Barabasi

N. Dehmamy, S. Milanlouei, A.-L. Barabasi

A structural transition in physical networks

Nature 563, 676-680 (2018)

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In many physical networks, including neurons in the brain, three-dimensional integrated circuits and underground hyphal networks, the nodes and links are physical objects that cannot intersect or overlap with each other. To take this into account, non-crossing conditions can be imposed to constrain the geometry of networks, which consequently affects how they form, evolve and function. However, these constraints are not included in the theoretical frameworks that are currently used to characterize real networks. Most tools for laying out networks are variants of the force-directed layout algorithm—which assumes dimensionless nodes and links—and are therefore unable to reveal the geometry of densely packed physical networks. Here we develop a modelling framework that accounts for the physical sizes of nodes and links, allowing us to explore how non-crossing conditions affect the geometry of a network. For small link thicknesses, we observe a weakly interacting regime in which link crossings are avoided via local link rearrangements, without altering the overall geometry of the layout compared to the force-directed layout. Once the link thickness exceeds a threshold, a strongly interacting regime emerges in which multiple geometric quantities, such as the total link length and the link curvature, scale with the link thickness. We show that the crossover between the two regimes is driven by the non-crossing condition, which allows us to derive the transition point analytically and show that networks with large numbers of nodes will ultimately exist in the strongly interacting regime. We also find that networks in the weakly interacting regime display a solid-like response to stress, whereas in the strongly interacting regime they behave in a gel-like fashion. Networks in the weakly interacting regime are amenable to 3D printing and so can be used to visualize network geometry, and the strongly interacting regime provides insights into the scaling of the sizes of densely packed mammalian brains.
Barabasi

E. Towlson, P. E. Vértes, G. Yan, Y. L. Chew, D. S. Walker, W. R. Schaefer, A.-L. Barabasi

Caenorhabditis elegans and the network control framework—FAQs

Phil. Trans. R. Soc. B 373: 20170372

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Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system’s inputs and outputs. One may therefore hypothesize that the brain’s wiring is predetermined by the need to maintain control across multiple scales, maintaining the stability of key internal variables, and producing behaviour in response to environmental cues. Recent advances in network control have offered a powerful mathematical framework to explore the structure – function relationship in complex biological, social and technological networks, and are beginning to yield important and precise insights on neuronal systems. The network control paradigm promises a predictive, quantitative framework to unite the distinct datasets necessary to fully describe a nervous system, and provide mechanistic explanations for the observed structure and function relationships. Here, we provide a thorough review of the network control framework as applied to Caenorhabditis elegans (Yan et al. 2017 Nature 550, 519 –523. (doi:10.1038/nature24056)), in the style of Frequently Asked Questions.We present the theoretical, computational and experimental aspects of network control, and discuss its current capabilities and limitations, together with the next likely advances and improvements. We further present the Python code to enable exploration of control principles in a manner specific to this prototypical organism. This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’
Barabasi

G. Yan, P. E. Vertes, E. K. Towlson, Y. L. Chew, D. S. Walker, W. R. Shafer, A.-L. Barabasi

Network Control Principles Predict Neuron Function in the Caenorhabditis elegans Connectome

Nature 550: 519-533 (2017)

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Recent studies on the controllability of complex systems offer a powerful mathematical framework to systematically explore the structure–function relationship in biological, social, and technological networks 1–3. Despite theoretical advances, we lack direct experimental proof of the validity of these widely used control principles. Here we fill this gap by applying a control framework to the connectome of the nematode Caenorhabditis elegans 4–6, allowing us to predict the involvement of each C. elegans neuron in locomotor behaviours. We predict that control of the muscles or motor neurons requires 12 neuronal classes, which include neuronal groups previously implicated in locomotion by laser ablation 7–13, as well as one previously uncharacterized neuron, PDB. We validate this prediction experimentally, finding that the blation of PDB leads to a significant loss of dorsoventral polarity in large body bends. Importantly, control principles also allow us to investigate the involvement of individual neurons within each neuronal class. For example, we predict that, within the class of DD motor neurons, only three (DD04, DD05, or DD06) should affect locomotion when ablated individually. This prediction is also confirmed; single cell ablations of DD04 or DD05 specifically affect posterior body movements, whereas ablations of DD02 or DD03 do not. Our predictions are robust to deletions of weak connections, missing connections, and rewired connections in the current connectome, indicating the potential applicability of this analytical framework to larger and less well-characterized connectomes.
Barabasi

J. Menche, E. Guney, A. Sharma, P. J. Branigan, M. J. Loza, F. Baribaud, R. Dobrin, A.-L. Barabasi

Integrating personalized gene expression profiles into predictive disease-associated gene pools

Systems Biology and Applications 3:10 (2017)

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Gene expression data are routinely used to identify genes that on average exhibit different expression levels between a case and a control group. Yet, very few of such differentially expressed genes are detectably perturbed in individual patients. Here, we develop a framework to construct personalized perturbation profiles for individual subjects, identifying the set of genes that are significantly perturbed in each individual. This allows us to characterize the heterogeneity of the molecular manifestations of complex diseases by quantifying the expression-level similarities and differences among patients with the same phenotype. We show that despite the high heterogeneity of the individual perturbation profiles, patients with asthma, Parkinson and Huntington’s disease share a broadpool of sporadically disease-associated genes, and that individuals with statistically signi ficant overlap with this pool have a 80–100% chance of being diagnosed with the disease. The developed framework opens up the possibility to apply gene expression data in the context of precision medicine, with important implications for biomarker identifi cation, drug development, diagnosis and treatment.
Barabasi

D. Gomez-Cabrero, J. Menche, C. Vargas, I. Cano, D. Maier, A.-L. Barabasi, J. Tegner, J. Roca (Synergy-COPD Consortia)

From Comorbidities of Chronic Obstructive Pulmonary Disease to Identification of Shared Molecular Mechanisms by Data Integration

BMC Bioinformatics 17: 1291 (2016)

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Background Deep mining of healthcare data has provided maps of comorbidity relationships between diseases. In parallel, integrative multi-omics investigations have generated high-resolution molecular maps of putative relevance for understanding disease initiation and progression. Yet, it is unclear how to advance an observation of comorbidity relations (one disease to others) to a molecular understanding of the driver processes and associated biomarkers. Results Since Chronic Obstructive Pulmonary disease (COPD) has emerged as a central hub in temporal comorbidity networks, we developed a systematic integrative data-driven framework to identify shared disease-associated genes and pathways, as a proxy for the underlying generative mechanisms inducing comorbidity. We integrated records from approximately 13 M patients from the Medicare database with disease-gene maps that we derived from several resources including a semantic-derived knowledge-base. Using rank-based statistics we not only recovered known comorbidities but also discovered a novel association between COPD and digestive diseases. Furthermore, our analysis provides the first set of COPD co-morbidity candidate biomarkers, including IL15, TNF and JUP, and characterizes their association to aging and life-style conditions, such as smoking and physical activity. Conclusions The developed framework provides novel insights in COPD and especially COPD co-morbidity associated mechanisms. The methodology could be used to discover and decipher the molecular underpinning of other comorbidity relationships and furthermore, allow the identification of candidate co-morbidity biomarkers.
Barabasi

M. Kitsak, A. Sharma, J. Menche, E. Guney, S. D. Ghiassian, J. Loscalzo, A.-L. Barabasi

Tissue Specificity of Human Disease Module

Scientific Reports 6: 35241 (2016)

