Evolution and development of brain networks: from Caenorhabditis elegans to Homo sapiens

Relation of connectome topology to brain volume across 103 mammalian species

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains.

Change of motifs in C. elegans reveals developmental principle of neural network

Revealing the organizing principles of developing neural networks is a difficult but significant task in neuroscience. As a creature with a rather compact and well-studied neural network, C. elegans is an ideal subject for neuroscience study. However, the researches on its developing neural network remain challenging. The changes in specific properties of neural network across development may uncover part of its principles. Motif is a typical structure property that can be well applied to various complex networks. Here, we study the motif changes in C. elegans neural network across development. By counting the occurrence number of all three-node subgraph motif structures in its neural network at different stages of C. elegans development, along with those in corresponding random networks, we determine which of these structures are motifs for C. elegans, finding out the regular changes of motifs during its development. Combined with the potential function of these subgraph motifs and synaptic information, we gain insight into the organizing principle of neural network during development, which may increase our understanding of neuroscience and inspire the construction of artificial neural network.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Identification of Young High-Functioning Autism Individuals Based on Functional Connectome Using Graph Isomorphism Network: A Pilot Study

Accumulated studies have determined the changes in functional connectivity in autism spectrum disorder (ASD) and spurred the application of machine learning for classifying ASD. Graph Neural Network provides a new method for network analysis in brain disorders to identify the underlying network features associated with functional deficits. Here, we proposed an improved model of Graph Isomorphism Network (GIN) that implements the Weisfeiler-Lehman (WL) graph isomorphism test to learn the graph features while taking into account the importance of each node in the classification to improve the interpretability of the algorithm. We applied the proposed method on multisite datasets of resting-state functional connectome from Autism Brain Imaging Data Exchange (ABIDE) after stringent quality control. The proposed method outperformed other commonly used classification methods on five different evaluation metrics. We also identified salient ROIs in visual and frontoparietal control networks, which could provide potential neuroimaging biomarkers for ASD identification.

Rare long-range cortical connections enhance human information processing

What are the key topological features of connectivity critically relevant for generating the dynamics underlying efficient cortical function? A candidate feature that has recently emerged is that the connectivity of the mammalian cortex follows an exponential distance rule, which includes a small proportion of long-range high-weight anatomical exceptions to this rule. Whole-brain modeling of large-scale human neuroimaging data in 1,003 participants offers the unique opportunity to create two models, with and without long-range exceptions, and explicitly study their functional consequences. We found that rare long-range exceptions are crucial for significantly improving information processing. Furthermore, modeling in a simplified ring architecture shows that this improvement is greatly enhanced by the turbulent regime found in empirical neuroimaging data. Overall, the results provide strong empirical evidence for the immense functional benefits of long-range exceptions combined with turbulence for information processing.

Environmental influences on the pace of brain development

Childhood socio-economic status (SES), a measure of the availability of material and social resources, is one of the strongest predictors of lifelong well-being. Here we review evidence that experiences associated with childhood SES affect not only the outcome but also the pace of brain development. We argue that higher childhood SES is associated with protracted structural brain development and a prolonged trajectory of functional network segregation, ultimately leading to more efficient cortical networks in adulthood. We hypothesize that greater exposure to chronic stress accelerates brain maturation, whereas greater access to novel positive experiences decelerates maturation. We discuss the impact of variation in the pace of brain development on plasticity and learning. We provide a generative theoretical framework to catalyse future basic science and translational research on environmental influences on brain development.

Multi-scale structural rich-club organization of the brain in full-term newborns: a combined DWI and fMRI study

