Imperial College London

ProfessorMauricioBarahona

Faculty of Natural SciencesDepartment of Mathematics

Chair in Biomathematics
 
 
 
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Contact

 

m.barahona Website

 
 
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Location

 

6M31Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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118 results found

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

Beguerisse-Díaz M, Bosque G, Oyarzún D, Picó J, Barahona Met al., 2017, Flux-dependent graphs for metabolic networks

Cells adapt their metabolic fluxes in response to changes in the environment.We present a systematic flux-based framework for the construction of graphs torepresent organism-wide metabolic networks. Our graphs encode thedirectionality of metabolic fluxes via links that represent the flow ofmetabolites from source to target reactions. The methodology can be applied inthe absence of a specific biological context by modelling fluxesprobabilistically, or can be tailored to different environmental conditions byincorporating flux distributions computed from constraint-based modelling suchas Flux Balance Analysis. We illustrate our approach on the central carbonmetabolism of Escherichia coli, and on a larger metabolic model of humanhepatocytes, and study the proposed graphs under various environmentalconditions and genetic perturbations. The results reveal drastic changes in thetopological and community structure of the metabolic graphs, which capture there-routing of metabolic fluxes under each growth and genetic condition. Byintegrating constraint-based models and tools from network science, ourframework allows for the interrogation of context-specific metabolic responsesbeyond fixed, standard pathway descriptions.

JOURNAL ARTICLE

Branch T, Barahona M, Dodson CA, Ying Let al., 2017, Kinetic Analysis Reveals the Identity of Aβ-Metal Complex Responsible for the Initial Aggregation of Aβ in the Synapse., ACS Chem Neurosci, Vol: 8, Pages: 1970-1979

The mechanism of Aβ aggregation in the absence of metal ions is well established, yet the role that Zn(2+) and Cu(2+), the two most studied metal ions, released during neurotransmission, paly in promoting Aβ aggregation in the vicinity of neuronal synapses remains elusive. Here we report the kinetics of Zn(2+) binding to Aβ and Zn(2+)/Cu(2+) binding to Aβ-Cu to form ternary complexes under near physiological conditions (nM Aβ, μM metal ions). We find that these reactions are several orders of magnitude slower than Cu(2+) binding to Aβ. Coupled reaction-diffusion simulations of the interactions of synaptically released metal ions with Aβ show that up to a third of Aβ is Cu(2+)-bound under repetitive metal ion release, while any other Aβ-metal complexes (including Aβ-Zn) are insignificant. We therefore conclude that Zn(2+) is unlikely to play an important role in the very early stages (i.e., dimer formation) of Aβ aggregation, contrary to a widely held view in the subject. We propose that targeting the specific interactions between Cu(2+) and Aβ may be a viable option in drug development efforts for early stages of AD.

JOURNAL ARTICLE

Colijn C, Jones N, Johnston IG, Yaliraki S, Barahona Met al., 2017, Toward Precision Healthcare: Context and Mathematical Challenges, FRONTIERS IN PHYSIOLOGY, Vol: 8, ISSN: 1664-042X

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

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 AssimilationS, BIOPHYSICAL JOURNAL, Vol: 112, Pages: 2219-2230, ISSN: 0006-3495

JOURNAL ARTICLE

Kiselev VY, 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-+, ISSN: 1548-7091

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

Liu Z, Barahona M, 2017, Geometric multiscale community detection: Markov stability and vector partitioning, Journal of Complex Networks, 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

Amor B, Vuik S, Callahan R, Darzi A, Yaliraki SN, Barahona Met 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: 978-1-60558752-3

With 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.

BOOK CHAPTER

Amor BRC, Schaub MT, Yaliraki S, Barahona Met al., 2016, Prediction of allosteric sites and mediating interactions through bond-to-bond propensities, Nature Communications, Vol: 7, ISSN: 2041-1723

Allostery 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.

JOURNAL ARTICLE

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.

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.

