of specific behaviors. Despite ample knowledge of task-specific functional networks, general rules governing global phase relations have not been investigated. To discover such general rules, we focused on phase modularity, measured as the degree to which global phase relations in EEG comprised distinct synchronized clusters interacting with one another at large phase lags. Synchronized clusters were detected with a standard community-detection algorithm, and the degree of phase modularity was quantified by the index q. Notably, we found that the mechanism controlling phase modularity is remarkably simple. A network comprising anterior-posterior long-distance connectivity coherently shifted phase relations from low-angles (|Δθ| < π/4) in low-modularity states (bottom 5% in q) to high-angles (|Δθ| > 3π/4) in high-modularity states (top 5% in q), accounting for fluctuations in phase modularity. This anterior-posterior network may play a fundamental functional role as (1) it controls phase modularity across a broad range of frequencies (3-50 Hz examined) in different behavioral conditions (resting with the eyes closed or watching a silent nature video) and (2) neural interactions (measured as power correlations) in beta-to-gamma bands were consistently elevated in high-modularity states. These results may motivate future investigations into the functional roles of phase modularity as well as the anterior-posterior network that controls it.

Dynamics in interbrain synchronization while playing a piano duet

Humans interact with each other through actions that are implemented by sensory and motor processes. To investigate the role of interbrain synchronization emerging during interpersonal action coordination, electroencephalography data from 13 pairs of pianists were recorded simultaneously while they performed a duet together. The study aimed to investigate whether interbrain phase couplings can be reduced to similar bottom-up driven processes during synchronous play, or rather represent cognitive top-down control required during periods of higher coordination demands. To induce such periods, one of the musicians acted as a confederate who deliberately desynchronized the play. As intended, on the behavioral level, the perturbation caused a breakdown in the synchronization of the musicians' play and in its stability across trials. On the brain level, interbrain synchrony, as measured by the interbrain phase coherence (IPC), increased in the delta and theta frequency bands during perturbation as compared to non-perturbed trials. Interestingly, this increase in IPC in the delta band was accompanied by the shift of the phase difference angle from in-phase toward anti-phase synchrony. In conclusion, the current study demonstrates that interbrain synchronization is based on the interpersonal temporal alignment of different brain mechanisms and is not simply reducible to similar sensory or motor responses.

The influence of inter-regional delays in generating large-scale brain networks of phase synchronization

Large-scale networks of phase synchronization are considered to regulate the communication between brain regions fundamental to cognitive function, but the mapping to their structural substrates, i.e., the structure-function relationship, remains poorly understood. Biophysical Network Models (BNMs) have demonstrated the influences of local oscillatory activity and inter-regional anatomical connections in generating alpha-band (8-12 Hz) networks of phase synchronization observed with Electroencephalography (EEG) and Magnetoencephalography (MEG). Yet, the influence of inter-regional conduction delays remains unknown. In this study, we compared a BNM with standard "distance-dependent delays", which assumes constant conduction velocity, to BNMs with delays specified by two alternative methods accounting for spatially varying conduction velocities, "isochronous delays" and "mixed delays". We followed the Approximate Bayesian Computation (ABC) workflow, i) specifying neurophysiologically informed prior distributions of BNM parameters, ii) verifying the suitability of the prior distributions with Prior Predictive Checks, iii) fitting each of the three BNMs to alpha-band MEG resting-state data (N = 75) with Bayesian optimization for Likelihood-Free Inference (BOLFI), and iv) choosing between the fitted BNMs with ABC model comparison on a separate MEG dataset (N = 30). Prior Predictive Checks revealed the range of dynamics generated by each of the BNMs to encompass those seen in the MEG data, suggesting the suitability of the prior distributions. Fitting the models to MEG data yielded reliable posterior distributions of the parameters of each of the BNMs. Finally, model comparison revealed the BNM with "distance-dependent delays", as the most probable to describe the generation of alpha-band networks of phase synchronization seen in MEG. These findings suggest that distance-dependent delays might contribute to the neocortical architecture of human alpha-band networks of phase synchronization. Hence, our study illuminates the role of inter-regional delays in generating the large-scale networks of phase synchronization that might subserve the communication between regions vital to cognition.

White-matter degradation and dynamical compensation support age-related functional alterations in human brain

Structural connectivity of the brain at different ages is analyzed using diffusion-weighted magnetic resonance imaging (MRI) data. The largest decrease of streamlines is found in frontal regions and for long inter-hemispheric links. The average length of the tracts also decreases, but the clustering is unaffected. From functional MRI we identify age-related changes of dynamic functional connectivity (dFC) and spatial covariation features of functional connectivity (FC) links captured by metaconnectivity. They indicate more stable dFC, but wider range and variance of MC, whereas static features of FC did not show any significant differences with age. We implement individual connectivity in whole-brain models and test several hypotheses for the mechanisms of operation among underlying neural system. We demonstrate that age-related functional fingerprints are only supported if the model accounts for: (i) compensation of the individual brains for the overall loss of structural connectivity and (ii) decrease of propagation velocity due to the loss of myelination. We also show that with these 2 conditions, it is sufficient to decompose the time-delays as bimodal distribution that only distinguishes between intra- and inter-hemispheric delays, and that the same working point also captures the static FC the best, and produces the largest variability at slow time-scales.

