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Journal articleKuntz J, Ottobre M, Stan G-B, et al., 2016,
Bounding stationary averages of polynomial diffusions via semidefinite programming
, SIAM Journal on Scientific Computing, Vol: 38, Pages: A3891-A3920, ISSN: 1095-7197We introduce an algorithm based on semidefinite programming that yields increasing (resp.decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusionswith polynomial drift vector and diffusion coefficients. The bounds are obtained byoptimising an objective, determined by the stationary average of interest, over the set of realvectors defined by certain linear equalities and semidefinite inequalities which are satisfied bythe moments of any stationary measure of the diffusion. We exemplify the use of the approachthrough several applications: a Bayesian inference problem; the computation of Lyapunov exponentsof linear ordinary differential equations perturbed by multiplicative white noise; and areliability problem from structural mechanics. Additionally, we prove that the bounds convergeto the infimum and supremum of the set of stationary averages for certain SDEs associated withthe computation of the Lyapunov exponents, and we provide numerical evidence of convergencein more general settings.
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Journal articleWeisse AY, Mannan AA, Oyarzun DA, 2016,
Signaling tug-of-war delivers the whole message
, Cell Systems, Vol: 3, Pages: 414-46, ISSN: 2405-4720How do cells transmit biochemical signals accurately? It turns out,pushing and pulling can go a long way.
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Journal articleJohnston 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: 1537-6605Populations of physiologically vital mitochondrial DNA (mtDNA) molecules evolve in cells under control from the nucleus. The evolution of populations of mixed mtDNA types is complicated and poorly understood, and variability of these controlled admixtures plays a central role in the inheritance and onset of genetic disease. Here, we develop a mathematical theory describing the evolution of, and variability in, these stochastic populations for any type of cellular control, showing that cell-to-cell variability in mtDNA and mutant load inevitably increases with time, according to rates that we derive and which are notably independent of the mechanistic details of feedback signaling. We show with a set of experimental case studies that this theory explains disparate quantitative results from classical and modern experimental and computational research on heteroplasmy variance in different species. We demonstrate that our general model provides a host of specific insights, including a modification of the often-used but hard-to-interpret Wright formula to correspond directly to biological observables, the ability to quantify selective and mutational pressure in mtDNA populations, and characterization of the pronounced variability inevitably arising from the action of possible mtDNA quality-control mechanisms. Our general theoretical framework, supported by existing experimental results, thus helps us to understand and predict the evolution of stochastic mtDNA populations in cell biology.
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Journal articleLarson HJ, de Figueiredo A, Xiahong Z, et al., 2016,
The state of vaccine confidence 2016: global insights through a 67-country survey
, EBioMedicine, Vol: 12, Pages: 295-301, ISSN: 2352-3964BackgroundPublic trust in immunization is an increasingly important global health issue. Losses in confidence in vaccines and immunization programmes can lead to vaccine reluctance and refusal, risking disease outbreaks and challenging immunization goals in high- and low-income settings. National and international immunization stakeholders have called for better monitoring of vaccine confidence to identify emerging concerns before they evolve into vaccine confidence crises.MethodsWe perform a large-scale, data-driven study on worldwide attitudes to immunizations. This survey – which we believe represents the largest survey on confidence in immunization to date – examines perceptions of vaccine importance, safety, effectiveness, and religious compatibility among 65,819 individuals across 67 countries. Hierarchical models are employed to probe relationships between individual- and country-level socio-economic factors and vaccine attitudes obtained through the four-question, Likert-scale survey.FindingsOverall sentiment towards vaccinations is positive across all 67 countries, however there is wide variability between countries and across world regions. Vaccine-safety related sentiment is particularly negative in the European region, which has seven of the ten least confident countries, with 41% of respondents in France and 36% of respondents in Bosnia & Herzegovina reporting that they disagree that vaccines are safe (compared to a global average of 13%). The oldest age group (65 +) and Roman Catholics (amongst all faiths surveyed) are associated with positive views on vaccine sentiment, while the Western Pacific region reported the highest level of religious incompatibility with vaccines. Countries with high levels of schooling and good access to health services are associated with lower rates of positive sentiment, pointing to an emerging inverse relationship between vaccine sentiments and socio-economic status.ConclusionsRegular monitoring of vaccine
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Journal articleSchaub MT, O'Clery N, Billeh YN, et al., 2016,
Graph partitions and cluster synchronization in networks of oscillators
, Chaos: an interdisciplinary journal of nonlinear science, Vol: 26, ISSN: 1054-1500Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.
