Network morphospace

Exploring the Influence of Neomorphic Gekkotan Paraphalanges on Limb Modularity and Integration

Digital specializations of geckos are widely associated with their climbing abilities. A recurring feature that has independently emerged within the sister families Gekkonidae and Phyllodactylidae is the presence of neomorphic paraphalanges (PPEs), usually paired, paraxial skeletal structures lying adjacent to interphalangeal and metapodial-phalangeal joints. The incorporation of PPEs into gekkotan autopodia has the potential to modify the modularity and integration of the ancestral limb pattern by affecting information flow among skeletal limb parts. Here we explore the influence of PPEs on limb organization using anatomical networks. We modeled the fore- and hindlimbs in species ancestrally devoid of PPEs (Iguana iguana and Gekko gecko) and paraphalanx-bearing species (Hemidactylus mabouia and Uroplatus fimbriatus). To further clarify the impact of PPEs we also expunged PPEs from paraphalanx-bearing network models. We found that PPEs significantly increase modularity, giving rise to tightly integrated sub-modules along the digits, suggesting functional specialization. Species-specific singularities also emerged, such as the trade-off between the presence of PPEs favoring modularity (along the proximodistal axis) and the interdigital webbing favoring integration (across the lateromedial axis) in the limbs of U. fimbriatus. The PPEs are characterized by low connectivity compared with other skeletal elements; nevertheless, this varies based on their specific location and seemingly reflects developmental constraints. Our results also highlight the importance of the fifth metatarsal in generating a shift in lepidosaurian hindlimb polarity that contrasts with the more symmetrical bauplan of tetrapods. Our findings support extensive modification of the autopodial system in association with the addition of the neomorphic and intriguing PPEs.

Angiosperm flowers reached their highest morphological diversity early in their evolutionary history

Flowers are the complex and highly diverse reproductive structures of angiosperms. Because of their role in sexual reproduction, the evolution of flowers is tightly linked to angiosperm speciation and diversification. Accordingly, the quantification of floral morphological diversity (disparity) among angiosperm subgroups and through time may give important insights into the evolutionary history of angiosperms as a whole. Based on a comprehensive dataset focusing on 30 characters describing floral structure across angiosperms, we used 1201 extant and 121 fossil flowers to measure floral disparity and explore patterns of floral evolution through time and across lineages. We found that angiosperms reached their highest floral disparity in the Early Cretaceous. However, decreasing disparity toward the present likely has not precluded the innovation of other complex traits at other morphological levels, which likely played a key role in the outstanding angiosperm species richness. Angiosperms occupy specific regions of the theoretical morphospace, indicating that only a portion of the possible floral trait combinations is observed in nature. The ANA grade, the magnoliids, and the early-eudicot grade occupy large areas of the morphospace (higher disparity), whereas nested groups occupy narrower regions (lower disparity).

Brain network communication: concepts, models and applications

Understanding communication and information processing in nervous systems is a central goal of neuroscience. Over the past two decades, advances in connectomics and network neuroscience have opened new avenues for investigating polysynaptic communication in complex brain networks. Recent work has brought into question the mainstay assumption that connectome signalling occurs exclusively via shortest paths, resulting in a sprawling constellation of alternative network communication models. This Review surveys the latest developments in models of brain network communication. We begin by drawing a conceptual link between the mathematics of graph theory and biological aspects of neural signalling such as transmission delays and metabolic cost. We organize key network communication models and measures into a taxonomy, aimed at helping researchers navigate the growing number of concepts and methods in the literature. The taxonomy highlights the pros, cons and interpretations of different conceptualizations of connectome signalling. We showcase the utility of network communication models as a flexible, interpretable and tractable framework to study brain function by reviewing prominent applications in basic, cognitive and clinical neurosciences. Finally, we provide recommendations to guide the future development, application and validation of network communication models.

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.

Multivariate information theory uncovers synergistic subsystems of the human cerebral cortex

One of the most well-established tools for modeling the brain is the functional connectivity network, which is constructed from pairs of interacting brain regions. While powerful, the network model is limited by the restriction that only pairwise dependencies are considered and potentially higher-order structures are missed. Here, we explore how multivariate information theory reveals higher-order dependencies in the human brain. We begin with a mathematical analysis of the O-information, showing analytically and numerically how it is related to previously established information theoretic measures of complexity. We then apply the O-information to brain data, showing that synergistic subsystems are widespread in the human brain. Highly synergistic subsystems typically sit between canonical functional networks, and may serve an integrative role. We then use simulated annealing to find maximally synergistic subsystems, finding that such systems typically comprise ≈10 brain regions, recruited from multiple canonical brain systems. Though ubiquitous, highly synergistic subsystems are invisible when considering pairwise functional connectivity, suggesting that higher-order dependencies form a kind of shadow structure that has been unrecognized by established network-based analyses. We assert that higher-order interactions in the brain represent an under-explored space that, accessible with tools of multivariate information theory, may offer novel scientific insights.

