Constraints structural similarity

The concept of the similarity of molecules has important ramifications for physical, chemical, and biological systems. Grunwald (7) has recently pointed out the constraints of molecular similarity on linear free energy relations and observed that Their accuracy depends upon the quality of the molecular similarity. The use of quantitative structure-activity relationships (2-6) is based on the assumption that similar molecules have similar properties. Herein we present a general and rigorous definition of molecular structural similarity. Previous research in this field has usually been concerned with sequence comparisons of macromolecules, primarily proteins and nucleic acids (7-9). In addition, there have appeared a number of ad hoc definitions of molecular similarity (10-15), many of which are subsumed in the present work. Difficulties associated with attempting to obtain precise numerical indices for qualitative molecular structural concepts have already been extensively discussed in the literature and will not be reviewed here. 

Although no single crystal X-ray work has been done on the cyclopentadienide complexes of the trivalent actinides, it is clear that they have structures similar to those of the known homologous lanthanides. Both the trivalent lanthanides and actinides behave as Lewis acids and form adducts to complete their coordination spheres. An optimum formal coordination number of ten is indicated and their structures seem to be dictated by a maximization of electrostatic interactions within the steric constraints of the ligands. 

The formation of mixed crystals by means of a solid-state reaction occurs under kinetic control and may be subject to different constraints than the formation of mixed crystals grown closer to equilibrium conditions from the melt or from solvents. However, whether or not mixed crystallization is possible, and to what extent, is still determined by the structural similarity of the reactant and the product. Kitaigorodskii suggested guidelines based on a volume analysis which indicate that chemically compatible compounds which have optimized overlapping volumes larger than ca. 75% are likely to form solid solutions [66],... 

Finally, the type of mapping described above is consistent with the constraints laid out in Gattis (this volume) for mapping between conceptual and spatial schemas. For example, the principle of iconicity constrains the mapping from the location and movement of the hands to the location and movement of objects described (whether abstract or concrete). Structural similarities constrain the mapping of relational structures, e.g., elements are mapped to elements (the hands to concepts) and relations are mapped to relations (the spatial relation of the hands is mapped to the relation of concepts, as in the poetry example). 

A third plausible relation between the four constraints, which is also consistent with the results of Gattis and Holyoak is a hierarchical relation, perhaps with iconicity at the bottom and structural similarity at the top. A hierarchical view would predict that iconicity exerts an influence on mapping if it is the only similarity present, or if it is consistent with the higher-order constraints. In this view, structural similarity would be able to override any conflicting mappings created by iconicity, associations, or polarity. 

Structural similarities can be seen, however, when the hydropathy profiles of the tobacco and Arabidopsis ALS transit peptides are compared (not shown). This suggests that a functional transit sequence depends more on secondary or higher order structural constraints than on primary sequence information. The in vitro uptake system described above can be used to further investigate the transit peptide domain. 

The detailed catalytic mechanism of dihydrolases remains an open question. Considering the mechanistic constraints above, at least three possible reaction pathways can be proposed for SADH (Figure 28). The first hydrolysis step could form urea (path a), -succinylcitrulline (path b), or A -succinylornithine (path c). The urea route (path a) is disfavored because no urease activity is detected. Based on structural similarities of SADH to ADI, the -succinylcitrulline route (path b) was proposed. This mechanism predicts that... 

These recommendations and those resulting from other thoroughly investigated accidents also provide an excellent resource to assist in generating the system safety requirements and constraints for similar types of systems and in designing improved safety control structures. 

Sol 1. (a) Selective formation of the cw-disubstituted cyclopentane via intramolecular ene reaction is due to the fact that the transition state will be of lower energy if the hydrogen atoms are on the same side of the folded bicyclic structure. This constraint is similar in a way that a five-membered ring fused to a six-membered ring is lower in energy if it is c -fused. 

Applications of spectrum prediction to the evaluation of candidate structures have some special requirements. First, comparisons are to be between predicted and experimental spectra, not relative comparisons between predicted spectra therefore, the predicted spectrum of a compound must closely approximate its experimentally determined spectrum. Second, the methods must be applicable to larger, complex, highly functionalized compounds as well as smaller, simpler ones. Third, spectrum prediction must be sufficiently refined to yield spectral distinctions between isomeric compounds that possess structural similarities (structural building units and constraints), which at times can be substantial. If they are to be of value, the techniques should be more discriminating than those used in spectrum interpretation. Finally, since at times there may be many structures whose spectral properties are to be predicted, the methods should be computationally efficient. 

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