Noise-modulated multistable synapses in a Wilson-Cowan-based model of plasticity

Frequency-dependent plasticity refers to changes in synaptic strength in response to different stimulation frequencies. Resonance is a factor known to be of importance in such frequency dependence, however, the role of neural noise in the process remains elusive. Considering the brain is an inherently noisy system, understanding its effects may prove beneficial in shaping therapeutic interventions based on non-invasive brain stimulation protocols. The Wilson-Cowan (WC) model is a well-established model to describe the average dynamics of neural populations and has been shown to exhibit bistability in the presence of noise. However, the important question of how the different stable regimes in the WC model can affect synaptic plasticity when cortical populations interact has not yet been addressed. Therefore, we investigated plasticity dynamics in a WC-based model of interacting neural populations coupled with activity-dependent synapses in which a periodic stimulation was applied in the presence of noise of controlled intensity. The results indicate that for a narrow range of the noise variance, synaptic strength can be optimized. In particular, there is a regime of noise intensity for which synaptic strength presents a triple-stable state. Regulating noise intensity affects the probability that the system chooses one of the stable states, thereby controlling plasticity. These results suggest that noise is a highly influential factor in determining the outcome of plasticity induced by stimulation.

Whole-Brain Propagation Delays in Multiple Sclerosis, a Combined Tractography-Magnetoencephalography Study

Two structurally connected brain regions are more likely to interact, with the lengths of the structural bundles, their widths, myelination, and the topology of the structural connectome influencing the timing of the interactions. We introduce an in vivo approach for measuring functional delays across the whole brain in humans (of either sex) using magneto/electroencephalography (MEG/EEG) and integrating them with the structural bundles. The resulting topochronic map of the functional delays/velocities shows that larger bundles have faster velocities. We estimated the topochronic map in multiple sclerosis patients, who have damaged myelin sheaths, and controls, demonstrating greater delays in patients across the network and that structurally lesioned tracts were slowed down more than unaffected ones. We provide a novel framework for estimating functional transmission delays in vivo at the single-subject and single-tract level.SIGNIFICANCE STATEMENT This article provides a straightforward way to estimate patient-specific delays and conduction velocities in the CNS, at the individual level, in healthy and diseased subjects. To do so, it uses a principled way to merge magnetoencephalography (MEG)/electroencephalography (EEG) and tractography.

Pattern of frustration formation in the functional brain network

The brain is a frustrated system that contains conflictual link arrangements named frustration. The frustration as a source of disorder prevents the system from settling into low-energy states and provides flexibility for brain network organization. In this research, we tried to identify the pattern of frustration formation in the brain at the levels of region, connection, canonical network, and hemisphere. We found that frustration formation has no uniform pattern. Some subcortical elements have an active role in frustration formation, despite low contributions from many cortical elements. Frustrating connections are mostly between-network connections, and triadic frustrations are mainly formed between three regions from three distinct canonical networks. We did not find any significant differences between brain hemispheres or any robust differences between the frustration formation patterns of various life-span stages. Our results may be interesting for those who study the organization of brain links and promising for those who want to manipulate brain networks.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.

Modelling the perception of music in brain network dynamics

We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report an increase of coherence between the global dynamics in our network and the input signal induced by a specific music song. We show that the level of coherence depends crucially on the frequency band. We compare our results with experimental data, which also describe global neural synchronization between different brain regions in the gamma-band range in a time-dependent manner correlated with musical large-scale form, showing increased synchronization just before transitions between different parts in a musical piece (musical high-level events). The results also suggest a separation in musical form-related brain synchronization between high brain frequencies, associated with neocortical activity, and low frequencies in the range of dance movements, associated with interactivity between cortical and subcortical regions.

Normalizing the brain connectome for communication through synchronization

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.

Biophysical mechanism underlying compensatory preservation of neural synchrony over the adult lifespan

We propose that the preservation of functional integration, estimated from measures of neural synchrony, is a key objective of neurocompensatory mechanisms associated with healthy human ageing. To support this proposal, we demonstrate how phase-locking at the peak alpha frequency in Magnetoencephalography recordings remains invariant over the lifespan in a large cohort of human participants, aged 18-88 years. Using empirically derived connection topologies from diffusion tensor imaging data, we create an in-silico model of whole-brain alpha dynamics. We show that enhancing inter-areal coupling can cancel the effect of increased axonal transmission delays associated with age-related degeneration of white matter tracts, albeit at slower network frequencies. By deriving analytical solutions for simplified connection topologies, we further establish the theoretical principles underlying compensatory network re-organization. Our findings suggest that frequency slowing with age- frequently observed in the alpha band in diverse populations- may be viewed as an epiphenomenon of the underlying compensatory mechanism.

Analysis of MEG data from healthy participants and whole-brain network modeling suggests that the brain compensates for age-related disruptions in connectivity by slowing down the frequency of neural synchronization.

