Chirality Codes

420 I 8.6 Tuionoi Conformatior -lnctependei i and Conformation-Dependent Chirality Codei [34] 

Neural networks were trained on the basis of these codes to predict chiralit -dependent properties in enantioselective reactions [42] and in chiral chromatography [43]. A detailed description of the chirality codes is given in the Tutorial in Section 8,6, 

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Tutorial Conformation-Independent and Conformation-Dependent Chirality Codes [34]... 

Chirality codes are used to represent molecular chirality by a fixed number of de-.scriptors. Thc.se descriptors can then be correlated with molecular properties by way of statistical methods or artificial neural networks, for example. The importance of using descriptors that take different values for opposite enantiomers resides in the fact that observable properties are often different for opposite enantiomers. 

In most common chiral molecules, chirality arises from chiral tetravalent atoms. A conformation-independent chirality code (CICC) was developed that encodes the molecular chirality originating from a chiral tetravalent atom [42], For more generality, a conformation-dependent chirality code (CDCC) is used [43]. CDCC ti cats a molecule as a rigid set of points (atoms) linked by bonds, and it accounts for chirality generated by chirality centers, chirality axes, or chirality planes. 

The calculation of the chirality code starts from a molccnlar structure, requires some preparatory calculations, and follows several steps that are described in detail below. 

The chirality code of a molecule is based on atomic properties and on the 3D structure. Examples of atomic properties arc partial atomic charges and polarizabilities, which are easily accessible by fast empirical methods contained in the PETRA package. Other atomic properties, calculated by other methods, can in principle be used. It is convenient, however, if the chosen atomic property discriminates as much as possible between non-equivalent atoms. 3D molecular structures are easily generated by the GORINA software package (see Section 2.13), but other sources of 3D structures can be used as well. 

In order to consider the 3D structure but make the chirality code independent of a specific conformer, r- is taken as the sum of the bond lengths between atoms i and j on the path with a minimum number of bond counts. 

The number of discrete points of /cicc( ) determines the resolution of the chirality code is a smoothing factor which in practice controls the width of the peaks obtained by a graphical representation versus u. An example of a chir-... 

The conformation-dependent chirality code constitutes a more general description of molecular chirality, which is formally comparable with the CICC [43], The main difference is that chiral carbon atoms arc now not explicitly considered, and combinations of any four atoms are now used, independently of the existence or nonexistence of chiial centers, and of their belonging or not belonging to ligands of chiral centers. 

The two values, e and c, calculated for all combinations of four atoms, are then combined to generate a conformation-dependent chirality code. fc )QO using Eq. (30), where n is the number of atoms in each molecule, and r introduces the conformation dependence ... 

The number of discrete values of/cocc(i ) determines the resolution of the chirality code. Again, is a smoothing factor. An example with the conformation-dependent chirality codes for the enantiomers of 4 in two different conformations is shown in Eigurc 8-1 f. 

Twenty-eight chiral compounds were separated from their enantiomers by HPLC on a teicoplanin chiral stationary phase. Figure 8-12 shows some of the structures contained in the data set. This is a very complex stationary phase and modeling of the possible interactions with the analytes is impracticable. In such a situation, learning from known examples seemed more appropriate, and the chirality code looked quite appealing for representing such data. 

Therefore the 28 analytes and their enantiomers were encoded by the conformation-dependent chirality code (CDCC) and submitted to a Kohoiien neural network (Figure 8-1 3). They were divided into a test set of six compounds that were chosen to cover a variety of skeletons and were not used for the training. That left a training set containing the remaining 50 compounds. 

Figure 8-1J. Training ofa Kohonen neural network with a chirality code, The number of weights in a neuron is the same as the number of elements in the chirality code vector, When a chirality code is presented to the network, the neuron with the most similar weights to the chirality code is excited (this is the ivinning or central neuron) (see Section 9.5,3),...

Aires-de-Sousa, J., Gasteiger, J., Gutman, I., Vidovic, D. Chirality code and molecular structure, j. Chem. Inf. Comput. Sci. 2004, 44, 831-836. 

The conformational-independent chirality code face is a modification of the radial distribution junction code g(R) to account for chirality ... 

The two values, E and S, calculated for all the combinations of the four atoms are then combined to generate the chirality code fcicc(R)i where the function is calculated at a number of discrete points R with defined intervals to obtain the same number of descriptors, irrespective of the size of the molecule. The actual range of R is chosen according to the range of the studied properties related to the range of observed interatomic distances for the data set molecules. 

The number of discrete points determines the resolution of the chirality code. 

Moreover, the Conformational-Dependent Chirality Code (/cdcc) was defined to account for conformational behavior of molecules, replacing the chirality signal Syki by a conformational-dependent geometric parameter Qjia [Caetano, Aires-de-Sousa et al., 2005]. The occ code is calculated as... 

Conformational-Dependent Chirality Code chirality descriptors (0 Chirality Codes) conformational global sensitivity molecular descriptors (0 invariance properties of... 

To account for stereochemistry of molecules, the —> Chirality Code was proposed as a modification of the RDF code [Aires-de-Sousa and Gasteiger, 2001]. 

Caetano, S., Aires-de-Sousa, J., Daszykowski, M. and Vander Heyden, Y. (2005) Prediction of enantioselectivity using chirality codes and classification and regression trees. Anal. Chim. Acta, 544, 315-326. 

Aires-de-Sousa and Gasteiger used four regression techniques [multiple linear regression, perceptron (a MLF ANN with no hidden layer), MLF ANN, and v-SVM regression] to obtain a quantitative structure-enantioselectivity relationship (QSER). The QSER models the enantiomeric excess in the addition of diethyl zinc to benzaldehyde in the presence of a racemic catalyst and an enan-tiopure chiral additive. A total of 65 reactions constituted the dataset. Using 11 chiral codes as model input and a three-fold cross-validation procedure, a neural network with two hidden neurons gave the best predictions ANN 2 hidden neurons, R pred = 0.923 ANN 1 hidden neurons, R pred = 0.906 perceptron, R pred = 0.845 MLR, R p .d = 0.776 and v-SVM regression with RBF kernel, R pred = 0.748. 

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