Brain modularity controls the critical behavior of spontaneous activity

Enhanced brain network flexibility by physical exercise in female methamphetamine users

Methamphetamine (MA) abuse is increasing worldwide, and evidence indicates that MA causes degraded cognitive functions such as executive function, attention, and flexibility. Recent studies have shown that regular physical exercise can ameliorate the disturbed functions. However, the potential functional network alterations resulting from physical exercise have not been extensively studied in female MA users. We collaborated with a drug rehabilitation center for this study to investigate changes in brain activity and network dynamics after two types of acute and long-term exercise interventions based on 64-channel electroencephalogram recordings of seventy-nine female MA users, who were randomly divided into three groups: control group (CG), dancing group (DG) and bicycling group (BG). Over a 12-week period, we observed a clear drop in the rate of brain activity in the exercise groups, especially in the frontal and temporal regions in the DG and the frontal and occipital regions in the BG, indicating that exercise might suppress hyperactivity and that different exercise types have distinct impacts on brain networks. Importantly, both exercise groups demonstrated enhancements in brain flexibility and network connectivity entropy, particularly after the acute intervention. Besides, a significantly negative correlation was found between Δattentional bias and Δbrain flexibility after acute intervention in both DG and BG. Analysis strongly suggested that exercise programs can reshape patient brains into a highly energy-efficient state with a lower activity rate but higher information communication capacity and more plasticity for potential cognitive functions. These results may shed light on the potential therapeutic effects of exercise interventions for MA users.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09848-5.

A novel conceptual model of heart rate autonomic modulation based on a small-world modular structure of the sinoatrial node

The present view on heartbeat initiation is that a primary pacemaker cell or a group of cells in the sinoatrial node (SAN) center paces the rest of the SAN and the atria. However, recent high-resolution imaging studies show a more complex paradigm of SAN function that emerges from heterogeneous signaling, mimicking brain cytoarchitecture and function. Here, we developed and tested a new conceptual numerical model of SAN organized similarly to brain networks featuring a modular structure with small-world topology. In our model, a lower rate module leads action potential (AP) firing in the basal state and during parasympathetic stimulation, whereas a higher rate module leads during β-adrenergic stimulation. Such a system reproduces the respective shift of the leading pacemaker site observed experimentally and a wide range of rate modulation and robust function while conserving energy. Since experimental studies found functional modules at different scales, from a few cells up to the highest scale of the superior and inferior SAN, the SAN appears to feature hierarchical modularity, i.e., within each module, there is a set of sub-modules, like in the brain, exhibiting greater robustness, adaptivity, and evolvability of network function. In this perspective, our model offers a new mainframe for interpreting new data on heterogeneous signaling in the SAN at different scales, providing new insights into cardiac pacemaker function and SAN-related cardiac arrhythmias in aging and disease.

The unbalanced reorganization of weaker functional connections induces the altered brain network topology in schizophrenia

Network neuroscience shed some light on the functional and structural modifications occurring to the brain associated with the phenomenology of schizophrenia. In particular, resting-state functional networks have helped our understanding of the illness by highlighting the global and local alterations within the cerebral organization. We investigated the robustness of the brain functional architecture in 44 medicated schizophrenic patients and 40 healthy comparators through an advanced network analysis of resting-state functional magnetic resonance imaging data. The networks in patients showed more resistance to disconnection than in healthy controls, with an evident discrepancy between the two groups in the node degree distribution computed along a percolation process. Despite a substantial similarity of the basal functional organization between the two groups, the expected hierarchy of healthy brains' modular organization is crumbled in schizophrenia, showing a peculiar arrangement of the functional connections, characterized by several topologically equivalent backbones. Thus, the manifold nature of the functional organization's basal scheme, together with its altered hierarchical modularity, may be crucial in the pathogenesis of schizophrenia. This result fits the disconnection hypothesis that describes schizophrenia as a brain disorder characterized by an abnormal functional integration among brain regions.