"It's a beer!": Brain functional hyperconnectivity during processing of alcohol-related images in young binge drinkers

Alcohol attentional bias has been pointed as a major marker of alcohol misuse. Recent evidence has revealed that brain functional connectivity (FC) may be a valuable index of the brain networks' integrity in young binge drinkers (BDs). However, there is no study to date examining the FC networks linked to the processing of alcohol-related images in this population. The present study aimed to explore the FC signatures underlying alcohol attention bias in young BDs. Thus, electroencephalographic (EEG) activity was recorded in 54 college students (55.5% females; 27 non/low-drinkers and 27 BDs) while performing a visual alcohol cue-reactivity task. We evaluated whole-brain FC profiles during the processing of alcoholic and non-alcoholic cues, as well as their potential relationship with craving and severity of alcohol use. Results showed that, at the behavioural level, BDs rated alcohol-related images as more pleasant/attractive than non/low-drinkers. Furthermore, at the electrophysiological level, BDs exhibited increased beta-band FC-particularly in the fronto-parieto-occipital network-when processing alcoholic cues. Conversely, they displayed reduced theta-band FC relatively to non/low-drinkers for non-alcoholic images. These hyper-/hypo-connectivity patterns were associated with higher alcohol craving levels. Findings are congruent with previous neurofunctional studies reporting an attentional bias towards alcohol-related information in BDs. These results may have important clinical implications as this neural reactivity to alcoholic cues may contribute to the maintenance and/or escalation of the drinking pattern. Finally, the present study constitutes the first evidence showing that FC networks may be a sensitive indicator to alcohol attentional bias in BDs.

Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling

We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling determines the phase lag of the characteristic sine coupling function of the KM and critically determines the synchronization properties of the network. We apply our results to uncover the presence of chimera states in two coupled populations of identical QIF neurons. We find that the presence of both electrical and chemical coupling is a necessary condition for chimera states to exist. Finally, we numerically demonstrate that chimera states gradually disappear as coupling strengths cease to be weak.

High-resolution Virtual Brain Modeling Personalizes Deep Brain Stimulation for Treatment-Resistant Depression: Spatiotemporal Response Characteristics Following Stimulation of Neural Fiber Pathways

Over the past 15 years, deep brain stimulation (DBS) has been actively investigated as a groundbreaking therapy for patients with treatment-resistant depression (TRD); nevertheless, outcomes have varied from patient to patient, with an average response rate of ∼50%. The engagement of specific fiber tracts at the stimulation site has been hypothesized to be an important factor in determining outcomes, however, the resulting individual network effects at the whole-brain scale remain largely unknown. Here we provide a computational framework that can explore each individual's brain response characteristics elicited by selective stimulation of fiber tracts. We use a novel personalized in-silico approach, the Virtual Big Brain, which makes use of high-resolution virtual brain models at a mm-scale and explicitly reconstructs more than 100 000 fiber tracts for each individual. Each fiber tract is active and can be selectively stimulated. Simulation results demonstrate distinct stimulus-induced event-related potentials as a function of stimulation location, parametrized by the contact positions of the electrodes implanted in each patient, even though validation against empirical patient data reveals some limitations (i.e., the need for individual parameter adjustment, and differential accuracy across stimulation locations). This study provides evidence for the capacity of personalized high-resolution virtual brain models to investigate individual network effects in DBS for patients with TRD and opens up novel avenues in the personalized optimization of brain stimulation.

A Non-spiking Neuron Model With Dynamic Leak to Avoid Instability in Recurrent Networks

Recurrent circuitry components are distributed widely within the brain, including both excitatory and inhibitory synaptic connections. Recurrent neuronal networks have potential stability problems, perhaps a predisposition to epilepsy. More generally, instability risks making internal representations of information unreliable. To assess the inherent stability properties of such recurrent networks, we tested a linear summation, non-spiking neuron model with and without a “dynamic leak”, corresponding to the low-pass filtering of synaptic input current by the RC circuit of the biological membrane. We first show that the output of this neuron model, in either of its two forms, follows its input at a higher fidelity than a wide range of spiking neuron models across a range of input frequencies. Then we constructed fully connected recurrent networks with equal numbers of excitatory and inhibitory neurons and randomly distributed weights across all synapses. When the networks were driven by pseudorandom sensory inputs with varying frequency, the recurrent network activity tended to induce high frequency self-amplifying components, sometimes evident as distinct transients, which were not present in the input data. The addition of a dynamic leak based on known membrane properties consistently removed such spurious high frequency noise across all networks. Furthermore, we found that the neuron model with dynamic leak imparts a network stability that seamlessly scales with the size of the network, conduction delays, the input density of the sensory signal and a wide range of synaptic weight distributions. Our findings suggest that neuronal dynamic leak serves the beneficial function of protecting recurrent neuronal circuitry from the self-induction of spurious high frequency signals, thereby permitting the brain to utilize this architectural circuitry component regardless of network size or recurrency.

Emergence of Neuronal Synchronisation in Coupled Areas

One of the most fundamental questions in the field of neuroscience is the emergence of synchronous behaviour in the brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how the connectivity between brain areas can influence the phase angle and the neuronal synchronisation. To do this, we consider brain areas connected by means of excitatory and inhibitory synapses, in which the neuron dynamics is given by the adaptive exponential integrate-and-fire model. Our simulations suggest that excitatory and inhibitory connections from one area to another play a crucial role in the emergence of these types of synchronisation. Thus, in the case of unidirectional interaction, we observe that the phase angles of the neurons in the receiver area depend on the excitatory and inhibitory synapses which arrive from the sender area. Moreover, when the neurons in the sender area are synchronised, the phase angle variability of the receiver area can be reduced for some conductance values between the areas. For bidirectional interactions, we find that phase and anti-phase synchronisation can emerge due to excitatory and inhibitory connections. We also verify, for a strong inhibitory-to-excitatory interaction, the existence of silent neuronal activities, namely a large number of excitatory neurons that remain in silence for a long time.