Objective.Our understanding of early brain development is limited due to rapid changes in white matter pathways after birth. In this study, we introduced a multi-scale cross-modal approach to investigate the rich club (RC) organization and topology of the structural brain networks in 40 healthy neonates using diffusion-weighted imaging and resting-state fMRI data.Approach.A group independent component analysis was first performed to identify eight resting state networks (RSNs) used as functional modules. A groupwise whole-brain functional parcellation was also performed at five scales comprising 100-900 parcels. The distribution of RC nodes was then investigated within and between the RSNs. We further assessed the distribution of short and long-range RC, feeder and local connections across different parcellation scales.Main results.Sharing the scale-free characteristic of small-worldness, the neonatal structural brain networks exhibited an RC organization at different nodal scales (NSs). The subcortical, sensory-motor and default mode networks were found to be strongly involved in the RC organization of the structural brain networks, especially in the zones where the RSNs overlapped, with an average cross-scale proportion of 45.9%, 28.5% and 10.5%, respectively. A large proportion of the connector hubs were found to be RC members for the coarsest (73%) to finest (92%) NSs. Our results revealed a prominent involvement of cortico-subcortical and cortico-cerebellar white matter pathways in the RC organization of the neonatal brain. Regardless of the NS, the majority (more than 65.2%) of the inter-RSN connections were long distance RC or feeder with an average physical connection of 105.5 and 97.4 mm, respectively. Several key RC regions were identified, including the insula and cingulate gyri, middle and superior temporal gyri, hippocampus and parahippocampus, fusiform gyrus, precuneus, superior frontal and precentral gyri, calcarine fissure and lingual gyrus.Significance.Our results emphasize the importance of the multi-scale connectivity analysis in assessing the cross-scale reproducibility of the connectivity results concerning the global and local topological properties of the brain networks. Our findings may improve our understanding of the early brain development.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Adaptive rewiring evolves brain-like structure in weighted networks

Activity-dependent plasticity refers to a range of mechanisms for adaptively reshaping neuronal connections. We model their common principle in terms of adaptive rewiring of network connectivity, while representing neural activity by diffusion on the network: Where diffusion is intensive, shortcut connections are established, while underused connections are pruned. In binary networks, this process is known to steer initially random networks robustly to high levels of structural complexity, reflecting the global characteristics of brain anatomy: modular or centralized small world topologies. We investigate whether this result extends to more realistic, weighted networks. Both normally- and lognormally-distributed weighted networks evolve either modular or centralized topologies. Which of these prevails depends on a single control parameter, representing global homeostatic or normalizing regulation mechanisms. Intermediate control parameter values exhibit the greatest levels of network complexity, incorporating both modular and centralized tendencies. The simulation results allow us to propose diffusion based adaptive rewiring as a parsimonious model for activity-dependent reshaping of brain connectivity structure.

Morphological Coordination: A Common Ancestral Function Unifying Neural and Non-Neural Signaling

Nervous systems are traditionally thought of as providing sensing and behavioral coordination functions at the level of the whole organism. What is the evolutionary origin of the mechanisms enabling the nervous systems’ information processing ability? Here, we review evidence from evolutionary, developmental, and regenerative biology suggesting a deeper, ancestral function of both pre-neural and neural cell-cell communication systems: the long-distance coordination of cell division and differentiation required to create and maintain body-axis symmetries. This conceptualization of the function of nervous system activity sheds new light on the evolutionary transition from the morphologically rudimentary, non-neural Porifera and Placazoa to the complex morphologies of Ctenophores, Cnidarians, and Bilaterians. It further allows a sharp formulation of the distinction between long-distance axis-symmetry coordination based on external coordinates, e.g., by whole-organism scale trophisms as employed by plants and sessile animals, and coordination based on body-centered coordinates as employed by motile animals. Thus we suggest that the systems that control animal behavior evolved from ancient mechanisms adapting preexisting ionic and neurotransmitter mechanisms to regulate individual cell behaviors during morphogenesis. An appreciation of the ancient, non-neural origins of bioelectrically mediated computation suggests new approaches to the study of embryological development, including embryological dysregulation, cancer, regenerative medicine, and synthetic bioengineering.

Proper spatial heterogeneities expand the regime of scale-free behavior in a lattice of excitable elements

Signatures of criticality, such as power law scaling of observables, have been empirically found in a plethora of real-life settings, including biological systems. The presence of critical states is believed to have many functional advantages and is associated with optimal operational abilities. Typically, critical dynamics arises in the proximity of phase transition points between absorbing disordered states (subcriticality) and ordered active regimes (supercriticality) and requires a high degree of fine tuning to emerge, which is unlikely to occur in real biological systems. In the present study we propose a rather simple, and biologically relevant mechanism that profoundly expands the critical-like region. In particular, by means of numerical simulation we show that incorporating spatial heterogeneities into the square lattice of map-based excitable oscillators broadens the parameter space in which the distribution of excitation wave sizes follows closely a power law. Most importantly, this behavior is only observed if the spatial profile exhibits intermediate-sized patches with similar excitability levels, whereas for large and small spatial clusters only marginal widening of the critical state is detected. Furthermore, it turned out that the presence of spatial disorder in general amplifies the size of excitation waves, whereby the relatively highest contributions are observed in the proximity of the critical point. We argue that the reported mechanism is of particular importance for excitable systems with local interactions between individual elements.