The Morphospace of Consciousness: Three Kinds of Complexity for Minds and Machines

In this perspective article, we show that a morphospace, based on information-theoretic measures, can be a useful construct for comparing biological agents with artificial intelligence (AI) systems. The axes of this space label three kinds of complexity: (i) autonomic, (ii) computational and (iii) social complexity. On this space, we map biological agents such as bacteria, bees, C. elegans, primates and humans; as well as AI technologies such as deep neural networks, multi-agent bots, social robots, Siri and Watson. A complexity-based conceptualization provides a useful framework for identifying defining features and classes of conscious and intelligent systems. Starting with cognitive and clinical metrics of consciousness that assess awareness and wakefulness, we ask how AI and synthetically engineered life-forms would measure on homologous metrics. We argue that awareness and wakefulness stem from computational and autonomic complexity. Furthermore, tapping insights from cognitive robotics, we examine the functional role of consciousness in the context of evolutionary games. This points to a third kind of complexity for describing consciousness, namely, social complexity. Based on these metrics, our morphospace suggests the possibility of additional types of consciousness other than biological; namely, synthetic, group-based and simulated. This space provides a common conceptual framework for comparing traits and highlighting design principles of minds and machines.

Socioconnectomics: Connectomics Should Be Extended to Societies to Better Understand Evolutionary Processes

Connectomics, which is the network study of connectomes or maps of the nervous system of an organism, should be applied and expanded to human and animal societies, resulting in the birth of the domain of socioconnectomics compared to neuroconnectomics. This new network study framework would open up new perspectives in evolutionary biology and add new elements to theories, such as the social and cultural brain hypotheses. Answering questions about network topology, specialization, and their connections with functionality at one level (i.e., neural or societal) may help in understanding the evolutionary trajectories of these patterns at the other level. Expanding connectomics to societies should be done in comparison and combination with multilevel network studies and the possibility of multiorganization selection processes. The study of neuroconnectomes and socioconnectomes in animals, from simpler to more advanced ones, could lead to a better understanding of social network evolution and the feedback between social complexity and brain complexity.

A connectomics-based taxonomy of mammals

Mammalian taxonomies are conventionally defined by morphological traits and genetics. How species differ in terms of neural circuits and whether inter-species differences in neural circuit organization conform to these taxonomies is unknown. The main obstacle to the comparison of neural architectures has been differences in network reconstruction techniques, yielding species-specific connectomes that are not directly comparable to one another. Here, we comprehensively chart connectome organization across the mammalian phylogenetic spectrum using a common reconstruction protocol. We analyse the mammalian MRI (MaMI) data set, a database that encompasses high-resolution ex vivo structural and diffusion MRI scans of 124 species across 12 taxonomic orders and 5 superorders, collected using a unified MRI protocol. We assess similarity between species connectomes using two methods: similarity of Laplacian eigenspectra and similarity of multiscale topological features. We find greater inter-species similarities among species within the same taxonomic order, suggesting that connectome organization reflects established taxonomic relationships defined by morphology and genetics. While all connectomes retain hallmark global features and relative proportions of connection classes, inter-species variation is driven by local regional connectivity profiles. By encoding connectomes into a common frame of reference, these findings establish a foundation for investigating how neural circuits change over phylogeny, forging a link from genes to circuits to behaviour.

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.

Multidimensional Assessment of Electroencephalography in the Neuromodulation of Disorders of Consciousness

In the present study, we aimed to elucidate changes in electroencephalography (EEG) metrics during recovery of consciousness and to identify possible clinical markers thereof. More specifically, in order to assess changes in multidimensional EEG metrics during neuromodulation, we performed repeated stimulation using a high-density transcranial direct current stimulation (HD-tDCS) protocol in 42 patients with disorders of consciousness (DOC). Coma Recovery Scale-Revised (CRS-R) scores and EEG metrics [brain network indicators, spectral energy, and normalized spatial complexity (NSC)] were obtained before as well as fourteen days after undergoing HD-tDCS stimulation. CRS-R scores increased in the responders (R +) group after HD-tDCS stimulation. The R + group also showed increased spectral energy in the alpha2 and beta1 bands, mainly at the frontal and parietal electrodes. Increased graphical metrics in the alpha1, alpha2, and beta1 bands combined with increased NSC in the beta2 band in the R + group suggested that improved consciousness was associated with a tendency toward stronger integration in the alpha1 band and greater isolation in the beta2 band. Following this, using NSC as a feature to predict responsiveness through machine learning, which yielded a prediction accuracy of 0.929, demonstrated that the NSC of the alpha and gamma bands at baseline successfully predicted improvement in consciousness. According to our findings reported herein, we conclude that neuromodulation of the posterior lobe can lead to an EEG response related to consciousness in DOC, and that the posterior cortex may be one of the key brain areas involved in the formation or maintenance of consciousness.

Competency in Navigating Arbitrary Spaces as an Invariant for Analyzing Cognition in Diverse Embodiments

One of the most salient features of life is its capacity to handle novelty and namely to thrive and adapt to new circumstances and changes in both the environment and internal components. An understanding of this capacity is central to several fields: the evolution of form and function, the design of effective strategies for biomedicine, and the creation of novel life forms via chimeric and bioengineering technologies. Here, we review instructive examples of living organisms solving diverse problems and propose competent navigation in arbitrary spaces as an invariant for thinking about the scaling of cognition during evolution. We argue that our innate capacity to recognize agency and intelligence in unfamiliar guises lags far behind our ability to detect it in familiar behavioral contexts. The multi-scale competency of life is essential to adaptive function, potentiating evolution and providing strategies for top-down control (not micromanagement) to address complex disease and injury. We propose an observer-focused viewpoint that is agnostic about scale and implementation, illustrating how evolution pivoted similar strategies to explore and exploit metabolic, transcriptional, morphological, and finally 3D motion spaces. By generalizing the concept of behavior, we gain novel perspectives on evolution, strategies for system-level biomedical interventions, and the construction of bioengineered intelligences. This framework is a first step toward relating to intelligence in highly unfamiliar embodiments, which will be essential for progress in artificial intelligence and regenerative medicine and for thriving in a world increasingly populated by synthetic, bio-robotic, and hybrid beings.

