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J Theor Biol. 2015 Jun 7;374:125-37. doi: 10.1016/j.jtbi.2015.03.026. Epub 2015 Apr 3.

Novel 3D bio-macromolecular bilinear descriptors for protein science: Predicting protein structural classes.

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Facultad de Química Farmacéutica, Universidad de Cartagena, Cartagena de Indias, Bolívar, Colombia; Unidad de Investigación de Diseño de Fármacos y Conectividad Molecular, Departamento de Química Física, Facultad de Farmacia, Universitat de València, Spain.; Grupo de Investigación en Estudios Químicos y Biológicos, Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena de Indias, Bolívar, Colombia. Electronic address: ymarrero77@yahoo.e.
Grupo de Investigación de Bioinformática, Centro de Estudio de Matemática Computacional (CEMC), Universidad de las Ciencias Informáticas (UCI), La Habana, Cuba; Departamento de Técnicas de Programacion, Facultad 6, Universidad de las Ciencias Informáticas (UCI), La Habana, Cuba.
Grupo de Investigación de Bioinformática, Centro de Estudio de Matemática Computacional (CEMC), Universidad de las Ciencias Informáticas (UCI), La Habana, Cuba.
Departamento de Química, Universidade Federal de Lavras, CP 3037, 37200-000 Lavras, MG, Brazil.
Laboratorio de Electrónica Molecular, Universidad del Zulia, Facultad Experimental de Ciencias, Departamento de Química, Maracaibo, República Bolivariana de Venezuela.
Laboratorio de Caracterización Molecular y Biomolecular, Departamento de Investigación en Tecnología de los Materiales y el Ambiente (DITeMA), Instituto Venezolano de Investigaciones Científicas (IVIC), Avenida 74 con calle 14A, Maracaibo, República Bolivariana de Venezuela.


In the present study, we introduce novel 3D protein descriptors based on the bilinear algebraic form in the ℝ(n) space on the coulombic matrix. For the calculation of these descriptors, macromolecular vectors belonging to ℝ(n) space, whose components represent certain amino acid side-chain properties, were used as weighting schemes. Generalization approaches for the calculation of inter-amino acidic residue spatial distances based on Minkowski metrics are proposed. The simple- and double-stochastic schemes were defined as approaches to normalize the coulombic matrix. The local-fragment indices for both amino acid-types and amino acid-groups are presented in order to permit characterizing fragments of interest in proteins. On the other hand, with the objective of taking into account specific interactions among amino acids in global or local indices, geometric and topological cut-offs are defined. To assess the utility of global and local indices a classification model for the prediction of the major four protein structural classes, was built with the Linear Discriminant Analysis (LDA) technique. The developed LDA-model correctly classifies the 92.6% and 92.7% of the proteins on the training and test sets, respectively. The obtained model showed high values of the generalized square correlation coefficient (GC(2)) on both the training and test series. The statistical parameters derived from the internal and external validation procedures demonstrate the robustness, stability and the high predictive power of the proposed model. The performance of the LDA-model demonstrates the capability of the proposed indices not only to codify relevant biochemical information related to the structural classes of proteins, but also to yield suitable interpretability. It is anticipated that the current method will benefit the prediction of other protein attributes or functions.


3D protein descriptor; Bilinear form; Coulombic matrix; LDA; Protein structural classes

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