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Genes carrying mutations associated with genetic diseases are present in all human cells; yet, clinical manifestations of genetic diseases are usually highly tissue-specific. Although some disease genes are expressed only in selected tissues, the expression patterns of disease genes alone cannot explain the observed tissue specificity of human diseases. Here we hypothesize that for a disease to manifest itself in a particular tissue, a whole functional subnetwork of genes (disease module) needs to be expressed in that tissue. Driven by this hypothesis, we conducted a systematic study of the expression patterns of disease genes within the human interactome. We find that genes expressed in a specific tissue tend to be localized in the same neighborhood of the interactome. By contrast, genes expressed in different tissues are segregated in distinct network neighborhoods. Most important, we show that it is the integrity and the completeness of the expression of the disease module that determines disease manifestation in selected tissues. This approach allows us to construct a disease-tissue network that confirms known and predicts unexpected disease-tissue associations.
Barabasi

G. Basler, Z. Nikoloski, A. Larhlimi, A.-L. Barabasi, and Y.-Y. Liu

Control of Fluxes in Metabolic Networks

Genome Research 7: 26, 956-968 (2016)

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Understanding the control of large-scale metabolic networks is central to biology and medicine. However, existing approaches either require specifying a cellular objective or can only be used for small networks. We introduce new coupling types describing the relations between reaction activities, and develop an efficient computational framework, which does not require any cellular objective for systematic studies of large-scale metabolism. We identify the driver reactions facilitating control of 23 metabolic networks from all kingdoms of life. We find that unicellular organisms require a smaller degree of control than multicellular organisms. Driver reactions are under complex cellular regulation in Escherichia coli, indicating their preeminent role in facilitating cellular control. In human cancer cells, driver reactions play pivotal roles in malignancy and represent potential therapeutic targets. The developed framework helps us gain insights into regulatory principles of diseases and facilitates design of engineering strategies at the interface of gene regulation, signaling, and metabolism.
Barabasi

S. D. Ghiassian, J. Menche, D. I. Chasman, F. Giulianini, R. Wang, P. Ricchiuto, M. Aikawa, H. Iwata, C. Muller, T. Zeller, A. Sharma, P. Wild, K. Lackner, S. Singh, P. M. Ridker, S. Blankenberg, A.-L. Barabasi, J. Loscalzo

Endophenotype Network Models: Common Core of Complex Diseases

Scientific Reports 6: 27414, 1-13 (2016)

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Historically, human diseases have been differentiated and categorized based on the organ system in which they primarily manifest. Recently, an alternative view is emerging that emphasizes that different diseases often have common underlying mechanisms and shared intermediate pathophenotypes, or endo(pheno)types. Within this framework, a specific disease’s expression is a consequence of the interplay between the relevant endophenotypes and their local, organ-based environment. Important examples of such endophenotypes are inflammation, fibrosis, and thrombosis and their essential roles in many developing diseases. In this study, we construct endophenotype network models and explore their relation to different diseases in general and to cardiovascular diseases in particular. We identify the local neighborhoods (module) within the interconnected map of molecular components, i.e., the subnetworks of the human interactome that represent the inflammasome, thrombosome, and fibrosome. We find that these neighborhoods are highly overlapping and significantly enriched with disease-associated genes. In particular they are also enriched with differentially expressed genes linked to cardiovascular disease (risk). Finally, using proteomic data, we explore how macrophage activation contributes to our understanding of inflammatory processes and responses. The results of our analysis show that inflammatory responses initiate from within the cross-talk of the three identified endophenotypic modules.
Barabasi

A. Vinayagama, T.E. Gibsonb, H.-J. Lee, B. Yilmazeld, C. Roeseld, Y. Hua, Y. Kwona, A. Sharma, Y.-Y. Liu, N. Perrimona, A.-L. Barabasi

Controllability Analysis of the Directed Human Protein Interaction Network Identifies Disease Genes and Drug Targets

Proceedings of the National Academy of Sciences 10.1073/pnas.1603992113, 1-6 (2016)

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The protein-protein interaction (PPI) network is crucial for cellular information processing and decision-making. With suitable inputs, PPI networks drive the cells to diverse functional outcomes such as cell proliferation or cell death. Here, we characterize the structural controllability of a large directed human PPI network comprising 6,339 proteins and 34,813 interactions. This network allows us to classify proteins as "indispensable," "neutral," or "dispensable," which correlates to increasing, no effect, or decreasing the number of driver nodes in the network upon removal of that protein. We find that 21% of the proteins in the PPI network are indispensable. Interestingly, these indispensable proteins are the primary targets of disease-causing mutations, human viruses, and drugs, suggesting that altering a networks control property is critical for the transition between healthy and disease states. Furthermore, analyzing copy number alterations data from 1,547 cancer patients reveals that 56 genes that are frequently amplified or deleted in nine different cancers are indispensable. Among the 56 genes, 46 of them have not been previously associated with cancer. This suggests that controllability analysis is very useful in identifying novel disease genes and potential drug targets.
Barabasi

M. Hawrylycz, J. A. Miller, V. Menon, D. Feng, T. Dolbeare, A. L. Guillozet-Bongaarts, A. G. Jegga, B. J. Aronow, C.-K. Lee, A. Bernard, M. F. Glasser, D. L. Dierker, J. Menche, A. Szafer, F. Collman, P. Grange, K. A. Berman, S. Mihalas, Z. Yao, L. Stewart, A.-L. Barabási, J. Schulkin, J. Phillips, L. Ng, C. Dang, D. R. Haynor, A. Jones, D. C. Van Essen, C. Koch, D. Lein

Canonical genetic signatures of the adult human brain

Nature Neuroscience 4171, 1-15 (2015)

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The structure and function of the human brain are highly stereotyped, implying a conserved molecular program responsible for its development, cellular structure and function. We applied a correlation-based metric called differential stability to assess reproducibility of gene expression patterning across 132 structures in six individual brains, revealing mesoscale genetic organization. The genes with the highest differential stability are highly biologically relevant, with enrichment for brain-related annotations, disease associations, drug targets and literature citations. Using genes with high differential stability, we identified 32 anatomically diverse and reproducible gene expression signatures, which represent distinct cell types, intracellular components and/or associations with neurodevelopmental and neurodegenerative disorders. Genes in neuron-associated compared to non-neuronal networks showed higher preservation between human and mouse; however, many diversely patterned genes displayed marked shifts in regulation between species. Finally, highly consistent transcriptional architecture in neocortex is correlated with resting state functional connectivity, suggesting a link between conserved gene expression and functionally relevant circuitry.
Barabasi

B. Barzel, Y.-Y. Liu, A.-L. Barabási

Constructing minimal models for complex system dynamics

Nature Communications 6:7186, 1-8 (2015)

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One of the strengths of statistical physics is the ability to reduce macroscopic observations into microscopic models, offering a mechanistic description of a system’s dynamics. This paradigm, rooted in Boltzmann’s gas theory, has found applications from magnetic phenomena to subcellular processes and epidemic spreading. Yet, each of these advances were the result of decades of meticulous model building and validation, which are impossible to replicate in most complex biological, social or technological systems that lack accurate microscopic models. Here we develop a method to infer the microscopic dynamics of a complex system from observations of its response to external perturbations, allowing us to construct the most general class of nonlinear pairwise dynamics that are guaranteed to recover the observed behavior. The result, which we test against both numerical and empirical data, is an effective dynamic model that can predict the system’s behavior and provide crucial insights into its inner workings.
Barabasi

