Optimum Search Strategies or Novel 3D Molecular Descriptors: is there a Stalemate?

Marrero-Ponce, Yovani; García-Jacas, César R.; Barigye, Stephen J.; Valdés-Martiní, José R.; Rivera-Borroto, Oscar Miguel; Pino-Urias, Ricardo W.; Cubillán, Néstor; Alvarado, Ysaías J.; Le-Thi-Thu, Huong

doi:10.2174/1574893610666151008011457

Cited by 19 publications

(43 citation statements)

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“…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%

“…Moreover,

{_{n s (s s, d s, m p)} ((), ℕ, ℚ) 𝔾}_{((), F)}^{a, k}

{_{n s (s s, m p)} ((), ℕ, ℚ) 𝔾 𝕋}_{((), F)}^{a, k}

and

{_{n s (s s, m p)} ((), ℕ, ℚ) 𝔾 ℚ}_{((), F)}^{a, k}

represent the atom‐level matrices computed for a specific atom a . The notations

ℕ ℚ

, F and ns ( ss , ds , mp ) denote neighborhood‐quotient, local‐fragment, and normalized matrices,, respectively.…”

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

confidence: 99%

“…From the atom‐level matrices, atom‐level descriptors for each atom a are computed (see Equation 16–18), whose values constitute entries (

L_{a}

) in the corresponding vectors of atom‐level descriptors

L^{k}

(LOVIs). Once LOVIs vectors are computed, then the global k‐th two‐linear , three‐linear and four‐linear QuBiLS‐MIDAS MDs can be determined using one or several aggregation operators based on the Minkowski definition (e. g. Euclidean norm), central tendency statistics (e. g. harmonic mean) and dispersion statistics (e. g. variance) ,. Scheme depicts a flowchart regarding the overall QuBiLS MIDAS 3D‐MDs calculation.…”

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

confidence: 99%

“…Moreover,

{_{n s (s s, d s, m p)} ((), ℕ, ℚ) 𝔾}_{((), F)}^{a, k}

{_{n s (s s, m p)} ((), ℕ, ℚ) 𝔾 𝕋}_{((), F)}^{a, k}

and

{_{n s (s s, m p)} ((), ℕ, ℚ) 𝔾 ℚ}_{((), F)}^{a, k}

represent the atom‐level matrices computed for a specific atom a . The notations

ℕ ℚ

, F and ns ( ss , ds , mp ) denote neighborhood‐quotient, local‐fragment, and normalized matrices,, respectively.…”

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

confidence: 99%

“…From the atom‐level matrices, atom‐level descriptors for each atom a are computed (see Equation 16–18), whose values constitute entries (

L_{a}

) in the corresponding vectors of atom‐level descriptors

L^{k}

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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“…The QuBiLS‐MIDAS molecular 3D (geometric) indices (see Supporting Information 1) are computed from the atomic contribution of each atom in a molecule. In this way, if a molecule consists of n atoms, then the k th two‐linear (bilinear, quadratic, and linear), three‐linear (threelinear, threelinear‐quadratic‐bilinear, threelinear‐bilinear, threelinear‐linear, and threelinear‐cubic), and four‐linear (fourlinear, fourlinear‐quadratic‐threelinear, fourlinear‐threelinear, fourlinear‐cubic‐bilinear, fourlinear‐bilinear, fourlinear‐linear, and fourlinear‐quadruple) indices for atom “ a ” are calculated as N‐ linear algebraic maps (forms) in

normalℝ

n , in a canonical basis set, and are expressed by the following equations, respectively:

{}_{b}L_{a} = b^{a} = b^{a, k} (\overset{}{\overset{x}{true}}, \overset{}{\overset{y}{true}}) = {true \sum}_{i = 1}^{n} {true \sum}_{j = 1}^{n} g_{i j}^{a, k} x^{i} y^{j} = {[X]}^{T} {double-struckG}^{a, k} true[Y true] \forall a = 1, 2, \dots, n

{{}_{t r}L}_{a} = {t r}^{a, k} true(\overset{}{\overset{x}{true}}, \overset{}{\overset{y}{true}}, \overset{}{\overset{z}{true}} true) = {true \sum}_{i = 1}^{n} {true \sum}_{j = 1}^{n} {true \sum}_{l = 1}^{n} g t_{i j l}^{a, k} x^{i} y^{j} z^{l} = G {double-struckT}^{a, k} \cdot \overset{}{\overset{x}{true}} \cdot \overset{}{\overset{y}{true}} \cdot \overset{}{\overset{z}{true}}

…”

Section: Qubils‐midas 3d‐descriptorsmentioning

confidence: 99%

“…In recent reports, Marrero‐Ponce et al inspired by the successful results achieved by the application of the algebraic two‐dimensional (2D)‐MDs, have proposed the QuBiLS‐MIDAS [acronym for Quadratic, Bilinear, and N ‐Linear Maps based on N ‐tuple Spatial Metric [(Dis)‐Similarity] Matrices and Atomic Weightings] indices to consider geometric [three‐dimensional (3D)] features. These novel molecular parameters utilize the bilinear, quadratic and linear algebraic forms to codify the 3D‐information of chemical structures using several (dis‐)similarity metrics when analysis between atom‐pairs is performed.…”

Section: Introductionmentioning

confidence: 99%

QuBiLS‐MIDAS: A parallel free‐software for molecular descriptors computation based on multilinear algebraic maps

et al. 2014

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The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and employs the Chemical Development Kit library for the manipulation of the chemical structures and the calculation of the atomic properties. This software is composed by a desktop user-friendly interface and an Abstract Programming Interface library. The former was created to simplify the configuration of the different options of the MDs, whereas the library was designed to allow its easy integration to other software for chemoinformatics applications. This program provides functionalities for data cleaning tasks and for batch processing of the molecular indices. In addition, it offers parallel calculation of the MDs through the use of all available processors in current computers. The studies of complexity of the main algorithms demonstrate that these were efficiently implemented with respect to their trivial implementation. Lastly, the performance tests reveal that this software has a suitable behavior when the amount of processors is increased. Therefore, the QuBiLS-MIDAS software constitutes a useful application for the computation of the molecular indices based on N-linear algebraic maps and it can be used freely to perform chemoinformatics studies.

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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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Optimum Search Strategies or Novel 3D Molecular Descriptors: is there a Stalemate?

Cited by 19 publications

References 0 publications

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

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

QuBiLS‐MIDAS: A parallel free‐software for molecular descriptors computation based on multilinear algebraic maps

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

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