Ensemble synchronization in the reassembly of Hydra's nervous system

Although much is known about how the structure of the nervous system develops, it is still unclear how its functional modularity arises. A dream experiment would be to observe the entire development of a nervous system, correlating the emergence of functional units with their associated behaviors. This is possible in the cnidarian Hydra vulgaris, which, after its complete dissociation into individual cells, can reassemble itself back together into a normal animal. We used calcium imaging to monitor the complete neuronal activity of dissociated Hydra as they reaggregated over several days. Initially uncoordinated neuronal activity became synchronized into coactive neuronal ensembles. These local modules then synchronized with others, building larger functional ensembles that eventually extended throughout the entire reaggregate, generating neuronal rhythms similar to those of intact animals. Global synchronization was not due to neurite outgrowth but to strengthening of functional connections between ensembles. We conclude that Hydra's nervous system achieves its functional reassembly through the hierarchical modularity of neuronal ensembles.

Brain network modularity predicts cognitive training-related gains in young adults

The brain operates via networked activity in separable groups of regions called modules. The quantification of modularity compares the number of connections within and between modules, with high modularity indicating greater segregation, or dense connections within sub-networks and sparse connections between sub-networks. Previous work has demonstrated that baseline brain network modularity predicts executive function outcomes in older adults and patients with traumatic brain injury after cognitive and exercise interventions. In healthy young adults, however, the functional significance of brain modularity in predicting training-related cognitive improvements is not fully understood. Here, we quantified brain network modularity in young adults who underwent cognitive training with casual video games that engaged working memory and reasoning processes. Network modularity assessed at baseline was positively correlated with training-related improvements on untrained tasks. The relationship between baseline modularity and training gain was especially evident in initially lower performing individuals and was not present in a group of control participants that did not show training-related gains. These results suggest that a more modular brain network organization may allow for greater training responsiveness. On a broader scale, these findings suggest that, particularly in low-performing individuals, global network properties can capture aspects of brain function that are important in understanding individual differences in learning.

Modular co-organization of functional connectivity and scale-free dynamics in the human brain

Scale-free neuronal dynamics and interareal correlations are emergent characteristics of spontaneous brain activity. How such dynamics and the anatomical patterns of neuronal connectivity are mutually related in brain networks has, however, remained unclear. We addressed this relationship by quantifying the network colocalization of scale-free neuronal activity-both neuronal avalanches and long-range temporal correlations (LRTCs)-and functional connectivity (FC) by means of intracranial and noninvasive human resting-state electrophysiological recordings. We found frequency-specific colocalization of scale-free dynamics and FC so that the interareal couplings of LRTCs and the propagation of neuronal avalanches were most pronounced in the predominant pathways of FC. Several control analyses and the frequency specificity of network colocalization showed that the results were not trivial by-products of either brain dynamics or our analysis approach. Crucially, scale-free neuronal dynamics and connectivity also had colocalized modular structures at multiple levels of network organization, suggesting that modules of FC would be endowed with partially independent dynamic states. These findings thus suggest that FC and scale-free dynamics-hence, putatively, neuronal criticality as well-coemerge in a hierarchically modular structure in which the modules are characterized by dense connectivity, avalanche propagation, and shared dynamic states.

Model of brain activation predicts the neural collective influence map of the brain

Efficient complex systems have a modular structure, but modularity does not guarantee robustness, because efficiency also requires an ingenious interplay of the interacting modular components. The human brain is the elemental paradigm of an efficient robust modular system interconnected as a network of networks (NoN). Understanding the emergence of robustness in such modular architectures from the interconnections of its parts is a longstanding challenge that has concerned many scientists. Current models of dependencies in NoN inspired by the power grid express interactions among modules with fragile couplings that amplify even small shocks, thus preventing functionality. Therefore, we introduce a model of NoN to shape the pattern of brain activations to form a modular environment that is robust. The model predicts the map of neural collective influencers (NCIs) in the brain, through the optimization of the influence of the minimal set of essential nodes responsible for broadcasting information to the whole-brain NoN. Our results suggest intervention protocols to control brain activity by targeting influential neural nodes predicted by network theory.