S. D. Ghiassian, J. Menche, A.-L. Barabási

A DIseAse MOdule Detection (DIAMOnD) Algorithm Derived from a Systematic Analysis of Connectivity Patterns of Disease Proteins in the Human Interactome

PLOS Computational Biology pcbi.1004120, 1-21 (2015)

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The observation that disease associated proteins often interact with each other has fueled the development of network-based approaches to elucidate the molecular mechanisms of human disease. Such approaches build on the assumption that protein interaction networks can be viewed as maps in which diseases can be identified with localized perturbation within a certain neighborhood. The identification of these neighborhoods, or disease modules, is therefore a prerequisite of a detailed investigation of a particular pathophenotype. While numerous heuristic methods exist that successfully pinpoint disease associated modules, the basic underlying connectivity patterns remain largely unexplored. In this work we aim to fill this gap by analyzing the network properties of a comprehensive corpus of 70 complex diseases. We find that disease associated proteins do not reside within locally dense communities and instead identify connectivity significance as the most predictive quantity. This quantity inspires the design of a novel Disease Module Detection (DIAMOnD) algorithm to identify the full disease module around a set of known disease proteins. We study the performance of the algorithm using well-controlled synthetic data and systematically validate the identified neighborhoods for a large corpus of diseases.
Barabasi

J. Menche, A. Sharma, M. Kitsak, D. Ghiassian, M. Vidal, J. Loscazlo, A.-L. Barabasi

Uncovering disease-disease relationships through the incomplete interactome

Science 347:6224, 1257601-1 (2015)

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According to the disease module hypothesis, the cellular components associated with a disease segregate in the same neighborhood of the human interactome, the map of biologically relevant molecular interactions. Yet, given the incompleteness of the interactome and the limited knowledge of disease-associated genes, it is not obvious if the available data have sufficient coverage to map out modules associated with each disease. Here we derive mathematical conditions for the identifiability of disease modules and show that the network-based location of each disease module determines its pathobiological relationship to other diseases. For example, diseases with overlapping network modules show significant coexpression patterns, symptom similarity, and comorbidity, whereas diseases residing in separated network neighborhoods are phenotypically distinct. These tools represent an interactome-based platform to predict molecular commonalities between phenotypically related diseases, even if they do not share primary disease genes.
Barabasi

J. Mench, A. Sharma, M. H. Cho, R. J. Mayer, S. I. Rennard, B. Celli, B. E. Miller, N. Locantore, R. Tal-Singer, S. Ghosh, C. Larminie, G. Bradley, J. H. Riley, A. Agusti, E. K. Silverman, A.-L. Barabási

A diVIsive Shuffling Approach (VIStA) for gene expression analysis to identify subtypes in Chronic Obstructive Pulmonary Disease

BMC Systems Biology 8, 1-13 (2014)

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Background: An important step toward understanding the biological mechanisms underlying a complex disease is a refined understanding of its clinical heterogeneity. Relating clinical and molecular differences may allow us to define more specific subtypes of patients that respond differently to therapeutic interventions. Results: We developed a novel unbiased method called diVIsive Shuffling Approach (VIStA) that identifies subgroups of patients by maximizing the difference in their gene expression patterns. We tested our algorithm on 140 subjects with Chronic Obstructive Pulmonary Disease (COPD) and found four distinct, biologically and clinically meaningful combinations of clinical characteristics that are associated with large gene expression differences. The dominant characteristic in these combinations was the severity of airflow limitation. Other frequently identified measures included emphysema, fibrinogen levels, phlegm, BMI and age. A pathway analysis of the differentially expressed genes in the identified subtypes suggests that VIStA is capable of capturing specific molecular signatures within in each group. Conclusions: The introduced methodology allowed us to identify combinations of clinical characteristics that correspond to clear gene expression differences. The resulting subtypes for COPD contribute to a better understanding of its heterogeneity.
Barabasi

B. Barzel, A.-L. Barabási

Network link prediction by global silencing of indirect correlations

Nature Biotechnology 31: Num 8, 1-8 (2013)

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Predictions of physical and functional links between cellular components are often based on correlations between experimental measurements, such as gene expression. However, correlations are affected by both direct and indirect paths, confounding our ability to identify true pairwise interactions. Here we exploit the fundamental properties of dynamical correlations in networks to develop a method to silence indirect effects. The method receives as input the observed correlations between node pairs and uses a matrix transformation to turn the correlation matrix into a highly discriminative silenced matrix, which enhances only the terms associated with direct causal links. Against empirical data for Escherichia coli regulatory interactions, the method enhanced the discriminative power of the correlations by twofold, yielding >50% predictive improvement over traditional correlation measures and 6% over mutual information. Overall this silencing method will help translate the abundant correlation data into insights about a system's interactions, with applications ranging from link prediction to inferring the dynamical mechanisms governing biological networks.
Barabasi

O. Rozenblatt-Rosen, R. C. Deo, M. Padi, G. Adelmant, T. Rolland, M. Grace, A. Dricot, M. Askenazi, M. Tavares, S. J. Pevzner, F. Abderazzaq, D. Byrdsong, A.-R. Carvunis, A. A. Chen, J. Cheng, M. Correll, M. Durate, C. Fan, M. C. Feltkamp, S. B. Ficarro, R. Franchi, B. K. Garg, N. Gulbahce, T. Hao, A. M. Holthaus, R. James, A. Korkhin, L. Litovchick, J. C. Mar, T. R. Pak, S. Rabello, R. Rubio, Y. Shen, S. Singh, J. M. Spangle, M. Tasan, S. Wanamakter, J. T. Webber, J. Roecklein-Canfield,, E. Johannsen, A.-L. Barabasi,, R. Beroukhim, E. Kieff,, M. E. Cusick, D. E. Hill,, K. Munger, J. A. Marto,, J. Quackenbush, F. P. Roth,, J. A. DeCaprio, M. Vidal

Interpreting cancer genomes using systematic host network perturbations by tumour virus proteins

Nature 487, 491-495 (2012)

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Genotypic differences greatly influence susceptibility and resistance to disease. Understanding genotype–phenotype relationships requires that phenotypes be viewed as manifestations of network properties, rather than simply as the result of individual genomic variations. Genome sequencing efforts have identified numerous germline mutations, and large numbers of somatic genomic alterations, associated with a predisposition to cancer. However, it remains difficult to distinguish background, or ‘passenger’, cancer mutations from causal, or ‘driver’, mutations in these data sets. Human viruses intrinsically depend on their host cell during the course of infection and can elicit pathological phenotypes similar to those arising from mutations. Here we test the hypothesis that genomic variations and tumour viruses may cause cancer through related mechanisms, by systematically examining host interactome and transcriptome network perturbations caused by DNA tumour virus proteins. The resulting integrated viral perturbation data reflects rewiring of the host cell networks, and highlights pathways, such as Notch signalling and apoptosis, that go awry in cancer. We show that systematic analyses of host targets of viral proteins can identify cancer genes with a success rate on a par with their identification through functional genomics and large-scale cataloguing of tumour mutations. Together, these complementary approaches increase the specificity of cancer gene identification. Combining systems-level studies of pathogen-encoded gene products with genomic approaches will facilitate the prioritization of cancer causing driver genes to advance the understanding of the genetic basis of human cancer.
Barabasi

