Equivalence Among Different Systems

Equivalence Among Different Systems, Conversion Factor gc, and Prefixes... 

One might have assumed that among different processes there would be a vast range of different levels of computational sophistication. But the remarkable assertion that the Principle of Computational Equivalence makes is that in practice this is not the case, and that instead there is essentially just one highest level of computational sophistication, and this is achieved by almost all processes that do not seem obviously simple. . . For the essence of this phenomenon is that it is possible to construct universal systems that can perform essentially any computation—and which must therefore all in a sense be capable of exhibiting the highest level of computational sophistication (Wolfram,... 

The overall form of each of these equations is fairly simple, ie, energy = a constant times a displacement. In most cases the focus is on differences in energy, because these are the quantities which help discriminate reactivity among similar stmctures. The computational requirement for molecular mechanics calculations grows as where n is the number of atoms, not the number of electrons or basis functions. Immediately it can be seen that these calculations will be much faster than an equivalent quantum mechanical study. The size of the systems which can be studied can also substantially ecHpse those studied by quantum mechanics. 

Many researchers refer to stems 1, 2, and 3 using their Roman numeral equivalents—that is, stems I, II, and III. These motifs are also denoted as helices I, II, and III. It should be noted at the beginning of this hammerhead ribozyme discussion that structure-function relationships, the role of various nucleobases, metal ion participation in catalysis, and other features of the system have not been completely delineated and in some cases remain controversial. Globally, the hammerhead fold appears to be similar in both solution and solid-state studies. In solution, however, the central core of the hammerhead construct appears to be highly dynamic. This may account for different experimental results among the analytical techniques used in solution and certainly explains some distinct differences seen between solution and solid-state (X-ray crystallographic) structures. 

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