Inferring effective computational connectivity using incrementally conditioned multivariate transfer entropy

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Maximized directed information transfer in critical neuronal networks

Critical dynamics in complex systems emerge at the transition from random to ordered dynamics and are characterized by power-law distributions of spatial and temporal properties of system events. The occurrence of critical dynamics in neuronal networks is increasingly supported by multielectrode array recordings of spontaneous activity in organotypic cortical slice cultures [1]. System events in these neuronal networks are typically defined as activations of neuronal ensembles, or “neuronal avalanches”. Interestingly, studies associate critical neuronal network avalanche dynamics with optimized information transfer [1, 2]. However, studies have not previously examined the directed nature of information transfer in these networks. Here, we present three novel transfer-entropy [3] based measures of directed information transfer between neuronal avalanches. Our measures compute the amount of predictive information present in avalanches properties (avalanche size, avalanche duration and inter-avalanche period) of the source region about avalanche properties of the destination region and are suitable for detecting information transfer at multiple spatial scales, from individual neurons to neuronal ensembles. We apply these measures to compute directed information transfer in large, sparse, modular networks of leaky integrate-and-fire neurons with spike timing-dependent synaptic plasticity and axonal conduction delays. We characterize dynamics in our networks by distributions of neuronal avalanches and assess these distributions for power-law scaling. We compute directed information transfer between two halves of eac

Wiring cost and topological participation of the mouse brain connectome.

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of "wiring cost" explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.Funding was provided by a NARSAD Young Investigator award and Isaac Newton Trust (to M.R.); a Rubicon Fellowship (to R.J.F.Y.); the Medical Research Council and the Wellcome Trust (Behavioural & Clinical Neuroscience Institute); and the National Institute for Health Research Cambridge Biomedical Research Centre (high-performance computing facilities).This is the accepted manuscript of a paper published in the Proceedings of the National Academy of Sciences (Rubinov M, Ypma RJF, Watson C, Bullmore ET, PNAS, 2015, 112, 10032-10037, doi:10.1073/pnas.1420315112). The final version is available at http://dx.doi.org/10.1073/pnas.142031511

A unifying framework for measuring weighted rich clubs.

Network analysis can help uncover meaningful regularities in the organization of complex systems. Among these, rich clubs are a functionally important property of a variety of social, technological and biological networks. Rich clubs emerge when nodes that are somehow prominent or 'rich' (e.g., highly connected) interact preferentially with one another. The identification of rich clubs is non-trivial, especially in weighted networks, and to this end multiple distinct metrics have been proposed. Here we describe a unifying framework for detecting rich clubs which intuitively generalizes various metrics into a single integrated method. This generalization rests upon the explicit incorporation of randomized control networks into the measurement process. We apply this framework to real-life examples, and show that, depending on the selection of randomized controls, different kinds of rich-club structures can be detected, such as topological and weighted rich clubs.J.A. is supported by the NIH-Oxford-Cambridge Scholarship Program. P.P. is employed by Queen Mary University of London. M.R. is supported by the NARSAD Young Investigator and Isaac Newton Trust grants. E.T.B. is employed half-time by the University of Cambridge, UK, and half-time by GlaxoSmithKline (GSK). P.E.V. is supported by the Medical Research Council (grant number MR/K020706/1).This is the final version of the article. It first appeared from NPG via http://dx.doi.org/10.1038/srep0725

Degree Distribution of Human Brain Functional Connectivity is Generalized Pareto: A Multi-Scale Analysis