What would a synthetic connectome look like?

A major challenge of contemporary neuroscience is to unravel the structure of the connectome, the ensemble of neural connections that link between different functional units of the brain, and to reveal how this structure relates to brain function. This thriving area of research largely follows the general tradition in biology of reverse-engineering, which consists of first observing and characterizing a biological system or process, and then deconstructing it into its fundamental building blocks in order to infer its modes of operation. However, a complementary form of biology has emerged, synthetic biology, which emphasizes construction-based forward-engineering. The synthetic biology approach comprises the assembly of new biological systems out of elementary biological parts. The rationale is that the act of building a system can be a powerful method for gaining deep understanding of how that system works. As the fields of connectomics and synthetic biology are independently growing, I propose to consider the benefits of combining the two, to create synthetic connectomics, a new form of neuroscience and a new form of synthetic biology. The goal of synthetic connectomics would be to artificially design and construct the connectomes of live behaving organisms. Synthetic connectomics could serve as a unifying platform for unraveling the complexities of brain operation and perhaps also for generating new forms of artificial life, and, in general, could provide a valuable opportunity for empirically exploring theoretical predictions about network function. What would a synthetic connectome look like? What purposes would it serve? How could it be constructed? This review delineates the novel notion of a synthetic connectome and aims to lay out the initial steps towards its implementation, contemplating its impact on science and society.

A Game-Theoretical Network Formation Model for C. elegans Neural Network

Studying and understanding human brain structures and functions have become one of the most challenging issues in neuroscience today. However, the mammalian nervous system is made up of hundreds of millions of neurons and billions of synapses. This complexity made it impossible to reconstruct such a huge nervous system in the laboratory. So, most researchers focus on C. elegans neural network. The C. elegans neural network is the only biological neural network that is fully mapped. This nervous system is the simplest neural network that exists. However, many fundamental behaviors like movement emerge from this basic network. These features made C. elegans a convenient case to study the nervous systems. Many studies try to propose a network formation model for C. elegans neural network. However, these studies could not meet all characteristics of C. elegans neural network, such as significant factors that play a role in the formation of C. elegans neural network. Thus, new models are needed to be proposed in order to explain all aspects of C. elegans neural network. In this paper, a new model based on game theory is proposed in order to understand the factors affecting the formation of nervous systems, which meet the C. elegans frontal neural network characteristics. In this model, neurons are considered to be agents. The strategy for each neuron includes either making or removing links to other neurons. After choosing the basic network, the utility function is built using structural and functional factors. In order to find the coefficients for each of these factors, linear programming is used. Finally, the output network is compared with C. elegans frontal neural network and previous models. The results implicate that the game-theoretical model proposed in this paper can better predict the influencing factors in the formation of C. elegans neural network compared to previous models.

Rich club disturbances of the human connectome from subjective cognitive decline to Alzheimer's disease

Alzheimer's disease (AD) has a preclinical phase that can last for decades prior to clinical dementia onset. Subjective cognitive decline (SCD) is regarded as the last preclinical AD stage prior to the development of amnestic mild cognitive decline (aMCI) and AD dementia (d-AD). The analysis of brain structural networks based on diffusion tensor imaging (DTI) has identified the so-called 'rich club', a set of cortical regions highly connected to each other, with other regions referred to as peripheral. It has been reported that rich club architecture is affected by regional atrophy and connectivity, which are reduced in patients with aMCI and d-AD. Methods: We recruited 62 normal controls, 47 SCD patients, 60 aMCI patients and 55 d-AD patients and collected DTI data to analyze rich-club organization. Results: We demonstrated that rich club organization was disrupted, with reduced structural connectivity among rich club nodes, in aMCI and d-AD patients but remained stable in SCD patients. In addition, SCD, aMCI and d-AD patients showed similar patterns of disrupted peripheral regions and reduced connectivity involving these regions, suggesting that peripheral regions might contribute to cognitive decline and that disruptions here could be regarded as an early marker of SCD. This organization could provide the fundamental structural architecture for complex cognitive functions and explain the low prevalence of cognitive problems in SCD patients. Conclusions: These findings reveal a disrupted pattern of the AD connectome that starts in peripheral regions and then hierarchically propagates to rich club regions, when patients show clinical symptoms. This pattern provides evidence that disruptions in rich club organization are a key factor in the progression of AD that can dynamically reflect the progression of AD, thus representing a potential biomarker for early diagnosis.