Null models in network neuroscience

Recent advances in imaging and tracing technology provide increasingly detailed reconstructions of brain connectomes. Concomitant analytic advances enable rigorous identification and quantification of functionally important features of brain network architecture. Null models are a flexible tool to statistically benchmark the presence or magnitude of features of interest, by selectively preserving specific architectural properties of brain networks while systematically randomizing others. Here we describe the logic, implementation and interpretation of null models of connectomes. We introduce randomization and generative approaches to constructing null networks, and outline a taxonomy of network methods for statistical inference. We highlight the spectrum of null models - from liberal models that control few network properties, to conservative models that recapitulate multiple properties of empirical networks - that allow us to operationalize and test detailed hypotheses about the structure and function of brain networks. We review emerging scenarios for the application of null models in network neuroscience, including for spatially embedded networks, annotated networks and correlation-derived networks. Finally, we consider the limits of null models, as well as outstanding questions for the field.

Evolution of Brains and Computers: The Roads Not Taken

When computers started to become a dominant part of technology around the 1950s, fundamental questions about reliable designs and robustness were of great relevance. Their development gave rise to the exploration of new questions, such as what made brains reliable (since neurons can die) and how computers could get inspiration from neural systems. In parallel, the first artificial neural networks came to life. Since then, the comparative view between brains and computers has been developed in new, sometimes unexpected directions. With the rise of deep learning and the development of connectomics, an evolutionary look at how both hardware and neural complexity have evolved or designed is required. In this paper, we argue that important similarities have resulted both from convergent evolution (the inevitable outcome of architectural constraints) and inspiration of hardware and software principles guided by toy pictures of neurobiology. Moreover, dissimilarities and gaps originate from the lack of major innovations that have paved the way to biological computing (including brains) that are completely absent within the artificial domain. As it occurs within synthetic biocomputation, we can also ask whether alternative minds can emerge from A.I. designs. Here, we take an evolutionary view of the problem and discuss the remarkable convergences between living and artificial designs and what are the pre-conditions to achieve artificial intelligence.

A consideration of brain networks modulating social behavior

A primary goal of the field of behavioral neuroendocrinology is to understand how the brain modulates complex behavior. Over the last 20 years we have proposed various brain networks to explain behavioral regulation, however, the parameters by which these networks are identified are often ill-defined and reflect our personal scientific biases based on our area of expertise. In this perspective article, I question our characterization of brain networks underlying behavior and their utility. Using the Social Behavior Network as a primary example, I outline issues with brain networks commonly discussed in the field of behavioral neuroendocrinology, argue that we reconsider how we identify brain networks underlying behavior, and urge the future use of analytical tools developed by the field of Network Neuroscience. With modern statistical/mathematical tools and state of the art technology for brain imaging, we can strive to minimize our bias and generate brain networks that may more accurately reflect how the brain produces behavior.

Efficient coding in the economics of human brain connectomics

In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and highly connected hubs remains sparse. The principle of efficient coding proposes that the brain transmits maximal information in a metabolically economical or compressed form to improve future behavior. To determine how structural connectivity supports efficient coding, we develop a theory specifying minimum rates of message transmission between brain regions to achieve an expected fidelity, and we test five predictions from the theory based on random walk communication dynamics. In doing so, we introduce the metric of compression efficiency, which quantifies the trade-off between lossy compression and transmission fidelity in structural networks. In a large sample of youth (n = 1,042; age 8-23 years), we analyze structural networks derived from diffusion-weighted imaging and metabolic expenditure operationalized using cerebral blood flow. We show that structural networks strike compression efficiency trade-offs consistent with theoretical predictions. We find that compression efficiency prioritizes fidelity with development, heightens when metabolic resources and myelination guide communication, explains advantages of hierarchical organization, links higher input fidelity to disproportionate areal expansion, and shows that hubs integrate information by lossy compression. Lastly, compression efficiency is predictive of behavior-beyond the conventional network efficiency metric-for cognitive domains including executive function, memory, complex reasoning, and social cognition. Our findings elucidate how macroscale connectivity supports efficient coding and serve to foreground communication processes that utilize random walk dynamics constrained by network connectivity.

A morphospace of functional configuration to assess configural breadth based on brain functional networks

The quantification of human brain functional (re)configurations across varying cognitive demands remains an unresolved topic. We propose that such functional configurations may be categorized into three different types: (a) network configural breadth, (b) task-to task transitional reconfiguration, and (c) within-task reconfiguration. Such functional reconfigurations are rather subtle at the whole-brain level. Hence, we propose a mesoscopic framework focused on functional networks (FNs) or communities to quantify functional (re)configurations. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, trapping efficiency (TE) and exit entropy (EE), which capture topology and integration of information within and between a reference set of FNs. We use this framework to quantify the network configural breadth across different tasks. We show that the metrics defining this morphospace can differentiate FNs, cognitive tasks, and subjects. We also show that network configural breadth significantly predicts behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence, and general intelligence. In essence, we put forth a framework to explore the cognitive space in a comprehensive manner, for each individual separately, and at different levels of granularity. This tool that can also quantify the FN reconfigurations that result from the brain switching between mental states.

