Natural equivalent

Acyloins (a-hydroxy ketones) are formed enzymatically by a mechanism similar to the classical benzoin condensation. The enzymes that can catalyze reactions of this type arc thiamine dependent. In this sense, the cofactor thiamine pyrophosphate may be regarded as a natural- equivalent of the cyanide catalyst needed for the umpolung step in benzoin condensations. Thus, a suitable carbonyl compound (a -synthon) reacts with thiamine pyrophosphate to form an enzyme-substrate complex that subsequently cleaves to the corresponding a-carbanion (d1-synthon). The latter adds to a carbonyl group resulting in an a-hydroxy ketone after elimination of thiamine pyrophosphate. Stereoselectivity of the addition step (i.e., addition to the Stand Re-face of the carbonyl group, respectively) is achieved by adjustment of a preferred active center conformation. A detailed discussion of the mechanisms involved in thiamine-dependent enzymes, as well as a comparison of the structural similarities, is found in references 1 -4. 

Oleosomes — Also called oil bodies, oleosomes are the natural equivalents of liposomes. They are found in plant seeds or fruits, filled with oils, pigments, and vitamins, and serve as specific organelles to store lipid molecules. A protocol to... 

The classical Lagrange formula is not efficient numerically. One can derive more efficient, but otherwise naturally equivalent interpolation formulas by introducing finite differences. The first order divided differences are defined by... 

Equivalent atoms in a molecule are those that may all be interchanged with one another by symmetry operations. Naturally, equivalent atoms must be of... 

Section 2.1 above). These functional fibrils suggest that designed fibrils can be developed as compatible materials. Toxicology will be a potential issue for all structures that self-assemble on a nanoscale. However, the natural building blocks used to construct protein fibers may increase the biocompatibility of these structures compared to other man-made materials. Polypeptide self-assembly also represents a route for generating ECM-like structures that are not only simpler than their natural equivalents but also easier to prepare. 

Theorem. Let R- S be faithfully flat. Then R-modules are naturally equivalent to S-modules with descent data. 

Such a representation is particularly useful when one recalls that there is a natural equivalence relation on die set of edges contained in a cycle [5l]-... 

In a much later stage of development, other ceramics that were not clay-or silicate-based depended on much more sophisticated raw materials, such as binary oxides, carbides, perovskites, and even completely synthetic materials for which there are no natural equivalents. The microstructures of these modern ceramics were at least an order of magnitude finer and more homogeneous and much less porous than those of their traditional counterparts. It is the latter — the modern or technical ceramics — with which this book is mainly concerned. 

Other oxidizing agents which were ineffective in this system were NAD, NADP, riboflavin monophosphate, FAD, ferricyanlde ion, and cytochrome c. The inference should be made that in vivo transformation with Ps. testosteroni can be run anaerobically with ai degree of efficiency. Since the necessary oxidizing reagent species are rarely present in stoichiometric quantities, oxygen is required to regenerate the natural equivalent(s) of phenazine methosulfate. 

Variable Applied To Symbol Nature Equivalent Tensor... 

The symmetry point group of the molecule in the quadrupolar field is thus C2v, which bears the same relation to Coov as D2/1 does to Doo/i- The reduction of symmetry from Doo/i to Coov or from D2/1 to C2V - is a result of a dipolar field along the z axis. The greater electronegativity of oxygen than carbon is the natural equivalent of the artificial dipolar field introduced in Section 2.2.6, the effect of which on an isolated atom was illustrated in Fig. 2.9. 

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