Y. Shen, L. Liu, G. Estiu, B. Isin, Y.-Y. Ahn, D.-S. Lee, A.-L. Barabásii, v. Kapatral, O. Wiest, Z. N. Oltvai

Blueprint for antimicrobial hit discovery targeting metabolic networks

Proceedings of the National Academy of Sciences of the United States of America 10.1073, 1-6 (2010)

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Advances in genome analysis, network biology, and computational chemistry have the potential to revolutionize drug discovery by combining system-level identification of drug targets with the atomistic modeling of small molecules capable of modulating their activity. To demonstrate the effectiveness of such a discovery pipeline, we deduced common antibiotic targets in Escherichia coli and Staphylococcus aureus by identifying shared tissue-specific or uniformly essential metabolic reactions in their metabolic networks. We then predicted through virtual screening dozens of potential inhibitors for several enzymes of these reactions and showed experimentally that a subset of these inhibited both enzyme activities in vitro and bacterial cell viability. This blueprint is applicable for any sequenced organism with high-quality metabolic reconstruction and suggests a general strategy for strain-specific antiinfective therapy.
Barabasi

A.-L. Barabási

Scale-Free Networks: A Decade and Beyond

Science 325, 412-413 (2009)

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For decades, we tacitly assumed that the components of such complex systems as the cell, the society, or the Internet are randomly wired together. In the past decade, an avalanche of research has shown that many real networks, independent of their age, function, and scope, converge to similar architectures, a universality that allowed researchers from different disciplines to embrace network theory as a common paradigm. The decade-old discovery of scale-free networks was one of those events that had helped catalyze the emergence of network science, a new research field with its distinct set of challenges and accomplishments.
Barabasi

D.-S. Lee, H. Burd, J. Liu, E. Almass, O. Weist, A.-L. Barabási, Z. N. Oltvai, V. Kapatra

Comparative Genome-Scale Metabolic Reconstruction and Flux Balance Analysis of Multiple Staphylococcus aureus Genomes Identify Novel Antimicrobial Drug Targets

Journal of Bacteriology 191:12, 4015–4024 (2009)

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Mortality due to multidrug-resistant Staphylococcus aureus infection is predicted to surpass that of human immunodeficiency virus/AIDS in the United States. Despite the various treatment options for S. aureus infections, it remains a major hospital- and community-acquired opportunistic pathogen. With the emergence of multidrug-resistant S. aureus strains, there is an urgent need for the discovery of new antimicrobial drug targets in the organism. To this end, we reconstructed the metabolic networks of multidrug-resistant S. aureus strains using genome annotation, functional-pathway analysis, and comparative genomic approaches, followed by flux balance analysis-based in silico single and double gene deletion experiments. We identified 70 single enzymes and 54 pairs of enzymes whose corresponding metabolic reactions are predicted to be unconditionally essential for growth. Of these, 44 single enzymes and 10 enzyme pairs proved to be common to all 13 S. aureus strains, including many that had not been previously identified as being essential for growth by gene deletion experiments in S. aureus. We thus conclude that metabolic reconstruction and in silico analyses of multiple strains of the same bacterial species provide a novel approach for potential antibiotic target identification.
Barabasi

C. A. Hidalgo, N. Blumm, A.-L. Barabási, N. A. Christakis

A dynamic network approach for the study of human phenotypes

PLoS Computational Biology 5:4, 1-11 (2009)

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The use of networks to integrate different genetic, proteomic, and metabolic datasets has been proposed as a viable path toward elucidating the origins of specific diseases. Here we introduce a new phenotypic database summarizing correlations obtained from the disease history of more than 30 million patients in a Phenotypic Disease Network (PDN). We present evidence that the structure of the PDN is relevant to the understanding of illness progression by showing that (1) patients develop diseases close in the network to those they already have; (2) the progression of disease along the links of the network is different for patients of different genders and ethnicities; (3) patients diagnosed with diseases which are more highly connected in the PDN tend to die sooner than those affected by less connected diseases; and (4) diseases that tend to be preceded by others in the PDN tend to be more connected than diseases that precede other illnesses, and are associated with higher degrees of mortality. Our findings show that disease progression can be represented and studied using network methods, offering the potential to enhance our understanding of the origin and evolution of human diseases. The dataset introduced here, released concurrently with this publication, represents the largest relational phenotypic resource publicly available to the research community.
Barabasi

J. Park, D. S. Lee, N. A. Christakis, A.-L. Barabási

The impact of cellular networks on disease comorbidity

Molecular Systems Biology 5:262, 1-7 (2009)

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The impact of disease-causing defects is often not limited to the products of a mutated gene but, thanks to interactions between the molecular components, may also affect other cellular functions, resulting in potential comorbidity effects. By combining information on cellular interactions, disease--gene associations, and population-level disease patterns extracted from Medicare data, we find statistically significant correlations between the underlying structure of cellular networks and disease comorbidity patterns in the human population. Our results indicate that such a combination of population-level data and cellular network information could help build novel hypotheses about disease mechanisms.
Barabasi

H. Yu, P. Braun, M. A. Yildirim, I. Lemmens, K. Venkatesan, J. Sahalie, T. Hirozane-Kishikawa, F. Gebreab, N. Li, N. Simonis, T. Hao, J.-F. Raul, A. Dricot, A. Vazquez, R. R. Murray, C. Simon, L. Tardivo, S. Tam, N. Svrzikapa, C. Fan, A.-S. de Semt, A. Motyl, M. E. Hudson, J. Park, X. Xin, M. E. Cusick, T. Moore, C. Boone, M. Snyder, F. P. Roth, A.-L. Barabási, J. Tavernier, D. E. Hill, M. Vidal

High-Quality Binary Protein Interaction Map of the Yeast Interactome Network

Science 322, 104-110 (2008)

Barabasi

D.-S. Lee, J. Park, K. A. Kay, N. A. Christakis, Z. N. Oltvai, A.-L. Barabási

The implications of human metabolic network topology for disease comorbidity

Proceedings of the National Academy of Sciences 105, 9880-9885 (2008)

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Most diseases are the consequence of the breakdown of cellular processes, but the relationships among genetic/epigenetic defects, the molecular interaction networks underlying them, and the disease phenotypes remain poorly understood. To gain insights into such relationships, here we constructed a bipartite human disease association network in which nodes are diseases and two diseases are linked if mutated enzymes associated with them catalyze adjacent metabolic reactions. We find that connected disease pairs display higher correlated reaction flux rate, corresponding enzyme-encoding gene coexpression, and higher comorbidity than those that have no metabolic link between them. Furthermore, the more connected a disease is to other diseases, the higher is its prevalence and associated mortality rate. The network topology-based approach also helps to
Barabasi

J. Park, A-L. Barabási

Distribution of node characteristics in complex networks

Proceedings of the National Academy of Sciences 104, 17916-17920 (2007)

