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  • Journal article
    Liu Z, Barahona M, 2017,

    Geometric multiscale community detection: Markov stability and vector partitioning

    , Journal of Complex Networks, Vol: 6, Pages: 157-172, ISSN: 2051-1329

    Multiscale community detection can be viewed from a dynamical perspective within the Markov stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov stability in terms of a time-dependent spectral embedding, where the Markov time acts as an inhomogeneous geometric resolution factor that zooms the components of the node vectors at different rates. Our geometric formulation encompasses both modularity and the multi-resolution Potts model, which are shown to correspond to vector partitioning in a pseudo-Euclidean space, and is also linked to spectral partitioning methods, where the number of eigenvectors used corresponds to the dimensionality of the underlying embedding vector space. Inspired by the Louvain optimization for community detection, we then propose an algorithm based on a graph-theoretical heuristic for the vector partitioning problem. We apply the algorithm to the spectral optimization of modularity and Markov stability community detection. The spectral embedding based on the transition matrix eigenvectors leads to improved partitions with higher information content and higher modularity than the eigen-decomposition of the modularity matrix. We illustrate the results with random network benchmarks.

  • Journal article
    Aryaman J, hoitzing H, burgstaller J, johnston I, Jones NSet al., 2017,

    Mitochondrial heterogeneity, metabolic scaling and cell death

    , Bioessays, Vol: 39, ISSN: 1521-1878

    Heterogeneity in mitochondrial content has been previously suggested as a major contributor to cellular noise, with multiple studies indicating its direct involvement in biomedically important cellular phenomena. A recently published dataset explored the connection between mitochondrial functionality and cell physiology, where a non-linearity between mitochondrial functionality and cell size was found. Using mathematical models, we suggest that a combination of metabolic scaling and a simple model of cell death may account for these observations. However, our findings also suggest the existence of alternative competing hypotheses, such as a non-linearity between cell death and cell size. While we find that the proposed non-linear coupling between mitochondrial functionality and cell size provides a compelling alternative to previous attempts to link mitochondrial heterogeneity and cell physiology, we emphasise the need to account for alternative causal variables, including cell cycle, size, mitochondrial density and death, in future studies of mitochondrial physiology.

  • Journal article
    Johnson S, Jones NS, 2017,

    Looplessness in networks is linked to trophic coherence

    , Proceedings of the National Academy of Sciences of USA, Vol: 114, Pages: 5618-5623, ISSN: 0027-8424

    Many natural, complex systems are remarkably stable thanks to anabsence of feedback acting on their elements. When described as net-works, these exhibit few or no cycles, and associated matrices have smallleading eigenvalues. It has been suggested that this architecture can con-fer advantages to the system as a whole, such as ‘qualitative stability’,but this observation does not in itself explain how a loopless structuremight arise. We show here that the number of feedback loops in a net-work, as well as the eigenvalues of associated matrices, are determined bya structural property called trophic coherence, a measure of how neatlynodes fall into distinct levels. Our theory correctly classifies a variety ofnetworks – including those derived from genes, metabolites, species, neu-rons, words, computers and trading nations – into two distinct regimesof high and low feedback, and provides a null model to gauge the signifi-cance of related magnitudes. Since trophic coherence suppresses feedback,whereas an absence of feedback alone does not lead to coherence, our worksuggests that the reasons for ‘looplessness’ in nature should be sought incoherence-inducing mechanisms.

  • Journal article
    Kiselev V, Kirschner K, Schaub MT, Andrews T, Yiu A, Chandra T, Natarajan KN, Reik W, Barahona M, Green AR, Hemberg Met al., 2017,

    SC3: consensus clustering of single-cell RNA-seq data

    , Nature Methods, Vol: 14, Pages: 483-486, ISSN: 1548-7105

    Single-cell RNA-seq enables the quantitative characterization of cell types based on global transcriptome profiles. We present single-cell consensus clustering (SC3), a user-friendly tool for unsupervised clustering, which achieves high accuracy and robustness by combining multiple clustering solutions through a consensus approach (http://bioconductor.org/packages/SC3). We demonstrate that SC3 is capable of identifying subclones from the transcriptomes of neoplastic cells collected from patients.

