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AuthorGoriely, Alain (19)Byrne, Helen M. (18)Erban, Radek (17)Goriely, A. (17)Vella, Dominic (14)View MoreJournalPhysical Review E (18)Bulletin of Mathematical Biology (15)SIAM Journal on Applied Mathematics (14)Journal of Fluid Mechanics (12)Journal of Theoretical Biology (12)View MoreKAUST Grant Number

KUK-C1-013-04 (327)

PublisherElsevier BV (50)Springer Nature (49)Society for Industrial & Applied Mathematics (SIAM) (36)American Physical Society (APS) (27)AIP Publishing (19)View MoreSubjectAsymptotic analysis (10)Preconditioning (7)lubrication theory (6)capillary flows (5)Elasticity (5)View MoreTypeArticle (319)Book Chapter (5)Conference Paper (3)Year (Issue Date)2017 (3)2016 (2)2015 (21)2014 (54)2013 (83)View MoreItem AvailabilityMetadata Only (314)Open Access (13)

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A Metabolite-Sensitive, Thermodynamically Constrained Model of Cardiac Cross-Bridge Cycling: Implications for Force Development during Ischemia

Tran, Kenneth; Smith, Nicolas P.; Loiselle, Denis S.; Crampin, Edmund J. (Biophysical Journal, Elsevier BV, 2010-01) [Article]

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on a model of cross-bridge kinetics that was developed by others, reproduces many of the observed effects of MgATP, MgADP, Pi, and H(+) on force development while retaining the force/length/Ca(2+) properties of the original model. We introduce three new parameters to account for the competitive binding of H(+) to the Ca(2+) binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters, along with the Pi and H(+) regulatory steps within the cross-bridge cycle, were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H(+)]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.

A pinned or free-floating rigid plate on a thin viscous film

Trinh, Philippe H.; Wilson, Stephen K.; Stone, Howard A. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014-11-11) [Article]

© 2014 Cambridge University Press. A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid-structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.

A constrained approach to multiscale stochastic simulation of chemically reacting systems

Cotter, Simon L.; Zygalakis, Konstantinos C.; Kevrekidis, Ioannis G.; Erban, Radek (The Journal of Chemical Physics, AIP Publishing, 2011) [Article]

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems. © 2011 American Institute of Physics.

The problem of pseudoreplication in neuroscientific studies: is it affecting your analysis?

Lazic, Stanley E (BMC Neuroscience, Springer Nature, 2010-01-14) [Article]

BACKGROUND: Pseudoreplication occurs when observations are not statistically independent, but treated as if they are. This can occur when there are multiple observations on the same subjects, when samples are nested or hierarchically organised, or when measurements are correlated in time or space. Analysis of such data without taking these dependencies into account can lead to meaningless results, and examples can easily be found in the neuroscience literature. RESULTS: A single issue of Nature Neuroscience provided a number of examples and is used as a case study to highlight how pseudoreplication arises in neuroscientific studies, why the analyses in these papers are incorrect, and appropriate analytical methods are provided. 12% of papers had pseudoreplication and a further 36% were suspected of having pseudoreplication, but it was not possible to determine for certain because insufficient information was provided. CONCLUSIONS: Pseudoreplication can undermine the conclusions of a statistical analysis, and it would be easier to detect if the sample size, degrees of freedom, the test statistic, and precise p-values are reported. This information should be a requirement for all publications.

A Comparison of Fully Automated Methods of Data Analysis and Computer Assisted Heuristic Methods in an Electrode Kinetic Study of the Pathologically Variable [Fe(CN) 6 ] 3–/4– Process by AC Voltammetry

Morris, Graham P.; Simonov, Alexandr N.; Mashkina, Elena A.; Bordas, Rafel; Gillow, Kathryn; Baker, Ruth E.; Gavaghan, David J.; Bond, Alan M. (Analytical Chemistry, American Chemical Society (ACS), 2013-12-17) [Article]

Fully automated and computer assisted heuristic data analysis approaches have been applied to a series of AC voltammetric experiments undertaken on the [Fe(CN)6]3-/4- process at a glassy carbon electrode in 3 M KCl aqueous electrolyte. The recovered parameters in all forms of data analysis encompass E0 (reversible potential), k0 (heterogeneous charge transfer rate constant at E0), α (charge transfer coefficient), Ru (uncompensated resistance), and Cdl (double layer capacitance). The automated method of analysis employed time domain optimization and Bayesian statistics. This and all other methods assumed the Butler-Volmer model applies for electron transfer kinetics, planar diffusion for mass transport, Ohm's Law for Ru, and a potential-independent Cdl model. Heuristic approaches utilize combinations of Fourier Transform filtering, sensitivity analysis, and simplex-based forms of optimization applied to resolved AC harmonics and rely on experimenter experience to assist in experiment-theory comparisons. Remarkable consistency of parameter evaluation was achieved, although the fully automated time domain method provided consistently higher α values than those based on frequency domain data analysis. The origin of this difference is that the implemented fully automated method requires a perfect model for the double layer capacitance. In contrast, the importance of imperfections in the double layer model is minimized when analysis is performed in the frequency domain. Substantial variation in k0 values was found by analysis of the 10 data sets for this highly surface-sensitive pathologically variable [Fe(CN) 6]3-/4- process, but remarkably, all fit the quasi-reversible model satisfactorily. © 2013 American Chemical Society.

A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell

Wright, G. B.; Flyer, N.; Yuen, D. A. (Geochemistry, Geophysics, Geosystems, Wiley-Blackwell, 2010-07) [Article]

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth's mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 10<sup>3</sup> and 10<sup>5</sup>. Results from a Ra = 10<sup>6</sup> simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature. Copyright 2010 by the American Geophysical Union.

