Novel global and local 3D atom-based linear descriptors of the Minkowski distance matrix: theory, diversity–variability analysis and QSPR applications

Cubillán, Néstor; Marrero-Ponce, Yovani; Ariza-Rico, Harold; Barigye, Stephen J.; García-Jacas, César R.; Valdés-Martiní, José R.; Alvarado, Ysaías J.

doi:10.1007/s10910-015-0533-3

Cited by 9 publications

(6 citation statements)

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“…This section is dedicated to assessing the introduction of the new truncation method based on FMFs, specifically in the molecular encoding. To this end, the QuBiLS‐MIDAS 3D‐MDs were considered, with the purpose of performing cheminformatics studies related to variability analysis, linear independence and modeling. The QuBiLS‐MIDAS 3D‐MDs are based on multilinear (tensor) algebraic forms (maps).…”

Section: Validation Of the Smoothed Spherical Truncation Methods Basedmentioning

confidence: 99%

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

et al. 2019

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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.

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Section: Validation Of the Smoothed Spherical Truncation Methods Basedmentioning

confidence: 99%

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

et al. 2019

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“…The QuBiLS‐MIDAS framework is one of the novel strategies introduced for the MDs computation based on atoms (LOVIs) –. This framework enables to determine geometric molecular descriptors (3D‐MDs) based on multi‐linear algebraic maps.…”

Section: Practical Example: Gowawa Operator‐based Qubils‐midas Molecumentioning

confidence: 99%

“…This framework enables to determine geometric molecular descriptors (3D‐MDs) based on multi‐linear algebraic maps. These 3D‐MDs are the only ones that codify chemical information between two atoms using several metrics other than the Euclidean distance,, as well as structural information regarding the relations between three and four atoms by means of multi‐metrics . Several studies have demonstrated that these 3D‐MDs encode information with high variability and linear independence with regard to other MDs reported, and, in addition, they yield superior performances in QSAR modeling ,…”

Section: Practical Example: Gowawa Operator‐based Qubils‐midas Molecumentioning

confidence: 99%

“…In short, the QuBiLS‐MIDAS 3D‐MDs are computed from the contribution of each atom (LOVI) in a molecule– (see Equations 16–18). So, if a molecule consists of n atoms, then the k th atom‐level two‐linear

([], _{n s (s s, d s, m p)}, ^{(*) (N Q)}, b_{(F)}^{a, k}, (\overset{x}{true}, \overset{y}{true}))

, three‐linear

([], _{n s (s s, m p)}, ^{(*) (N Q)}, {t r}_{(F)}^{a, k}, (\overset{x}{true}, \overset{y}{true}, \overset{z}{true}))

and four‐linear

([], _{n s (s s, m p)}, ^{(*) (N Q)}, {q u}_{(F)}^{a, k}, (\overset{x}{true}, \overset{y}{true}, \overset{z}{true}, \overset{w}{true}))

QuBiLS‐ MIDAS 3D‐MDs are calculated as N ‐linear algebraic forms in

ℝ^{n}

, in a canonical basis set, when relations among two ( N =2), three ( N =3) and four ( N =4) atoms are considered, respectively.…”

Section: Practical Example: Gowawa Operator‐based Qubils‐midas Molecumentioning

confidence: 99%

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GOWAWA Aggregation Operator‐based Global Molecular Characterizations: Weighting Atom/bond Contributions (LOVIs/LOEIs) According to their Influence in the Molecular Encoding