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Our enhanced ability to map the structure of various complex networks is increasingly accompanied by the possibility of independently identifying the functional characteristics of each node. Although this led to the observation that nodes with similar characteristics have a tendency to link to each other, in general we lack the tools to quantify the interplay between node properties and the structure of the underlying network. Here we show that when nodes in a network belong to two distinct classes, two independent parameters are needed to capture the detailed interplay between the network structure and node properties. We find that the network structure significantly limits the values of these parameters, requiring a phase diagram to uniquely characterize the configurations available to the system. The phase diagram shows a remarkable independence from the network size, a finding that, together with a proposed heuristic algorithm, allows us to determine its shape even for large networks. To test the usefulness of the developed methods, we apply them to biological and socioeconomic systems, finding that protein functions and mobile phone usage occupy distinct regions of the phase diagram, indicating that the proposed parameters have a strong discriminating power.
Barabasi

M. A. Yildirim, K.-L. Goh, M.E. Cusick, A.-L. Barabási, M. Vidal

Drug-target network

Nature Biotechnology 25:10, 1119-1126 (2007)

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The global set of relationships between protein targets of all drugs and all disease-gene products in the human protein–protein interaction or ‘interactome’ network remains uncharacterized. We built a bipartite graph composed of US Food and Drug Administration–approved drugs and proteins linked by drug–target binary associations. The resultingnetwork connects most drugs into a highly interlinked giant component, with strong local clustering of drugs of similar types according to Anatomical Therapeutic Chemical classification. Topological analyses of this network quantitatively showed an overabundance of ‘follow-on’ drugs, that is, drugs that target already targeted proteins. By including drugs currently under investigation, we identified a trend toward more functionally diverse targets improving polypharmacology. To analyze the relationships between drug targets and disease-gene products, we measured the shortest distance between both sets of proteins in current models of the human interactome network. Significant differences in distance were found between etiological and palliative drugs. A recent trend toward more rational drug design was observed.
Barabasi

Q. K. Beg, A. Vazquez, J. Ernst, M. A. de Menezes, Z. Bar-Joseph, A.-L. Barabási, Z. N. Oltvai

Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity

Proceedings of the National Academy of Sciences 104, 31 (2007)

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The influence of the high intracellular concentration of macromolecules on cell physiology is increasingly appreciated, but its impact on system-level cellular functions remains poorly quantified. To assess its potential effect, here we develop a flux balance model of Escherichia coli cell metabolism that takes into account a systemslevel constraint for the concentration of enzymes catalyzing the various metabolic reactions in the crowded cytoplasm. We demonstrate that the model’s predictions for the relative maximum growth rate of wild-type and mutant E. coli cells in single substratelimited media, and the sequence and mode of substrate uptake and utilization from a complex medium are in good agreement with subsequent experimental observations. These results suggest that molecular crowding represents a bound on the achievable functional states of a metabolic network, and they indicate that models incorporating this constraint can systematically identify alterations in cellular metabolism activated in response to environmental change.
Barabasi

V. Vermeirssen, M. Inmaculada Barrasa, C. Hidalgo, J.-A. B. Babon, R. Sequerra, L. Doucette-Stamm, A.-L. Barabási, A. J.M. Walhout

Transcription factor modularity in a Gene-Centered C. elegans Protein-DNA interaction network

Genome Research 17, 061-1071 (2007)

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Transcription regulatory networks play a pivotal role in the development, function, and pathology of metazoan organisms. Such networks are comprised of protein–DNA interactions between transcription factors (TFs) and their target genes. An important question pertains to how the architecture of such networks relates to network functionality. Here, we show that a Caenorhabditis elegans core neuronal protein–DNA interaction network is organized into two TF modules. These modules contain TFs that bind to a relatively small number of target genes and are more systems specific than the TF hubs that connect the modules. Each module relates to different functional aspects of the network. One module contains TFs involved in reproduction and target genes that are expressed in neurons as well as in other tissues. The second module is enriched for paired homeodomain TFs and connects to target genes.
Barabasi

K.-I. Goh, M. E. Cusick, D. Valle, B. Childs, M. Vidal, A.-L. Barabási

The human disease network

Proceedings of the National Academy of Sciences 104:21, 8685 (2007)

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A network of disorders and disease genes linked by known disorder–gene associations offers a platform to explore in a single graphtheoretic framework all known phenotype and disease gene associations, indicating the common genetic origin of many diseases. Genes associated with similar disorders show both higher likelihood of physical interactions between their products and higher expression profiling similarity for their transcripts, supporting the existence of distinct disease-specific functional modules. We find that essential human genes are likely to encode hub proteins and are expressed widely in most tissues. This suggests that disease genes also would play a central role in the human interactome. In contrast, we find that the vast majority of disease genes are nonessential and show no tendency to encode hub proteins, and their expression pattern indicates that they are localized in the functional periphery of the network. A selection-based model explains the observed difference between essential and disease genes and also suggests that diseases caused by somatic mutations should not be peripheral, a prediction we confirm for cancer genes.
Barabasi

J. Lim, T. Hao, C. Shaw, A.J. Patel, G. Szabo, J.F. Rual, C.J. Fisk, N. Li, A. Smolyar, D.E. Hill, A.-L. Barabási, M. Vidal, H.Y. Zoghbi

A protein-protein interaction network for human inherited ataxias and disorders of Purkinje cell degeneration

Cell 125, 801-814 (2006)

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Many human inherited neurodegenerative disorders are characterized by loss of balance due to cerebellar Purkinje cell (PC) degeneration. Although the disease-causing mutations have been identified for a number of these disorders, the normal functions of the proteins involved remain, in many cases, unknown. To gain insight into the function of proteins involved in PC degeneration, we developed an interaction network for 54 proteins involved in 23 inherited ataxias and expanded the network by incorporating literature-curated and evolutionarily conserved interactions. We identified 770 mostly novel protein–protein interactions using a stringent yeast two-hybrid screen; of 75 pairs tested, 83% of the interactions were verified in mammalian cells. Many ataxia-causing proteins share interacting partners, a subset of which have been found to modify neurodegeneration in animal models. This interactome thus provides a tool for understanding pathogenic mechanisms common for this class of neurodegenerative disorders and for identifying candidate genes for inherited ataxias.
Barabasi

S. Wuchty, A.-L. Barabási, M.T. Ferdig

Stable evolutionary signal in a Yeast protein interaction network

BMC Evolutionary Biology 60, 8 (2006)

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Background: The recently emerged protein interaction network paradigm can provide novel and important insights into the innerworkings of a cell. Yet, the heavy burden of both false positive and false negative protein-protein interaction data casts doubt on the broader usefulness of these interaction sets. Approaches focusing on one-protein-at-a-time have been powerfully employed to demonstrate the high degree of conservation of proteins participating in numerous interactions; here, we expand his 'node' focused paradigm to investigate the relative persistence of 'link' based evolutionary signals in a protein interaction network of S. cerevisiae and point out the value of this relatively untapped source of information. Results: The trend for highly connected proteins to be preferably conserved in evolution is stable, even in the context of tremendous noise in the underlying protein interactions as well as in the assignment of orthology among five higher eukaryotes. We find that local clustering around interactions correlates with preferred evolutionary conservation of the participating proteins; furthermore the correlation between high local clustering and evolutionary conservation is accompanied by a stable elevated degree of coexpression of the interacting proteins. We use this conserved interaction data, combined with P. falciparum /Yeast orthologs, as proof-of-principle that high-order network topology can be used comparatively to deduce local network structure in nonmodel organisms. Conclusion: High local clustering is a criterion for the reliability of an interaction and coincides with preferred evolutionary conservation and significant coexpression. These strong and stable correlations indicate that evolutionary units go beyond a single protein to include the interactions among them. In particular, the stability of these signals in the face of extreme noise suggests that empirical protein interaction data can be integrated with orthologous clustering around these protein interactions to reliably infer local network structures in non-model organisms.
Barabasi

