Membrane bending

This issue was addressed in 1979 by McBride and Jacobs. Jacobs was from Fluor in Houston. The principle was to calculate stresses in two distinct areas, membrane and bending. Membrane stresses are based on pressure area times metal urea. Bending is based on AISC beam formulas. The neck-and-shell section (and sometimes the flange as well) is assumed as bent on the hard axis. This is not a beam-on-elastic-foundation calculation. It is more of a brute-force approach. 

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Evans E A 1974 Bending resistanoe and ohemioally induoed moments in membrane bilayers Biophys. J. 14 923... 

Kev>erse Osmosis (RO) Membranes A type of membrane system for treating oily wastewater is currently undergoing commercialization by Bend Research, Inc. The system uses a tube-side feed module that yields high fluxes while being able to handle high-sohds-content waste streams (Ref. 25). Another type of reverse osmosis technique is being designed to yield ultrapurified HF recovered from... 

The double bonds found in fatty acids are nearly always in the cis configuration. As shown in Figure 8.1, this causes a bend or kink in the fatty acid chain. This bend has very important consequences for the structure of biological membranes. Saturated fatty acid chains can pack closely together to form ordered, rigid arrays under certain conditions, but unsaturated fatty acids prevent such close packing and produce flexible, fluid aggregates. 

Hydrophobicity plots of AQPs indicated that these proteins consist of six transmembrane a-helices (Hl-H6 in Fig. la) connected by five connecting loops (A-E), and flanked by cytosolic N- and C-termini. The second half of the molecule is an evolutionary duplicate and inverse orientation of the first half of the molecule. Loops B and E of the channel bend into the membrane with an a-helical conformation (HB, HE in Fig. lb) and meet and each other at their so-called Asn-Pro-Ala (NPA) boxes. These NPA motifs are the hallmark of AQPs and form the actual selective pore of the channel, as at this location, the diameter is of that of a water molecule (3 A Fig. la and b). Based on the narrowing of the channel from both membrane sides to this small... 

Tape >System of Analysis. A tape system which is used widely for analysis in the Pediatric Laboratory is a system whose principle was developed by the author. A reagent is placed on a paper tape. The paper is covered with a membrane, such as cellophane, cellulose nitrate or cellulose acetate, porous to low molecular weight substances. Finally, the serum is placed above the porous membrane, so that diffusion of the components of serum take place and a stain is produced on the paper (60). This principle has been incorporated for example, with glucose oxidase, in the conmercially available Dextro-Sticks. In addition, a similar principle is being applied by some for the analysis of components in urine (Ames Co., South Bend, Indiana). 

Polymer-metal composites Cationic mobility activated electrically in membranes of the Nafion (DuPont) and Flemion (Asahi Glass) type leads to a bending response, again mimicking muscle action. 

It follows from previous discussion that the destabilizing electrostatic contribution grows in absolute value with x (with increasing A.). But the influence of the nonuniform electrical force is overwhelmed by the stabilizing bending and stretching contributions. As a result, the traditional smectic model cannot explain how a small transmembrane voltage can lead to membrane breakdown. The obvious solution is to abandon this approach and to develop an alternative, such as the pore formation model. However, as we noticed before, this approach postulates rather than proves the appearance of hydrophobic pores. 

The walls of thin vessels can be considered to be membranes supporting loads without significant bending or shear stresses similar to the walls of a balloon. 

In the stress analysis of pressure vessels and pressure vessel components stresses are classified as primary or secondary. Primary stresses can be defined as those stresses that are necessary to satisfy the conditions of static equilibrium. The membrane stresses induced by the applied pressure and the bending stresses due to wind loads are examples of primary stresses. Primary stresses are not self-limiting if they exceed the yield point of the material, gross distortion, and in the extreme situation, failure of the vessel will occur. 

We would like to point out that an order parameter indicates the static property of the lipid bilayer, whereas the rotational motion, the oxygen transport parameter (Section 4.1), and the chain bending (Section 4.4) characterize membrane dynamics (membrane fluidity) that report on rotational diffusion of alkyl chains, translational diffusion of oxygen molecules, and frequency of alkyl chain bending, respectively. The EPR spin-labeling approach also makes it possible to monitor another bulk property of lipid bilayer membranes, namely local membrane hydrophobicity. 

Figure 3.6 compares iso-pH permeabilities of ketoprofen at various pH values in a 2% DOPC-dodecane model (open circles) and the 20% soy lecithin with SLS in the acceptor compartment (filled circles, data in Table 3.5). In the presence of the latter negatively charged lipids (with the make-up similar to that of BBM in Table 3.1), ketoprofen is intrinsically more permeable, by a factor of 17. The UWL limit, indicated by the solid curves in low-pH solutions, and consistent with the permeability Pu 19.8 x 10-6 cm s 1 (log Pu —4.7), masks the true intrinsic permeability of the membranes, P0. However, it is possible to deduce the membrane permeability if the pKa is known. In Fig. 3.6, the bending in the dashed (calculated) curves at pH 4 corresponds to the pKa of the molecule. Due to the UWL, the point of bending is shifted to higher pH values in the solid (measured) curves. The difference between the apparent pKa (pK 5.3 for DOPC and 6.3 for soy) and the true pKa (4.12) is the same as the difference between log P0 and log Pu [23],... 

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