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Journal articleFröhlich F, Thomas P, Kazeroonian A, et al., 2016,
Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion
, PLOS Computational Biology, Vol: 12, ISSN: 1553-734XQuantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity.
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Journal articleVoliotis M, Thomas P, Grima R, et al., 2016,
Stochastic simulation of biomolecular networks in dynamic environments
, PLOS Computational Biology, Vol: 12, ISSN: 1553-734XSimulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.
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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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Journal articleGeorgiou PS, Yaliraki SN, Drakakis EM, et al., 2016,
Window functions and sigmoidal behaviour of memristive systems
, International Journal of Circuit Theory and Applications, Vol: 44, Pages: 1685-1696, ISSN: 0098-9886Summary: A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner.
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Conference paperBranch T, Girvan P, Barahona M, et al., 2015,
Kinetics of amyloid-beta/metal ions interactions in the synaptic cleft: experiment and simulation
, 10th EBSA European Biophysics Congress, Publisher: Springer Verlag, Pages: S230-S230, ISSN: 0175-7571 -
Journal articleSim A, Yaliraki SN, Barahona M, et al., 2015,
Great cities look small.
, Journal of the Royal Society Interface, Vol: 12, ISSN: 1742-5689Great 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.
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Journal articleThomas P, Grima R, 2015,
Approximate probability distributions of the master equation
, Physical Review E, Vol: 92, Pages: 012120-012120-12, ISSN: 1539-3755Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
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Journal articleNoseda M, Harada M, McSweeney S, et al., 2015,
PDGFRα demarcates the cardiogenic clonogenic Sca1(+) stem/progenitor cell in adult murine myocardium
, Nature Communications, Vol: 6, ISSN: 2041-1723Cardiac 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.
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Journal articleWang 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 -
Conference paperBranch 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
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