Complex lamellar components

In this final section, it is shown that the three magnetic field components of electromagnetic radiation in 0(3) electrodynamics are Beltrami vector fields, illustrating the fact that conventional Maxwell-Heaviside electrodynamics are incomplete. Therefore Beltrami electrodynamics can be regarded as foundational, structuring the vacuum fields of nature, and extending the point of view of Heaviside, who reduced the original Maxwell equations to their presently accepted textbook form. In this section, transverse plane waves are shown to be solenoidal, complex lamellar, and Beltrami, and to obey the Beltrami equation, of which B is an identically nonzero solution. In the Beltrami electrodynamics, therefore, the existence of the transverse 1 = implies that of , as in 0(3) electrodynamics. 

Beltrami fields have been advanced [4] as theoretical models for astrophy-sical phenomena such as solar flares and spiral galaxies, plasma vortex filaments arising from plasma focus experiments, and superconductivity. Beltrami electrodynamic fields probably have major potential significance to theoretical and empirical science. In plasma vortex filaments, for example, energy anomalies arise that cannot be described with the Maxwell-Heaviside equations. The three magnetic components of 0(3) electrodynamics are Beltrami fields as well as being complex lamellar and solenoidal fields. The component is identically nonzero in Beltrami electrodynamics if is so. In the Beltrami... 

The three components of the cyclic theorem (411) are solenoidal, complex lamellar, and Beltrami. This is a remarkable property of Beltrami electrodynamics when recognized as 0(3) electrodynamics for the special case when... 

The Bii] component [which is nonzero only on the 0(3) level] is a solution of the Beltrami equation (885) with k = 0. Therefore, in Beltrami electrodynamics, Bii] is a solenoidal, irrotational, complex lamellar and Beltrami field in the vacuum, and is also a propagating field. The B 1 component in Beltrami... 

There are two known standard methods for decomposition of any smooth (differentiable) vector field. One is that attributed to Helmholtz, which splits any vector field into a lamellar (curl-free) component, and a solenoidal (divergenceless) component. The second, which divides a general vector field into lamellar and complex lamellar parts, is that popularized by Monge. However, the relatively recent discovery by Moses [7] shows that any smooth vector field— general or with restraints to be determined—may also be separable into circularly polarized vectors. Furthermore, this third method simplifies the otherwise difficult analysis of three-dimensional classical flow fields. The Beltrami flow field, which has a natural chiral structure, is particularly amenable to this type analysis. 

Plants were probably the first to have polyester outerwear, as the aerial parts of higher plants are covered with a cuticle whose structural component is a polyester called cutin. Even plants that live under water in the oceans, such as Zoestra marina, are covered with cutin. This lipid-derived polyester covering is unique to plants, as animals use carbohydrate or protein polymers as their outer covering. Cutin, the insoluble cuticular polymer of plants, is composed of inter-esterified hydroxy and hydroxy epoxy fatty acids derived from the common cellular fatty acids and is attached to the outer epidermal layer of cells by a pectinaceous layer (Fig. 1). The insoluble polymer is embedded in a complex mixture of soluble lipids collectively called waxes [1], Electron microscopic examination of the cuticle usually shows an amorphous appearance but in some plants the cuticle has a lamellar appearance (Fig. 2). 

Lxotmpii liquid crystals possess at least two components. One of these is water and the other is amphihle (a polar head group attached to one or more long hydrocarbon chains). In the lamellar form, water molecules are sandwiched between the polar heads of adjacent layers while the hydrocarbon tails lie in a nonpolar environment. Lyotropic liquid crystals have very complex structures, but occur abundantly in nature, particularly in living systems. See Fig. 3. 

In two-component systems of association of colloid and water the sequence of phases, as the water content decreases, is micellar solution - hexagonally packed polar rods complex phases with rod-shaped aggregates lamellar mesophase D - crystalline surfactant. Some of these steps may be absent, depending, for example, on the temperature. 

Motivated by its important role in gene delivery, we have studied the effect of cholesterol (chol) and several analogs on the transfection efficiency of lamellar CL-DNA complexes in vitro [27]. As evident from the results on DOPC/DOTAP and DOPE/DOTAP vectors, the nature of the neutral lipid component is an important parameter that is worth further exploration. Conveniently, a number of neutral lipids are commercially available. In addition, modifying the neutral lipid component has the potential to improve TE in a regime (at low aM) where DNA dissociation from the complex in the cytosol is not yet a barrier to transfection. 

The structure of the interfacial layers in food colloids can be quite complex as these are usually comprised of mixtures of a variety of surfactants and all are probably at least partly adsorbed at interfaces which even individually, can form complex adsorption layers. The layers can be viscoelastic. Phospholipids form multi-lamellar structures at the interface and proteins, such as casein, can adsorb in a variety of conformations [78]. Lecithins not only adsorb also at interfaces, but can affect the conformations of adsorbed casein. The situation in food emulsions can be complicated further by the additional presence of solid particles. For example, the fat droplets in homogenized milk are surrounded by a membrane that contains phospholipid, protein and semi-solid casein micelles [78,816], Similarly, the oil droplets in mayonnaise are partly coated with granular particles formed from the phospho and lipo-protein components of egg yolk [78]. Finally, the phospholipids can also interact with proteins and lecithins to form independent vesicles [78], thus creating an additional dispersed phase. 

