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    Colijn C, Jones N, Johnston I, Yaliraki SN, Barahona Met al.,

    Towards precision healthcare: context and mathematical challenges

    , Frontiers in Physiology, 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.

    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.

    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, 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.

    Kuntz J, Thomas P, Stan G-B, Barahona Met al., 2017,

    Rigorous bounds on the stationary distributions of the chemical master equation via mathematical programming

    The stochastic dynamics of networks of biochemical reactions in living cellsare typically modelled using chemical master equations (CMEs). The stationarydistributions of CMEs are seldom solvable analytically, and few methods existthat yield numerical estimates with computable error bounds. Here, we presenttwo such methods based on mathematical programming techniques. First, we usesemidefinite programming to obtain increasingly tighter upper and lower boundson the moments of the stationary distribution for networks with rationalpropensities. Second, we employ linear programming to compute convergent upperand lower bounds on the stationary distributions themselves. The boundsobtained provide a computational test for the uniqueness of the stationarydistribution. In the unique case, the bounds collectively form an approximationof the stationary distribution accompanied with a computable $\ell^1$-errorbound. In the non-unique case, we explain how to adapt our approach so that ityields approximations of the ergodic distributions, also accompanied withcomputable error bounds. We illustrate our methodology through two biologicalexamples: Schl\"ogl's model and a toggle switch model.

    Amor BRC, Schaub MT, Yaliraki SN, Barahona Met al., 2016,

    Prediction of allosteric sites and mediating interactions through bond-to-bond propensities

    , NATURE COMMUNICATIONS, Vol: 7, ISSN: 2041-1723
    Bacik KA, Schaub MT, Beguerisse-Diaz M, Billeh YN, Barahona Met al., 2016,

    Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

    , PLOS Computational Biology, Vol: 12, ISSN: 1553-734X

    We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios.

    Beguerisse Diaz M, Desikan R, Barahona M, 2016,

    Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

    , Journal of the Royal Society Interface, Vol: 13, ISSN: 1742-5689

    Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal-gain cascades (i.e., when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

    Johnston IG, Jones NS, 2016,

    Evolution of Cell-to-Cell Variability in Stochastic, Controlled, Heteroplasmic mtDNA Populations

    , AMERICAN JOURNAL OF HUMAN GENETICS, Vol: 99, Pages: 1150-1162, ISSN: 0002-9297
    Kuntz J, Ottobre M, Stan G-B, Barahona Met al., 2016,


    , SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 38, Pages: A3891-A3920, ISSN: 1064-8275
    Larson HJ, de Figueiredo A, Xiahong Z, Schulz WS, Verger P, Johnston IG, Cook AR, Jones NSet al., 2016,

    The State of Vaccine Confidence 2016: Global Insights Through a 67-Country Survey

    , EBioMedicine, Vol: 12, Pages: 295-301, ISSN: 2352-3964

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