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    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, Zhao X, 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
    Schaub MT, O'Clery N, Billeh YN, Delvenne J-C, Lambiotte R, Barahona Met al., 2016,

    Graph partitions and cluster synchronization in networks of oscillators

    , CHAOS, Vol: 26, ISSN: 1054-1500
    de Figueiredo A, Johnston IG, Smith DMD, Agarwal S, Larson HJ, Jones NSet al., 2016,

    Forecasting time-series trends in vaccination coverage and their links with socio-economic factors: A global analysis over 30 years

    , Lancet Global Health, ISSN: 2214-109X

    Background Incomplete immunisation coverage causes preventable illness and death in both the developing anddeveloped world. Identifying factors that may modulate coverage can inform effective immunisation programmes andpolicies.Methods We perform a data-driven analysis of unprecedented scale, examining time-varying trends in Diphtheriatetanus-pertussiscoverage across 190 countries over the past three decades. Gaussian process regression is employedto forecast future coverage rates and provide a Vaccine Performance Index: a summary measure of the strength ofimmunisation coverage in a country.Findings Overall vaccine coverage has increased in all five world regions between 1980 and 2010, with markedvariation in volatility and trends. Our Vaccine Performance Index identifies 53 countries with a less than 50% chanceof missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide DTP3 coverage by 2015, in agreementwith recent immunisation data. These countries are mostly sub-Saharan and South Asian, but Austria and Ukraine inEurope also feature. Factors associated with DTP3 immunisation coverage vary by world-region: personal income(! = 0.66, ' < 0.001) and government health spending (! = 0.66, ' < 0.01) are particularly informative in theEastern Mediterranean between 1980 and 2010, whilst primary school completion is informative in Africa (! =0.56, ' < 0.001) over the same time. The fraction of births attended by skilled health staff is significantly informativeacross many world regionsInterpretation A Vaccine Performance Index can highlight countries at risk identifying the strength and resilience ofimmunisation programmes. Weakening correlations with socio-economic factors indicate a need to tackle vaccineconfidence whereas strengthening correlations points to clear factors to address.

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