From Maps to Multi-dimensional Network Mechanisms of Mental Disorders

The development of advanced neuroimaging techniques and their deployment in large cohorts has enabled an assessment of functional and structural brain network architecture at an unprecedented level of detail. Across many temporal and spatial scales, network neuroscience has emerged as a central focus of intellectual efforts, seeking meaningful descriptions of brain networks and explanatory sets of network features that underlie circuit function in health and dysfunction in disease. However, the tools of network science commonly deployed provide insight into brain function at a fundamentally descriptive level, often failing to identify (patho-)physiological mechanisms that link system-level phenomena to the multiple hierarchies of brain function. Here we describe recently developed techniques stemming from advances in complex systems and network science that have the potential to overcome this limitation, thereby contributing mechanistic insights into neuroanatomy, functional dynamics, and pathology. Finally, we build on the Research Domain Criteria framework, highlighting the notion that mental illnesses can be conceptualized as dysfunctions of neural circuitry present across conventional diagnostic boundaries, to sketch how network-based methods can be combined with pharmacological, intermediate phenotype, genetic, and magnetic stimulation studies to probe mechanisms of psychopathology.

Mechanisms of Connectome Development

At the centenary of D'Arcy Thompson's seminal work 'On Growth and Form', pioneering the description of principles of morphological changes during development and evolution, recent experimental advances allow us to study change in anatomical brain networks. Here, we outline potential principles for connectome development. We will describe recent results on how spatial and temporal factors shape connectome development in health and disease. Understanding the developmental origins of brain diseases in individuals will be crucial for deciding on personalized treatment options. We argue that longitudinal studies, experimentally derived parameters for connection formation, and biologically realistic computational models are needed to better understand the link between brain network development, network structure, and network function.

Species-conserved reconfigurations of brain network topology induced by ketamine

Species-conserved (intermediate) phenotypes that can be quantified and compared across species offer important advantages for translational research and drug discovery. Here, we investigate the utility of network science methods to assess the pharmacological alterations of the large-scale architecture of brain networks in rats and humans. In a double-blind, placebo-controlled, cross-over study in humans and a placebo-controlled two-group study in rats, we demonstrate that the application of ketamine leads to a topological reconfiguration of large-scale brain networks towards less-integrated and more-segregated information processing in both the species. As these alterations are opposed to those commonly observed in patients suffering from depression, they might indicate systems-level correlates of the antidepressant effect of ketamine.

A simple generative model of the mouse mesoscale connectome

Recent technological advances now allow for the collection of vast data sets detailing the intricate neural connectivity patterns of various organisms. Oh et al. (2014) recently published the most complete description of the mouse mesoscale connectome acquired to date. Here we give an in-depth characterization of this connectome and propose a generative network model which utilizes two elemental organizational principles: proximal attachment ‒ outgoing connections are more likely to attach to nearby nodes than to distant ones, and source growth ‒ nodes with many outgoing connections are likely to form new outgoing connections. We show that this model captures essential principles governing network organization at the mesoscale level in the mouse brain and is consistent with biologically plausible developmental processes.

Emerging hubs in phantom perception connectomics

Brain networks are small-world networks typically characterized by the presence of hubs, i.e. nodes that have significantly greater number of links in comparison to other nodes in the network. These hubs act as short cuts in the network and promote long-distance connectivity. Long-distance connections increase the efficiency of information transfer but also increase the cost of the network. Brain disorders are associated with an altered brain connectome which reflects either as a complete change in the network topology, as in, the replacement of hubs or as an alteration in the connectivity between the hubs while retaining network structure. The current study compares the network topology of binary and weighted networks in tinnitus patients and healthy controls by studying the hubs of the two networks in different oscillatory bands. The EEG of 311 tinnitus patients and 256 control subjects are recorded, pre-processed and source-localized using sLORETA. The hubs of the different binary and weighted networks are identified using different measures of network centrality. The results suggest that the tinnitus and control networks are distinct in all the frequency bands but substantially overlap in the gamma frequency band. The differences in network topology in the tinnitus and control groups in the delta, theta and the higher beta bands are driven by a change in hubs as well as network connectivity; in the alpha band by changes in hubs alone and in the gamma band by changes in network connectivity. Thus the brain seems to employ different frequency band-dependent adaptive mechanisms trying to compensate for auditory deafferentation.

