Abstract
In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor’s Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.
Highlights
The use of 3D molecular descriptors (MDs) can be considered as an approach for inferring information about structural properties and their related quantities
A good number of prediction models that link 3D chemical structures with activity or properties (QSAR/QSPR) have been generated from 3D-MDs, which have been extensively used for the characterization of organic molecules and small chemical systems[12]
Marrero-Ponce et al introduced a new set of MDs that consider topology (2D) related characteristics for organic molecules[19,20,21,22,23], which has been included in QuBiLs MAS (Quadratic, Bilinear and N-Linear Maps based on graph-theoretic electronic-density Matrices and Atomic Weightings) software[24]
Summary
The use of 3D molecular descriptors (MDs) can be considered as an approach for inferring information about structural properties and their related quantities. Marrero-Ponce et al introduced a new set of MDs that consider topology (2D) related characteristics for organic molecules[19,20,21,22,23], which has been included in QuBiLs MAS (Quadratic, Bilinear and N-Linear Maps based on graph-theoretic electronic-density Matrices and Atomic Weightings) software[24]. These 0-2D and chiral MDs were obtained codifying the structural information, using algebraic bilinear forms, and considering electronic density graph-based matrices. Concerning protein folding rate, there are several indices that consider the topology/ geometry of proteins and the number of contacts between amino acids for the prediction of this property[15,30,41,42,43]
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