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.

Frequency-Resolved Functional Connectivity: Role of Delay and the Strength of Connections

The brain functional network extracted from the BOLD signals reveals the correlated activity of the different brain regions, which is hypothesized to underlie the integration of the information across functionally specialized areas. Functional networks are not static and change over time and in different brain states, enabling the nervous system to engage and disengage different local areas in specific tasks on demand. Due to the low temporal resolution, however, BOLD signals do not allow the exploration of spectral properties of the brain dynamics over different frequency bands which are known to be important in cognitive processes. Recent studies using imaging tools with a high temporal resolution has made it possible to explore the correlation between the regions at multiple frequency bands. These studies introduce the frequency as a new dimension over which the functional networks change, enabling brain networks to transmit multiplex of information at any time. In this computational study, we explore the functional connectivity at different frequency ranges and highlight the role of the distance between the nodes in their correlation. We run the generalized Kuramoto model with delayed interactions on top of the brain's connectome and show that how the transmission delay and the strength of the connections, affect the correlation between the pair of nodes over different frequency bands.

Enhancing GABAergic signaling ameliorates aberrant gamma oscillations of olfactory bulb in AD mouse models

Background

Before the deposition of amyloid-beta plaques and the onset of learning memory deficits, patients with Alzheimer’s disease (AD) experience olfactory dysfunction, typified by a reduced ability to detect, discriminate, and identify odors. Rodent models of AD, such as the Tg2576 and APP/PS1 mice, also display impaired olfaction, accompanied by aberrant in vivo or in vitro gamma rhythms in the olfactory pathway. However, the mechanistic relationships between the electrophysiological, biochemical and behavioral phenomena remain unclear.

Methods

To address the above issues in AD models, we conducted in vivo measurement of local field potential (LFP) with a combination of in vitro electro-olfactogram (EOG), whole-cell patch and field recordings to evaluate oscillatory and synaptic function and pharmacological regulation in the olfactory pathway, particularly in the olfactory bulb (OB). Levels of protein involved in excitation and inhibition of the OB were investigated by western blotting and fluorescence staining, while behavioral studies assessed olfaction and memory function.

Results

LFP measurements demonstrated an increase in gamma oscillations in the OB accompanied by altered olfactory behavior in both APP/PS1 and 3xTg mice at 3–5 months old, i.e. an age before the onset of plaque formation. Fewer olfactory sensory neurons (OSNs) and a reduced EOG contributed to a decrease in the excitatory responses of M/T cells, suggesting a decreased ability of M/T cells to trigger interneuron GABA release indicated by altered paired-pulse ratio (PPR), a presynaptic parameter. Postsynaptically, there was a compensatory increase in levels of GABA_AR α1 and β3 subunits and subsequent higher amplitude of inhibitory responses. Strikingly, the GABA uptake inhibitor tiagabine (TGB) ameliorated abnormal gamma oscillations and levels of GABA_AR subunits, suggesting a potential therapeutic strategy for early AD symptoms. These findings reveal increased gamma oscillations in the OB as a core indicator prior to onset of AD and uncover mechanisms underlying aberrant gamma activity in the OB.

Conclusions

This study suggests that the concomitant dysfunction of both olfactory behavior and gamma oscillations have important implications for early AD diagnosis: in particular, awareness of aberrant GABAergic signaling mechanisms might both aid diagnosis and suggest therapeutic strategies for olfactory damage in AD.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13024-021-00434-7.

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

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

Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity

An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart-Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.

Stochastic synchronization of dynamics on the human connectome

Synchronization is a collective mechanism by which oscillatory networks achieve their functions. Factors driving synchronization include the network's topological and dynamical properties. However, how these factors drive the emergence of synchronization in the presence of potentially disruptive external inputs like stochastic perturbations is not well understood, particularly for real-world systems such as the human brain. Here, we aim to systematically address this problem using a large-scale model of the human brain network (i.e., the human connectome). The results show that the model can produce complex synchronization patterns transitioning between incoherent and coherent states. When nodes in the network are coupled at some critical strength, a counterintuitive phenomenon emerges where the addition of noise increases the synchronization of global and local dynamics, with structural hub nodes benefiting the most. This stochastic synchronization effect is found to be driven by the intrinsic hierarchy of neural timescales of the brain and the heterogeneous complex topology of the connectome. Moreover, the effect coincides with clustering of node phases and node frequencies and strengthening of the functional connectivity of some of the connectome's subnetworks. Overall, the work provides broad theoretical insights into the emergence and mechanisms of stochastic synchronization, highlighting its putative contribution in achieving network integration underpinning brain function.

Abnormal organization of inhibitory control functional networks in future binge drinkers

BACKGROUND AND AIMS

Adolescent Binge drinking has become an increasing health and social concern, which cause several detrimental consequences for brain integrity. However, research on neurophysiological traits of vulnerability for binge drinking predisposition is limited at this time. In this work, we conducted a two-year longitudinal study with magnetoencephalography (MEG) over a cohort of initially alcohol-naive adolescents with the purpose of characterize inhibitory cortical networks' anomalies prior to alcohol consumption onset in those youths who will transit into binge drinkers years later.