Kuramoto model simulation of neural hubs and dynamic synchrony in the human cerebral connectome

Background

The topological structure of the wiring of the mammalian brain cortex plays an important role in shaping the functional dynamics of large-scale neural activity. Due to their central embedding in the network, high degree hub regions and their connections (often referred to as the ‘rich club’) have been hypothesized to facilitate intermodular neural communication and global integration of information by means of synchronization. Here, we examined the theoretical role of anatomical hubs and their wiring in brain dynamics. The Kuramoto model was used to simulate interaction of cortical brain areas by means of coupled phase oscillators—with anatomical connections between regions derived from diffusion weighted imaging and module assignment of brain regions based on empirically determined resting-state data.

Results

Our findings show that synchrony among hub nodes was higher than any module’s intramodular synchrony (p < 10⁻⁴, for cortical coupling strengths, λ, in the range 0.02 < λ < 0.05), suggesting that hub nodes lead the functional modules in the process of synchronization. Furthermore, suppressing structural connectivity among hub nodes resulted in an elevated modular state (p < 4.1 × l0⁻³, 0.015 < λ < 0.04), indicating that hub-to-hub connections are critical in intermodular synchronization. Finally, perturbing the oscillatory behavior of hub nodes prevented functional modules from synchronizing, implying that synchronization of functional modules is dependent on the hub nodes’ behavior.

Conclusion

Our results converge on anatomical hubs having a leading role in intermodular synchronization and integration in the human brain.

Electronic supplementary material

The online version of this article (doi:10.1186/s12868-015-0193-z) contains supplementary material, which is available to authorized users.

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic, functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether the connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.

Developmental time windows for axon growth influence neuronal network topology

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation during early development, either starting at the same time for all neurons (parallel, i.e., maximally overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e., no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: Neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening up the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.

Latching chains in K-nearest-neighbor and modular small-world networks

Latching dynamics retrieve pattern sequences successively by neural adaption and pattern correlation. We have previously proposed a modular latching chain model in Song et al. (2014) to better accommodate the structured transitions in the brain. Different cortical areas have different network structures. To explore how structural parameters like rewiring probability, threshold, noise and feedback connections affect the latching dynamics, two different connection schemes, K-nearest-neighbor network and modular network both having modular structure are considered. Latching chains are measured using two proposed measures characterizing length of intra-modular latching chains and sequential inter-modular association transitions. Our main findings include: (1) With decreasing threshold coefficient and rewiring probability, both the K-nearest-neighbor network and the modular network experience quantitatively similar phase change processes. (2) The modular network exhibits selectively enhanced latching in the small-world range of connectivity. (3) The K-nearest-neighbor network is more robust to changes in rewiring probability, while the modular network is more robust to the presence of noise pattern pairs and to changes in the strength of feedback connections. According to our findings, the relationships between latching chains in K-nearest-neighbor and modular networks and different forms of cognition and information processing emerging in the brain are discussed.

Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.

Abnormal cortical growth in schizophrenia targets normative modules of synchronized development

BACKGROUND

Schizophrenia is a disorder of brain connectivity and altered neurodevelopmental processes. Cross-sectional case-control studies in different age groups have suggested that deficits in cortical thickness in childhood-onset schizophrenia may normalize over time, suggesting a disorder-related difference in cortical growth trajectories.

METHODS

We acquired magnetic resonance imaging scans repeated over several years for each subject, in a sample of 106 patients with childhood-onset schizophrenia and 102 age-matched healthy volunteers. Using semiparametric regression, we modeled the effect of schizophrenia on the growth curve of cortical thickness in ~80,000 locations across the cortex, in the age range 8 to 30 years. In addition, we derived normative developmental modules composed of cortical regions with similar maturational trajectories for cortical thickness in typical brain development.

RESULTS

We found abnormal nonlinear growth processes in prefrontal and temporal areas that have previously been implicated in schizophrenia, distinguishing for the first time between cortical areas with age-constant deficits in cortical thickness and areas whose maturational trajectories are altered in schizophrenia. In addition, we showed that when the brain is divided into five normative developmental modules, the areas with abnormal cortical growth overlap significantly only with the cingulo-fronto-temporal module.

