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Novel global and local 3D atom-based linear descriptors of the Minkowski distance matrix: theory, diversity–variability analysis and QSPR applications

Abstract

A new family of alignment-free 3D descriptors based on TOMOCOMD-CARDD framework has been designed, namely 3D-linear indices. In this report, we have proposed the use of a generalized form of the geometric pairwise atom-atom distance matrix as structural information matrix. This matrix, denominated as non-stochastic, uses as matrix form of linear maps as well as their algebraic transformations: stochastic, double stochastic and mutual probabilities matrices. The methodology for 3D-QSAR studies is based on the combined use of global and local approaches. Principal component analysis reveals that the novel indices are capable of capturing structural information not codified by the indices implemented in the DRAGON’s software. Moreover, Shannon’s entropy based variability analysis comparing the 3D-linear indices with some relevant descriptors suggests that the former encode similar-to-better amount of structural information than these descriptors. Finally, a search for the best regressions for congeneric databases in QSPR modeling was performed. The overall results demonstrates satisfactory behavior.

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Acknowledgments

Cubillán, N. thanks Consejo de Desarrollo Científico y Humanístico (CONDES-LUZ, Grant CC-0593-10), Fondo Nacional de Ciencia, Tecnología e Innovación (FONACIT, Grant G-2005000403), Misión Ciencia (Grant 2007000881) and Instituto Zuliano de Investigaciones Tecnológicas (INZIT, Project LOCTI) for partial financial support of this work. Marrero-Ponce, Yovani thanks the program ‘Estades Temporals per an Investigadors Convidats’ for a fellowship to work at Valencia University. The authors acknowledge also the partial financial support from Spanish Ministry of Science and Innovation (MICINN, Project Reference: SAF2009-10399). Last, but not least, the authors want to express their acknowledgements to Prof. Jorge Galvez (VU) and Prof. Ramón García-Domenech (VU) for their help and useful comments about these new MDs.

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Correspondence to Néstor Cubillán.

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10910_2015_533_MOESM1_ESM.doc

Supplementary Information: The Table S1 shows the values of the atomic weights used for molecular vectors. Table S2 reports the factor loadings (varimax normalized rotation) for the 0D--3D DRAGON MDs as well as the total and local (atom type) 3D-Linear indices for 41 heterogeneous chemicals. And, Table S3 shows the chemical structure and numbering of atoms in 2-furylethylene database. (DOC 4791KB)

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Cubillán, N., Marrero-Ponce, Y., Ariza-Rico, H. et al. Novel global and local 3D atom-based linear descriptors of the Minkowski distance matrix: theory, diversity–variability analysis and QSPR applications. J Math Chem 53, 2028–2064 (2015). https://doi.org/10.1007/s10910-015-0533-3

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Keywords

  • TOMOCOMD-CARDD
  • 3D-linear index
  • Variability analysis
  • QSPR study