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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The journal of membrane biology 90 (1986), S. 89-96 
    ISSN: 1432-1424
    Keywords: frog skin ; membrane potential ; voltage clamp ; K+ depolarization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary In studies of apical membrane current-voltage relationships, in order to avoid laborious intracellular microelectrode techniques, tight epithelia are commonly exposed to high serosal K concentrations. This approach depends on the assumptions that high serosal K reduces the basolateral membrane resistance and potential to insignificantly low levels, so that transepithelial values can be attributed to the apical membrane. We have here examined the validity of these assumptions in frog skins (Rana pipiens pipiens). The skins were equilibrated in NaCl Ringer's solutions, with transepithelial voltageV t clamped (except for brief perturbations ΔV t) at zero. The skins were impaled from the outer surface with 1.5m KCl-filled microelectrodes (R el〉30 MΩ). The transepithelial (short-circuit) currentl i and conductanceg t=−ΔI t/ΔV t, the outer membrane voltageV o (apical reference) and voltage-divider ratio (F o=ΔV o/ΔV t), and the microelectrode resistanceR el were recorded continuously. Intermittent brief apical exposure to 20 μm amiloride permitted estimation of cellular (c) and paracellular (p) currents and conductances. The basolateral (inner) membrane conductance was estimated by two independent means: either from values ofg i andF o before and after amiloride or as the ratio of changes (−ΔI c/ΔV i) induced by amiloride. On serosal substitution of Na by K, within about 10 min,I c declined andg t increased markedly, mainly as a consequence of increase ing p. The basolateral membrane voltage (V i(=−V o) was depolarized from 75±4 to 2±1 mV [mean±sem (n=6)], and was partially repolarized following amiloride to 5±2 mV. The basolateral conductance increased in high serosal K, as estimated by both methods. Essentially complete depolarization of the basolateral membrane and increase in its conductance in response to high [K] were obtained also when the main serosal anion was SO4 or NO3 instead of Cl. On clampingV t over the range 0 to +125 mV in K2SO4-depolarized skins, the quasi-steady-stateV o V t relationship was linear, with a mean slope of 0.88±0.03. The above results demonstrate that, in a variety of conditions, exposure to high serosal K results in essentially complete depolarization of the basolateral membrane and a large increase in its conductance.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The journal of membrane biology 85 (1985), S. 143-158 
    ISSN: 1432-1424
    Keywords: frog skin ; anions and sodium transport ; membrane potential ; K activity ; pump current ; constant current source
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary Cell K activity,a k, was measured in the short-circuited frog skin by simultaneous cell punctures from the apical surface with open-tip and K-selective microelectrodes. Strict criteria for acceptance of impalements included constancy of the open-tip microelectrode resistance, agreement within 3% of the fractional apical voltage measured with open-tip and K-selective microelectrodes, and constancy of the differential voltage recorded between the open-tip and the K microelectrodes 30–60 sec after application of amiloride or substitution of apical Na. Skins were bathed on the serosal surface with NaCl Ringer and, to reduce paracellular Cl conductance and effects of amiloride on paracellular conductance, with NaNO3 Ringer on the apical surface. Under control conditionsa k r was nearly constant among skins (mean±SD=92±8mM, 14 skins) in spite of a wide range of cellular currents (5 to 70 μA/cm2). Cell current (and transcellular Na transport) was inhibited by either apical addition of amiloride or substitution of Na by other cations. Although in some experiments the expected small increase ina k r after inhibition of cell current was observed, on the average the change was not significant (98±11mM after amiloride, 101±12mM after Na substitution), even 30 min after the inhibition of cell current. The membrane potential, which in the control state ranged from −42 to −77 mV, hyperpolarized after inhibition of cell current, initially to −109±5mV, then depolarizing to a stable value (−88±5mV) after 15–25 min. At this time K was above equilibrium (E k=98±2mV), indicating that the active pump mechanism is still operating after inhibition of transcellular Na transport. The measurement ofa k r permitted the calculation of the passive K current and pump current under control conditions. assuming a “constant current source” with almost all of the basolateral conductance attributable to K. We found a significant correlation between pump current and cell current with a slope of 0.31, indicating that about one-third of the cell current is carried by the pump, i.e., a pump stoichiometry of 3Na/2K.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    The journal of membrane biology 92 (1986), S. 37-46 
    ISSN: 1432-1424
    Keywords: frog skin ; cell Na activity ; membrane potential ; Na pump flux ; Na microelectrodes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary Cell Na activity,a Na c , was measured in the short-circuited frog skin by simulaneous cell punctures from the apical surface with open-tip and Na-selective microelectrodes. Skins were bathed on the serosal surface with NaCl Ringer and, to reduce paracellular conductance, with NaNO3 Ringer on the apical surface. Under control conditionsa Na c averaged 8±2mm (n=9,sd). Apical addition of amiloride (20 μm) or Na replacement reduceda Na c to 3mm in 6–15 min. Sequential decreases in apical [Na] induced parallel reductions ina Na c and cell current,I c . On restoring Na after several minutes of exposure to apical Na-free solutionI c rose rapidly $$(\tilde〈 30\sec )$$ to a stable value whilea Na c increased exponentially, with a time constant of 1.8±0.7 min (n=8). Analysis of the time course ofa Na c indicates that the pump Na flux is linearly related toa Na c in the range 2–12mm. These results indicate thata Na c plays an important role in relating apical Na entry to basolateral active Na flux.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 501-522 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We used a conjugate gradient type method, with preconditioning, to solve the sparse linear systems arising from the discretization of PDEs. With such methods, the main obstacles for complete vectorization have been the preconditioning calculation and its application step within the iteration: for the matrices obtained using 5- or 9-point discretization operators, some well known existing preconditionings (like ILU) require a block-recursive procedure which prevents vectorization. Preconditioners based on nested incomplete factorization, which require the calculation of approximate inverses of tridiagonal matrices, allow complete vectorization of the application step. We present a formulation of such a preconditioning, using a Frobenius norm minimization to calculate the inverses, which also allows complete vectorization of the inverses' calculation, thus making the iterative solver completely vectorizable. Numerical experiments show that the method is robust over a range of symmetric and non-symmetric problems, and up to 4 times faster than other existing methods, such as ILU, depending on the computer and compiler being used. We also show the importance of diagonal scaling used in conjunction with other preconditionings and present some theoretical results concerning the approximate inverses of tridiagonal matrices, calculated using the Frobenius norm minimization.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 1 (1985), S. 263-267 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Linear equations arising from reservoir simulation are closely coupled at the local-cell level, and the variables and equations tend to be poorly equilibrated. Scaling by the inverse of the diagonal block has an equilibrating effect. It usually improves the condition of the matrix for solution by linear iteration. The effects of block diagonal scaling are illustrated for a thermal reservoir simulator, where the original matrix may be indefinite. These results illustrate that for difficult problems block diagonal scaling can significantly enhance the convergence rate of the iterative method. It is also illustrated that preconditioned generated by block incomplete LU decomposition (ILU) and block symmetric Gauss Seidel (BSGS) methods are effective preconditioned for use in thermal simulation.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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