Linear indices of the ‘macromolecular graph’s nucleotides adjacency matrix’ as a promising approach for bioinformatics studies. Part 1: Prediction of paromomycin’s affinity constant with HIV-1 Ψ-RNA packaging region

doi:10.1016/j.bmc.2005.03.010

Bioorganic & Medicinal Chemistry

Volume 13, Issue 10, 16 May 2005, Pages 3397-3404

https://doi.org/10.1016/j.bmc.2005.03.010 Get rights and content

Abstract

The design of novel anti-HIV compounds has now become a crucial area for scientists around the world. In this paper a new set of macromolecular descriptors (that are calculated from the macromolecular graph’s nucleotide adjacency matrix) of relevance to nucleic acid QSAR/QSPR studies, nucleic acids’ linear indices. A study of the interaction of the antibiotic Paromomycin with the packaging region of the HIV-1 Ψ-RNA has been performed as example of this approach. A multiple linear regression model predicted the local binding affinity constants [Log K (10⁻⁴ M⁻¹)] between a specific nucleotide and the aforementioned antibiotic. The linear model explains more than 87% of the variance of the experimental Log K (R = 0.93 and s = 0.102 × 10⁻⁴ M⁻¹) and leave-one-out press statistics evidenced its predictive ability (q² = 0.82 and s_cv = 0.108 × 10⁻⁴ M⁻¹). The comparison with other approaches (macromolecular quadratic indices, Markovian Negentropies and ‘stochastic’ spectral moments) reveals a good behavior of our method.

Graphical abstract

Introduction

The number of new discovered genomes has dramatically increased in recent years and this has once again highlighted the problem of protein and nucleic acid functions.1, 2 The complete sequencing of the genomes of various species will undoubtedly contribute to a better understanding of its evolution. Public databases such as GenBank are growing in size at an exponential rate.¹ A significant proportion of the data corresponds to genomic sequences containing the structures not only of many genes but also of RNA.3, 4

The study of the interactions of drugs with biomolecules is now the hot topic in modern bioinformatics. This kind of study constitutes a significant step toward rational drug design. In this sense, the use of footprinting techniques has proven to be an important experimental method for the discovery of significant processes in molecular biology and specifically the field of genomics.5, 6, 7, 8, 9 The interactions between aminoglycosides and the packaging region of type-1 HIV (human immunodeficiency virus) appear to represent a promising route for antiviral discoveries.¹⁰ Aminoglycoside drugs are cationic natural products that interact with RNA.¹¹ The bactericidal effects inherent in these compounds stem from their ability to block protein synthesis by binding to the A site on ribosomal RNA.¹²

Recently, a novel scheme to the rational in silico molecular design (or selection/identification of chemicals) and to QSAR/QSPR studies has been introduced by our group. The so-called TOpological MOlecular COMputer Design (TOMOCOMD).¹³ This method generates molecular fingerprints based on the Discrete Mathematic and Linear Algebra Theory. In this sense, atom, atom type and total quadratic and linear molecular fingerprints have been defined in analogy to the quadratic and linear mathematical maps.14, 15 This approach has been successfully employed in QSPR and QSAR studies,14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 including studies related to nucleic acid–drug interactions.²⁵

The TOMOCOMD–CARDD (acronym of the Computed-Aided ‘Rational’ Drug Design) strategy is very useful for the selection of novel subsystems of compounds having a desired property/activity,22, 23, 24 which can be further optimized by using some of the many molecular modeling methods available for medicinal chemists. The method has also demonstrated flexibility in relation to many different problems. In this sense, the TOMOCOMD–CARDD approach has been applied to the fast-track experimental discovery of novel anthelmintic compounds.22, 24 The prediction of the physical, chem-physical and chemical properties of organic compounds is a problem that can also be addressed using this approach.14, 19, 21 Codification of chirality and other 3D structural features constitutes another advantage of this method.²⁰ This latter opportunity allows the description of the significance interpretation and the comparison to other molecular descriptors.15, 19 Additionally, promising results have been found in the modeling of the interaction between drugs and HIV packaging-region RNA in the field of bioinformatics using TOMOCOMD-CANAR (Computed-Aided Nucleic Acid Research) approach.²⁵ Finally, an alternative formulation of our approach for structural characterization of proteins was carried out recently.²⁶ This extends methodology [TOMOCOMD-CAMPS (Computed-Aided Modelling in Protein Science)] which was used to encompass protein stability studies—specifically how alanine scan on Arc repressor wild-type protein affects protein stability—by means of a combination of protein quadratic indices (macromolecular fingerprints) and statistical (linear and nonlinear models) methods.²⁶

Therefore, describing an extended TOMOCOMD-CANAR approach to account for RNA structure constitutes the main aim of this paper. In the present study, we propose a total and local definition of nucleic acid linear indices of the ‘macromolecular graph’s nucleotides adjacency matrix’. Besides, the present work is focused on developing quantitative structure–property relationships to predict the affinity with which paromomycin binds to the HIV-1 Ψ-RNA packaging region and compare our results with other cheminformatic methods previously reported.