Topological analysis of differential effects of ketamine and propofol anaesthesia on brain dynamics

Research has found that the vividness of conscious experience is related to brain dynamics. Despite both being anaesthetics, propofol and ketamine produce different subjective states: we explore the different effects of these two anaesthetics on the structure of dynamic attractors reconstructed from electrophysiological activity recorded from cerebral cortex of two macaques. We used two methods: the first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find that the awake condition generally had the 'richest' structure, visiting the most states, the presence of pronounced higher-order structures, and the least deterministic dynamics. By contrast, the propofol condition had the most dissimilar dynamics, transitioning to a more impoverished, constrained, low-structure regime. The ketamine condition, interestingly, seemed to combine aspects of both: while it was generally less complex than the awake condition, it remained well above propofol in almost all measures. These results provide deeper and more comprehensive insights than what is typically gained by using point-measures of complexity.

Cost-efficiency trade-offs of the human brain network revealed by a multiobjective evolutionary algorithm

It is widely believed that the formation of brain network architecture is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the questions of whether this trade-off exists in empirical human brain structural networks and, if so, how it takes effect are still not well understood. Here, we employed a multiobjective evolutionary algorithm to directly and quantitatively explore the cost-efficiency trade-off in human brain structural networks. Using this algorithm, we generated a population of synthetic networks with optimal but diverse cost-efficiency trade-offs. It was found that these synthetic networks could not only reproduce a large portion of connections in the empirical brain structural networks but also embed a resembling small-world organization. Moreover, the synthetic and empirical brain networks were found similar in terms of the spatial arrangement of hub regions and the modular structure, which are two important topological features widely assumed to be outcomes of cost-efficiency trade-offs. The synthetic networks had high robustness against random attacks as the empirical brain networks did. Additionally, we also revealed some differences between the synthetic networks and the empirical brain networks, including lower segregated processing capacity and weaker robustness against targeted attacks in the synthetic networks. These findings provide direct and quantitative evidence that the structure of human brain networks is indeed largely influenced by optimal cost-efficiency trade-offs. We also suggest that some additional factors (e.g., segregated processing capacity) might jointly determine the network organization with cost and efficiency.

A Connectomic Hypothesis for the Hominization of the Brain

Cognitive abilities of the human brain, including language, have expanded dramatically in the course of our recent evolution from nonhuman primates, despite only minor apparent changes at the gene level. The hypothesis we propose for this paradox relies upon fundamental features of human brain connectivity, which contribute to a characteristic anatomical, functional, and computational neural phenotype, offering a parsimonious framework for connectomic changes taking place upon the human-specific evolution of the genome. Many human connectomic features might be accounted for by substantially increased brain size within the global neural architecture of the primate brain, resulting in a larger number of neurons and areas and the sparsification, increased modularity, and laminar differentiation of cortical connections. The combination of these features with the developmental expansion of upper cortical layers, prolonged postnatal brain development, and multiplied nongenetic interactions with the physical, social, and cultural environment gives rise to categorically human-specific cognitive abilities including the recursivity of language. Thus, a small set of genetic regulatory events affecting quantitative gene expression may plausibly account for the origins of human brain connectivity and cognition.

Morphospace analysis leads to an evo-devo model of digit patterning

Biological forms occupy a constrained portion of theoretical morphospaces. Developmental models accounting for empirical morphospaces are necessary to achieve a better understanding of this phenomenon. We analyzed the phalangeal formulas (PFs) in lizards and relatives' hands by comparing them with a set of simulated PFs that compose a theoretical morphospace. We detected that: (1) the empirical morphospace is severely limited in size, (2) the PFs comply with two properties of phalangeal count per digit, namely the ordering rule (DI ≤ DII ≤ DIII ≤ DIV ≥ DV), and the contiguity relationship (neighbor digits differ on average in one phalanx), (3) the totality of the PFs can be categorized into four categories of hands aligned along a feasibility gradient. We also reconstructed the evolution of PFs and found a stepwise trajectory from the plesiomorphic PF towards reduced conditions. Finally, we propose a developmental model as the generative mechanism behind the PFs. It is consistent with the bulk of evidence managed and involves an ordered digit primordia initialization timed with periodic signals of joint formation coming from digit tips. Our approach is also useful to address the study of other meristic sequences in nature such as dental, floral, and branchial formulas.

Network topology of the marmoset connectome

The brain is a complex network of interconnected and interacting neuronal populations. Global efforts to understand the emergence of behavior and the effect of perturbations depend on accurate reconstruction of white matter pathways, both in humans and in model organisms. An emerging animal model for next-generation applied neuroscience is the common marmoset (Callithrix jacchus). A recent open respository of retrograde and anterograde tract tracing presents an opportunity to systematically study the network architecture of the marmoset brain (Marmoset Brain Architecture Project; http://www.marmosetbrain.org). Here we comprehensively chart the topological organization of the mesoscale marmoset cortico-cortical connectome. The network possesses multiple nonrandom attributes that promote a balance between segregation and integration, including near-minimal path length, multiscale community structure, a connective core, a unique motif composition, and multiple cavities. Altogether, these structural attributes suggest a link between network architecture and function. Our findings are consistent with previous reports across a range of species, scales, and reconstruction technologies, suggesting a small set of organizational principles universal across phylogeny. Collectively, these results provide a foundation for future anatomical, functional, and behavioral studies in this model organism.