Dynamical systems, attractors, and neural circuits

Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

Scaling in topological properties of brain networks

The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks. The modular organization, in terms of modular mass, inter-modular, and intra-modular interaction, also obeys fractal nature. The parameters which characterize topological properties of brain networks follow one parameter scaling theory in all levels of network structure, which reveals the self-similar rules governing the network structure. Further, the calculated fractal dimensions of brain networks of different species are found to decrease when one goes from lower to higher level species which implicates the more ordered and self-organized topography at higher level species. The sparsely distributed hubs in brain networks may be most influencing nodes but their absence may not cause network breakdown, and centrality parameters characterizing them also follow one parameter scaling law indicating self-similar roles of these hubs at different levels of organization in brain networks. The local-community-paradigm decomposition plot and calculated local-community-paradigm-correlation co-efficient of brain networks also shows the evidence for self-organization in these networks.

Studying Sub-Dendrograms of Resting-State Functional Networks with Voxel-Wise Hierarchical Clustering

Hierarchical clustering is a useful data-driven approach to classify complex data and has been used to analyze resting-state functional magnetic resonance imaging (fMRI) data and derive functional networks of the human brain at very large scale, such as the entire visual or sensory-motor cortex. In this study, we developed a voxel-wise, whole-brain hierarchical clustering framework to perform multi-stage analysis of group-averaged resting-state fMRI data in different levels of detail. With the framework we analyzed particularly the somatosensory motor and visual systems in fine details and constructed the corresponding sub-dendrograms, which corroborate consistently with the known modular organizations from previous clinical and experimental studies. The framework provides a useful tool for data-driven analysis of resting-state fMRI data to gain insight into the hierarchical organization and degree of functional modulation among the sub-units.

From functional to structural connectivity using partial correlation in neuronal assemblies

OBJECTIVE

Our goal is to re-introduce an optimized version of the partial correlation to infer structural connections from functional-effective ones in dissociated neuronal cultures coupled to microelectrode arrays.

APPROACH

We first validate our partialization procedure on in silico networks, mimicking different experimental conditions (i.e., different connectivity degrees and number of nodes) and comparing the partial correlation's performance with two gold-standard methods: cross-correlation and transfer entropy. Afterwards, to infer the structural connections in in vitro neuronal networks where the ground truth is unknown, we propose a thresholding heuristic approach. Then, to validate whether the partialization process correctly reconstructs macroscopic features of the network structure, we extract a modularity index from segregated in silico and in vitro models. Finally, as a case study, we apply our partialization procedure to analyze connectivity and topology on spontaneous developing and electrically stimulated in vitro cultures.

MAIN RESULTS

In simulated networks, partial correlation outperforms cross-correlation and transfer entropy at low and medium connectivity degrees, not only in relatively small (60 nodes) but also in larger (120-240 nodes) assemblies. Furthermore, partial correlation correctly identifies interconnected neuronal sub-populations and allows one to derive network topology in in vitro cortical networks.

SIGNIFICANCE

Our results support the idea that partial correlation is a good method for connectivity studies and can be applied to derive topological and structural features of neuronal assemblies.

Structural determinants of criticality in biological networks

Many adaptive evolutionary systems display spatial and temporal features, such as long-range correlations, typically associated with the critical point of a phase transition in statistical physics. Empirical and theoretical studies suggest that operating near criticality enhances the functionality of biological networks, such as brain and gene networks, in terms for instance of information processing, robustness, and evolvability. While previous studies have explained criticality with specific system features, we still lack a general theory of critical behavior in biological systems. Here we look at this problem from the complex systems perspective, since in principle all critical biological circuits have in common the fact that their internal organization can be described as a complex network. An important question is how self-similar structure influences self-similar dynamics. Modularity and heterogeneity, for instance, affect the location of critical points and can be used to tune the system toward criticality. We review and discuss recent studies on the criticality of neuronal and genetic networks, and discuss the implications of network theory when assessing the evolutionary features of criticality.

