The wall shear rate distribution for flow in random sphere packings

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1 <= phi <= 0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As phi --> 0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.Comment: 4 pages, 3 figures, 1 table, RevTeX 4; significantly revised with significantly extended scop

ENaC–Membrane Interactions: Regulation of Channel Activity by Membrane Order

Recently, it was reported that the epithelial Na+ channel (ENaC) is regulated by temperature (Askwith, C.C., C.J. Benson, M.J. Welsh, and P.M. Snyder. 2001. Proc. Natl. Acad. Sci. USA. 98:6459–6463). As these changes of temperature affect membrane lipid order and lipid–protein interactions, we tested the hypothesis that ENaC activity can be modulated by membrane lipid interactions. Two approaches were used to modulate membrane anisotropy, a lipid order–dependent parameter. The nonpharmacological approach used temperature changes, while the pharmacological one used chlorpromazine (CPZ), an agent known to decrease membrane order, and Gd+3. Experiments used Xenopus oocytes expressing human ENaC. Methods of impedance analysis were used to determine whether the effects of changing lipid order indirectly altered ENaC conductance via changes of membrane area. These data were further corroborated with quantitative morphology on micrographs from oocytes membranes studied via electron microscopy. We report biphasic effects of cooling (stimulation followed by inhibition) on hENaC conductance. These effects were relatively slow (minutes) and were delayed from the actual bath temperature changes. Peak stimulation occurred at a calculated Tmax of 15.2. At temperatures below Tmax, ENaC conductance was inhibited with cooling. The effects of temperature on gNa were distinct from those observed on ion channels endogenous to Xenopus oocytes, where the membrane conductance decreased monoexponentially with temperature (t = 6.2°C). Similar effects were also observed in oocytes with reduced intra- and extracellular [Na+], thereby ruling out effects of self or feedback inhibition. Addition of CPZ or the mechanosensitive channel blocker, Gd+3, caused inhibition of ENaC. The effects of Gd+3 were also attributed to its ability to partition into the outer membrane leaflet and to decrease anisotropy. None of the effects of temperature, CPZ, or Gd+3 were accompanied by changes of membrane area, indicating the likely absence of effects on channel trafficking. However, CPZ and Gd+3 altered membrane capacitance in an opposite manner to temperature, consistent with effects on the membrane-dielectric properties. The reversible effects of both Gd+3 and CPZ could also be blocked by cooling and trapping these agents in the rigidified membrane, providing further evidence for their mechanism of action. Our findings demonstrate a novel regulatory mechanism of ENaC

Annexin A4 Reduces Water and Proton Permeability of Model Membranes but Does Not Alter Aquaporin 2–mediated Water Transport in Isolated Endosomes

Annexin A4 (Anx4) belongs to a ubiquitous family of Ca2+-dependent membrane-binding proteins thought to be involved in membrane trafficking and membrane organization within cells. Anx4 localizes to the apical region in epithelia; however, its physiological role is unclear. We show that Anx4 exhibited binding to liposomes (phosphatidylcholine:phosphatidylserine, 1:1) in the presence of Ca2+ and binding was reversible with EDTA. Anx4 binding resulted in liposome aggregation and a reduction in membrane water permeability of 29% (P < 0.001) at 25°C. These effects were not seen in the presence of Ca2+ or Anx4 alone and were reversible with EDTA. Measurements of membrane fluidity made by monitoring fluorescence anisotropy of 2-(12-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)dodecanoyl-1-hexadecanoyl-sn-glycero-3-phosphocholine (NBD-HPC) demonstrated that Anx4 binding rigidified the outer leaflet of the bilayer (P < 0.001), thus providing a molecular explanation for the inhibition of water flux. To determine whether Anx4 would produce similar effects on physiological membranes we constructed liposomes which recapitulated the lipid composition of the inner leaflet of the MDCK apical membrane. These membranes exhibited reductions to water permeability upon Anx4 binding (19.5% at 25°C, 31% at 37°C; P < 0.01 and P < 0.001, respectively) and to proton permeability (15% at 25°C, 19.5% at 37°C; P < 0.05). Since our in vitro experiments indicated an effect on membrane permeability, we examined localization of Anx4 in the kidney collecting duct, a region of the nephron responsible for concentrating urine through water reabsorbtion. Anx4 was shown to colocalize apically with aquaporin 2 (AQP2) in collecting duct epithelia. To test for the existence of a functional interaction between Anx4 and AQP2 we isolated AQP2-containing endosomes and exposed them to Anx4/Ca2+. Water flux rates were unchanged, indicating Anx4 does not directly regulate AQP2. We conclude that Anx4 can alter the physical properties of membranes by associating with them and regulate passive membrane permeability to water and protons. These properties represent important new functions for Anx4