Section snippets

Computational methods

A nucleic acid is a long, unbranched polynucleotide, that is, a polymer consisting of nucleotides. Each nucleotide has the three following components: (1) A cyclic five-carbon sugar, (2) a purine or a pyrimidine base attached to the 1′-carbon atom of sugar by N-glycoside bond, and (3) a phosphate attached to the 5′-carbon of the sugar by a phosphoester linkage. The nucleotides in nucleic acids are covalently linked by a second phosphoester bond that joins the 5′-phosphate of one nucleotide and

Results and discussion

The data set of footprinted and binding nucleotides was extracted from the literature.³⁷ Figure 1 depicts the secondary structure of the HIV-1 Ψ-RNA packaging region as well as the binding sites of Paromomycin. The local affinity constant values [Log K(10⁻⁴ M⁻¹)] were also obtained from the literature.³⁷ Is very important to know the strength of each interaction in the studies of the drug–RNA interaction. In order to prove the applicability of this new approach, a quantitative linear model was

Conclusions

Although there have been many discoveries in the last years in the field of bioinformatics, it is necessary the definition of novel macromolecular descriptors that could explain different bio-macromolecular properties by means of a QSAR approach. In this sense, the approach described here represents a novel and very promising method for bioinformatics research. It presents a new set of macromolecular descriptors that are calculated from the macromolecular graph’s nucleotide adjacency matrix. We

Footprinting data

The data set of footprinted and binding nucleotides was extracted from the literature.³⁷ Figure 1 depicts the secondary structure of the HIV-1 Ψ-RNA packaging region as well as the binding sites of Paromomycin. A representation of the Ψ-RNA appears along with a summary of binding/enhancement information for Paromomycin. The RNA consists of the ‘main stem’, positions 213–238 and 361–388; SL-1, which contains the dimmer initiation site; SL-2, having the 5′ splice donor site; SL-3, and SL-4, the

Acknowledgements

The authors would like to offer their sincere thanks to the referees for their critical opinions about the manuscript, which have significantly contributed to improve its presentation and quality.

References and notes (41)

Z. Yuan
FEBS Lett.
(1999)
M. Brenowitz et al.
Methods Enzymol.
(1986)
J.M. Sullivan et al.
Bioorg. Med. Chem. Lett.
(2002)
S.R. Lynch et al.
Methods Enzymol.
(2000)
Y. Marrero-Ponce
Bioorg. Med. Chem.
(2004)
Y. Marrero-Ponce et al.
Bioorg. Med. Chem.
(2004)
Y. Marrero-Ponce et al.
Bioorg. Med. Chem.
(2005)
Y. Marrero-Ponce et al.
Bioorg. Med. Chem.
(2005)
A. Golbraikh et al.
J. Mol. Graphics Modell.
(2002)
D.A. Benson et al.
Nucleic Acids Res.
(2000)

S. Saxonov et al.

Nucleic Acids Res.

(2000)

N.J. Schisler et al.

Nucleic Acids Res.

(2000)

T.D. Tullius

Annu. Rev. Biophys. Biophys. Chem.

(1989)

A. Henn et al.

Nucleic Acids Res.

(2001)

D.J. Galas et al.

Nucleic Acid Res.

(1978)

O.N. Ozoline et al.

Nucleic Acids Res.

(2001)

E.F. Gale et al.

The Molecular Basis of Antibiotic Action

(1981)

Marrero-Ponce, Y.; Romero, V. TOMOCOMD software. Central University of Las Villas. 2002. TOMOCOMD (TOpological...

Y. Marrero-Ponce

Molecules

(2003)

Y. Marrero-Ponce

J. Chem. Inf. Comput. Sci.

(2004)

Cited by (50)

