Xanthene tetracarboxylic acid

Thus, if we allow pairs of enantiomorphic amino acids and the self-enantiomorphic amino acid glycine, i.e. total sets of 3, 5,..., up to 39 amino acids, we find that the combinatorial libraries of all the possible amidation products consist of 25,169,..., up to 579,121 tetra-amides of this particular xanthene-tetracarboxylic acid. The libraries contain 20,156,..., and 578,360 enantiomorph amidation products, and 5, D..., 761 self-enantiomorphic ones, respectively. 

Exercise Give a complete table of numbers of amidation products of the above xanthene-tetracarboxylic acid (total number, number of enantiomorphs and number of self-enantiomorphs) for 3 < y < 15, Y consisting of glycine and pairs of enantiomorphic amino acids. 

In the previous section we obtained sizes of combinatorial bbraries, e.g. numbers of eunidations of xanthene-tetracarboxylic acid chloride, euid also sizes of sublibraries contauiing achiral or chiral amidations only. Some of these numbers can be obtained in one step, e.g. the number of permutational isomers with racemic content. The answer to such problems will be a generating Junction, a polynomial in the indetermi-nates y Y that has the desired numbers as coefficients of monomial summands. Generating firnctions for the numbers of simple graphs with given number of bonds were obtained above. The number of permutational isomers of content con S) will be the coefficient of the monomial summand... 

The crucial point is that this generating function for the numbers of permutational isomers by content and with respect to R suffices when we use the notion of racemic content. We demonstrate this using the amidation of xanthene-tetracarboxylic acid chloride, using three types of ligands, a pair of enantiomorphic ones, x and y and the self-enantiomorphic glycine, indicated by z. 

Example (Amidations by content) Recalling that the rotation group of the skeleton of xanthene-tetracarboxylic acid chloride consists of the permutations 1 = (0)(1)(2)(3) and (03)(12) of the four substitutable positions, and putting Y = x, y, z, where = z, Y i, = x, y and x = y, we obtain the generating function for the numbers of permutational isomers by weight, with respect to the rotation group R from Example 3.19 ... 

Hence there are seventeen pairs of orbits with non-racemic contents. The union of the two components of such pairs forms a permutational isomer with non-racemic content. Replacing the orbit symbols < , and e by the contents, we obtain the following situation for the amidation of xanthene-tetracarboxylic acid chloride using types of substituents contained in x, y, z and indicating the placement of the types of substituents x, y, z on the substitutable positions 0,1,2,3 ... 

Exercise Evaluate the number of amidations of xanthene-tetracarboxylic acid chloride with respect to a set of types of substituents consisting of five elements, two different pairs of enan-tiomorphs and the achiral amino acid. Evaluate the numbers of amidations with racemic content as well as of non-racemic content. In order to make life easier, you can use the online version of AMGAM at http //magma.maths.usyd.edu.au/calc/ For this reason you should know the form of input that MAGMA accepts. For example, you may submit as input the following three command lines ... 

Template-based approaches to combinatorial libraries have been explored by a few research groups. The macrocyclic lysine-derived template of Houghten (library 1.2) is an early example of this library concept. More recently, less peptidic scaffolds have been employed in libraries including the Kemp triacid (library 1.6), a xanthene tetracarboxylic acid (library 1.7), 2,4-dichloro-6-methylpyrimidine (library 3.23), pyridinotriamines (library 4.13) and the polyazapyridinophanes (library 4.14). 

Other popular scaffolds have been derivatives of biphenyls which are now readily prepared using solid phase methods [265,464-469]. A solution phase approach has been to react a polyfunctional ised core containing reactive groupings - acid chlorides or isocyanates are easily prepared examples -with a mixture of reagents. One of the earliest synthetic examples showed the use of cubane tetracarboxylic acid chloride [151]. Two recent methods have used functionalised xanthene (library 71) [470] or diphenylmethane cores (library 72) [471] to identify DNA and urokinase receptor antagonists respectively. 

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