Models of communication and control for brain networks: distinctions, convergence, and future outlook

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Fate of Duplicated Neural Structures

Statistical physics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under specific conditions, self-replicating and computationally complex patterns become favored, yielding life, cognition, and Darwinian evolution. Neurons and neural circuits sit at a crossroads between statistical physics, computation, and (through their role in cognition) natural selection. Can we establish a statistical physics of neural circuits? Such theory would tell what kinds of brains to expect under set energetic, evolutionary, and computational conditions. With this big picture in mind, we focus on the fate of duplicated neural circuits. We look at examples from central nervous systems, with stress on computational thresholds that might prompt this redundancy. We also study a naive cost-benefit balance for duplicated circuits implementing complex phenotypes. From this, we derive phase diagrams and (phase-like) transitions between single and duplicated circuits, which constrain evolutionary paths to complex cognition. Back to the big picture, similar phase diagrams and transitions might constrain I/O and internal connectivity patterns of neural circuits at large. The formalism of statistical physics seems to be a natural framework for this worthy line of research.

Altered inter-frequency dynamics of brain networks in disorder of consciousness

OBJECTIVE

Growing evidence have linked disorders of consciousness (DOC) with the changes in frequency-specific functional networks. However, the alteration of inter-frequency dynamics in brain networks remain largely unknown. In this study, we investigated the network integration and segregation across frequency bands in a multiplex network framework.

APPROACH

Resting-state EEG data were recorded and analysed from 19 patients in minimally conscious state, 35 patients in unresponsive wakefulness syndrome (UWS) and 23 healthy controls. Frequency-based multiplex (cross-frequency) networks were reconstructed by integrating the five frequency-specific networks. Multiplex graph metrics, named multiplex participation coefficient and multiplex clustering coefficient, were employed to assess the network topology of subjects with different levels of consciousness.

MAIN RESULTS

Results revealed DOC networks, compared to those of healthy controls, may work at a less optimal point (closer to complete disorder) with increased integration and decreased segregation considering inter-frequency dynamics. Both metrics show increased spatial and temporal variability with the consciousness levels. Moreover, significant correlation can be found between the alteration of cross-frequency networks in DOC patients and their behavioural performance at both local and global scales.

SIGNIFICANCE

These findings may contribute to the development of EEG network study and benefit our understanding of the processes of consciousness and their pathophysiology for DOC.

Characterization of network switching in disorder of consciousness at multiple time scales

OBJECTIVE

Recent works have shown that flexible information processing is closely related to the reconfiguration of human brain networks underlying brain functions. However, the role of network switching for consciousness is poorly explored and whether such transition can indicate the behavioral performance of patients with disorders of consciousness (DOC) remains unknown. Here, we investigate the relationship between the switching of brain networks (states) over time and the consciousness levels.

APPROACH

By applying multilayer network methods, we calculated time-resolved functional connectivity from source-level EEG data in different frequency bands. At various time scales, we explored how the human brain changes its community structure and traverses across defined network states (integrated and segregated states) in subjects with different consciousness levels.

MAIN RESULTS

Network switching in the human brain is decreased with increasing time scale opposite to that in random systems. Transitions of community assignment (denoted by flexibility) are negatively correlated with the consciousness levels (particularly in the alpha band) at short time scales. At long time scales, the opposite trend is found. Compared to healthy controls, patients show a new balance between dynamic segregation and integration, with decreased proportion and mean duration of segregated state (contrary to those of integrated state) at small scales.

SIGNIFICANCE

These findings may contribute to the development of EEG-based network analysis and shed new light on the pathological mechanisms of neurological disorders like DOC.

Evolving complexity: how tinkering shapes cells, software and ecological networks

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organization (more than the parts) that largely conditions most higher-level properties, which are not reducible to the properties of the individual parts. Can the topological organization of these webs provide some insight into their evolutionary origins? Both biological and artificial networks share some common architectural traits. They are often heterogeneous and sparse, and most exhibit different types of correlations, such as nestedness, modularity or hierarchical patterns. These properties have often been attributed to the selection of functionally meaningful traits. However, a proper formulation of generative network models suggests a rather different picture. Against the standard selection-optimization argument, some networks reveal the inevitable generation of complex patterns resulting from reuse and can be modelled using duplication-rewiring rules lacking functionality. These give rise to the observed heterogeneous, scale-free and modular architectures. Here, we examine the evidence for tinkering in cellular, technological and ecological webs and its impact in shaping their architecture. Our analysis suggests a serious consideration of the role played by selection as the origin of network topology. Instead, we suggest that the amplification processes associated with reuse might shape these graphs at the topological level. In biological systems, selection forces would take advantage of emergent patterns. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Emergence of Hierarchical Modularity in Evolving Networks Uncovered by Phylogenomic Analysis

Networks describe how parts associate with each other to form integrated systems which often have modular and hierarchical structure. In biology, network growth involves two processes, one that unifies and the other that diversifies. Here, we propose a biphasic (bow-tie) theory of module emergence. In the first phase, parts are at first weakly linked and associate variously. As they diversify, they compete with each other and are often selected for performance. The emerging interactions constrain their structure and associations. This causes parts to self-organize into modules with tight linkage. In the second phase, variants of the modules diversify and become new parts for a new generative cycle of higher level organization. The paradigm predicts the rise of hierarchical modularity in evolving networks at different timescales and complexity levels. Remarkably, phylogenomic analyses uncover this emergence in the rewiring of metabolomic and transcriptome-informed metabolic networks, the nanosecond dynamics of proteins, and evolving networks of metabolism, elementary functionomes, and protein domain organization.