CONCLUSIONS

These findings suggest that abnormal cortical development in schizophrenia may be modularized or constrained by the normal community structure of developmental modules of the human brain connectome.

Structural and functional aspects relating to cost and benefit of rich club organization in the human cerebral cortex

Recent findings have demonstrated that a small set of highly connected brain regions may play a central role in enabling efficient communication between cortical regions, together forming a densely interconnected "rich club." However, the density and spatial layout of the rich club also suggest that it constitutes a costly feature of brain architecture. Here, combining anatomical T1, diffusion tensor imaging, magnetic transfer imaging, and functional MRI, several aspects of structural and functional connectivity of the brain's rich club were examined. Our findings suggest that rich club regions and rich club connections exhibit high levels of wiring volume, high levels of white matter organization, high levels of metabolic energy usage, long maturational trajectories, more variable regional time series, and more inter-regional functional couplings. Taken together, these structural and functional measures extend the notion that rich club organization represents a high-cost feature of brain architecture that puts a significant strain on brain resources. The high cost of the rich club may, however, be offset by significant functional benefits that the rich club confers to the brain network as a whole.

Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained ('random'), connection length preserving ('spatial'), and connection length optimised ('reduced') surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain.

Systematic network lesioning reveals the core white matter scaffold of the human brain

Brain connectivity loss due to traumatic brain injury, stroke or multiple sclerosis can have serious consequences on life quality and a measurable impact upon neural and cognitive function. Though brain network properties are known to be affected disproportionately by injuries to certain gray matter regions, the manner in which white matter (WM) insults affect such properties remains poorly understood. Here, network-theoretic analysis allows us to identify the existence of a macroscopic neural connectivity core in the adult human brain which is particularly sensitive to network lesioning. The systematic lesion analysis of brain connectivity matrices from diffusion neuroimaging over a large sample (N = 110) reveals that the global vulnerability of brain networks can be predicated upon the extent to which injuries disrupt this connectivity core, which is found to be quite distinct from the set of connections between rich club nodes in the brain. Thus, in addition to connectivity within the rich club, the brain as a network also contains a distinct core scaffold of network edges consisting of WM connections whose damage dramatically lowers the integrative properties of brain networks. This pattern of core WM fasciculi whose injury results in major alterations to overall network integrity presents new avenues for clinical outcome prediction following brain injury by relating lesion locations to connectivity core disruption and implications for recovery. The findings of this study contribute substantially to current understanding of the human WM connectome, its sensitivity to injury, and clarify a long-standing debate regarding the relative prominence of gray vs. WM regions in the context of brain structure and connectomic architecture.

An anatomical substrate for integration among functional networks in human cortex

The human brain shows several characteristics of an efficient communication network architecture, including short communication paths and the existence of modules interlinked by a small set of highly connected regions. Studies of structural networks comprising macroscopic white matter projections have shown that these putative hubs are densely interconnected, giving rise to a spatially distributed and topologically central collective called the "rich club." In parallel, studies of intrinsic brain activity have consistently revealed distinct functional communities or resting-state networks (RSNs), indicative of specialized processing and segregation of neuronal information. However, the pattern of structural connectivity interconnecting these functional RSNs and how such inter-RSN structural connections might bring about functional integration between RSNs remain largely unknown. Combining high-resolution diffusion weighted imaging with resting-state fMRI, we present novel evidence suggesting that the rich club structure plays a central role in cross-linking macroscopic RSNs of the human brain. Rich club hub nodes were present in all functional networks, accounted for a large proportion of "connector nodes," and were found to coincide with regions in which multiple networks overlap. In addition, a large proportion of all inter-RSN connections were found to involve rich club nodes, and these connections participated in a disproportionate number of communication paths linking nodes in different RSNs. Our findings suggest that the brain's rich club serves as a macroscopic anatomical substrate to cross-link functional networks and thus plays an important role in the integration of information between segregated functional domains of the human cortex.

The rich club of the C. elegans neuronal connectome

There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N = 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.

