Extracting the hierarchical organization of complex systems

Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract the hierarchical organization of complex biological, social, and technological networks. We define an ensemble of hierarchically nested random graphs, which we use to validate the method. We then apply our method to real-world networks, including the air-transportation network, an electronic circuit, an email exchange network, and metabolic networks. We find that our method enables us to obtain an accurate multi-scale descriptions of a complex system.Comment: Figures in screen resolution. Version with full resolution figures available at http://amaral.chem-eng.northwestern.edu/Publications/Papers/sales-pardo-2007.pd

Mesoscopic structure conditions the emergence of cooperation on social networks

We study the evolutionary Prisoner's Dilemma on two social networks obtained from actual relational data. We find very different cooperation levels on each of them that can not be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding perfect agreement with the observations in the real networks. Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.Comment: Largely improved version, includes an artificial network model that fully confirms the explanation of the results in terms of inter- and intra-community structur

Bayesian modeling of recombination events in bacterial populations

Background: We consider the discovery of recombinant segments jointly with their origins within multilocus DNA sequences from bacteria representing heterogeneous populations of fairly closely related species. The currently available methods for recombination detection capable of probabilistic characterization of uncertainty have a limited applicability in practice as the number of strains in a data set increases. Results: We introduce a Bayesian spatial structural model representing the continuum of origins over sites within the observed sequences, including a probabilistic characterization of uncertainty related to the origin of any particular site. To enable a statistically accurate and practically feasible approach to the analysis of large-scale data sets representing a single genus, we have developed a novel software tool (BRAT, Bayesian Recombination Tracker) implementing the model and the corresponding learning algorithm, which is capable of identifying the posterior optimal structure and to estimate the marginal posterior probabilities of putative origins over the sites. Conclusion: A multitude of challenging simulation scenarios and an analysis of real data from seven housekeeping genes of 120 strains of genus Burkholderia are used to illustrate the possibilities offered by our approach. The software is freely available for download at URL http://web.abo.fi/fak/ mnf//mate/jc/software/brat.html

Mesoscopic organization reveals the constraints governing C. elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.Comment: Published version, Minor modifications, 16 pages, 9 figure

Functional cartography of complex metabolic networks

High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that one can (i) find functional modules in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a ``cartographic representation'' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability. We use our method to analyze the metabolic networks of twelve organisms from three different super-kingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that low-degree metabolites that connect different modules are more conserved than hubs whose links are mostly within a single module.Comment: 17 pages, 4 figures. Go to http://amaral.northwestern.edu for the PDF file of the reprin

Drosophila Neurotrophins Reveal a Common Mechanism for Nervous System Formation

Neurotrophic interactions occur in Drosophila, but to date, no neurotrophic factor had been found. Neurotrophins are the main vertebrate secreted signalling molecules that link nervous system structure and function: they regulate neuronal survival, targeting, synaptic plasticity, memory and cognition. We have identified a neurotrophic factor in flies, Drosophila Neurotrophin (DNT1), structurally related to all known neurotrophins and highly conserved in insects.By investigating with genetics the consequences of removing DNT1 or adding it in excess, we show that DNT1 maintains neuronal survival, as more neurons die in DNT1 mutants and expression of DNT1 rescues naturally occurring cell death, and it enables targeting by motor neurons. We show that Spa¨ tzle and a further fly neurotrophin superfamily member, DNT2, also have neurotrophic functions in flies. Our findings imply that most likely a neurotrophin was present in the common ancestor of all bilateral organisms, giving rise to invertebrate and vertebrate neurotrophins through gene or whole-genome duplications. This work provides a missing link between aspects of neuronal function in flies and vertebrates, and it opens the opportunity to use Drosophila to investigate further aspects of neurotrophin function and to model related diseases

Neurocognitive function in HIV infected patients on antiretroviral therapy

OBJECTIVE To describe factors associated with neurocognitive (NC) function in HIV-positive patients on stable combination antiretroviral therapy. DESIGN We undertook a cross-sectional analysis assessing NC data obtained at baseline in patients entering the Protease-Inhibitor-Monotherapy-Versus-Ongoing-Triple therapy (PIVOT) trial. MAIN OUTCOME MEASURE NC testing comprised of 5 domains. Raw results were z-transformed using standard and demographically adjusted normative datasets (ND). Global z-scores (NPZ-5) were derived from averaging the 5 domains and percentage of subjects with test scores >1 standard deviation (SD) below population means in at least two domains (abnormal Frascati score) calculated. Patient characteristics associated with NC results were assessed using multivariable linear regression. RESULTS Of the 587 patients in PIVOT, 557 had full NC results and were included. 77% were male, 68% Caucasian and 28% of Black ethnicity. Mean (SD) baseline and nadir CD4+ lymphocyte counts were 553(217) and 177(117) cells/µL, respectively, and HIV RNA was <50 copies/mL in all. Median (IQR) NPZ-5 score was -0.5 (-1.2/-0) overall, and -0.3 (-0.7/0.1) and -1.4 (-2/-0.8) in subjects of Caucasian and Black ethnicity, respectively. Abnormal Frascati scores using the standard-ND were observed in 51%, 38%, and 81%, respectively, of subjects overall, Caucasian and Black ethnicity (p<0.001), but in 62% and 69% of Caucasian and Black subjects using demographically adjusted-ND (p = 0.20). In the multivariate analysis, only Black ethnicity was associated with poorer NPZ-5 scores (P<0.001). CONCLUSIONS In this large group of HIV-infected subjects with viral load suppression, ethnicity but not HIV-disease factors is closely associated with NC results. The prevalence of abnormal results is highly dependent on control datasets utilised. TRIAL REGISTRY ClinicalTrials.gov, NCT01230580

Wisdom of groups promotes cooperation in evolutionary social dilemmas

Whether or not to change strategy depends not only on the personal success of each individual, but also on the success of others. Using this as motivation, we study the evolution of cooperation in games that describe social dilemmas, where the propensity to adopt a different strategy depends both on individual fitness as well as on the strategies of neighbors. Regardless of whether the evolutionary process is governed by pairwise or group interactions, we show that plugging into the "wisdom of groups" strongly promotes cooperative behavior. The more the wider knowledge is taken into account the more the evolution of defectors is impaired. We explain this by revealing a dynamically decelerated invasion process, by means of which interfaces separating different domains remain smooth and defectors therefore become unable to efficiently invade cooperators. This in turn invigorates spatial reciprocity and establishes decentralized decision making as very beneficial for resolving social dilemmas.Comment: 8 two-column pages, 7 figures; accepted for publication in Scientific Report