E. Almaas, Z.N. Oltvai, A.-L. Barabási

The activity reaction core and plasticity of metabolic networks

PLOS Computational Biology 1, 557-563 (2005)

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Understanding the system-level adaptive changes taking place in an organism in response to variations in the environment is a key issue of contemporary biology. Current modeling approaches, such as constraint-based fluxbalance analysis, have proved highly successful in analyzing the capabilities of cellular metabolism, including its capacity to predict deletion phenotypes, the ability to calculate the relative flux values of metabolic reactions, and the capability to identify properties of optimal growth states. Here, we use flux-balance analysis to thoroughly assess the activity of Escherichia coli, Helicobacter pylori, and Saccharomyces cerevisiae metabolism in 30,000 diverse simulated environments. We identify a set of metabolic reactions forming a connected metabolic core that carry non-zero fluxes under all growth conditions, and whose flux variations are highly correlated. Furthermore, we find that the enzymes catalyzing the core reactions display a considerably higher fraction of phenotypic essentiality and evolutionary conservation than those catalyzing noncore reactions. Cellular metabolism is characterized by a large number of species-specific conditionally active reactions organized around an evolutionary conserved, but always active, metabolic core. Finally, we find that most current antibiotics interfering with bacterial metabolism target the core enzymes, indicating that our findings may have important implications for antimicrobial drug-target discovery.
Barabasi

G. Balazsi, A.-L. Barabási, Z.N. Oltvai

Topological units of environmental signal processing in the transcriptional regulatory network of Escherichia coli

Proceedings of the National Academy of Sciences 102, 7841-7846 (2005)

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Recent evidence indicates that potential interactions within metabolic, protein–protein interaction, and transcriptional regulatory networks are used differentially according to the environmental conditions in which a cell exists. However, the topological units underlying such differential utilization are not understood. Here we use the transcriptional regulatory network of Escherichia coli to identify such units, called origons, representing regulatory subnetworks that originate at a distinct class of sensor transcription factors. Using microarray data, we find that specific environmental signals affect mRNA expression levels significantly only within the origons responsible for their detection and processing. We also show that small regulatory interaction patterns, called subgraphs and motifs, occupy distinct positions in and between origons, offering insights into their dynamical role in information processing. The identified features are likely to represent a general framework for environmental signal processing in prokaryotes.
Barabasi

A. Vazquez, R. Dobrin, D. Sergi, J.-P. Eckmann, Z. N. Oltvai, A.-L. Barabási

The topological relationship between the large-scale attributes and local interactions patterns of complex networks

Proceedings of the National Academy of Sciences 101, 17940-17945 (2004)

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Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks’ global organization remain poorly understood. Here we show that a network’s large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.
Barabasi

G. Palla, I. Farkas, I. Derenyi, A.-L. Barabási, T. Vicsek

Reverse engineering of linking preferences from network restructuring

Physical Review E 70, 046115 (2004)

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We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a single-vertex energy function with fskd being the contribution of a node of degree k to the total energy, and the dynamics obeys the detailed balance. The method is first tested by Monte Carlo simulations of restructuring graphs with known energies; then it is used to study variations of real network systems ranging from the coauthorship network of scientific publications to the asset graphs of the New York Stock Exchange. The empirical energies obtained from the restructuring can be described by a universal function fskd,−k ln k, which is consistent with and justifies the validity of the preferential attachment rule proposed for growing networks.
Barabasi

S. Y. Yook, Z. N. Oltvai, A.-L. Barabási

Functional and topological characterization of protein interaction networks

Proteomics 4, 928-942 (2004)

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The elucidation of the cell’s large-scale organization is a primary challenge for post-genomic biology, and understanding the structure of protein interaction networks offers an important starting point for such studies. We compare four available databases that approximate the protein interaction network of the yeast, Saccharomyces cerevisiae, aiming to uncover the network’s generic large-scale properties and the impact of the proteins’ function and cellular localization on the network topology. We show how each database supports a scale-free, topology with hierarchical modularity, indicating that these features represent a robust and generic property of the protein interactions network. We also find strong correlations between the network’s structure and the functional role and subcellular localization of its protein constituents, concluding that most functional and/or localization classes appear as relatively segregated subnetworks of the full protein interaction network. The uncovered systematic differences between the four protein interaction databases reflect their relative coverage for different functional and localization classes and provide a guide for their utility in various bioinformatics studies.
Barabasi

E. Almaas, B. Kovacs, T. Vicsek, Z.N. Oltvai, A.-L. Barabási

Global organization of metabolic fluxes in the bacterium Escherichia coli

Nature 427, 839-843 (2004)

Barabasi

R. Dobrin, Q. K. Beg, A.-L. Barabási

Aggregation of topological motifs in the Escherichia coli transcriptional regulatory networks

BMC Bioinformatics 5, 10 (2004)

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Background: Transcriptional regulation of cellular functions is carried out through a complex network of interactions among transcription factors and the promoter regions of genes and operons regulated by them.To better understand the system-level function of such networks simplification of their architecture was previously achieved by identifying the motifs present in the network, which are small, overrepresented, topologically distinct regulatory interaction patterns (subgraphs). However, the interaction of such motifs with each other, and their form of integration into the full network has not been previously examined. Results: By studying the transcriptional regulatory network of the bacterium, Escherichia coli, we demonstrate that the two previously identified motif types in the network (i.e., feed-forward loops and bi-fan motifs) do not exist in isolation, but rather aggregate into homologous motif clusters that largely overlap with known biological functions. Moreover, these clusters further coalesce into a supercluster, thus establishing distinct topological hierarchies that show global statistical properties similar to the whole network. Targeted removal of motif links disintegrates the network into small, isolated clusters, while random disruptions of equal number of links do not cause such an effect. Conclusion: Individual motifs aggregate into homologous motif clusters and a supercluster forming the backbone of the E. coli transcriptional regulatory network and play a central role in defining its global topological organization.
Barabasi

M. A. de Menezes, A.-L. Barabási

Fluctuations in network dynamics

Physical Review Letters 92, 28701 (2004)

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Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet.We collected data on the time dependent activity of five natural and technological networks, finding that for each the coupling of the flux fluctuations with the total flux on individual nodes obeys a unique scaling law. We show that the observed scaling can explain the competition between the system’s internal collective dynamics and changes in the external environment, allowing us to predict the relevant scaling exponents.
Barabasi

Z. Dezso, Z. N. Oltvai, A.-L. Barabási

Bioinformatics analysis of experimentally determined protein complexes in the yeast Saccharomyces cerevisiae

Genome Research 13, 2450-2454 (2003)

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Many important cellular functions are implemented by protein complexes that act as sophisticated molecular machines of varying size and temporal stability. Here we demonstrate quantitatively that protein complexes in the yeast Saccharomyces cerevisiae are comprised of a core in which subunits are highly coexpressed, display the same deletion phenotype (essential or nonessential), and share identical functional classification and cellular localization. This core is surrounded by a functionally mixed group of proteins, which likely represent short-lived or spurious attachments. The results allow us to define the deletion phenotype and cellular task of most known complexes, and to identify with high confidence the biochemical role of hundreds of proteins with yet unassigned functionality.
Barabasi

