Extension phase

Figure A2.5.7. Constant temperature isothenns of reduced Helmlioltz free energy A versus reduced volume V. The two-phase region is defined by the line simultaneously tangent to two points on the curve. The dashed parts of the smooth curve are metastable one-phase extensions while the dotted curves are unstable regions. (The isothenns are calculated for an unphysical r = 0.1, the only effect of which is to separate the isothenns...

Values of the mass-transfer coefficient k have been obtained for single drops rising (or falling) through a continuous immiscible Hquid phase. Extensive Hterature data have been summarized (40,42). The mass-transfer coefficient is often expressed in dimensionless form as the Sherwood number ... 

Xiang, S., Carter Jr., C.W., Bricogne, G. and Gilmore, C.J. (1993) Entropy maximization constrained by solvent flatness a new method for macromolecular phase extension and map improvement, Acta Cryst., D49, 193-212. 

It is emphasized that the final result is the structure map of the examined crystal rather than a pseudo structure map. This is because the difftaction intensities have been pushed towards the corresponding kinematical values during the calculation of partial structure factor in each cycle of the correction. In addition, in the final step, structure refinement by Fourier synthesis modifies the peak heights towards the true values to some extent. It is obvious that all the missing structure information due to the CTF zero transfer is mended after phase extension. The amplitudes are provided by the electron diffraction data, and the phases are derived from the phase extension. As a result, the resolution of the structure analysis by this method is determined by the electron diffraction resolution limit. 

The success of electron diffraction data correction is vital to phase extension because, if they are not properly corrected, the projected potential map is not linear with the atomic weight. This makes it difficult to study the atomic substitution. Obviously the success of diffraction data correction depends, to a great extent, on the proposed structure from which the F p(u) is calculated. It is believed that a better match of the proposed model to the tme structure would lead to a better solution for phase extension. 

Phase extension proves that the second model gives better and more reasonable results. Fig. 3c shows the final projected potential map of the crystal along [010] with resolution up to 1 A that is obtained after performing the phase extension for two cycles in combination with the diffraction data correction based on the second proposed mode. Hence, it is supposed that, in the examined structure, B atoms replace those Cu atoms sited in the Cu-0 chains. Image simulations based on the multislice theory were performed to confirm the proposed model in Fig. 3e. The simulated image calculated with the crystal thickness of 46 A and defocus value of -650 A is presented in Fig. 3d, which matches the contrast of the averaged experimental image (Fig. 3a) pretty well. 

Hai-Fu, F., Zi-Yang, Z., Chao-De, Z. and Fang-Hua, L. (1985). Image processing in high-resolution electron microscopy using the direct method. 1.Phase extension Acta Cryst. A41,163-165. 

Gilmore, C.J., Shatikland, K. and Fryer, J.R. (1993), Phase extension in electron crystallography using the maximum entropy method and its application to two-dimensional purple membrane data fromHalobacterium halobium. Ultramicroscopy, 49, 147-178. 

There are six subunits in the asymmetric unit of the Panuliris structure, arranged in a particle best described as a trimer of dimers. The 3-2 symmetry was good enough to be useful in a phase extension technique commonly used in the structure determination of highly symmetric viruses. Unfortunately, these crystals diffract only to 3.2 A, so that there cannot be a high level of detail available for description of the active site. Nevertheless, because there are six independent copies of the molecule in the asymmetric unit, there is more information than might normally be available at this resolution. The structure has been carefully refined at this resolution, with and without the 3-2 symmetry restraint. The estimated coordinate error is —0.35 A. The overall R is 0.201 for data between 8 and 3.2 A. Surprisingly, while the overalls for subunits 1 and... 

The most demanding element of macromolecular crystallography (except, perhaps, for dealing with macromolecules that resist crystallization) is the so-called phase problem, that of determining the phase angle ahkl for each reflection. In the remainder of this chapter, I will discuss some of the common methods for overcoming this obstacle. These include the heavy-atom method (also called isomorphous replacement), anomalous scattering (also called anomalous dispersion), and molecular replacement. Each of these techniques yield only estimates of phases, which must be improved before an interpretable electron-density map can be obtained. In addition, these techniques usually yield estimates for a limited number of the phases, so phase determination must be extended to include as many reflections as possible. In Chapter 7,1 will discuss methods of phase improvement and phase extension, which ultimately result in accurate phases and an interpretable electron-density map. 

Finally, the derivative crystal must diffract to reasonably high resolution, although the resolution of derivative data need not be as high as that of native data. Methods of phase extension (Chapter 7) can produce phases for higher-angle reflections from good phases of reflections at lower angles. 

Another example was reported by Ugi and co-workers in a study concerning the synthetic applications of convertible (jS-isocyanoethyl)alkyl carbonates [7a]. A solid-phase extension of the same procedure has been reported by the Kennedy group [20] at Array BioPharma who employed the resin-bound carbonate convertible isocyanide. 

A solid-phase extension of the UDC strategy for the preparation of highly pure and diverse arrays of l,4-benzodiazepine-2,5-diones has been reported. The method employed Wang resin-bound a-amino adds [75]. Another interesting solid-phase synthesis of l,4-benzodiazepine-2,5-diones was reported by Chen et al. [18b] that employed the Rink-isocyanide resin as the convertible isocyanide. 

Halo ketones react with enamines 177 to form pyrroles (the Hantzsch pyrrole synthesis, ) and with -keto esters 179 under basic conditions to give furans 180 (the FeistBenary furan synthesis, ). The orientation in the Hantzsch pyrrole synthesis 177 178 differs from that in the FeistBenary furan synthesis 179 180 (Scheme 99). In an example of a modified Hantzsch synthesis, the -aminoacrylonitrile 182 reacts with ketone 181 to give pyrrole 183 in a moderate yield (Scheme 100) a series of similar compounds can be synthesized using this approach <1997S530>. A solid-phase extension of the Hantzsch synthesis has also been reported <1998BML2381>. 

Two-phase, Four-wire.—Two complete single-phase circuits. The neutrals of the two circuits may be connected, in which case the voltage across circuits is 71 per cent of that between the wires of a phase. Extensively used. In the five-wire system, the common neutral is extended as a fifth wire. 

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