  • Journal article
    Dawes T, Simoes monteiro de marvao A, Shi W, Fletcher T, Watson G, Wharton J, Rhodes C, Howard L, Gibbs J, Rueckert D, Cook S, Wilkins M, O'Regan DPet al., 2017,

    Machine learning of three-dimensional right ventricular motion enables outcome prediction in pulmonary hypertension: a cardiac MR imaging study

    , Radiology, Vol: 283, Pages: 381-390, ISSN: 1527-1315

    Purpose: To determine if patient survival and mechanisms of right ventricular (RV) failure in pulmonary hypertension (PH) could be predicted using supervised machine learning of three dimensional patterns of systolic cardiac motion. Materials and methods: The study was approved by a research ethics committee and participants gave written informed consent. 256 patients (143 females, mean age 63 ± 17) with newly diagnosed PH underwent cardiac MR imaging, right heart catheterization (RHC) and six minute walk testing (6MWT) with a median follow up of 4.0 years. Semi automated segmentation of short axis cine images was used to create a three dimensional model of right ventricular motion. Supervised principal components analysis identified patterns of systolic motion which were most strongly predictive of survival. Survival prediction was assessed by the difference in median survival time and the area under the curve (AUC) using time dependent receiver operator characteristic for one year survival. Results: At the end of follow up 33% (93/256) died and one underwent lung transplantation. Poor outcome was predicted by a loss of effective contraction in the septum and freewall coupled with reduced basal longitudinal motion. When added to conventional imaging, hemodynamic, functional and clinical markers, three dimensional cardiac motion improved survival prediction (area under the curve 0.73 vs 0.60, p<0.001) and provided greater differentiation by difference in median survival time between high and low risk groups (13.8 vs 10.7 years, p<0.001). Conclusion:Three dimensional motion modeling with machine learning approaches reveal the adaptations in function that occur early in right heart failure and independently predict outcomes in newly diagnosed PH patients.

  • Journal article
    Gosztolai A, Schumacher J, Behrends V, Bundy JG, Heydenreich F, Bennett MH, Buck M, Barahona Met al., 2017,

    GlnK Facilitates the Dynamic Regulation of Bacterial Nitrogen Assimilation.

    , Biophysical journal, Vol: 112, Pages: 2219-2230, ISSN: 0006-3495

    Ammonium assimilation in Escherichia coli is regulated by two paralogous proteins (GlnB and GlnK), which orchestrate interactions with regulators of gene expression, transport proteins, and metabolic pathways. Yet how they conjointly modulate the activity of glutamine synthetase, the key enzyme for nitrogen assimilation, is poorly understood. We combine experiments and theory to study the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We measure time-resolved in vivo concentrations of metabolites, total and posttranslationally modified proteins, and develop a concise biochemical model of GlnB and GlnK that incorporates competition for active and allosteric sites, as well as functional sequestration of GlnK. The model predicts the responses of glutamine synthetase, GlnB, and GlnK under time-varying external ammonium level in the wild-type and two genetic knock-outs. Our results show that GlnK is tightly regulated under nitrogen-rich conditions, yet it is expressed during ammonium run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen shock after starvation, and provides a further functional link between nitrogen and carbon metabolisms.

  • Journal article
    Colijn C, Jones N, Johnston I, Yaliraki SN, Barahona Met al., 2017,

    Towards precision healthcare: context and mathematical challenges

    , Frontiers in Physiology, Vol: 8, ISSN: 1664-042X

    Precision medicine refers to the idea of delivering the right treatment to the right patient at the right time, usually with a focus on a data-centred approach to this task. In this perspective piece, we use the term "precision healthcare" to describe the development of precision approaches that bridge from the individual to the population, taking advantage of individual-level data, but also taking the social context into account. These problems give rise to a broad spectrum of technical, scientific, policy, ethical and social challenges, and new mathematical techniques will be required to meet them. To ensure that the science underpin-ning "precision" is robust, interpretable and well-suited to meet the policy, ethical and social questions that such approaches raise, the mathematical methods for data analysis should be transparent, robust and able to adapt to errors and uncertainties. In particular, precision methodologies should capture the complexity of data, yet produce tractable descriptions at the relevant resolution while preserving intelligibility and traceability, so that they can be used by practitioners to aid decision-making. Through several case studies in this domain of precision healthcare, we argue that this vision requires the development of new mathematical frameworks, both in modelling and in data analysis and interpretation.