S. Wuchty, Z. N. Oltvai, A.-L. Barabási

Evolutionary conservation of motif constituents in the yeast protein interaction network

Nature Genetics 35, 176-179 (2003)

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Understanding why some cellular components are conserved across species but others evolve rapidly is a key question of modern biology1-3. Here we show that in Saccharomyces cerevisiae, proteins organized in cohesive patterns of interactions are conserved to a substantially higher degree than those that do not participate in such motifs. We find that the conservation of proteins in distinct topological motifs correlates with the interconnectedness and function of that motif and also depends on the structure of the overall interactome topology. These findings indicate that motifs may represent evolutionary conserved topological units of cellular networks molded in accordance with the specific biological function in which they participate.
Barabasi

S. Y. Gerdes, M. D. Scholle, J. W. Campbell, G. Balazsi, E. Ravasz, M. D. Daugherty, A. L. Somera, N. C. Kyrpides, I. Anderson, M. S. Gelfand, A. Bhattacharya, V. Kapatral, M. D'Souza, M. V. Baev, Y. Grechkin, F. Mseeh, M. Y. Fonstein, R. Overbeek, A.-L. Barabási, Z. N. Oltvai, A. L. Osterman

Experimental determination and system level analysis of essential genes in Escherichia coli MG1655

Journal of Bacteriology 185, 5673-5684 (2003)

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Defining the gene products that play an essential role in an organism’s functional repertoire is vital to understanding the system level organization of living cells. We used a genetic footprinting technique for a genome-wide assessment of genes required for robust aerobic growth of Escherichia coli in rich media. We identified 620 genes as essential and 3,126 genes as dispensable for growth under these conditions. Functional context analysis of these data allows individual functional assignments to be refined. Evolutionary context analysis demonstrates a ignificant tendency of essential E. coli genes to be preserved throughout the bacterial kingdom. Projection of these data over metabolic subsystems reveals topologic modules with essential and evolutionarily preserved enzymes with reduced capacity for error tolerance.
Barabasi

H. Jeong, Z. N. Oltvai, A.-L. Barabási

Prediction of protein essentiality based on genomic data

ComPlexUs 1, 19-28 (2003)

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A major goal of pharmaceutical bioinformatics is to develop computational tools for systematic in silico molecular target identification. Here we demonstrate that in the yeast Saccharomyces cerevisiae the phenotypic effect of single gene deletions simultaneously correlates with fluctuations in mRNA expression profiles, the functional categorization of the gene products, and their connectivity in the yeast’s protein-protein interaction network. Building on these quantitative correlations, we developed a computational method for predicting the phenotypic effect of a given gene’s functional disabling or removal. Our subsequent analyses were in good agreement with the results of systematic gene deletion experiments, allowing us to predict the deletion phenotype of a number of untested yeast genes. The results underscore the utility oflarge genomic databases for in silico systematic drug target identification in the postgenomic era.
Barabasi

G. Balazsi, K. A. Kay, A.-L. Barabási, Z. N. Oltvai

Spurious spatial periodicity of co-expression in microarray data due to printing design

Nucleic Acids Research 31, 4425-4433 (2003)

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Global transcriptome data is increasingly combined with sophisticated mathematical analyses to extract information about the functional state of a cell. Yet the extent to which the results re¯ect experimental bias at the expense of true biological information remains largely unknown. Here we show that the spatial arrangement of probes on microarrays and the particulars of the printing procedure signi®- cantly affect the log-ratio data of mRNA expression levels measured during the Saccharomyces cerevisiae cell cycle. We present a numerical method that ®lters out these technology-derived contributions from the existing transcriptome data, leading to improved functional predictions. The example presented here underlines the need to routinely search and compensate for inherent experimental bias when analyzing systematically collected,internally consistent biological data sets.
Barabasi

I. Farkas, H. Jeong, T. Vicsek, A.-L. Barabási, Z. N. Oltvai

The topology of the transcription regulatory network in the yeast Saccharomyces cerevisiae

Physica A 318, 601-612 (2003)

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A central goal of postgenomic biology is the elucidation of the regulatory relationships among all cellular constituents that together comprise the ‘genetic network’ of a cell or microorganism. Experimental manipulation of gene activity coupled with the assessment of perturbed transcriptome (i.e., global mRNA expression) patterns represents one approach toward this goal, and may provide a backbone into which other measurements can be later integrated. We use microarray data on 287 single gene deletion Saccharomyces cerevisiae mutant strains to elucidate generic relationships among perturbed transcriptomes. Their comparison with a method that preferentially recognizes distinct expression subpatterns allows us to pair those transcriptomes that share localized similarities. Analyses of the resulting transcriptome similarity network identify a continuum hierarchy among the deleted genes, and in the frequency of local similarities that establishes the links among their reorganized transcriptomes. We also find a combinatorial utilization of shared expression subpatterns within individual links, with increasing quantitative similarity among those that connect transcriptome states induced by the deletion of functionally related gene products. This suggests a distinct hierarchical and combinatorial organization of the S. cerevisiae transcriptional activity, and may represent a pattern that is generic to the transcriptional organization of all eukaryotic organisms.
Barabasi

Z. N. Oltvai, A.-L. Barabási

Life’s complexity pyramid

Science 298, 763-764 (2002)

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Cells and microorganisms have an impressive capacity for adjusting their intracellular machinery in response to changes in their environment, food availability, and developmental state. Add to this an amazing ability to correct internal errors — battling the effects of such mistakes as mutations or misfolded proteins — and we arrive at a major issue of contemporary cell biology: our need to comprehend the staggering complexity, versatility, and robustness of living systems. Although molecular biology offers many spectacular successes, it is clear that the detailed inventory of genes, proteins, and metabolites is not sufficient to understand the cell’s complexity (1). As demonstrated by two papers in this issue—Lee et al. (2) on page 799 and Milo et al. (3) on page 824—viewing the cell as a network of genes and proteins offers a viable strategy for addressing the complexity of living systems.
Barabasi

R. J. Williams, N. D. Martinez, E. L. Berlow, J. A. Dunne, A.-L. Barabási

Two degrees of separation in complex food webs

Proceedings of the National Academy of Sciences 99, 12913-12916 (2002)

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Feeding relationships can cause invasions, extirpations, and population fluctuations of a species to dramatically affect other species within a variety of natural habitats. Empirical evidence suggests that such strong effects rarely propagate through food webs more than three links away from the initial perturbation. However, the size of these spheres of potential influence within complex communities is generally unknown. Here, we show for that species within large communities from a variety of aquatic and terrestrial ecosystems are on average two links apart, with >95% of species typically within three links of each other. Species are drawn even closer as network complexity and, more unexpectedly, species richness increase. Our findings are based on seven of the largest and most complex food webs available as well as a food-web model that extends the generality of the empirical results. These results indicate that the dynamics of species within ecosystems may be more highly interconnected and that biodiversity loss and species invasions may affect more species than previously thought.
Barabasi

Z. Dezso, A.-L. Barabási

Halting viruses in scale-free networks

Physical Review E 65, 055103 (2002)