METHODS

Sixty-seven participant's inhibitory functional networks, and dysexecutive/impulsivity traits were measured by means of inhibitory task (go/no-go) and questionnaires battery. After a follow-up period of two years, we evaluated their alcohol consumption habits, sub-dividing them in two groups according to their alcohol intake patterns: future binge drinkers (fBD): n = 22; future Light/non-drinkers (fLD): n = 17. We evaluated whole-brain and seed-based functional connectivity profiles, as well as its correlation with impulsive and dysexecutive behaviours, searching for early abnormalities before consumption onset.

RESULTS

For the first time, abnormalities in MEG functional networks and higher dysexecutive and impulsivity profiles were detected in alcohol-naïve adolescents who two years later became binge drinkers. Concretely, fBD exhibit a distinctive pattern of beta band hyperconnectivity among crucial regions of inhibitory control networks, positively correlated with behavioral traits and future alcohol intake rate.

CONCLUSIONS

These findings strongly support the idea of early neurobiological vulnerabilities for substances consumption initiation, with inhibitory functional networks' abnormalities as a relevant neurophysiological marker of subjects at risk- we hypothesize this profile is due to neurodevelopmental and neurobiological differences involving cognitive control networks and neurotransmission pathways.

Coupled Möbius maps as a tool to model Kuramoto phase synchronization

We propose Möbius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.

Synchronization and resilience in the Kuramoto white matter network model with adaptive state-dependent delays

White matter pathways form a complex network of myelinated axons that regulate signal transmission in the nervous system and play a key role in behaviour and cognition. Recent evidence reveals that white matter networks are adaptive and that myelin remodels itself in an activity-dependent way, during both developmental stages and later on through behaviour and learning. As a result, axonal conduction delays continuously adjust in order to regulate the timing of neural signals propagating between different brain areas. This delay plasticity mechanism has yet to be integrated in computational neural models, where conduction delays are oftentimes constant or simply ignored. As a first approach to adaptive white matter remodeling, we modified the canonical Kuramoto model by enabling all connections with adaptive, phase-dependent delays. We analyzed the equilibria and stability of this system, and applied our results to two-oscillator and large-dimensional networks. Our joint mathematical and numerical analysis demonstrates that plastic delays act as a stabilizing mechanism promoting the network's ability to maintain synchronous activity. Our work also shows that global synchronization is more resilient to perturbations and injury towards network architecture. Our results provide key insights about the analysis and potential significance of activity-dependent myelination in large-scale brain synchrony.

Synchronization of complex human networks

The synchronization of human networks is essential for our civilization and understanding its dynamics is important to many aspects of our lives. Human ensembles were investigated, but in noisy environments and with limited control over the network parameters which govern the network dynamics. Specifically, research has focused predominantly on all-to-all coupling, whereas current social networks and human interactions are often based on complex coupling configurations. Here, we study the synchronization between violin players in complex networks with full and accurate control over the network connectivity, coupling strength, and delay. We show that the players can tune their playing period and delete connections by ignoring frustrating signals, to find a stable solution. These additional degrees of freedom enable new strategies and yield better solutions than are possible within current models such as the Kuramoto model. Our results may influence numerous fields, including traffic management, epidemic control, and stock market dynamics.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Dynamical Mechanisms of Interictal Resting-State Functional Connectivity in Epilepsy

Drug-resistant focal epilepsy is a large-scale brain networks disorder characterized by altered spatiotemporal patterns of functional connectivity (FC), even during interictal resting state (RS). Although RS-FC-based metrics can detect these changes, results from RS functional magnetic resonance imaging (RS-fMRI) studies are unclear and difficult to interpret, and the underlying dynamical mechanisms are still largely unknown. To better capture the RS dynamics, we phenomenologically extended the neural mass model of partial seizures, the Epileptor, by including two neuron subpopulations of epileptogenic and nonepileptogenic type, making it capable of producing physiological oscillations in addition to the epileptiform activity. Using the neuroinformatics platform The Virtual Brain, we reconstructed 14 epileptic and 5 healthy human (of either sex) brain network models (BNMs), based on individual anatomical connectivity and clinically defined epileptogenic heatmaps. Through systematic parameter exploration and fitting to neuroimaging data, we demonstrated that epileptic brains during interictal RS are associated with lower global excitability induced by a shift in the working point of the model, indicating that epileptic brains operate closer to a stable equilibrium point than healthy brains. Moreover, we showed that functional networks are unaffected by interictal spikes, corroborating previous experimental findings; additionally, we observed higher excitability in epileptogenic regions, in agreement with the data. We shed light on new dynamical mechanisms responsible for altered RS-FC in epilepsy, involving the following two key factors: (1) a shift of excitability of the whole brain leading to increased stability; and (2) a locally increased excitability in the epileptogenic regions supporting the mixture of hyperconnectivity and hypoconnectivity in these areas.

SIGNIFICANCE STATEMENT Advances in functional neuroimaging provide compelling evidence for epilepsy-related brain network alterations, even during the interictal resting state (RS). However, the dynamical mechanisms underlying these changes are still elusive. To identify local and network processes behind the RS-functional connectivity (FC) spatiotemporal patterns, we systematically manipulated the local excitability and the global coupling in the virtual human epileptic patient brain network models (BNMs), complemented by the analysis of the impact of interictal spikes and fitting to the neuroimaging data. Our results suggest that a global shift of the dynamic working point of the brain model, coupled with locally hyperexcitable node dynamics of the epileptogenic networks, provides a mechanistic explanation of the epileptic processes during the interictal RS period. These, in turn, are associated with the changes in FC.