Connection strength of the macaque connectome augments topological and functional network attributes

Mammalian brains constitute complex organized networks of neural projections. On top of their binary topological organization, the strength (or weight) of these neural projections can be highly variable across connections and is thus likely of additional importance to the overall topological and functional organization of the network. Here we investigated the specific distribution pattern of connection strength in the macaque connectome. We performed weighted and binary network analysis on the cortico-cortical connectivity of the macaque provided by the unique tract-tracing dataset of Markov and colleagues (2014) and observed in both analyses a small-world, modular and rich club organization. Moreover, connectivity strength showed a distribution augmenting the architecture identified in the binary network version by enhancing both local network clustering and the central infrastructure for global topological communication and integration. Functional consequences of this topological distribution were further examined using the Kuramoto model for simulating interactions between brain regions and showed that the connectivity strength distribution across connections enhances synchronization within modules and between rich club hubs. Together, our results suggest that neural pathway strength promotes topological properties in the macaque connectome for local processing and global network integration.

Evolutionary aspects of reservoir computing

Reservoir computing (RC) is a powerful computational paradigm that allows high versatility with cheap learning. While other artificial intelligence approaches need exhaustive resources to specify their inner workings, RC is based on a reservoir with highly nonlinear dynamics that does not require a fine tuning of its parts. These dynamics project input signals into high-dimensional spaces, where training linear readouts to extract input features is vastly simplified. Thus, inexpensive learning provides very powerful tools for decision-making, controlling dynamical systems, classification, etc. RC also facilitates solving multiple tasks in parallel, resulting in a high throughput. Existing literature focuses on applications in artificial intelligence and neuroscience. We review this literature from an evolutionary perspective. RC's versatility makes it a great candidate to solve outstanding problems in biology, which raises relevant questions. Is RC as abundant in nature as its advantages should imply? Has it evolved? Once evolved, can it be easily sustained? Under what circumstances? (In other words, is RC an evolutionarily stable computing paradigm?) To tackle these issues, we introduce a conceptual morphospace that would map computational selective pressures that could select for or against RC and other computing paradigms. This guides a speculative discussion about the questions above and allows us to propose a solid research line that brings together computation and evolution with RC as test model of the proposed hypotheses. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Multicellular Systems Biology: Quantifying Cellular Patterning and Function in Plant Organs Using Network Science

Organ function is at least partially shaped and constrained by the organization of their constituent cells. Extensive investigation has revealed mechanisms explaining how these patterns are generated, with less being known about their functional relevance. In this paper, a methodology to discretize and quantitatively analyze cellular patterning is described. By performing global organ-scale cellular interaction mapping, the organization of cells can be extracted and analyzed using network science. This provides a means to take the developmental analysis of cellular organization in complex organisms beyond qualitative descriptions and provides data-driven approaches to inferring cellular function. The bridging of a structure-function relationship in hypocotyl epidermal cell patterning through global topological analysis provides support for this approach. The analysis of cellular topologies from patterning mutants further enables the contribution of gene activity toward the organizational properties of tissues to be linked, bridging molecular and tissue scales. This systems-based approach to investigate multicellular complexity paves the way to uncovering the principles of complex organ design and achieving predictive genotype-phenotype mapping.

Spatiotemporal ontogeny of brain wiring

The wiring of vertebrate and invertebrate brains provides the anatomical skeleton for cognition and behavior. Connections among brain regions are characterized by heterogeneous strength that is parsimoniously described by the wiring cost and homophily principles. Moreover, brains exhibit a characteristic global network topology, including modules and hubs. However, the mechanisms resulting in the observed interregional wiring principles and network topology of brains are unknown. Here, with the aid of computational modeling, we demonstrate that a mechanism based on heterochronous and spatially ordered neurodevelopmental gradients, without the involvement of activity-dependent plasticity or axonal guidance cues, can reconstruct a large part of the wiring principles (on average, 83%) and global network topology (on average, 80%) of diverse adult brain connectomes, including fly and human connectomes. In sum, space and time are key components of a parsimonious, plausible neurodevelopmental mechanism of brain wiring with a potential universal scope, encompassing vertebrate and invertebrate brains.

Travel in city road networks follows similar transport trade-off principles to neural and plant arbors

Both engineered and biological transportation networks face trade-offs in their design. Network users desire to quickly get from one location in the network to another, whereas network planners need to minimize costs in building infrastructure. Here, we use the theory of Pareto optimality to study this design trade-off in the road networks of 101 cities, with wide-ranging population sizes, land areas and geographies. Using a simple one parameter trade-off function, we find that most cities lie near the Pareto front and are significantly closer to the front than expected by alternate design structures. To account for other optimization dimensions or constraints that may be important (e.g. traffic congestion, geography), we performed a higher-order Pareto optimality analysis and found that most cities analysed lie within a region of design space bounded by only four archetypal cities. The trade-offs studied here are also faced and well-optimized by two biological transport networks-neural arbors in the brain and branching architectures of plant shoots-suggesting similar design principles across some biological and engineered transport systems.

Rich-club neurocircuitry: function, evolution, and vulnerability

Over the past decades, network neuroscience has played a fundamental role in the understanding of large-scale brain connectivity architecture. Brains, and more generally nervous systems, can be modeled as sets of elements (neurons, assemblies, or cortical chunks) that dynamically interact through a highly structured and adaptive neurocircuitry. An interesting property of neural networks is that elements rich in connections are central to the network organization and tend to interconnect strongly with each other, forming so-called rich clubs. The ubiquity of rich-club organization across different species and scales of investigation suggests that this topology could be a distinctive feature of biological systems with information processing capabilities. This review surveys recent neuroimaging, computational, and cross-species comparative literature to offer an insight into the function and origin of rich-club architecture in nervous systems, discussing its relevance to human cognition and behavior, and vulnerability to brain disorders.

