Conformation sphere

Substitution of (19) into (18) makes the semi-axes Xt of equilibrium ellipsoid the same and equal to radius Rm of the conformational sphere the same distribution density o(X) corresponds to the surface of this conformational sphere ... 

Figure 3. The conformational sphere for pyranoid rings. The perfect chairs are at the north and south poles (0=0 and 180 , respectively). The boat and skew (B and S designations) at the equator permit pseudorotation that is slightly hindered, at least for cyclohexane. The envelopes, E (also called sofas and half-boats), and half-chairs, H, are not observed for rings coiqposed of saturated carbon and oxygen atoms, but are iiqportant forms for rings with unsaturated carbon atoms. The aiqplitude of puckering corresponds to the radius of the sphere.

FIG. 7 Snapshot of a bilayer conformation with a pore in the bond-fluctuation model. The dark spheres represent head particles, the light spheres tail particles. Around the pore, the amphiphiles rearrange so as to shield the bilayer interior from the solvent. (From Muller and Schick [133].)... 

Baumgartner and coworkers [145,146] study lipid-protein interactions in lipid bilayers. The lipids are modeled as chains of hard spheres with heads tethered to two virtual surfaces, representing the two sides of the bilayer. Within this model, Baumgartner [145] has investigated the influence of membrane curvature on the conformations of a long embedded chain (a protein ). He predicts that the protein spontaneously localizes on the inner side of the membrane, due to the larger fluctuations of lipid density there. Sintes and Baumgartner [146] have calculated the lipid-mediated interactions between cylindrical inclusions ( proteins ). Apart from the... 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

The simplest indicator of conformation comes not from but the sedimentation concentration dependence coefficient, ks. Wales and Van Holde [106] were the first to show that the ratio of fcs to the intrinsic viscosity, [/ ] was a measure of particle conformation. It was shown empirically by Creeth and Knight [107] that this has a value of 1.6 for compact spheres and non-draining coils, and adopted lower values for more extended structures. Rowe [36,37] subsequently provided a derivation for rigid particles, a derivation later supported by Lavrenko and coworkers [10]. The Rowe theory assumed there were no free-draining effects and also that the solvent had suf-... 

Fig. 8 The Haug triangle. The three extremes of conformation compact sphere, random coil and rigid rod) are placed at the apices of a triangle. The conformation of a given macromolecule is represented by a locus along the sides of the triangle between these extremes. Knowledge of the power law exponents (see text) can help to give us an idea of the conformation type. From [61]...

A step closer toward realism is taken by off-lattice models in which the backbone is specified in some detail, while side chains, if they are represented at all, are taken to be single, unified spheres [44-50]. One indication that this approach is too simplistic was given in [51], which proved that for a backbone representation in which only Ca carbons were modeled, no contact potential could stabilize the native conformation of a single protein against its nonnative ( decoy ) conformations. However, Irback and co-workers were able to fold real protein sequences, albeit short ones, using a detailed backbone representation, with coarse-grained side chains modeled as spheres [49, 52-54]. 

HzPO . The values are 0.24, 0.21, 0.16 and 0.13, respectively. The values span a range of a factor of two which must be admitted to be a little larger than the experimental uncertainty and also easily within the differences among the anions in their probability of occupancy of the crucial outer sphere site adjacent to the leaving water molecule. All are nearly a factor of five below the water exchange rate. These results conform neatly to the predictions. 

In conforming to an expected linear free energy relationship, the Ce(lV) oxidation of various 1,10-phenanthroline and bipyridyl complexes of Ru(II) in 0.5 M sulphuric acid are consistent with the requirements of the Marcus treatment . The results for the oxidation of the 3- and 5-sulphonic-substituted ferroin complexes by Ce(IV) suggest that the ligand does not function as an electron mediator, and that the mechanism is outer-sphere in type. Second-order rate coefficients for the oxidation of Ru(phen)j, Ru(bipy)3, and Ru(terpy)3 are 5.8x10, 8,8 X 10, and 7.0 x 10 l.mole . sec, respectively, in 0.5 M H2SO4 at 25 °C a rapid-mixing device was employed. 

A simplified analysis of the effect of particle shape or molecular conformation on SEC calibration has led to the prediction that the more open structure of rigid rod shaped solutes gives a relatively flat SEC-MW calibration curve. As the solute conformation becomes more compact (random-coil to solid-sphere), the SEC-MW calibration curve becomes increasingly steep... 

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