Fuzzy spherical truncation-based multi-linear protein descriptors: From their definition to application in structural-related predictions - Contreras-Torres, Ernesto; Marrero-Ponce, Yovani; Terán, Julio E.; Agüero-Chapin, Guillermin; Antunes, Agostinho; García-Jacas, César R. (Frontiers in Chemistry, 2022)
This study introduces a set of fuzzy spherically truncated three-dimensional (3D) multi-linear descriptors for proteins. These molecular descriptors (MDs) are based on the two-linear and three-linear algebraic forms, as specific cases of the N-linear (tensor) algebraic forms. These indices codify geometric structural information from kth spherically truncated spatial-(dis)similarity two-tuple and three-tuple tensors. The coefficients of these truncated tensors are calculated by applying a smoothing value to the 3D structural encoding based on the relationships between two and three amino acids of a protein embedded into a sphere. As, the geometrical center of the protein matches with center of the sphere, the distance between each amino acid involved in any specific interaction and the geometrical center of the protein can be computed. Then, the fuzzy membership degree of each amino acid with respect to a spherical region of interest is computed from fuzzy membership functions (FMFs). The truncation value is finally calculated by the combination (by using arithmetic mean as the fusion rule) of the membership degrees of the interacting amino acids. Several fuzzy membership functions having diverse biases on the calculation of amino acids memberships (e.g., Z-shaped (close to the center), PI-shaped (middle region), and A-Gaussian (far from the center)) were considered as well as traditional truncation functions (e.g., Switching). The truncation functions (i.e., FMFs) were compared by exploring: i) the frequency of membership degrees, ii) by the variability and orthogonality analyses among them based on the Shannon Entropy’s and Principal Component’s methods, respectively, and iii) by the alignment-free prediction of protein folding rates and structural classes. Such extensive evaluation unraveled the singularity of the proposed fuzzy spherically truncated MDs with respect to the classical (non-truncated) MDs and the MDs truncated with traditional functions. The best model developed for folding rate showed an external correlation coefficient equal to 95.82%; whereas the best model created for structural class discrimination attained 100% of accuracy on the corresponding test. These results are better than the ones attained by existing approaches, justifying the theoretical contribution of this work. Thus, the fuzzy spherically truncated-based MDs from MuLiMs-MCoMPAs (http://tomocomd.com/mulims-mcompas) are promising alignment-free predictors for protein.