Activity-dependent myelination: A glial mechanism of oscillatory self-organization in large-scale brain networks

Communication and oscillatory synchrony between distributed neural populations are believed to play a key role in multiple cognitive and neural functions. These interactions are mediated by long-range myelinated axonal fiber bundles, collectively termed as white matter. While traditionally considered to be static after development, white matter properties have been shown to change in an activity-dependent way through learning and behavior-a phenomenon known as white matter plasticity. In the central nervous system, this plasticity stems from oligodendroglia, which form myelin sheaths to regulate the conduction of nerve impulses across the brain, hence critically impacting neural communication. We here shift the focus from neural to glial contribution to brain synchronization and examine the impact of adaptive, activity-dependent changes in conduction velocity on the large-scale phase synchronization of neural oscillators. Using a network model based on primate large-scale white matter neuroanatomy, our computational and mathematical results show that such plasticity endows white matter with self-organizing properties, where conduction delay statistics are autonomously adjusted to ensure efficient neural communication. Our analysis shows that this mechanism stabilizes oscillatory neural activity across a wide range of connectivity gain and frequency bands, making phase-locked states more resilient to damage as reflected by diffuse decreases in connectivity. Critically, our work suggests that adaptive myelination may be a mechanism that enables brain networks with a means of temporal self-organization, resilience, and homeostasis.

White Matter Brain Network Research in Alzheimer's Disease Using Persistent Features

Despite the severe social burden caused by Alzheimer’s disease (AD), no drug than can change the disease progression has been identified yet. The structural brain network research provides an opportunity to understand physiological deterioration caused by AD and its precursor, mild cognitive impairment (MCI). Recently, persistent homology has been used to study brain network dynamics and characterize the global network organization. However, it is unclear how these parameters reflect changes in structural brain networks of patients with AD or MCI. In this study, our previously proposed persistent features and various traditional graph-theoretical measures are used to quantify the topological property of white matter (WM) network in 150 subjects with diffusion tensor imaging (DTI). We found significant differences in these measures among AD, MCI, and normal controls (NC) under different brain parcellation schemes. The decreased network integration and increased network segregation are presented in AD and MCI. Moreover, the persistent homology-based measures demonstrated stronger statistical capability and robustness than traditional graph-theoretic measures, suggesting that they represent a more sensitive approach to detect altered brain structures and to better understand AD symptomology at the network level. These findings contribute to an increased understanding of structural connectome in AD and provide a novel approach to potentially track the progression of AD.

Genuine cross-frequency coupling networks in human resting-state electrophysiological recordings

Phase synchronization of neuronal oscillations in specific frequency bands coordinates anatomically distributed neuronal processing and communication. Typically, oscillations and synchronization take place concurrently in many distinct frequencies, which serve separate computational roles in cognitive functions. While within-frequency phase synchronization has been studied extensively, less is known about the mechanisms that govern neuronal processing distributed across frequencies and brain regions. Such integration of processing between frequencies could be achieved via cross-frequency coupling (CFC), either by phase–amplitude coupling (PAC) or by n:m-cross–frequency phase synchrony (CFS). So far, studies have mostly focused on local CFC in individual brain regions, whereas the presence and functional organization of CFC between brain areas have remained largely unknown. We posit that interareal CFC may be essential for large-scale coordination of neuronal activity and investigate here whether genuine CFC networks are present in human resting-state (RS) brain activity. To assess the functional organization of CFC networks, we identified brain-wide CFC networks at mesoscale resolution from stereoelectroencephalography (SEEG) and at macroscale resolution from source-reconstructed magnetoencephalography (MEG) data. We developed a novel, to our knowledge, graph-theoretical method to distinguish genuine CFC from spurious CFC that may arise from nonsinusoidal signals ubiquitous in neuronal activity. We show that genuine interareal CFC is present in human RS activity in both SEEG and MEG data. Both CFS and PAC networks coupled theta and alpha oscillations with higher frequencies in large-scale networks connecting anterior and posterior brain regions. CFS and PAC networks had distinct spectral patterns and opposing distribution of low- and high-frequency network hubs, implying that they constitute distinct CFC mechanisms. The strength of CFS networks was also predictive of cognitive performance in a separate neuropsychological assessment. In conclusion, these results provide evidence for interareal CFS and PAC being 2 distinct mechanisms for coupling oscillations across frequencies in large-scale brain networks.

Genuine interareal cross-frequency coupling (CFC) can be identified from human resting state activity using magnetoencephalography, stereoelectroencephalography, and novel network approaches. CFC couples slow theta and alpha oscillations to faster oscillations across brain regions.

