Smoothed Spherical Truncation based on Fuzzy Membership Functions: Application to the Molecular Encoding

Abstract

A novel spherical truncation method, based on fuzzy membership functions, is introduced to truncate interatomic (or interaminoacid) relations according to smoothing values computed from fuzzy membership degrees. In this method, the molecules are circumscribed into a sphere, so that the geometric centers of the molecules are the centers of the spheres. The fuzzy membership degree of each atom (or aminoacid) is computed from its distance with respect to the geometric center of the molecule, by using a fuzzy membership function. So, the smoothing value to be applied in the truncation of a relation (or interaction) is computed by averaging the fuzzy membership degrees of the atoms (or aminoacids) involved in the relation. This truncation method is rather different from the existing ones, at considering the geometric center for the whole molecule and not only for atom‐groups, as well as for using fuzzy membership functions to compute the smoothing values. A variability study on a set comprised of 20,469 compounds (15,050 drug‐like compounds, 2994 drugs approved, 880 natural products from African sources, and 1545 plant‐derived natural compounds exhibiting anti‐cancerous activity) demonstrated that the truncation method proposed allows to determine molecular encodings with better ability for discriminating among structurally different molecules than the encodings obtained without applying truncation or applying non‐fuzzy truncation functions. Moreover, a principal component analysis revealed that orthogonal chemical information of the molecules is encoded by using the method proposed. Lastly, a modeling study proved that the truncation method improves the modeling ability of existing geometric molecular descriptors, at allowing to develop more robust models than the ones built only using non‐truncated descriptors. In this sense, a comparison and statistical assessment were performed on eight chemical datasets. As a result, the models based on the truncated molecular encodings yielded statistically better results than 12 procedures considered from the literature. It can thus be stated that the proposed truncation method is a relevant strategy for obtaining better molecular encodings, which will be ultimately useful in enhancing the modeling ability of existing encodings both on small‐to‐medium size molecules and biomacromolecules. © 2019 Wiley Periodicals, Inc.

Fuzzy spherical truncation-based multi-linear protein descriptors: From their definition to application in structural-related predictions

“…The second largest amount of aas was located between 80% and 100% of the R values (surface region of the sphere), whereas the remaining aas are near to the geometric center. These results are in correspondence with the ones obtained elsewhere (García-Jacas et al, 2019).…”

“…Consequently, the truncation values can be deemed as defined r on -r off intervals (membership degree). This observation encouraged the recent development of a smoothing spherical truncation method based on fuzzy membership functions (FMFs) to truncate inter-atomic relationships in small-and mediumsized molecules (García-Jacas et al, 2019). This method determines a truncation value in the interval [0, 1] by averaging the fuzzy membership degrees of interacting atoms, depending on the distance of each atom to the molecule's geometrical center.…”

“…The utility of the previously-mentioned truncation scheme, implemented for the calculation of the QuBiLS-MIDAS 3D-MDs, has been shown through different chemometric studies, which have improved the modeling ability of extant 3D-MDs for small-and medium-sized molecules (García-Jacas et al, 2019). But the relevance of this truncation method has not been evaluated yet in the structural encoding of macromolecules, such as proteins.…”

Distributed and multicore QuBiLS‐MIDAS software v2.0: Computing chiral, fuzzy, weighted and truncated geometrical molecular descriptors based on tensor algebra

“…Schema shows a specific example of how the truncation method developed is applied. This truncation method was widely examined in the literature . This truncation is done by considering the spherical radius ( R ) of the molecule, which is calculated as the Euclidean distance between the geometric center ( o ) and the outermost atom of the molecule.…”

“…The truncation function for the NO relation ( d NO ) is depicted in the schema (also see section 2 in ref. ). On the one hand, it can be noted that if an S‐shaped FMF is used, then the membership degree ( μ A ) for the d No and d Oo distances tend to 1, since the N and O atoms are distant from the center o in the molecule accounted for; whereas if a Z‐shaped FMF is used, then the membership degrees obtained tend to 0.…”