Are degree distributions of human brain functional connectivity networks heavy-tailed? Initial claims based on least-square fitting suggested that brain functional connectivity networks obey power law scaling in their degree distributions. This interpretation has been challenged on methodological grounds. Subsequently, estimators based on maximum-likelihood and non-parametric tests involving surrogate data have been proposed. No clear consensus has emerged as results especially depended on data resolution. To identify the underlying topological distribution of brain functional connectivity calls for a closer examination of the relationship between resolution and statistics of model fitting. In this study, we analyze high-resolution functional magnetic resonance imaging (fMRI) data from the Human Connectome Project to assess its degree distribution across resolutions. We consider resolutions from one thousand to eighty thousand regions of interest (ROIs) and test whether they follow a heavy or short-tailed distribution. We analyze power law, exponential, truncated power law, log-normal, Weibull and generalized Pareto probability distributions. Notably, the Generalized Pareto distribution is of particular interest since it interpolates between heavy-tailed and short-tailed distributions, and it provides a handle on estimating the tail's heaviness or shortness directly from the data. Our results show that the statistics support the short-tailed limit of the generalized Pareto distribution, rather than a power law or any other heavy-tailed distribution. Working across resolutions of the data and performing cross-model comparisons, we further establish the overall robustness of the generalized Pareto model in explaining the data. Moreover, we account for earlier ambiguities by showing that down-sampling the data systematically affects statistical results. At lower resolutions models cannot easily be differentiated on statistical grounds while their plausibility consistently increases up to an upper bound. Indeed, more power law distributions are reported at low resolutions (5K) than at higher ones (50K or 80K). However, we show that these positive identifications at low resolutions fail cross-model comparisons and that down-sampling data introduces the risk of detecting spurious heavy-tailed distributions. This dependence of the statistics of degree distributions on sampling resolution has broader implications for neuroinformatic methodology, especially, when several analyses rely on down-sampled data, for instance, due to a choice of anatomical parcellations or measurement technique. Our findings that node degrees of human brain functional networks follow a short-tailed distribution have important implications for claims of brain organization and function. Our findings do not support common simplistic representations of the brain as a generic complex system with optimally efficient architecture and function, modeled with simple growth mechanisms. Instead these findings reflect a more nuanced picture of a biological system that has been shaped by longstanding and pervasive developmental and architectural constraints, including wiring-cost constraints on the centrality architecture of individual nodes

State and Trait Components of Functional Connectivity: Individual Differences Vary with Mental State.

Resting-state functional connectivity, as measured by functional magnetic resonance imaging (fMRI), is often treated as a trait, used, for example, to draw inferences about individual differences in cognitive function, or differences between healthy or diseased populations. However, functional connectivity can also depend on the individual's mental state. In the present study, we examined the relative contribution of state and trait components in shaping an individual's functional architecture. We used fMRI data from a large, population-based human sample (N = 587, age 18-88 years), as part of the Cambridge Centre for Aging and Neuroscience (Cam-CAN), which were collected in three mental states: resting, performing a sensorimotor task, and watching a movie. Whereas previous studies have shown commonalities across mental states in the average functional connectivity across individuals, we focused on the effects of states on the pattern of individual differences in functional connectivity. We found that state effects were as important as trait effects in shaping individual functional connectivity patterns, each explaining an approximately equal amount of variance. This was true when we looked at aging, as one specific dimension of individual differences, as well as when we looked at generic aspects of individual variation. These results show that individual differences in functional connectivity consist of state-dependent aspects, as well as more stable, trait-like characteristics. Studying individual differences in functional connectivity across a wider range of mental states will therefore provide a more complete picture of the mechanisms underlying factors such as cognitive ability, aging, and disease. SIGNIFICANCE STATEMENT: The brain's functional architecture is remarkably similar across different individuals and across different mental states, which is why many studies use functional connectivity as a trait measure. Despite these trait-like aspects, functional connectivity varies over time and with changes in cognitive state. We measured connectivity in three different states to quantify the size of the trait-like component of functional connectivity, compared with the state-dependent component. Our results show that studying individual differences within one state (such as resting) uncovers only part of the relevant individual differences in brain function, and that the study of functional connectivity under multiple mental states is essential to disentangle connectivity differences that are transient versus those that represent more stable, trait-like characteristics of an individual

Regional expression of the MAPT gene is associated with loss of hubs in brain networks and cognitive impairment in Parkinson disease and progressive supranuclear palsy.