Decoding the circuitry of consciousness: From local microcircuits to brain-scale networks

Identifying the physiological processes underlying the emergence and maintenance of consciousness is one of the most fundamental problems of neuroscience, with implications ranging from fundamental neuroscience to the treatment of patients with disorders of consciousness (DOCs). One major challenge is to understand how cortical circuits at drastically different spatial scales, from local networks to brain-scale networks, operate in concert to enable consciousness, and how those processes are impaired in DOC patients. In this review, we attempt to relate available neurophysiological and clinical data with existing theoretical models of consciousness, while linking the micro- and macrocircuit levels. First, we address the relationships between awareness and wakefulness on the one hand, and cortico-cortical and thalamo-cortical connectivity on the other hand. Second, we discuss the role of three main types of GABAergic interneurons in specific circuits responsible for the dynamical reorganization of functional networks. Third, we explore advances in the functional role of nested oscillations for neural synchronization and communication, emphasizing the importance of the balance between local (high-frequency) and distant (low-frequency) activity for efficient information processing. The clinical implications of these theoretical considerations are presented. We propose that such cellular-scale mechanisms could extend current theories of consciousness.

Natural rhythms of periodic temporal attention

That attention is a fundamentally rhythmic process has recently received abundant empirical evidence. The essence of temporal attention, however, is to flexibly focus in time. Whether this function is constrained by an underlying rhythmic neural mechanism is unknown. In six interrelated experiments, we behaviourally quantify the sampling capacities of periodic temporal attention during auditory or visual perception. We reveal the presence of limited attentional capacities, with an optimal sampling rate of ~1.4 Hz in audition and ~0.7 Hz in vision. Investigating the motor contribution to temporal attention, we show that it scales with motor rhythmic precision, maximal at ~1.7 Hz. Critically, motor modulation is beneficial to auditory but detrimental to visual temporal attention. These results are captured by a computational model of coupled oscillators, that reveals the underlying structural constraints governing the temporal alignment between motor and attention fluctuations.

Probing neural networks for dynamic switches of communication pathways

Dynamic communication and routing play important roles in the human brain in order to facilitate flexibility in task solving and thought processes. Here, we present a network perturbation methodology that allows investigating dynamic switching between different network pathways based on phase offsets between two external oscillatory drivers. We apply this method in a computational model of the human connectome with delay-coupled neural masses. To analyze dynamic switching of pathways, we define four new metrics that measure dynamic network response properties for pairs of stimulated nodes. Evaluating these metrics for all network pathways, we found a broad spectrum of pathways with distinct dynamic properties and switching behaviors. We show that network pathways can have characteristic timescales and thus specific preferences for the phase lag between the regions they connect. Specifically, we identified pairs of network nodes whose connecting paths can either be (1) insensitive to the phase relationship between the node pair, (2) turned on and off via changes in the phase relationship between the node pair, or (3) switched between via changes in the phase relationship between the node pair. Regarding the latter, we found that 33% of node pairs can switch their communication from one pathway to another depending on their phase offsets. This reveals a potential mechanistic role that phase offsets and coupling delays might play for the dynamic information routing via communication pathways in the brain.

A big challenge in elucidating information processing in the brain is to understand the neural mechanisms that dynamically organize the communication between different brain regions in a flexible and task-dependent manner. In this theoretical study, we present an approach to investigate the routing and gating of information flow along different pathways from one region to another. We show that stimulation of the brain at two sites with different frequencies and oscillatory phases can reveal the underlying effective connectivity. This yields new insights into the underlying processes that govern dynamic switches in the communication pathways between remote sites of the brain.

Low-dimensional dynamics for higher-order harmonic, globally coupled phase-oscillator ensembles

The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher-order modes. To demonstrate an application of the formulation, we use a second harmonic globally coupled model, with a mean-field equal to the square of the Kuramoto mean-field. This model is known to exhibit asymmetrical clustering in previous numerical studies. We try to explain the phenomenon of asymmetrical clustering using the analytical theory developed here, as well as discuss certain phenomena not observed at the level of first-order harmonic coupling.

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ-oscillations

Activity cascades are found in many complex systems. In the cortex, they arise in the form of neuronal avalanches that capture ongoing and evoked neuronal activities at many spatial and temporal scales. The scale-invariant nature of avalanches suggests that the brain is in a critical state, yet predictions from critical theory on the temporal unfolding of avalanches have yet to be confirmed in vivo. Here we show in awake nonhuman primates that the temporal profile of avalanches follows a symmetrical, inverted parabola spanning up to hundreds of milliseconds. This parabola constrains how avalanches initiate locally, extend spatially and shrink as they evolve in time. Importantly, parabolas of different durations can be collapsed with a scaling exponent close to 2 supporting critical generational models of neuronal avalanches. Spontaneously emerging, transient γ-oscillations coexist with and modulate these avalanche parabolas thereby providing a temporal segmentation to inherently scale-invariant, critical dynamics. Our results identify avalanches and oscillations as dual principles in the temporal organization of brain activity.

Transmission time delays organize the brain network synchronization

The timing of activity across brain regions can be described by its phases for oscillatory processes, and is of crucial importance for brain functioning. The structure of the brain constrains its dynamics through the delays due to propagation and the strengths of the white matter tracts. We use self-sustained delay-coupled, non-isochronous, nonlinearly damped and chaotic oscillators to study how spatio-temporal organization of the brain governs phase lags between the coherent activity of its regions. In silico results for the brain network model demonstrate a robust switching from in- to anti-phase synchronization by increasing the frequency, with a consistent lagging of the stronger connected regions. Relative phases are well predicted by an earlier analysis of Kuramoto oscillators, confirming the spatial heterogeneity of time delays as a crucial mechanism in shaping the functional brain architecture. Increased frequency and coupling are also shown to distort the oscillators by decreasing their amplitude, and stronger regions have lower, but more synchronized activity. These results indicate specific features in the phase relationships within the brain that need to hold for a wide range of local oscillatory dynamics, given that the time delays of the connectome are proportional to the lengths of the structural pathways. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Linking Molecular Pathways and Large-Scale Computational Modeling to Assess Candidate Disease Mechanisms and Pharmacodynamics in Alzheimer's Disease

