Correlation weight

Toropov AA, Benfenati E (2007) Optimisation of correlation weights of SMILES invariants for modelling oral quad toxicity. Eur J Med Chem 42(5) 606-613 Toropov AA, Benfenati E (2006) QSAR models of quail dietary toxicity based on the graph of atomic orbitals. Bioorg Med Chem Lett 16(7) 1941-1943... 

Optimization of Correlation Weights of Local Graph Invariants... 

Global SMILES attributes were defined as (%,0,l,2,3)-code of six symbols si, s2, s3, s4, s5, and s6. The first symbol (si) is % . This symbol indicates this SMILES attribute is global. The s2 is descriptor of a presence of fluorine 0 means F symbol is absent in the SMILES 1 means there is one F symbol 2 means there are two F symbols finally 3 means that there are three or more F symbols in the SMILES the s3, s4, s5 are the same descriptors for Cl , Br , and O , respectively the s6 is the descriptor for the ( symbol in the SMILES. The brackets are tools to reflect the branching of molecular skeleton (Weininger, 1988, 1990 Weininger et al., 1989). Thus, ( and ) are indicators of the same phenomenon These SMILES attributes (i.e., brackets) have common correlation weight. 

Having numerical data on the optimal correlation weights, one can calculate DCW for the training and the test sets. Using data on the training set one can derive model for the fullerene C60 solubility ... 

Numerical data on the correlation weights and numbers of SMILES attributes in the training and test sets are presented in Table 14.2. One can see from Table 14.2 that two SMILES attributes are absent in the training set. Their correlation weights are defined as being equal to zero. In other words, these attributes are removed from the modeling process. 

Table 14.1 Statistical characteristics of the models for fullerene C60 solubility for three runs of the Monte Carlo optimization of the correlation weights of SMILES attributes...

Table 14.2 Numerical data on correlation weights of local and global SMILES attributes numbers of the Ak in training (jVtrn) and test (jVtst) sets ...

Attributes which are absent in the training set. Their correlation weights are zero. 

An example of calculation of the DCW with correlation weights obtained in the first ran of the Monte Carlo optimization is shown in Table 14.3. 

Correlation weights of the global SMILES invariants improve statistical quality of the fullerene C60 solubility model for both the training and the test set. 

Castro EA, Toropov AA, Nesterova AI, Nabiev OM (2004) QSPR modeling aqueous solubility of polychlorinated biphenyls by optimization of correlation weights of local and global graph invariants. CEJC 2 500-523. 

Toropov AA, Benfenati E (2004) QSAR modelling of aldehyde toxicity against a protozoan, Tetrahymena pyriformis by optimization of correlation weights of nearest neighboring codes. J. Mol. Struct. (Theochem) 679 225-228. 

Toropov AA, Benfenati E (2006c) Correlation weighting of valence shells in QSAR analysis of toxicity. Bioorg. Med. Chem. 14 3923-3928. 

Toropov AA, Benfenati E (2007a) Optimisation of correlation weights of SMILES invariants for modelling oral quail toxicity Eur. J. Med. Chem. 42 606-613. 

Toropov AA, Leszczynski J (2006) A new approach to the characterization of nanomaterials Predicting young s modulus by correlation weighting of nanomaterials codes. Chem. Phys. Lett. 433, 29 125-129. 

Toropov AA, Roy K (2004) QSPR modeling of lipid-water partition coefficient by optimization of correlation weights of local graph invariants. J. Chem. Inf. Comput. Sci. 44 179-186. 

Toropov AA, Toropova AP (2001) Prediction of heteroaromatic amine mutagenicity by means of correlation weighting of atomic orbital graphs of local invariants. J. Mol. Struct. (Theochem) 538 287-293. 

Toropov AA, Toropova AP (2002) QSPR modeling of complex stability by optimization of correlation weights of the hydrogen bond index and the local graph invariants. Russ. J. Coord. Chem. 28 877-880. 

Toropov AA, Toropova AP, Nesterova AI, Nabiev OM (2004a) Prediction of alkane enthalpies by means of correlation weighting of Morgan extended connectivity in molecular graphs. Chem. Phys. Lett. 384 357-363. 

The descriptor was a product of the correlation weights, CW(Ik), calculated by the Monte Carlo method for each kth element of a special SMILES-like notation introduced by the authors. The notation codes the following characteristics the atom composition, the type of substance (bulk or not, ceramic or not), and the temperature of synthesis. The QSAR model constructed in this way was validated with the use of many different splits into training (n 21) and validation (n=8) sets. Individual sub-models are characterized by high goodness-of-fit (0.972 applicability domain of the model, it is not known if all the compounds (metal oxides, nitrides, mullite, and silicon carbide) can be truly modeled together. 

The glass was crushed, sieved, and leached for 24 hr with boiling distilled water in a Soxhlet-type extractor. Although there are variations, the values reported (Table X) would be reduced two to three orders of magnitude at ambient temperature, and the glasses would then have an acceptably low leach rate. Our program now is to determine the temperature dependence of leach rates and to correlate weight loss data with bulk leach rates based on specific elements. 

Correlation Weights of the Local Invariants of Molecular Graphs —> variable descriptors... 

By this approach, a family of fiexible molecular descriptors based on different mathematical functions obtained from the molecular graph <5 is defined. The basic idea is to vary the correlation weights CW ofthe different atom-types under consideration, aimed at obtaining an as high as possible correlation coefficient between experimental and calculated values of a selected molecular property. Atom-types are defined using chemical information and local vertex invariants. The general form of the molecular descriptor D in terms of a number of selected atom-types is... 

An example of molecular descriptors defined in terms of correlation weights is [Krenkel, Castro et al, 2001a]... 

Castro, E.A., Toropov, A.A., Netserova, A.l. and Nazarov, A.U. (2003) QSAR study of the toxic action of aliphatic compounds to the bacteria Vibrio fisheri based on correlation weighting of local graph... 

Duchowicz, P.R., Castro, E.A. and Toropov, A.A. (2002) Improved QSPR analysis of standard entropy of acyclic and aromatic compounds using optimized correlation weights of linear graph invariants. Computers Chem., 26, 327—332. 

---