Abnormalities of tau protein are central to the pathogenesis of progressive supranuclear palsy, whereas haplotype variation of the tau gene MAPT influences the risk of Parkinson disease and Parkinson's disease dementia. We assessed whether regional MAPT expression might be associated with selective vulnerability of global brain networks to neurodegenerative pathology. Using task-free functional magnetic resonance imaging in progressive supranuclear palsy, Parkinson disease, and healthy subjects (n = 128), we examined functional brain networks and measured the connection strength between 471 gray matter regions. We obtained MAPT and SNCA microarray expression data in healthy subjects from the Allen brain atlas. Regional connectivity varied according to the normal expression of MAPT. The regional expression of MAPT correlated with the proportionate loss of regional connectivity in Parkinson's disease. Executive cognition was impaired in proportion to the loss of hub connectivity. These effects were not seen with SNCA, suggesting that alpha-synuclein pathology is not mediated through global network properties. The results establish a link between regional MAPT expression and selective vulnerability of functional brain networks to neurodegeneration.Medical Research Council (Grant IDs: G1100464, MR/K020706/1, G0700503), Wellcome Trust (Grant ID: 103838), National Institute for Health Research Cambridge Biomedical Research Centre, Beverley Sackler fellowship scheme, NARSAD Young Investigator Award, Isaac Newton TrustThis is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.neurobiolaging.2016.09.00

Default Mode Hypoconnectivity Underlies a Sex-Related Autism Spectrum.

BACKGROUND: Females and males differ significantly in the prevalence and presentation of autism spectrum conditions. One theory of this effect postulates that autistic traits lie on a sex-related continuum in the general population, and autism represents the extreme male end of this spectrum. This theory predicts that any feature of autism in males should 1) be present in autistic females, 2) differentiate between the sexes in the typical population, and 3) correlate with autistic traits. We tested these three predictions for default mode network (DMN) hypoconnectivity during the resting state, one of the most robustly found neurobiological differences in autism. METHODS: We analyzed a primary dataset of adolescents (N = 121, 12-18 years of age) containing a relatively large number of females and a replication multisite dataset including children, adolescents, and adults (N = 980, 6-58 years of age). We quantified the average connectivity between DMN regions and tested for group differences and correlation with behavioral performance using robust regression. RESULTS: We found significant differences in DMN intraconnectivity between female controls and females with autism (p = .001 in the primary dataset; p = .009 in the replication dataset), and between female controls and male controls (p = .036 in the primary dataset; p = .002 in the replication dataset). We also found a significant correlation between DMN intraconnectivity and performance on a mentalizing task (p = .001) in the primary dataset. CONCLUSIONS: Collectively, these findings provide the first evidence for DMN hypoconnectivity as a behaviorally relevant neuroimaging phenotype of the sex-related spectrum of autistic traits, of which autism represents the extreme case.The authors thank the participants and their families for their participation and the autism support organizations who assisted with recruitment. We thank colleagues at the Brain Mapping Unit for methodological discussions. The present analysis was funded by a Rubicon Fellowship from the Netherlands Organization for Scientific Research (RJFY), a NARSAD Young Investigator award (MR) and by the Isaac Newton Trust (MR). Data collection was funded by a Clinical Scientist Fellowship from the UK Medical Research Council (MRC) (G0701919) to MDS, imaging data acquired from the depressed adolescents was from the MR-IMPACT study funded by the Medical Research Council. NR was supported by the Cambridge Trust; LRC was supported by the Gates Cambridge Scholarship Trust; RH was supported by the MRC and the Innovative Medicines Initiative (IMI) during the period of this work. The study was conducted in association with the National Institute for Health Research (NIHR) Collaboration for Leadership in Applied Health Research and Care (CLAHRC) for Cambridgeshire, and Peterborough National Health Service (NHS) Foundation Trust. The Brain Mapping Unit (RJFY, RLM, NR, JS, ETB and MR) is part of the Behavioral & Clinical Neuroscience Institute, which is funded by the MRC and the Wellcome Trust. High performance computing facilities were supported by the NIHR Cambridge Biomedical Research Centre.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Elsevier