A multiscale analysis of nutrient transport and biological tissue growth in vitro

O'Dea, R. D.; Nelson, M. R.; El Haj, A. J.; Waters, S. L.; Byrne, H. M. (Mathematical Medicine and Biology, Oxford University Press (OUP), 2014-10-15) [Article]

© The authors 2014. In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenization method to accommodate explicitly the influence of the underlying microscale structure of the material, and its evolution, on the macroscale dynamics. Such methods have been widely used to study porous and poroelastic materials; however, a distinguishing feature of biological tissue is its ability to remodel continuously in response to local environmental cues. Here, we present the derivation of a model broadly applicable to tissue engineering applications, characterized by cell proliferation and extracellular matrix deposition in porous scaffolds used within tissue culture systems, which we use to study coupling between fluid flow, nutrient transport, and microscale tissue growth. Attention is restricted to surface accretion within a rigid porous medium saturated with a Newtonian fluid; coupling between the various dynamics is achieved by specifying the rate of microscale growth to be dependent upon the uptake of a generic diffusible nutrient. The resulting macroscale model comprises a Darcy-type equation governing fluid flow, with flow characteristics dictated by the assumed periodic microstructure and surface growth rate of the porous medium, coupled to an advection-reaction equation specifying the nutrient concentration. Illustrative numerical simulations are presented to indicate the influence of microscale growth on macroscale dynamics, and to highlight the importance of including experimentally relevant microstructural information to correctly determine flow dynamics and nutrient delivery in tissue engineering applications.

A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection

Hennessy, Matthew G.; Münch, Andreas (SIAM Journal on Applied Mathematics, Society for Industrial & Applied Mathematics (SIAM), 2013-04-23) [Article]

This paper considers the stability of thin liquid layers of binary mixtures of a volatile (solvent) species and a nonvolatile (polymer) species. Evaporation leads to a depletion of the solvent near the liquid surface. If surface tension increases for lower solvent concentrations, sufficiently strong compositional gradients can lead to Bénard-Marangoni-type convection that is similar to the kind which is observed in films that are heated from below. The onset of the instability is investigated by a linear stability analysis. Due to evaporation, the base state is time dependent, thus leading to a nonautonomous linearized system which impedes the use of normal modes. However, the time scale for the solvent loss due to evaporation is typically long compared to the diffusive time scale, so a systematic multiple scales expansion can be sought for a finite-dimensional approximation of the linearized problem. This is determined to leading and to next order. The corrections indicate that the validity of the expansion does not depend on the magnitude of the individual eigenvalues of the linear operator, but it requires these eigenvalues to be well separated. The approximations are applied to analyze experiments by Bassou and Rharbi with polystyrene/toluene mixtures [Langmuir, 25 (2009), pp. 624-632]. © 2013 Society for Industrial and Applied Mathematics.

A panchromatic anthracene-fused porphyrin sensitizer for dye-sensitized solar cells

Ball, James M.; Davis, Nicola K. S.; Wilkinson, James D.; Kirkpatrick, James; Teuscher, Joël; Gunning, Robert; Anderson, Harry L.; Snaith, Henry J. (RSC Advances, Royal Society of Chemistry (RSC), 2012) [Article]

The development of ruthenium-free sensitizers which absorb light over a broad range of the solar spectrum is important for improving the power conversion efficiency of dye-sensitized solar cells. Here we study three chemically tailored porphyrin-based dyes. We show that by fusing the porphyrin core to an anthracene unit, we can extend the conjugation length and lower the optical gap, shifting the absorption spectrum into the near-infrared (NIR). All three dyes were tested in dye-sensitized solar cells, using both titanium dioxide and tin dioxide as the electron-transport material. Solar cells incorporating the anthracene-fused porphyrin dye exhibit photocurrent collection at wavelengths up to about 1100 nm, which is the longest reported for a porphyrin-based system. Despite extending the photon absorption bandwidth, device efficiency is found to be low, which is a common property of cells based on porphyrin dyes with NIR absorption. We show that in the present case the efficiency is reduced by inefficient electron injection into the oxide, as opposed to dye regeneration, and highlight some important design considerations for panchromatic sensitizers. © 2012 The Royal Society of Chemistry.

Stochastic simulations of normal aging and Werner's syndrome.

Qi, Qi; Wattis, Jonathan A D; Byrne, Helen M. (Bulletin of Mathematical Biology, Springer Science + Business Media, 2014-04-26) [Article]

Human cells typically consist of 23 pairs of chromosomes. Telomeres are repetitive sequences of DNA located at the ends of chromosomes. During cell replication, a number of basepairs are lost from the end of the chromosome and this shortening restricts the number of divisions that a cell can complete before it becomes senescent, or non-replicative. In this paper, we use Monte Carlo simulations to form a stochastic model of telomere shortening to investigate how telomere shortening affects normal aging. Using this model, we study various hypotheses for the way in which shortening occurs by comparing their impact on aging at the chromosome and cell levels. We consider different types of length-dependent loss and replication probabilities to describe these processes. After analyzing a simple model for a population of independent chromosomes, we simulate a population of cells in which each cell has 46 chromosomes and the shortest telomere governs the replicative potential of the cell. We generalize these simulations to Werner's syndrome, a condition in which large sections of DNA are removed during cell division and, amongst other conditions, results in rapid aging. Since the mechanisms governing the loss of additional basepairs are not known, we use our model to simulate a variety of possible forms for the rate at which additional telomeres are lost per replication and several expressions for how the probability of cell division depends on telomere length. As well as the evolution of the mean telomere length, we consider the standard deviation and the shape of the distribution. We compare our results with a variety of data from the literature, covering both experimental data and previous models. We find good agreement for the evolution of telomere length when plotted against population doubling.

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