Intracellular Ca2+ nonlinear wave behaviours in a three dimensional ventricular cell model

Intracellular Ca²⁺ activity regulates a wide range of cellular biochemical processes; in muscle cells, it links membrane excitation to contraction. Ca²⁺ dynamics includes both synchronous oscillations, and nonlinear wave phenomena, both arising from the superposition of spatially localised stochastic events, such as Ca²⁺ sparks. We incorporated individualised cell geometry reconstructed from confocal microscopy with realistic spatial distribution of RyR clusters into the three dimensional ventricular cell model, and reproduced complex spatio-temporal intracellular wave patterns from Ca²⁺ sparks. We also introduced a detailed nuclear Ca²⁺ handing model to simulate prolonged nuclear Ca²⁺ transient, and study the effects of cytosolic-nuclear coupling on intracellular Ca²⁺ dynamics. The model provides a computational platform to study intracellular Ca²⁺ with the ability to interact with experimental measurements of subcellular structures, and can be modified for other cell types.     

Lipschitz metric for the periodic Camassa-Holm equation

We study the stability of conservative solutions of the Cauchy problem for the Camassa-Holm equation ut−uxxt+κux+3uux−2uxuxx−uuxxx=0 with periodic initial data u₀. In particular, we derive a new Lipschitz metric dD with the property that for two solutions u and v of the equation we have dD(u(t),v(t))?eCtdD(u₀,v₀). The relationship between this metric and usual norms in and is clarified.     

Surface activation of electrocatalysis at oxide electrodes. Concerted electron-proton transfer

Dramatic rate enhancements are observed for the oxidation of phenols, including tyrosine, at indium-tin oxide electrodes modified by the addition of the electron-transfer relays [M(II)(bpy)(2)(4,4'-(HO)(2)P(O)CH(2))(2)bpy)](2+) (M = Ru, Os) with clear evidence for the importance of proton-coupled electron transfer and concerted electron-proton transfer.     

Distribution of wealth in a network model of the economy

We show, analytically and numerically, that wealth distribution in the Bouchaud–Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.     

Mimicking Photosystem I with a Transmembrane Light Harvester and Energy Transfer-Induced Photoreduction in Phospholipid Bilayers

Photosystem I (PS I) is a transmembrane protein that assembles perpendicular to the membrane, and performs light harvesting, energy transfer, and electron transfer to a final, water-soluble electron acceptor. We present here a supramolecular model of it formed by a bicationic oligofluorene 1²⁺ bound to the bisanionic photoredox catalyst eosin Y (EY²⁻) in phospholipid bilayers. According to confocal microscopy, molecular modeling, and time dependent density functional theory calculations, 1²⁺ prefers to align perpendicularly to the lipid bilayer. In presence of EY²⁻, a strong complex is formed (K_a=2.1±0.1×10⁶ m ⁻¹), which upon excitation of 1²⁺ leads to efficient energy transfer to EY²⁻. Follow-up electron transfer from the excited state of EY²⁻ to the water-soluble electron donor EDTA was shown via UV–Vis absorption spectroscopy. Overall, controlled self-assembly and photochemistry within the membrane provides an unprecedented yet simple synthetic functional mimic of PS I.     

Well-posedness of higher-order Camassa-Holm equations

We consider higher-order Camassa-Holm equations describing exponential curves of the manifold of smooth orientation-preserving diffeomorphisms of the unit circle in the plane. We establish the existence of global weak solutions. We also present some invariant spaces under the action of the equation. Moreover, we prove a “weak equals strong” uniqueness result.     

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.     

Solid-phase extraction of herbicides from well water for determination by gas chromatography-mass spectrometry

A simple, rapid method for isolating herbicides from well water was developed using disposable octadecyl (C₁₈) solid-phase extraction columns. Deuterium-labeled internal standards were used to compensate for any losses that may have occurred during sample preparation owing to matrix effects. Detection by capillary gas chromatography-mass spectrometry in the selected ion monitoring mode minimized the frequency of false-positive results. The accuracy of the method was ± 5% at concentrations > 0.20μg l^?1 for four of the five herbicides studied.