Relationship of fast- and slow-timescale neuronal dynamics in human MEG and SEEG

A growing body of evidence suggests that the neuronal dynamics are poised at criticality. Neuronal avalanches and long-range temporal correlations (LRTCs) are hallmarks of such critical dynamics in neuronal activity and occur at fast (subsecond) and slow (seconds to hours) timescales, respectively. The critical dynamics at different timescales can be characterized by their power-law scaling exponents. However, insight into the avalanche dynamics and LRTCs in the human brain has been largely obtained with sensor-level MEG and EEG recordings, which yield only limited anatomical insight and results confounded by signal mixing. We investigated here the relationship between the human neuronal dynamics at fast and slow timescales using both source-reconstructed MEG and intracranial stereotactical electroencephalography (SEEG). Both MEG and SEEG revealed avalanche dynamics that were characterized parameter-dependently by power-law or truncated-power-law size distributions. Both methods also revealed robust LRTCs throughout the neocortex with distinct scaling exponents in different functional brain systems and frequency bands. The exponents of power-law regimen neuronal avalanches and LRTCs were strongly correlated across subjects. Qualitatively similar power-law correlations were also observed in surrogate data without spatial correlations but with scaling exponents distinct from those of original data. Furthermore, we found that LRTCs in the autonomous nervous system, as indexed by heart-rate variability, were correlated in a complex manner with cortical neuronal avalanches and LRTCs in MEG but not SEEG. These scalp and intracranial data hence show that power-law scaling behavior is a pervasive but neuroanatomically inhomogeneous property of neuronal dynamics in central and autonomous nervous systems.

Progressive glucose stimulation of islet beta cells reveals a transition from segregated to integrated modular functional connectivity patterns

Collective beta cell activity in islets of Langerhans is critical for the supply of insulin within an organism. Even though individual beta cells are intrinsically heterogeneous, the presence of intercellular coupling mechanisms ensures coordinated activity and a well-regulated exocytosis of insulin. In order to get a detailed insight into the functional organization of the syncytium, we applied advanced analytical tools from the realm of complex network theory to uncover the functional connectivity pattern among cells composing the intact islet. The procedure is based on the determination of correlations between long temporal traces obtained from confocal functional multicellular calcium imaging of beta cells stimulated in a stepwise manner with a range of physiological glucose concentrations. Our results revealed that the extracted connectivity networks are sparse for low glucose concentrations, whereas for higher stimulatory levels they become more densely connected. Most importantly, for all ranges of glucose concentration beta cells within the islets form locally clustered functional sub-compartments, thereby indicating that their collective activity profiles exhibit a modular nature. Moreover, we show that the observed non-linear functional relationship between different network metrics and glucose concentration represents a well-balanced setup that parallels physiological insulin release.

Tuning pathological brain oscillations with neurofeedback: a systems neuroscience framework

Neurofeedback (NFB) is emerging as a promising technique that enables self-regulation of ongoing brain oscillations. However, despite a rise in empirical evidence attesting to its clinical benefits, a solid theoretical basis is still lacking on the manner in which NFB is able to achieve these outcomes. The present work attempts to bring together various concepts from neurobiology, engineering, and dynamical systems so as to propose a contemporary theoretical framework for the mechanistic effects of NFB. The objective is to provide a firmly neurophysiological account of NFB, which goes beyond traditional behaviorist interpretations that attempt to explain psychological processes solely from a descriptive standpoint whilst treating the brain as a “black box”. To this end, we interlink evidence from experimental findings that encompass a broad range of intrinsic brain phenomena: starting from “bottom-up” mechanisms of neural synchronization, followed by “top-down” regulation of internal brain states, moving to dynamical systems plus control-theoretic principles, and concluding with activity-dependent as well as homeostatic forms of brain plasticity. In support of our framework, we examine the effects of NFB in several brain disorders, including attention-deficit hyperactivity (ADHD) and post-traumatic stress disorder (PTSD). In sum, it is argued that pathological oscillations emerge from an abnormal formation of brain-state attractor landscape(s). The central thesis put forward is that NFB tunes brain oscillations toward a homeostatic set-point which affords an optimal balance between network flexibility and stability (i.e., self-organised criticality (SOC)).