An assertion language for constraint logic programs

In an advanced program development environment, such as that discussed in the introduction of this book, several tools may coexist which handle both the program and information on the program in different ways. Also, these tools may interact among themselves and with the user. Thus, the different tools and the user need some way to communicate. It is our design principie that such communication be performed in terms of assertions. Assertions are syntactic objects which allow expressing properties of programs. Several assertion languages have been used in the past in different contexts, mainly related to program debugging. In this chapter we propose a general language of assertions which is used in different tools for validation and debugging of constraint logic programs in the context of the DiSCiPl project. The assertion language proposed is parametric w.r.t. the particular constraint domain and properties of interest being used in each different tool. The language proposed is quite general in that it poses few restrictions on the kind of properties which may be expressed. We believe the assertion language we propose is of practical relevance and appropriate for the different uses required in the tools considered

Water Permeability of Asymmetric Planar Lipid Bilayers: Leaflets of Different Composition Offer Independent and Additive Resistances to Permeation

To understand how plasma membranes may limit water flux, we have modeled the apical membrane of MDCK type 1 cells. Previous experiments demonstrated that liposomes designed to mimic the inner and outer leaflet of this membrane exhibited 18-fold lower water permeation for outer leaflet lipids than inner leaflet lipids (Hill, W.G., and M.L. Zeidel. 2000. J. Biol. Chem. 275:30176–30185), confirming that the outer leaflet is the primary barrier to permeation. If leaflets in a bilayer resist permeation independently, the following equation estimates single leaflet permeabilities: 1/PAB = 1/PA + 1/PB (Eq. l), where PAB is the permeability of a bilayer composed of leaflets A and B, PA is the permeability of leaflet A, and PB is the permeability of leaflet B. Using for the MDCK leaflet–specific liposomes gives an estimated value for the osmotic water permeability (Pf) of 4.6 × 10−4 cm/s (at 25°C) that correlated well with experimentally measured values in intact cells. We have now constructed both symmetric and asymmetric planar lipid bilayers that model the MDCK apical membrane. Water permeability across these bilayers was monitored in the immediate membrane vicinity using a Na+-sensitive scanning microelectrode and an osmotic gradient induced by addition of urea. The near-membrane concentration distribution of solute was used to calculate the velocity of water flow (Pohl, P., S.M. Saparov, and Y.N. Antonenko. 1997. Biophys. J. 72:1711–1718). At 36°C, Pf was 3.44 ± 0.35 × 10−3 cm/s for symmetrical inner leaflet membranes and 3.40 ± 0.34 × 10−4 cm/s for symmetrical exofacial membranes. From , the estimated permeability of an asymmetric membrane is 6.2 × 10−4 cm/s. Water permeability measured for the asymmetric planar bilayer was 6.7 ± 0.7 × 10−4 cm/s, which is within 10% of the calculated value. Direct experimental measurement of Pf for an asymmetric planar membrane confirms that leaflets in a bilayer offer independent and additive resistances to water permeation and validates the use of

Using global analysis, partial specifications, and an extensible assertion language for program validation and debugging

We discuss a framework for the application of abstract interpretation as an aid during program development, rather than in the more traditional application of program optimization. Program validation and detection of errors is first performed statically by comparing (partial) specifications written in terms of assertions against information obtained from (global) static analysis of the program. The results of this process are expressed in the user assertion language. Assertions (or parts of assertions) which cannot be checked statically are translated into run-time tests. The framework allows the use of assertions to be optional. It also allows using very general properties in assertions, beyond the predefined set understandable by the static analyzer and including properties defined by user programs. We also report briefly on an implementation of the framework. The resulting tool generates and checks assertions for Prolog, CLP(R), and CHIP/CLP(fd) programs, and integrates compile-time and run-time checking in a uniform way. The tool allows using properties such as types, modes, non-failure, determinacy, and computational cost, and can treat modules separately, performing incremental analysis