García-Jacas

Cabrera-Leyva

Marrero-Ponce

et al. 2018

Molecular Informatics

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A different perspective to compute global weighted definitions of molecular descriptors from the contributions of each atom (LOVIs) or covalent bond (LOEIs) within a molecule is presented, using the generalized ordered weighted averaging - weighted averaging (GOWAWA) aggregation operator. This operator is rather different from the other norm-, mean- and statistic-based operators used up to date for the descriptors calculation from LOVIs/LOEIs. GOWAWA unifies the generalized ordered weighted averaging (GOWA) and the weighted generalized mean (WGM) functions and, in addition, it uses a smoothing parameter to assign different importance values to both functions depending on the problem under study. With the GOWAWA operator, diversity of novel global aggregations of molecular descriptors can be determined, where the influence that each atom (or covalent bond) has on the molecular characterization is taken into account. Therefore, this approach is completely different from the ones reported in the literature, where the values of LOVIs/LOEIs are considered equally important. To demonstrate the feasibility of using this operator, the QuBiLS-MIDAS descriptors (http://tomocomd.com/qubils-midas) were used and, as a result, a module was built into the corresponding software to compute them, being thus the only software reported in the literature that can be employed to determine weighted descriptors. Moreover, several modeling studies were performed on eight chemical datasets, which demonstrated that, with the GOWAWA aggregation operator, weighted QuBiLS-MIDAS descriptors that contribute to develop models with greater predictive power can be computed, if compared to the models based on the non-weighted descriptors calculated from the other operators used up to date. A non-parametric statistical assessment confirmed that the GOWAWA-based predictions are significantly superior to the others obtained. Therefore, all in all, it can be concluded that, from the results achieved, the GOWAWA operator constitutes a prominent alternative to codify relevant chemical information of the molecules, ultimately useful in improving the modeling ability of several old and recent descriptors whose definition is based on the LOVIs/LOEIs calculation.

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“…Inspired by the previous idea, recently the 3D N - linear algebraic molecular descriptors have been introduced as a novel mathematical procedure for computing the structural features of chemical compounds [ 24 – 26 ]. These MDs employ the bilinear , quadratic and linear algebraic maps [ 27 ] to codify information between atom-pairs by using several (dis - )similarity metrics [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

Examining the predictive accuracy of the novel 3D N-linear algebraic molecular codifications on benchmark datasets

et al. 2016

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BackgroundRecently, novel 3D alignment-free molecular descriptors (also known as QuBiLS-MIDAS) based on two-linear, three-linear and four-linear algebraic forms have been introduced. These descriptors codify chemical information for relations between two, three and four atoms by using several (dis-)similarity metrics and multi-metrics. Several studies aimed at assessing the quality of these novel descriptors have been performed. However, a deeper analysis of their performance is necessary. Therefore, in the present manuscript an assessment and statistical validation of the performance of these novel descriptors in QSAR studies is performed.ResultsTo this end, eight molecular datasets (angiotensin converting enzyme, acetylcholinesterase inhibitors, benzodiazepine receptor, cyclooxygenase-2 inhibitors, dihydrofolate reductase inhibitors, glycogen phosphorylase b, thermolysin inhibitors, thrombin inhibitors) widely used as benchmarks in the evaluation of several procedures are utilized. Three to nine variable QSAR models based on Multiple Linear Regression are built for each chemical dataset according to the original division into training/test sets. Comparisons with respect to leave-one-out cross-validation correlation coefficients reveal that the models based on QuBiLS-MIDAS indices possess superior predictive ability in 7 of the 8 datasets analyzed, outperforming methodologies based on similar or more complex techniques such as: Partial Least Square, Neural Networks, Support Vector Machine and others. On the other hand, superior external correlation coefficients are attained in 6 of the 8 test sets considered, confirming the good predictive power of the obtained models. For the values non-parametric statistic tests were performed, which demonstrated that the models based on QuBiLS-MIDAS indices have the best global performance and yield significantly better predictions in 11 of the 12 QSAR procedures used in the comparison. Lastly, a study concerning to the performance of the indices according to several conformer generation methods was performed. This demonstrated that the quality of predictions of the QSAR models based on QuBiLS-MIDAS indices depend on 3D structure generation method considered, although in this preliminary study the results achieved do not present significant statistical differences among them.ConclusionsAs conclusions it can be stated that the QuBiLS-MIDAS indices are suitable for extracting structural information of the molecules and thus, constitute a promissory alternative to build models that contribute to the prediction of pharmacokinetic, pharmacodynamics and toxicological properties on novel compounds.Graphical abstractComparative graphical representation of the performance of the novel QuBiLS-MIDAS 3D-MDs with respect to other methodologies in QSAR modeling of eight chemical datasetsElectronic supplementary materialThe online version of this article (doi:10.1186/s13321-016-0122-x) contains supplementary material, which is available to authorized users.

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Novel global and local 3D atom-based linear descriptors of the Minkowski distance matrix: theory, diversity–variability analysis and QSPR applications

Cited by 9 publications

References 113 publications

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

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

GOWAWA Aggregation Operator‐based Global Molecular Characterizations: Weighting Atom/bond Contributions (LOVIs/LOEIs) According to their Influence in the Molecular Encoding

Examining the predictive accuracy of the novel 3D N-linear algebraic molecular codifications on benchmark datasets

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