  • Journal article
    Didelot X, Fraser C, Gardy J, Colijn Cet al., 2017,

    Genomic infectious disease epidemiology in partially sampled and ongoing outbreaks

    , Molecular Biology and Evolution, Vol: 34, Pages: 997-1007, ISSN: 1537-1719

    Genomic data is increasingly being used to understand infectious disease epidemiology. Isolates from a given outbreak are sequenced, and the patterns of shared variation are used to infer which isolates within the outbreak are most closely related to each other. Unfortunately, thephylogenetic trees typically used to represent this variation are not directly informative about who infected whom { a phylogenetic tree is not a transmission tree. However, a transmission tree can be inferred from a phylogeny while accounting for within-host genetic diversity by colouring the branches of a phylogeny according to which host those branches were in. Here we extend this approach and show that it can be applied to partially sampled and ongoing outbreaks. This requires computing the correct probability of an observed transmission tree and we herein demonstrate how to do this for a large class of epidemiological models. Wealso demonstrate how the branch colouring approach can incorporate a variable number of unique colours to represent unsampled intermediates in transmission chains. The resulting algorithm is a reversible jump Monte-Carlo Markov Chain, which we apply to both simulated data and real data from an outbreak of tuberculosis. By accounting for unsampled cases and an outbreak which may not have reached its end, our method is uniquely suited to use in a public health environment during real-time outbreak investigations. We implemented this transmission tree inference methodology in an R package called TransPhylo, which is freely available from https://github.com/xavierdidelot/TransPhylo

  • Journal article
    Dattani J, Barahona M, 2017,

    Stochastic models of gene transcription with upstream drives: Exact solution and sample path characterisation

    , Journal of the Royal Society Interface, Vol: 14, ISSN: 1742-5689

    Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copynumber of a given gene is heterogeneous both between cells and across time. We present a frameworkto model gene transcription in populations of cells with time-varying (stochastic or deterministic)transcription and degradation rates. Such rates can be understood as upstream cellular drivesrepresenting the effect of different aspects of the cellular environment. We show that the full solutionof the master equation contains two components: a model-specific, upstream effective drive, whichencapsulates the effect of cellular drives (e.g., entrainment, periodicity or promoter randomness),and a downstream transcriptional Poissonian part, which is common to all models. Our analyticalframework treats cell-to-cell and dynamic variability consistently, unifying several approaches in theliterature. We apply the obtained solution to characterise different models of experimental relevance,and to explain the influence on gene transcription of synchrony, stationarity, ergodicity, as well asthe effect of time-scales and other dynamic characteristics of drives. We also show how the solutioncan be applied to the analysis of noise sources in single-cell data, and to reduce the computationalcost of stochastic simulations.

  • Journal article
    Beguerisse-Diaz M, McLennan AK, Garduño-Hernández G, Barahona M, Ulijaszek SJet al., 2017,

    The 'who' and 'what' of #diabetes on Twitter

    , Digital Health, Vol: 3, Pages: 1-29, ISSN: 2055-2076

    Social media are being increasingly used for health promotion, yet thelandscape of users, messages and interactions in such fora is poorlyunderstood. Studies of social media and diabetes have focused mostly onpatients, or public agencies addressing it, but have not looked broadly at allthe participants or the diversity of content they contribute. We study Twitterconversations about diabetes through the systematic analysis of 2.5 milliontweets collected over 8 months and the interactions between their authors. Weaddress three questions: (1) what themes arise in these tweets?; (2) who arethe most influential users?; (3) which type of users contribute to whichthemes? We answer these questions using a mixed-methods approach, integratingtechniques from anthropology, network science and information retrieval such asthematic coding, temporal network analysis, and community and topic detection.Diabetes-related tweets fall within broad thematic groups: health information,news, social interaction, and commercial. At the same time, humorous messagesand references to popular culture appear consistently, more than any other typeof tweet. We classify authors according to their temporal 'hub' and 'authority'scores. Whereas the hub landscape is diffuse and fluid over time, topauthorities are highly persistent across time and comprise bloggers, advocacygroups and NGOs related to diabetes, as well as for-profit entities withoutspecific diabetes expertise. Top authorities fall into seven interestcommunities as derived from their Twitter follower network. Our findings haveimplications for public health professionals and policy makers who seek to usesocial media as an engagement tool and to inform policy design.

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