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Journal articleBeguerisse 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: 1742-5689Cellular 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.
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Journal articleAmor BRC, Schaub MT, Yaliraki S, et al., 2016,
Prediction of allosteric sites and mediating interactions through bond-to-bond propensities
, Nature Communications, Vol: 7, Pages: 1-13, ISSN: 2041-1723Allostery is a fundamental mechanism of biological regulation, in which binding of a molecule at a distant location affects the active site of a protein. Allosteric sites provide targets to fine-tune protein activity, yet we lack computational methodologies to predict them. Here we present an efficient graph-theoretical framework to reveal allosteric interactions (atoms and communication pathways strongly coupled to the active site) without a priori information of their location. Using an atomistic graph with energy-weighted covalent and weak bonds, we define a bond-to-bond propensity quantifying the non-local effect of instantaneous bond fluctuations propagating through the protein. Significant interactions are then identified using quantile regression. We exemplify our method with three biologically important proteins: caspase-1, CheY, and h-Ras, correctly predicting key allosteric interactions, whose significance is additionally confirmed against a reference set of 100 proteins. The almost-linear scaling of our method renders it suitable for high-throughput searches for candidate allosteric sites.
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Journal articlede Figueiredo A, Johnston IG, Smith DM, et al., 2016,
Forecasted trends in vaccination coverage and correlations with socioeconomic factors: a global time-series analysis over 30 years.
, Lancet Global Health, Vol: 4, Pages: e726-e735, ISSN: 2214-109XBACKGROUND: Incomplete immunisation coverage causes preventable illness and death in both developing and developed countries. Identification of factors that might modulate coverage could inform effective immunisation programmes and policies. We constructed a performance indicator that could quantitatively approximate measures of the susceptibility of immunisation programmes to coverage losses, with an aim to identify correlations between trends in vaccine coverage and socioeconomic factors. METHODS: We undertook a data-driven time-series analysis to examine trends in coverage of diphtheria, tetanus, and pertussis (DTP) vaccination across 190 countries over the past 30 years. We grouped countries into six world regions according to WHO classifications. We used Gaussian process regression to forecast future coverage rates and provide a vaccine performance index: a summary measure of the strength of immunisation coverage in a country. FINDINGS: Overall vaccine coverage increased in all six world regions between 1980 and 2010, with variation in volatility and trends. Our vaccine performance index identified that 53 countries had more than a 50% chance of missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide coverage with three doses of DTP (DTP3) by 2015. These countries were mostly in sub-Saharan Africa and south Asia, but Austria and Ukraine also featured. Factors associated with DTP3 immunisation coverage varied by world region: personal income (Spearman's ρ=0·66, p=0·0011) and government health spending (0·66, p<0·0001) were informative of immunisation coverage in the Eastern Mediterranean between 1980 and 2010, whereas primary school completion was informative of coverage in Africa (0·56, p<0·0001) over the same period. The proportion of births attended by skilled health staff correlated significantly with immunisation coverage across many world regions. INTERPRETATION: Our vaccine performance inde
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Journal articleBacik KA, Schaub MT, Beguerisse-Diaz M, et al., 2016,
Flow-Based Network Analysis of the Caenorhabditis elegans Connectome
, PLOS Computational Biology, Vol: 12, ISSN: 1553-734XWe 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.
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Book chapterAmor B, Vuik S, Callahan R, et al., 2016,
Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate
, Dynamic Networks and Cyber-Security, Editors: Adams, Heard, Publisher: World Scientific, Pages: 111-136, ISBN: 978-1-60558752-3With the rise of social media as an important channel for the debate anddiscussion of public affairs, online social networks such as Twitter havebecome important platforms for public information and engagement by policymakers. To communicate effectively through Twitter, policy makers need tounderstand how influence and interest propagate within its network of users. Inthis chapter we use graph-theoretic methods to analyse the Twitter debatesurrounding NHS England's controversial care.data scheme. Directionality is acrucial feature of the Twitter social graph - information flows from thefollowed to the followers - but is often ignored in social network analyses;our methods are based on the behaviour of dynamic processes on the network andcan be applied naturally to directed networks. We uncover robust communities ofusers and show that these communities reflect how information flows through theTwitter network. We are also able to classify users by their differing roles indirecting the flow of information through the network. Our methods and resultswill be useful to policy makers who would like to use Twitter effectively as acommunication medium.
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