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The vanishing epidemic threshold for viruses spreading on scale-free networks indicate that traditional methods, aiming to decrease a virus’ spreading rate cannot succeed in eradicating an epidemic. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate a virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus’ spreading rate. Furthermore, such biased policies are more cost effective, requiring less cures to eradicate the virus.
Barabasi

H. Jeong, B. Tombor, R. Albert, Z. N. Oltvai, A.-L. Barabási

The large-scale organization of metabolic networks

Nature 407, 651–655 (2000)

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Here we present a systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life.We show that, despite significant variation in their individual constituents and pathways, these metabolic networks have the same topological scaling properties and show striking similarities to the inherent organization of complex non-biological systems. This may indicate that metabolic organization is not only identical for all living organisms, but also complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.
Barabasi

H. Jeong, S. P. Mason, A.-L. Barabási, Z. N. Oltvai

Lethality and centrality in protein networks

Nature 411, 41-42 (2001)

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The most highly connected proteins in the cell are the most important for its survival. Proteins are traditionally identified on the basis of their individual actions as catalysts, signalling molecules, or building blocks in cells and microorganisms. But our post-genomic view is expanding the protein’s role into an element in a network of protein–protein interactions as well, in which it has a contextual or cellular function within functional modules1,2. Here we provide quantitative support for this idea by demonstrating that the phenotypic consequence of a single gene deletion in the yeast Saccharomyces cerevisiae is affected to a large extent by the topological position of its protein product in the complex hierarchical web of molecular interactions.
Barabasi

A.-L. Barabási, Z. N. Oltvai

Network biology: understanding the cell’s functional organization

Nature Reviews Genetics 5, 101-113 (2004)

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A key aim of postgenomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a clear need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. Rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize our view of biology and disease pathologies in the twenty-first century.
Barabasi

E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, A.-L. Barabási

Hierarchical organization of modularity in metabolic networks

Science 297, 1551-1555 (2002)

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Spatially or chemically isolated functional modules composed of several cellular components and carrying discrete functions are considered fundamental building blocks of cellular organization, but their presence in highly integrated biochemical networks lacks quantitative support. Here, we show that the metabolic networks of 43 distinct organisms are organized into many small, highly connected topologic modules that combine in a hierarchical manner into larger, less cohesive units, with their number and degree of clustering following a power law. Within Escherichia coli, the uncovered hierarchical modularity closely overlaps with known metabolic functions. The identified network architecture may be generic to system-level cellular organization.
Barabasi

U. Frey, M. Silverman, A.-L. Barabási, B. Suki

Irregularities and power law distributions in the breathing pattern in preterm and term infants

Journal of Applied Physiology 85, 789–797 (1998)

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Irregularities and power law distributions in the breathing pattern in preterm and term infants. J. Appl. Physiol. 86(3): 789–797, 1998.—Unlike older children, young infants are prone to develop unstable respiratory patterns, suggesting important differences in their control of breathing. We examined the irregular breathing pattern in infants by measuring the time interval between breaths (‘‘interbreath interval; IBI) assessed from abdominal movement during 2 h of sleep in 25 preterm infants at a postconceptional age of 40.5 6 5.2 (SD) wk and in 14 term healthy infants at a postnatal age of 8.2 6 4 wk. In 10 infants we performed longitudinal measurements on two occasions. We developed a threshold algorithm for the detection of a breath so that an IBI included an apneic period and potentially some periods of insufficient tidal breathing excursions (hypopneas). The probability density distribution (P) of IBIs follows a power law, P(IBI),IBI2a, with the exponent a providing a statistical measurement of the relative risk of insufficient breathing.With maturation, a increased from 2.62 6 0.4 at 41.2 6 3.6 wk to 3.22 6 0.4 at 47.3 6 6.4 wk postconceptional age, indicating a decrease in long hypopneas (for paired data P 5 0.002). The statistical properties of IBI were well reproduced in a model of the respiratory oscillator on the basis of two hypotheses: 1) tonic neural inputs to the respiratory oscillator are noisy; and 2) the noise explores a critical region where IBI diverges with decreasing tonic inputs. Accordingly, maturation of infant respiratory control can be explained by the tonic inputs moving away from this critical region. We conclude that breathing irregularities in infants can be characterized by a, which provides a link between clinically accessible data and the neurophysiology of the respiratory oscillator.
Barabasi

A.-L. Barabási, S.V. Buldyrev, H.E. Stanley, B. Suki

Avalanches in the lung: a statistical mechanical approach

Physical Review Letters 76, 2192–2195 (1996)

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We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche problem onto percolation on a Cayley tree, we analytically derive the exponents describing the size distribution of the first avalanches and test the analytical solution by numerical simulations. We find that the treelike structure of the airways, together with the simplest assumptions concerning opening threshold pressures of each airway, is sufficient to explain the existence of power-law distributions observed experimentally.
Barabasi

B. Suki, A.-L. Barabási, K. Lutchen

Lung tissue viscoelasticity: a mathematical framework and its molecular basis

Journal of Applied Physiology 76, 2749–2759 (1994)

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Recent studies indicated that lung tissue stress relaxation is well represented by a simple empirical equation involving a power law, t+ (where t is time). Likewise, tissue impedance is well described by a model having a frequency-independent (constant) phase with impedance proportional to 0 -(r (where w is angular frequency and a! is a constant). These models provide superior descriptions over conventional springdashpot systems. Here we offer a mathematical framework and explore its mechanistic basis for using the power law relaxation function and constant-phase impedance. We show that replacing ordinary time derivatives with fractional time derivatives in the constitutive equation of conventional spring-dashpot systems naturally leads to power law relaxation function, the Fourier transform of which is the constant-phase impedance with a! = 1 - @. We further establish that fractional derivatives have a mechanistic basis with respect to the viscoelasticity of certain polymer systems. This mechanistic basis arises from molecular theories that take into account the complexity and statistical nature of the system at the molecular level. Moreover, because tissues are composed of long flexible biopolymers, we argue that these molecular theories may also apply for soft tissues. In our approach a key parameter is the exponent & which is shown to be directly related to dynamic processes at the tissue fiber and matrix level. By exploring statistical properties of various polymer systems, we offer a molecular basis for several salient features of the dynamic passive mechanical properties of soft tissues.
Barabasi

B. Suki, A.-L. Barabási, Z. Hantos, F. Petak, H.E. Stanley

Avalanches and power law behavior in lung inflation

Nature 368, 615–618 (1994)

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When lunkg are emptied during exhalation, peripheral airways close up. For people with lung disease, they mey not reopen for a significant portion of inhalation, impairing gas exchange. A knowledge of the mechanisms that govern reinflation of collapsed regions of lungs is therefore central to the development of ventilation strategies for combating respiratory problems. Here we report measurements of the terminal airway resistance, Rt, during the opening of isolated dog lungs. When inflated by a constant flow, Rt decreases in discrete jumps. We find that the probability distribution of the sizes of the jumps and of the time intervals between them exhibit power-law behavior over two decades. We develop a model of the inflation process in which 'avalanches' of airway openings are seen--with power-law distributions of both the size of avalanches and the time intervals between them--which agree quantitatively with those seen experimentally, and are reminiscent of the power-law behavior observed for self-organized critical systems. Thus power-law distributions, arising from avalanches associated with threshold phenomena propagating down a branching tree structure, appear to govern the recruitment of terminal airspaces.