The morphospace of language networks

What is the nature of language? How has it evolved in different species? Are there qualitative, well-defined classes of languages? Most studies of language evolution deal in a way or another with such theoretical contraption and explore the outcome of diverse forms of selection on the communication matrix that somewhat optimizes communication. This framework naturally introduces networks mediating the communicating agents, but no systematic analysis of the underlying landscape of possible language graphs has been developed. Here we present a detailed analysis of network properties on a generic model of a communication code, which reveals a rather complex and heterogeneous morphospace of language graphs. Additionally, we use curated data of English words to locate and evaluate real languages within this morphospace. Our findings indicate a surprisingly simple structure in human language unless particles with the ability of naming any other concept are introduced in the vocabulary. These results refine and for the first time complement with empirical data a lasting theoretical tradition around the framework of least effort language.

Low-dimensional morphospace of topological motifs in human fMRI brain networks

We present a low-dimensional morphospace of fMRI brain networks, where axes are defined in a data-driven manner based on the network motifs. The morphospace allows us to identify the key variations in healthy fMRI networks in terms of their underlying motifs, and we observe that two principal components (PCs) can account for 97% of the motif variability. The first PC of the motif distribution is correlated with efficiency and inversely correlated with transitivity. Hence this axis approximately conforms to the well-known economical small-world trade-off between integration and segregation in brain networks. Finally, we show that the economical clustering generative model proposed by Vértes et al. (2012) can approximately reproduce the motif morphospace of the real fMRI brain networks, in contrast to other generative models. Overall, the motif morphospace provides a powerful way to visualize the relationships between network properties and to investigate generative or constraining factors in the formation of complex human brain functional networks.

Rich-club neurocircuitry: function, evolution, and vulnerability

Over the past decades, network neuroscience has played a fundamental role in the understanding of large-scale brain connectivity architecture. Brains, and more generally nervous systems, can be modeled as sets of elements (neurons, assemblies, or cortical chunks) that dynamically interact through a highly structured and adaptive neurocircuitry. An interesting property of neural networks is that elements rich in connections are central to the network organization and tend to interconnect strongly with each other, forming so-called rich clubs. The ubiquity of rich-club organization across different species and scales of investigation suggests that this topology could be a distinctive feature of biological systems with information processing capabilities. This review surveys recent neuroimaging, computational, and cross-species comparative literature to offer an insight into the function and origin of rich-club architecture in nervous systems, discussing its relevance to human cognition and behavior, and vulnerability to brain disorders.

The topology of evolutionary novelty and innovation in macroevolution

Sewall Wright's fitness landscape introduced the concept of evolutionary spaces in 1932. George Gaylord Simpson modified this to an adaptive, phenotypic landscape in 1944 and since then evolutionary spaces have played an important role in evolutionary theory through fitness and adaptive landscapes, phenotypic and functional trait spaces, morphospaces and related concepts. Although the topology of such spaces is highly variable, from locally Euclidean to pre-topological, evolutionary change has often been interpreted as a search through a pre-existing space of possibilities, with novelty arising by accessing previously inaccessible or difficult to reach regions of a space. Here I discuss the nature of evolutionary novelty and innovation within the context of evolutionary spaces, and argue that the primacy of search as a conceptual metaphor ignores the generation of new spaces as well as other changes that have played important evolutionary roles.This article is part of the themed issue 'Process and pattern in innovations from cells to societies'.

Generic assembly patterns in complex ecological communities

The study of ecological communities often involves detailed simulations of complex networks. However, our empirical knowledge of these networks is typically incomplete and the space of simulation models and parameters is vast, leaving room for uncertainty in theoretical predictions. Here we show that a large fraction of this space of possibilities exhibits generic behaviors that are robust to modeling choices. We consider a wide array of model features, including interaction types and community structures, known to generate different dynamics for a few species. We combine these features in large simulated communities, and show that equilibrium diversity, functioning, and stability can be predicted analytically using a random model parameterized by a few statistical properties of the community. We give an ecological interpretation of this "disordered" limit where structure fails to emerge from complexity. We also demonstrate that some well-studied interaction patterns remain relevant in large ecosystems, but their impact can be encapsulated in a minimal number of additional parameters. Our approach provides a powerful framework for predicting the outcomes of ecosystem assembly and quantifying the added value of more detailed models and measurements.

Diversity of meso-scale architecture in human and non-human connectomes

Brain function is reflected in connectome community structure. The dominant view is that communities are assortative and segregated from one another, supporting specialized information processing. However, this view precludes the possibility of non-assortative communities whose complex inter-community interactions could engender a richer functional repertoire. We use weighted stochastic blockmodels to uncover the meso-scale architecture of Drosophila, mouse, rat, macaque, and human connectomes. We find that most communities are assortative, though others form core-periphery and disassortative structures, which better recapitulate observed patterns of functional connectivity and gene co-expression in human and mouse connectomes compared to standard community detection techniques. We define measures for quantifying the diversity of communities in which brain regions participate, showing that this measure is peaked in control and subcortical systems in humans, and that inter-individual differences are correlated with cognitive performance. Our report paints a more diverse portrait of connectome communities and demonstrates their cognitive relevance.

