Title: Fuzzy spherical truncation-based multilinear descriptors for protein structural prediction
Abstract:
This work introduces a family of fuzzy spherically truncated 3D multilinear descriptors for protein structure representation. The proposed indices encode geometric information derived from k-th order spherically truncated spatial dissimilarity two-tuple and three-tuple tensors. These tensors are constructed by embedding protein structures into a spherical coordinate system centered at the protein’s geometric centroid. Within this framework, distances between amino acids and the protein center are used to quantify spatial relationships. A fuzzy membership function is then applied to model the membership degree of each residue within spherical regions of interest.
Truncation coefficients are obtained by aggregating membership degrees of interacting amino acids using an arithmetic mean fusion rule. Several fuzzy membership functions are explored, including Z-shaped (center-focused), PI-shaped (mid-region), and A-Gaussian (surface-focused) functions, alongside classical truncation schemes such as switching functions.
A comprehensive evaluation is conducted in terms of membership distribution, variability, and redundancy, using Shannon entropy and Principal Component Analysis to assess variability and diversity among descriptors. Predictive performance is further validated in alignment-free models for protein folding rate prediction and structural class classification.
Results demonstrate that the proposed fuzzy spherical truncation framework provides a richer and more discriminative representation than classical non-truncated and conventionally truncated descriptors. The best models achieve up to 95.82% external correlation in folding rate prediction and 100% accuracy in structural class discrimination, outperforming existing approaches.
These findings highlight the potential of fuzzy spherically truncated multilinear descriptors, implemented in MuLiMs-MCoMPAs (http://tomocomd.com/mulims-mcompas), as effective alignment-free representations for modeling protein structure–function relationships.
