Overall curvature

So far, Santos has been able to express the relation between a set of coefficients af, aj J 6 / describing a vector field and the overall curvature of the stream lines of this vector field. Based on the curvature field, they constructed the measure E of the curvature distribution in the simulation box. Provided that the homogeneous curvature field of curvature c0 is the one that minimizes E, the problem of packing has been recast as a minimization problem. However, the lack of information about the gradient of the error function to be minimized does not facilitate the search. Fortunately, appropriate computer simulation schemes for similar minimization problems have been proposed in the literature [105-109]. 

The total curvature energy of a spherical vesicle is given by 4tt(2/cc + k). As all experimental data on phospholipids indicate that kc is not small, one is inclined to conclude that the vesicles are thermodynamically unstable the reduction of the number of vesicles, e.g. by vesicle fusion or by Ostwald ripening, will reduce the overall curvature energy. However, such lines of thought overlook the possibility that k is sufficiently negative to allow the overall curvature free energy of vesicles to remain small. 

Block 1 Perform a 2 fraction factorial design plus 2 center points. Estimate the factor main effects (Srst-order effects) and the overall curvature effect. 

Block 2 Run the other half of the 2 - design plus 2 center points. A foldo-ver design estimate the three two-factor interaction effects, re-estimate main effects and overall curvature, and the block effect. 

Other oxidants like thallium(III) oxide, vanadium(V) oxyfluoride, palladium ) acetate, and ruthenium(IV) tetrakis(trifluoracetate) have been developed as powerful tools for the intramolecular biaryl coupling reaction [7,93,113]. Nevertheless, DDQ is still one of the most versatile reagents in oxidative coupling reactions (see Scheme 14 and 29 [82,114]). The highly strained dioxa[8](2,7)pyrenophane (65), portraying an overall curvature of nearly 90° for the pyrene subunit, was finally obtained from the mefa-cyclophanediene (66) by dehydrogenation with DDQ in refluxing benzene in 67% yield [114]. 

It was suggested [284] that the perforated lamellar phase may form via the growth of branched and multiconnected threadlike micelles. Interconnection of threadlike micelles reduces the overall curvature of the monolayer making up the micelles and thereby reflects a preference for microstructures of decreasing curvature [119]. The suggested morphological sequence for the system cetylpyridinium chloride-hexanol-brine is spheres, small disks, long capped cylinders, branched cylinders, perforated bilayers, smooth bilayers, loose network of connected bilayers (foamlike structure), and multiphasic domain [284]. 

Different lipid molecules associate together to form membrane structures with very different overall curvatures. When liposomes are made in the presence of sufficient concentrations of nonhydroxylated fatty-acid galactoceramides (NFA-GalCer) they form nanotubes (Wilson-Kubalek et al, 1998). We have used these preformed lipid nanotubes to examine the effect of GTP hydrolysis on the conformation of a dynamin helix (Marks et al, 2001 Stowell et al, 1999). Indeed, in the absence of GTP hydrolysis, purified dynamin aggregates to form helices and, as seen above, can tubulate liposomes. Also, dynamin interacts with lipid nanotubes to form ordered arrays with a diameter similar to the constricted necks of clathrin-coats pits observed in vivo (Stowell et al, 1999 Takei et al, 1995), suggesting that the nanotube acts as a good mimic of the neck of a vesicle. 

The curvature method also has some inherent limitations. Since the method entails determination of plastic response through the imposition of a temperature change or phase transformation, which is known to alter the plastic properties of metals, care should be exercised in the interpretation of strain relaxation phenomena from curvature measurements. There are also no clear means of isolating the individual contributions to overall curvature evolution seen experimentally from such factors as plastic yielding, strain hardening, diffusional creep, or microstructural changes, without recourse to other independent experimental and observational tools. 

If liquid crystalline phases can be obtained with a large variation in molar composition, the peak position shifts as a function of composition. The magnitude and the sign of this shift of periodicity allows us in all cases to determine whether the addition of solute induces an area increase at a low V increase, or a pure apolar volume V swelling. Most cases are intermediate in behaviour and correspond to an incorporation of solutes with a constant overall curvature. 

In the case of the non-planar assumption, the twcmod is determined from the a-cu relation, the overall curvature km and the length of the fictitious crack. 

---