Topological analysis of multicellular complexity in the plant hypocotyl

Multicellularity arose as a result of adaptive advantages conferred to complex cellular assemblies. The arrangement of cells within organs endows higher-order functionality through a structure-function relationship, though the organizational properties of these multicellular configurations remain poorly understood. We investigated the topological properties of complex organ architecture by digitally capturing global cellular interactions in the plant embryonic stem (hypocotyl), and analyzing these using quantitative network analysis. This revealed the presence of coherent conduits of reduced path length across epidermal atrichoblast cell files. The preferential movement of small molecules along this cell type was demonstrated using fluorescence transport assays. Both robustness and plasticity in this higher order property of atrichoblast patterning was observed across diverse genetic backgrounds, and the analysis of genetic patterning mutants identified the contribution of gene activity towards their construction. This topological analysis of multicellular structural organization reveals higher order functions for patterning and principles of complex organ construction.

Network neuroscience

Despite substantial recent progress, our understanding of the principles and mechanisms underlying complex brain function and cognition remains incomplete. Network neuroscience proposes to tackle these enduring challenges. Approaching brain structure and function from an explicitly integrative perspective, network neuroscience pursues new ways to map, record, analyze and model the elements and interactions of neurobiological systems. Two parallel trends drive the approach: the availability of new empirical tools to create comprehensive maps and record dynamic patterns among molecules, neurons, brain areas and social systems; and the theoretical framework and computational tools of modern network science. The convergence of empirical and computational advances opens new frontiers of scientific inquiry, including network dynamics, manipulation and control of brain networks, and integration of network processes across spatiotemporal domains. We review emerging trends in network neuroscience and attempt to chart a path toward a better understanding of the brain as a multiscale networked system.

Micro-connectomics: probing the organization of neuronal networks at the cellular scale

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.

Constraints and spandrels of interareal connectomes

Interareal connectomes are whole-brain wiring diagrams of white-matter pathways. Recent studies have identified modules, hubs, module hierarchies and rich clubs as structural hallmarks of these wiring diagrams. An influential current theory postulates that connectome modules are adequately explained by evolutionary pressures for wiring economy, but that the other hallmarks are not explained by such pressures and are therefore less trivial. Here, we use constraint network models to test these postulates in current gold-standard vertebrate and invertebrate interareal-connectome reconstructions. We show that empirical wiring-cost constraints inadequately explain connectome module organization, and that simultaneous module and hub constraints induce the structural byproducts of hierarchies and rich clubs. These byproducts, known as spandrels in evolutionary biology, include the structural substrate of the default-mode network. Our results imply that currently standard connectome characterizations are based on circular analyses or double dipping, and we emphasize an integrative approach to future connectome analyses for avoiding such pitfalls.

Whole-brain networks of long-range neuronal pathways are characterized by interdependencies between structural features. Here the author shows that module hierarchy and rich club features in these networks are structural byproducts (spandrels) of module and hub constraints, but not of wiring-cost constraints.

Topological and geometric measurements of force-chain structure

Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.

A morphospace for synthetic organs and organoids: the possible and the actual

Efforts in evolutionary developmental biology have shed light on how organs are developed and why evolution has selected some structures instead of others. These advances in the understanding of organogenesis along with the most recent techniques of organotypic cultures, tissue bioprinting and synthetic biology provide the tools to hack the physical and genetic constraints in organ development, thus opening new avenues for research in the form of completely designed or merely altered settings. Here we propose a unifying framework that connects the concept of morphospace (i.e. the space of possible structures) with synthetic biology and tissue engineering. We aim for a synthesis that incorporates our understanding of both evolutionary and architectural constraints and can be used as a guide for exploring alternative design principles to build artificial organs and organoids. We present a three-dimensional morphospace incorporating three key features associated to organ and organoid complexity. The axes of this space include the degree of complexity introduced by developmental mechanisms required to build the structure, its potential to store and react to information and the underlying physical state. We suggest that a large fraction of this space is empty, and that the void might offer clues for alternative ways of designing and even inventing new organs.

Single-subject morphological brain networks: connectivity mapping, topological characterization and test-retest reliability

INTRODUCTION

Structural MRI has long been used to characterize local morphological features of the human brain. Coordination patterns of the local morphological features among regions, however, are not well understood. Here, we constructed individual-level morphological brain networks and systematically examined their topological organization and long-term test-retest reliability under different analytical schemes of spatial smoothing, brain parcellation, and network type.

METHODS

This study included 57 healthy participants and all participants completed two MRI scan sessions. Individual morphological brain networks were constructed by estimating interregional similarity in the distribution of regional gray matter volume in terms of the Kullback-Leibler divergence measure. Graph-based global and nodal network measures were then calculated, followed by the statistical comparison and intra-class correlation analysis.

RESULTS

The morphological brain networks were highly reproducible between sessions with significantly larger similarities for interhemispheric connections linking bilaterally homotopic regions. Further graph-based analyses revealed that the morphological brain networks exhibited nonrandom topological organization of small-worldness, high parallel efficiency and modular architecture regardless of the analytical choices of spatial smoothing, brain parcellation and network type. Moreover, several paralimbic and association regions were consistently revealed to be potential hubs. Nonetheless, the three studied factors particularly spatial smoothing significantly affected quantitative characterization of morphological brain networks. Further examination of long-term reliability revealed that all the examined network topological properties showed fair to excellent reliability irrespective of the analytical strategies, but performing spatial smoothing significantly improved reliability. Interestingly, nodal centralities were positively correlated with their reliabilities, and nodal degree and efficiency outperformed nodal betweenness with respect to reliability.

CONCLUSIONS

Our findings support single-subject morphological network analysis as a meaningful and reliable method to characterize structural organization of the human brain; this method thus opens a new avenue toward understanding the substrate of intersubject variability in behavior and function and establishing morphological network biomarkers in brain disorders.