Principal networks

Graph representations of brain connectivity have attracted a lot of recent interest, but existing methods for dividing such graphs into connected subnetworks have a number of limitations in the context of neuroimaging. This is an important problem because most cognitive functions would be expected to involve some but not all brain regions. In this paper we outline a simple approach for decomposing graphs, which may be based on any measure of interregional association, into coherent “principal networks”. The technique is based on an eigendecomposition of the association matrix, and is closely related to principal components analysis. We demonstrate the technique using cortical thickness and diffusion tractography data, showing that the subnetworks which emerge are stable, meaningful and reproducible. Graph-theoretic measures of network cost and efficiency may be calculated separately for each principal network. Unlike some other approaches, all available connectivity information is taken into account, and vertices may appear in none or several of the subnetworks. Subject-by-subject “scores” for each principal network may also be obtained, under certain circumstances, and related to demographic or cognitive variables of interest.

The convergence of maturational change and structural covariance in human cortical networks

Large-scale covariance of cortical thickness or volume in distributed brain regions has been consistently reported by human neuroimaging studies. The mechanism of this population covariance of regional cortical anatomy has been hypothetically related to synchronized maturational changes in anatomically connected neuronal populations. Brain regions that grow together, i.e., increase or decrease in volume at the same rate over the course of years in the same individual, are thus expected to demonstrate strong structural covariance or anatomical connectivity across individuals. To test this prediction, we used a structural MRI dataset on healthy young people (N = 108; aged 9-22 years at enrollment), comprising 3-6 longitudinal scans on each participant over 6-12 years of follow-up. At each of 360 regional nodes, and for each participant, we estimated the following: (1) the cortical thickness in the median scan and (2) the linear rate of change in cortical thickness over years of serial scanning. We constructed structural and maturational association matrices and networks from these measurements. Both structural and maturational networks shared similar global and nodal topological properties, as well as mesoscopic features including a modular community structure, a relatively small number of highly connected hub regions, and a bias toward short distance connections. Using resting-state functional magnetic resonance imaging data on a subset of the sample (N = 32), we also demonstrated that functional connectivity and network organization was somewhat predictable by structural/maturational networks but demonstrated a stronger bias toward short distance connections and greater topological segregation. Brain structural covariance networks are likely to reflect synchronized developmental change in distributed cortical regions.

High-cost, high-capacity backbone for global brain communication

Network studies of human brain structural connectivity have identified a specific set of brain regions that are both highly connected and highly central. Recent analyses have shown that these putative hub regions are mutually and densely interconnected, forming a "rich club" within the human brain. Here we show that the set of pathways linking rich club regions forms a central high-cost, high-capacity backbone for global brain communication. Diffusion tensor imaging (DTI) data of two sets of 40 healthy subjects were used to map structural brain networks. The contributions to network cost and communication capacity of global cortico-cortical connections were assessed through measures of their topology and spatial embedding. Rich club connections were found to be more costly than predicted by their density alone and accounted for 40% of the total communication cost. Furthermore, 69% of all minimally short paths between node pairs were found to travel through the rich club and a large proportion of these communication paths consisted of ordered sequences of edges ("path motifs") that first fed into, then traversed, and finally exited the rich club, while passing through nodes of increasing and then decreasing degree. The prevalence of short paths that follow such ordered degree sequences suggests that neural communication might take advantage of strategies for dynamic routing of information between brain regions, with an important role for a highly central rich club. Taken together, our results show that rich club connections make an important contribution to interregional signal traffic, forming a central high-cost, high-capacity backbone for global brain communication.

Computational modeling of epilepsy for an experimental neurologist

Computational modeling can be a powerful tool for an experimentalist, providing a rigorous mathematical model of the system you are studying. This can be valuable in testing your hypotheses and developing experimental protocols prior to experimenting. This paper reviews models of seizures and epilepsy at different scales, including cellular, network, cortical region, and brain scales by looking at how they have been used in conjunction with experimental data. At each scale, models with different levels of abstraction, the extraction of physiological detail, are presented. Varying levels of detail are necessary in different situations. Physiologically realistic models are valuable surrogates for experimental systems because, unlike in an experiment, every parameter can be changed and every variable can be observed. Abstract models are useful in determining essential parameters of a system, allowing the experimentalist to extract principles that explain the relationship between mechanisms and the behavior of the system. Modeling is becoming easier with the emergence of platforms dedicated to neuronal modeling and databases of models that can be downloaded. Modeling will never be a replacement for animal and clinical experiments, but it should be a starting point in designing experiments and understanding their results.