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  • Journal article
    Georgiou PS, Yaliraki SN, Drakakis EM, Barahona Met al., 2012,

    Quantitative Measure of Hysteresis for Memristors through Explicit Dynamics

    , Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol: 468, Pages: 2210-2229, ISSN: 1471-2946
  • Conference paper
    Thomas P, Matuschek H, Grima R, 2012,

    Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA

    , Pages: 1-5
  • Journal article
    Strelkowa N, Barahona M, 2012,

    Stochastic Oscillatory Dynamics of Generalized Repressilators

    , NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, Vol: 1479, Pages: 662-666, ISSN: 0094-243X
  • Conference paper
    Dominguez-Huttinger E, Ono M, Barahona M, Tanaka Ret al., 2011,

    Mathematical modelling approach for systems-level understanding of skin barrier homeostasis in Atopic dermatitis

    , Annual Congress of the British-Society-for-Immunology, Publisher: WILEY-BLACKWELL, Pages: 36-36, ISSN: 0019-2805
  • Conference paper
    Yuan Y, Stan G-B, Barahona M, Shi L, Goncalves Jet al., 2011,

    Decentralised minimal-time consensus

    , Publisher: IEEE, Pages: 4282 -4289-4282 -4289, ISSN: 0743-1546

    This study considers the discrete-time dynamics of a network of agents that exchange information according to the nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We show that this minimal number of steps is related to a Jordan block decomposition of the network dynamics and present an algorithm to obtain the minimal number of steps in question by checking a rank condition on a Hankel matrix of the local observations. Furthermore, we prove that the minimal number of steps is related to other algebraic and graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the underlying graph topology.
  • Journal article
    Thomas P, Straube AV, Grima R, 2011,

    Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

    , Journal of Chemical Physics, Vol: 135, ISSN: 1089-7690

    It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.
  • Journal article
    Wu J, Barahona M, Tan Y-J, Deng H-Zet al., 2011,

    Spectral Measure of Structural Robustness in Complex Networks

    , Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, Vol: 41, Pages: 1244 -1252-1244 -1252, ISSN: 1083-4427

    We introduce the concept of natural connectivity as a measure of structural robustness in complex networks. The natural connectivity characterizes the redundancy of alternative routes in a network by quantifying the weighted number of closed walks of all lengths. This definition leads to a simple mathematical formulation that links the natural connectivity to the spectrum of a network. The natural connectivity can be regarded as an average eigenvalue that changes strictly monotonically with the addition or deletion of edges. We calculate both analytically and numerically the natural connectivity of three typical networks: regular ring lattices, random graphs, and random scale-free networks. We also compare the proposed natural connectivity to other structural robustness measures within a scenario of edge elimination and demonstrate that the natural connectivity provides sensitive discrimination of structural robustness that agrees with our intuition.
  • Journal article
    Delmotte A, Tate EW, Yaliraki SN, Barahona Met al., 2011,

    Protein multi-scale organization through graph partitioning and robustness analysis: application to the myosin-myosin light chain interaction

    , PHYSICAL BIOLOGY, Vol: 8, ISSN: 1478-3975

    Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.
  • Journal article
    Georgiou PS, Barahona M, Yaliraki SN, Drakakis EMet al., 2011,

    Device Properties of Bernoulli Memristors

    , Proceedings of the IEEE, Vol: 100, Pages: 1-13, ISSN: 0018-9219
  • Journal article
    Grima R, Thomas P, Straube AV, 2011,

    How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

    , Journal of Chemical Physics, Vol: 135, ISSN: 1089-7690

    The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.

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