Enumeration

Although the representation of these queries is very similar to a combinatorial library, there are some significant differences in both design and use. Since the exact compositions of the database structures are not determined until after the query has been posed, the query typically contains query features, such as fuzzy atoms and bonds and ambiguous connectivity. There is no need for these features to represent a combinatorial library, since all the structures are known. The syntax for representing R-groups in a query can also include features such as zero occurrences to reduce the retrieval of undesired records. Such a feature is unnecessary for a combinatorial library representation, since it is a complete set of specific structures and not an open-ended query. 

The enumeration process takes a generic structure and performs the substitutions defined by one or more of the R-groups to generate a number of more specific structures. 

If all the R-groups are expanded, then the result is a set of specific structures. If only some ofthe R-groups are expanded, then the result is a set of subgeneric structures. These subgeneric structures are useful in representing deconvolution experiments. This process is shown in Fig. 2. 

On the other hand, the enumerated structures themselves might be useful as input for other computer programs that generate computational data, such as QSAR or other chemical property predictions. Since these programs accept and work on individual specific structures, these structures must be generated both for input to these programs and for association with their output. This capability is important for the process of designing new combinatorial libraries. 

There might often be cause to limit the enumeration to less than every possible specific structure or subgeneric structure represented by the combinatorial library. If the library represents a real experiment, then perhaps not every combination of R-group members represents a compound that was actually synthesized. If the library is to be enumerated 

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The various types of synnnetry enumerated in section A1.4.F2 are discussed in detail here and the synnnetry groups containing such synnnetry operations are presented. 

At third order, one must expand + ) Ur=i enumerate the generators ... 

All of the symmetry classes compatible with the long-range periodic arrangement of atoms comprising crystalline surfaces and interfaces have been enumerated in table Bl.5,1. For each of these syimnetries, we indicate the corresponding fonn of the surface nonlinear susceptibility With the exception of surfaces... 

R N. The exponent v = 0.588 has been calculated using renonnalization group teclmiques [9, 10], enumeration teclmiques for short chain lengths and Monte Carlo simulations [13]. 

In order to summarize the procedures used for computing ionization constants of titratable residues in proteins, the steps used in our algorithm will be enumerated below ... 

This process is continued until all the atoms arc canonically enumerated. 

To reiterate a point that we made earlier, these problems of accurately calculating the free energy and entropy do not arise for isolated molecules that have a small number of well-characterised minima which can all be enumerated. The partition function for such systems can be obtained by standard statistical mechanical methods involving a summation over the mini mum energy states, taking care to include contributions from internal vibrational motion. 

A related study was the exhaustive enumeration of the global minimum energy structure for all iP possible sequences of the HP model described in Section 10.3.1 [Li et al. 1996 Ihis showed that 4 75% of these sequences have a unique ground state (i.e. just on... 

Pander J W and F M Richards 1987. Tertiary Templates for Proteins. Use of Packing Criteria in Enumeration of Allowed Sequences for Different Structural Classes. Journal of Molecular Bio 193 775-791. 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

The term enumeration when applied to a combinatorial library refers to the process by which the cormection tables for the product structures in a real or virtual library are produced. It should be noted that a single compound can be considered as a library of one and so enumeration can equally well be applied in this case. However, whereas it is considered reasonable for a chemist to draw the structure of a single compoimd manually (which may have taken days, if not months or years, to synthesise), it is clearly not practical to do so even for small combinatorial libraries. Hence the need for automated tools to perform this procedure. 

The alternative approach is to use the computational equivalent of a chemical reaction, or reaction transform. Here, one does not need to define a common template or to generate sets of clipped reagents. Rather, the library can be enumerated using as input the initial reagent structures and the chemical transforms required to operate upon them. In this... 

Comparison of the reaction transform (a) and fragment-marking (b) approaches to the enumeration of izoles. 

The rate of colour change will depend upon the activity of the enzyme preparation. The changes enumerated below are usually, however, easily observable. 

The aolventa, enumerated under 10 and 11, may contain traces of peroxides. These can be removed either by refiuxing over anhydrous stannous ofiloride (see concluding paragraph of Section VI, 12) or by filtration under slight pressure through a column of activated alumina. 

Triiodobenzoates. The derivatives enumerated above are unsatisfactory for alcohol - ethers, e.g., the mono-ethers of ethyleneglycol ( cellosolves ) and the mono-ethers of diethyleneglycol ( car-bitols ) (see Table 111,27). Crystalline derivatives of alcohol - ethers are readily obtained with 3 4 5-triiodobenzoyl chloride (for preparation, see Section VII,21), for example ... 

The experiments enumerated below illustrate the tautomeric character of ethyl acetoacetate. 

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