Introduction: While the prevalence of neurodegenerative diseases associated with dementia such as Alzheimer's disease (AD) increases, our knowledge on the underlying mechanisms, outcome predictors, or therapeutic targets is limited. In this work, we demonstrate how computational multi-scale brain modeling links phenomena of different scales and therefore identifies potential disease mechanisms leading the way to improved diagnostics and treatment. Methods: The Virtual Brain (TVB; thevirtualbrain.org) neuroinformatics platform allows standardized large-scale structural connectivity-based simulations of whole brain dynamics. We provide proof of concept for a novel approach that quantitatively links the effects of altered molecular pathways onto neuronal population dynamics. As a novelty, we connect chemical compounds measured with positron emission tomography (PET) with neural function in TVB addressing the phenomenon of hyperexcitability in AD related to the protein amyloid beta (Abeta). We construct personalized virtual brains based on an averaged healthy connectome and individual PET derived distributions of Abeta in patients with mild cognitive impairment (MCI, N = 8) and Alzheimer's Disease (AD, N = 10) and in age-matched healthy controls (HC, N = 15) using data from ADNI-3 data base (http://adni.loni.usc.edu). In the personalized virtual brains, individual Abeta burden modulates regional Excitation-Inhibition balance, leading to local hyperexcitation with high Abeta loads. We analyze simulated regional neural activity and electroencephalograms (EEG). Results: Known empirical alterations of EEG in patients with AD compared to HCs were reproduced by simulations. The virtual AD group showed slower frequencies in simulated local field potentials and EEG compared to MCI and HC groups. The heterogeneity of the Abeta load is crucial for the virtual EEG slowing which is absent for control models with homogeneous Abeta distributions. Slowing phenomena primarily affect the network hubs, independent of the spatial distribution of Abeta. Modeling the N-methyl-D-aspartate (NMDA) receptor antagonism of memantine in local population models, reveals potential functional reversibility of the observed large-scale alterations (reflected by EEG slowing) in virtual AD brains. Discussion: We demonstrate how TVB enables the simulation of systems effects caused by pathogenetic molecular candidate mechanisms in human virtual brains.

Null model exhibiting synchronized dynamics in uncoupled oscillators

The phenomenon of phase synchronization of oscillatory systems, arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by nonsynchronous dynamics. How does one guarantee that the observed transient epochs of synchronization are arising from an underlying feedback mechanism and not from some peculiar statistical properties of the system? This question is particularly important for complex biological systems, where the search for a nonexistent feedback mechanism may turn out to be an enormous waste of resources. In this article, we propose a null model for synchronization, motivated by expectations on the dynamical behavior of biological systems, to provide a quantitative measure of the confidence with which one can infer the existence of a feedback mechanism based on observation of transient synchronized behavior. We demonstrate the application of our null model to the phenomenon of gait synchronization in free-swimming nematodes, Caenorhabditis elegans.

Synchronization dependent on spatial structures of a mesoscopic whole-brain network

Complex structural connectivity of the mammalian brain is believed to underlie the versatility of neural computations. Many previous studies have investigated properties of small subsystems or coarse connectivity among large brain regions that are often binarized and lack spatial information. Yet little is known about spatial embedding of the detailed whole-brain connectivity and its functional implications. We focus on closing this gap by analyzing how spatially-constrained neural connectivity shapes synchronization of the brain dynamics based on a system of coupled phase oscillators on a mammalian whole-brain network at the mesoscopic level. This was made possible by the recent development of the Allen Mouse Brain Connectivity Atlas constructed from viral tracing experiments together with a new mapping algorithm. We investigated whether the network can be compactly represented based on the spatial dependence of the network topology. We found that the connectivity has a significant spatial dependence, with spatially close brain regions strongly connected and distal regions weakly connected, following a power law. However, there are a number of residuals above the power-law fit, indicating connections between brain regions that are stronger than predicted by the power-law relationship. By measuring the sensitivity of the network order parameter, we show how these strong connections dispersed across multiple spatial scales of the network promote rapid transitions between partial synchronization and more global synchronization as the global coupling coefficient changes. We further demonstrate the significance of the locations of the residual connections, suggesting a possible link between the network complexity and the brain’s exceptional ability to swiftly switch computational states depending on stimulus and behavioral context.

In a previous study, a data-driven large-scale model of mouse brain connectivity was constructed. This mouse brain connectivity model is estimated by a simplified model which only takes in account anatomy and distance dependence of connection strength which is best fit by a power law. The distance dependence model captures the connection strengths of the mouse whole-brain network well. But can it capture the dynamics? In this study, we show that a small number of connections which are missed by the simple spatial model lead to significant differences in dynamics. The presence of a small number of strong connections over longer distances increases sensitivity of synchronization to perturbations. Unlike the data-driven network, the network without these long-range connections, as well as the network in which these long range connections are shuffled, lose global synchronization while maintaining localized synchrony, underlining the significance of the exact topology of these distal connections in the data-driven brain network.