Like chlorophyll, plastoquinone A has a nonpolar terpenoid or isoprenoid tail, which can stabilize the molecule at the proper location in the lamellar membranes of chloroplasts via hydrophobic reactions with other membrane components. When donating or accepting electrons, plastoquinones have characteristic absorption changes in the UV near 250 to 260, 290, and 320 nm that can be monitored to study their electron transfer reactions. (Plastoquinone refers to a quinone found in a plastid such as a chloroplast these quinones have various numbers of isoprenoid residues, such as nine for plastoquinone A, the most common plastoquinone in higher plants see above.) The plastoquinones involved in photosynthetic electron transport are divided into two categories (1) the two plastoquinones that rapidly receive single electrons from Peso (Qa and Qb) and (2) a mobile group or pool of about 10 plastoquinones that subsequently receives two electrons (plus two H+ s) from QB (all of these quinones occur in the lamellar membranes see Table 5-3). From the plastoquinone pool, electrons move to the cytochrome b f complex. 

Because Photosystem II tends to occur in the grana and Photosystem I in the stromal lamellae, the intervening components of the electron transport chain need to diffuse in the lamellar membranes to link the two photosystems. We can examine such diffusion using the time-distance relationship derived in Chapter 1 (Eq. 1.6 x je = 4Djtife). In particular, the diffusion coefficient for plastocyanin in a membrane can be about 3 x 10 12 m2 s-1 and about the same in the lumen of the thylakoids, unless diffusion of plastocyanin is physically restricted in the lumen by the appres-sion of the membranes (Haehnel, 1984). For such a D , in 3 x 10-4 s (the time for electron transfer from the Cyt b(f complex to P ), plastocyanin could diffuse about [(4)(3 x 10-12 m2 s-1) (3 x 10-4 s)]1/2 or 60 nm, indicating that this complex in the lamellae probably occurs in relatively close proximity to its electron acceptor, Photosystem I. Plastoquinone is smaller and hence would diffuse more readily than plastocyanin, and a longer time (2 x 10-3 s) is apparently necessary to move electrons from Photosystem II to the Cyt b(f complex hence, these two components can be separated by greater distances than are the Cyt b f complex and Photosystem I. 

Most of the components involved in electron transport in mitochondria are contained in four supramolecular protein complexes that traverse the inner mitochondrial membrane. Complex I, which contains FMN and various iron-sulfur clusters as active sites, transfers electrons from NADH to ubiquinone (Fig. 6-8). Complex II, which contains FAD, various iron-sulfur clusters, and a Cyt >, transfers electrons from succinate also to a ubiquinone. Ubiquinone functions as a pool of two-electron carriers, analogous to the function of plastoquinone A in the lamellar membranes of chloroplasts, which accepts electrons from Complexes I and II and delivers them to the... 

Certainly, more complex lipid systems, such as the three-component "raft"-mixtures may represent more realistic models for biomembrane systems. Their pressure dependent lateral organization and phase behavior has not been studied yet, however. Some data are available on pressure effects on lipid extracts from natural membranes, such as bipolar tetraether liposomes composed of the polar lipid fraction E (PLFE) isolated from the thermoacidophilic archaeon Sulfolobus acidocaldarius. The SAXS data on PLFE multilamellar vesicles also exhibit several temperature dependent lamellar phases, and, in addition, the existence of cubic... 

In the lumen of the small intestine, dietary fat does not only meet bile salt but the much more complex bile in which bile salts are about half saturated with lecithin in a mixed micellar system of bile salt-lecithin-cholesterol. On dilution in the intestinal content, the micelles grow in size as the phase limit is approached and large disk-like micelles form which fold into vesicles [49]. These changes are due to the phase transition that occurs when the bile salt concentration is decreased and the solubility limit for lecithin in the mixed micelles is exceeded. The information is mostly derived from in vitro studies with model systems but most probably is applicable to the in vivo situation. What in fact takes place when the bile-derived lamellar bile salt-lecithin-cholesterol system meets the partly digested dietary fat can only be pictured. Most probably it involves an exchange of surface components, a continuous lipolysis at the interphase by pancreatic enzymes and the formation of amphiphilic products which go into different lamellar systems for further uptake by the enterocyte. Due to the relatively low bile salt concentration and the potentially high concentration of product phases in intestinal content early in fat digestion, the micellar and monomeric concentration of bile salt can be expected to be low but to increase towards the end of absorption. 

This fact is confirmed by the kinetics of enzymatic hydrolysis of the complex at 20°C which are intermediate in rate between the "quench precipitate" and that of a lamellar crystalline preparation of pure nigeran (Table III). SDS polyacrylamide gel electrophoresis of the solubilized protein fraction indicates it is composed of four components. The major one constituting probably 80% or more of the staining material has an apparent molecular weight of approximately 12,000 the 3 minor species present have molecular weights of 16,000 ... 

Microemulsions are prepared by the spontaneous anulsilication method (phase titration method) and can be depicted with the help of phase diagrams. Construction of phase diagram is a useful approach to study the complex series of interactions that can occur when different components are mixed. Microemulsions are formed along with varions association structures (including emulsion, micelles, lamellar, hexagonal, cubic, and varions gels and oily dispersion), depending on the chemical composition and concentration of each component. 

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