JOURNAL ARTICLE

Georgiou PS, Yaliraki SN, Drakakis EM, Barahona Met al., 2016, Window functions and sigmoidal behaviour of memristive systems, INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Vol: 44, Pages: 1685-1696, ISSN: 0098-9886

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: 1064-8275

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, Vol: 26, ISSN: 1054-1500

JOURNAL ARTICLE

Branch T, Barahona M, Ying L, 2015, Secondary Metal Binding to Amyloid-Beta Monomer is Insignificant under Synaptic Conditions, 59th Annual Meeting of the Biophysical-Society, Publisher: CELL PRESS, Pages: 385A-385A, ISSN: 0006-3495

CONFERENCE PAPER

Branch T, Girvan P, Barahona M, Ying Let al., 2015, Introduction of a Fluorescent Probe to Amyloid-beta to Reveal Kinetic Insights into Its Interactions with Copper(II), ANGEWANDTE CHEMIE-INTERNATIONAL EDITION, Vol: 54, Pages: 1227-1230, ISSN: 1433-7851

JOURNAL ARTICLE

Branch T, Girvan P, Barahona M, Ying Let al., 2015, Kinetics of amyloid-beta/metal ions interactions in the synaptic cleft: experiment and simulation, 10th European-Biophysical-Societies-Association (EBSA) European Biophysics Congress, Publisher: SPRINGER, Pages: S230-S230, ISSN: 0175-7571

CONFERENCE PAPER

Noseda M, Harada M, McSweeney S, Leja T, Belian E, Stuckey DJ, Abreu Paiva MS, Habib J, Macaulay I, de Smith AJ, Al-Beidh F, Sampson R, Lumbers RT, Rao P, Harding SE, Blakemore AI, Eirik Jacobsen S, Barahona M, Schneider MDet al., 2015, PDGFRα demarcates the cardiogenic clonogenic Sca1(+) stem/progenitor cell in adult murine myocardium., Nature Communications, Vol: 6, Pages: 6930-6930, ISSN: 2041-1723

Cardiac progenitor/stem cells in adult hearts represent an attractive therapeutic target for heart regeneration, though (inter)-relationships among reported cells remain obscure. Using single-cell qRT-PCR and clonal analyses, here we define four subpopulations of cardiac progenitor/stem cells in adult mouse myocardium all sharing stem cell antigen-1 (Sca1), based on side population (SP) phenotype, PECAM-1 (CD31) and platelet-derived growth factor receptor-α (PDGFRα) expression. SP status predicts clonogenicity and cardiogenic gene expression (Gata4/6, Hand2 and Tbx5/20), properties segregating more specifically to PDGFRα(+) cells. Clonal progeny of single Sca1(+) SP cells show cardiomyocyte, endothelial and smooth muscle lineage potential after cardiac grafting, augmenting cardiac function although durable engraftment is rare. PDGFRα(-) cells are characterized by Kdr/Flk1, Cdh5, CD31 and lack of clonogenicity. PDGFRα(+)/CD31(-) cells derive from cells formerly expressing Mesp1, Nkx2-5, Isl1, Gata5 and Wt1, distinct from PDGFRα(-)/CD31(+) cells (Gata5 low; Flk1 and Tie2 high). Thus, PDGFRα demarcates the clonogenic cardiogenic Sca1(+) stem/progenitor cell.

JOURNAL ARTICLE

Schaub MT, Billeh YN, Anastassiou CA, Koch C, Barahona Met al., 2015, Emergence of Slow-Switching Assemblies in Structured Neuronal Networks, PLOS COMPUTATIONAL BIOLOGY, Vol: 11, ISSN: 1553-734X

JOURNAL ARTICLE

Sim A, Yaliraki SN, Barahona M, Stumpf MPet al., 2015, Great cities look small., Journal of the Royal Society Interface, Vol: 12, ISSN: 1742-5689

Great cities connect people; failed cities isolate people. Despite the fundamental importance of physical, face-to-face social ties in the functioning of cities, these connectivity networks are not explicitly observed in their entirety. Attempts at estimating them often rely on unrealistic over-simplifications such as the assumption of spatial homogeneity. Here we propose a mathematical model of human interactions in terms of a local strategy of maximizing the number of beneficial connections attainable under the constraint of limited individual travelling-time budgets. By incorporating census and openly available online multi-modal transport data, we are able to characterize the connectivity of geometrically and topologically complex cities. Beyond providing a candidate measure of greatness, this model allows one to quantify and assess the impact of transport developments, population growth, and other infrastructure and demographic changes on a city. Supported by validations of gross domestic product and human immunodeficiency virus infection rates across US metropolitan areas, we illustrate the effect of changes in local and city-wide connectivities by considering the economic impact of two contemporary inter- and intra-city transport developments in the UK: High Speed 2 and London Crossrail. This derivation of the model suggests that the scaling of different urban indicators with population size has an explicitly mechanistic origin.

