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  • Book chapter
    Andreychenko A, Bortolussi L, Grima R, Thomas P, Wolf Vet al., 2017,

    Distribution approximations for the chemical master equation: comparisonof the method of moments and the system size expansion

    , Modeling Cellular Systems, Editors: Graw, Matthaus, Pahle, Publisher: Springer, Pages: 39-39, ISBN: 978-3-319-45833-5

    The stochastic nature of chemical reactions involving randomly fluctuatingpopulation sizes has lead to a growing research interest in discrete-statestochastic models and their analysis. A widely-used approach is the descriptionof the temporal evolution of the system in terms of a chemical master equation(CME). In this paper we study two approaches for approximating the underlyingprobability distributions of the CME. The first approach is based on anintegration of the statistical moments and the reconstruction of thedistribution based on the maximum entropy principle. The second approach relieson an analytical approximation of the probability distribution of the CME usingthe system size expansion, considering higher-order terms than the linear noiseapproximation. We consider gene expression networks with unimodal andmultimodal protein distributions to compare the accuracy of the two approaches.We find that both methods provide accurate approximations to the distributionsof the CME while having different benefits and limitations in applications.
  • 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
    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
    Schaub M, Billeh YN, Anastassiou CA, Koch C, Barahona Met al., 2017,

    Emergence of Slow-Switching Assemblies in Structured Neuronal Networks

    , PLOS COMPUTATIONAL BIOLOGY, Vol: 13, ISSN: 1553-734X
  • 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.
  • Journal article
    Kuntz J, Ottobre M, Stan G-B, Barahona Met al., 2016,

    Bounding stationary averages of polynomial diffusions via semidefinite programming

    , SIAM Journal on Scientific Computing, Vol: 38, Pages: A3891-A3920, ISSN: 1095-7197

    We 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.
  • Journal article
    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: an interdisciplinary journal of nonlinear science, Vol: 26, ISSN: 1054-1500

    Synchronization 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.
  • Journal article
    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.

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