JOURNAL ARTICLE

Stroud J, Barahona M, Pereira T, 2015, Dynamics of cluster synchronisation in modular networks: implications for structural and functional networks, Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4, Editors: Banerjee, Rondoni, Publisher: Springer International Publishing, Pages: 107-130, ISBN: 978-3-319-17036-7

Experimental results often do not assess network structure; rather, thenetwork structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. A fundamental question in the analysis of complex systems concerns the relation between functional and structural networks. Using synchronisation as a paradigm for network functionality, we study the dynamics of cluster formation in functional networks. We show that the functional network can drastically differ from the structural network. We uncover the mechanism driving these bifurcations by obtaining necessary conditions for modular synchronisation.

BOOK CHAPTER

Wang B, Barahona M, Buck M, 2015, Amplification of small molecule-inducible gene expression via tuning of intracellular receptor densities, NUCLEIC ACIDS RESEARCH, Vol: 43, Pages: 1955-1964, ISSN: 0305-1048

JOURNAL ARTICLE

Amor B, Yaliraki SN, Woscholski R, Barahona Met al., 2014, Uncovering allosteric pathways in caspase-1 using Markov transient analysis and multiscale community detection, MOLECULAR BIOSYSTEMS, Vol: 10, Pages: 2247-2258, ISSN: 1742-206X

JOURNAL ARTICLE

Beguerisse-Díaz M, Garduño-Hernández G, Vangelov B, Yaliraki SN, Barahona Met al., 2014, Interest communities and flow roles in directed networks: the Twitter network of the UK riots, J. R. Soc. Interface 6 December 2014, Vol: 11

Directionality is a crucial ingredient in many complex networks in whichinformation, energy or influence are transmitted. In such directed networks,analysing flows (and not only the strength of connections) is crucial to revealimportant features of the network that might go undetected if the orientationof connections is ignored. We showcase here a flow-based approach for communitydetection in networks through the study of the network of the most influentialTwitter users during the 2011 riots in England. Firstly, we use directed MarkovStability to extract descriptions of the network at different levels ofcoarseness in terms of interest communities, i.e., groups of nodes within whichflows of information are contained and reinforced. Such interest communitiesreveal user groupings according to location, profession, employer, and topic.The study of flows also allows us to generate an interest distance, whichaffords a personalised view of the attention in the network as viewed from thevantage point of any given user. Secondly, we analyse the profiles of incomingand outgoing long-range flows with a combined approach of role-based similarityand the novel relaxed minimum spanning tree algorithm to reveal that the usersin the network can be classified into five roles. These flow roles go beyondthe standard leader/follower dichotomy and differ from classifications based onregular/structural equivalence. We then show that the interest communities fallinto distinct informational organigrams characterised by a different mix ofuser roles reflecting the quality of dialogue within them. Our genericframework can be used to provide insight into how flows are generated,distributed, preserved and consumed in directed networks.

JOURNAL ARTICLE

Billeh YN, Schaub MT, Anastassiou CA, Barahona M, Koch Cet al., 2014, Revealing cell assemblies at multiple levels of granularity, JOURNAL OF NEUROSCIENCE METHODS, Vol: 236, Pages: 92-106, ISSN: 0165-0270

JOURNAL ARTICLE

Branch T, Barahona M, Ying L, 2014, Kinetics of the Interconversion Between Two Physiologically Important Copper-Bound Amyloid-Beta Species, 58th Annual Meeting of the Biophysical-Society, Publisher: CELL PRESS, Pages: 682A-682A, ISSN: 0006-3495

CONFERENCE PAPER

Branch T, Evans M, Barahona M, Ying Let al., 2014, Kinetics of Metal Amyloid-Beta Binding and Efficacy of Ligands Targeting Metal Amyloid-Beta Interactions, 58th Annual Meeting of the Biophysical-Society, Publisher: CELL PRESS, Pages: 39A-39A, ISSN: 0006-3495

CONFERENCE PAPER

Georgiou PS, Barahona M, Yaliraki SN, Drakakis EMet al., 2014, On memristor ideality and reciprocity, MICROELECTRONICS JOURNAL, Vol: 45, Pages: 1363-1371, ISSN: 0026-2692

JOURNAL ARTICLE

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