Ligand-based discovery of novel trypanosomicidal drug-like compounds: In silico identification and experimental support
2011, European Journal of Medicinal Chemistry
Citation Excerpt :
This approach, which is based on principles of novel methods in chemical graph and algebraic theories, has been successfully used for the description of different physical, chemo-physical, and chemical properties of organic compounds [20,24,25], as well as to the prediction of, pharmacokinetical [26,27], biological [28–35] and toxicological [36] properties. In addition, this method has been applied to studies in the field of proteomics and nucleic acid–drug interactions [37,38]. Furthermore, these molecular descriptors (MDs) have been extended to consider three-dimensional (3D) features of small/medium-sized molecules based on the trigonometric-3D-chirality-correction factor approach [39–43].
Two-dimensional bond-based linear indices and linear discriminant analysis are used in this report to perform a quantitative structure–activity relationship study to identify new trypanosomicidal compounds. A database with 143 anti-trypanosomal and 297 compounds having other clinical uses, are utilized to develop the theoretical models. The best discriminant models computed using bond-based linear indices provides accuracies greater than 90 for both training and test sets. Our models identify as anti-trypanosomals five out of nine compounds of a set of already-synthesized substances. The in vitro anti-trypanosomal activity of this set against epimastigote forms of Trypanosoma cruzi is assayed. Both models show a perfect agreement between theoretical predictions and experimental results. The compounds identified as active ones show more than 98% of anti-epimastigote elimination (AE) at a concentration of 100 μg/mL. Besides, three compounds show more than 70% of AE at a concentration of 10 μg/mL. Finally, compounds with the best “activity against epimastigote forms/unspecific cytotoxicity” ratio are evaluated using an amastigote susceptibility assay. It should be noticed that, compound Va7-71 exhibit a 100% of intracellular amastigote elimination and shows similar activity when compared to a standard trypanosomicidal as nifurtimox. Finally, we can emphasize that, the present algorithm constitutes a step forward in the search for efficient ways of discovering new anti-trypanosomal compounds.
Computational discovery of novel trypanosomicidal drug-like chemicals by using bond-based non-stochastic and stochastic quadratic maps and linear discriminant analysis
2010, European Journal of Pharmaceutical Sciences
Herein we present results of a quantitative structure–activity relationship (QSAR) studies to classify and design, in a rational way, new antitrypanosomal compounds by using non-stochastic and stochastic bond-based quadratic indices. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop QSAR models based on linear discriminant analysis (LDA). Non-stochastic model correctly classifies more than 93% and 95% of chemicals in both training and external prediction groups, respectively. On the other hand, the stochastic model shows an accuracy of about the 87% for both series. As an experiment of virtual lead generation, the present approach is finally satisfactorily applied to the virtual evaluation of 9 already synthesized in house compounds. The in vitro antitrypanosomal activity of this series against epimastigote forms of Trypanosoma cruzi is assayed. The model is able to predict correctly the behaviour for the majority of these compounds. Four compounds (FER16, FER32, FER33 and FER 132) showed more than 70% of epimastigote inhibition at a concentration of 100 μg/mL (86.74%, 78.12%, 88.85% and 72.10%, respectively) and two of these chemicals, FER16 (78.22% of AE) and FER33 (81.31% of AE), also showed good activity at a concentration of 10 μg/mL. At the same concentration, compound FER16 showed lower value of cytotoxicity (15.44%), and compound FER33 showed very low value of 1.37%. Taking into account all these results, we can say that these three compounds can be optimized in forthcoming works, but we consider that compound FER33 is the best candidate. Even though none of them resulted more active than Nifurtimox, the current results constitute a step forward in the search for efficient ways to discover new lead antitrypanosomals.
Plasmod-PPI: A web-server predicting complex biopolymer targets in plasmodium with entropy measures of protein-protein interactions
2010, Polymer
Citation Excerpt :
The model presents a good overall classification of pPPI and npPPI. This level of accuracy is generally accepted by other researchers that have applied LDA to find QSAR models useful in molecular parasitology and related areas; e.g., the works of García-Domenech, Marrero-Ponce, Bruno-Blanch, Galvez, Gozalbes and others predicting active compounds against Trypanosoma cruzi, Mycobacterium avium, Toxoplasma gondii, P. falciparum, Trichomonas vaginalis, Fasciola hepatica, and other parasites [96–100]; see also the works of Marrero-Ponce on protein and DNA/RNA QSAR studies [101–103]. The comparison of linear and non-linear models is essential to test how directly our parameters are correlated to the biological property [104].
We can define structural indices of polymer or biopolymer complex structures and use them in the prediction of new drug targets in parasites. For instance, Plasmodium falciparum causes the most severe form of Malaria and kills up to 2.7 million people annually whereas Plasmodium vivax is geographically the most widely distributed cause with more than 80 million clinical cases. Due to drug resistance and toxicity, discovering novel drug targets is mandatory; such as Protein–Protein Complexes unique in this pathogen and not present in human host (pPPCs). Additionally, the 3D structure of an increasing number of Plasmodium proteins is being reported in public databases making easier the development of bioinformatics models to predict pPPCs. In addition, some PPCs expressed both in parasite and human, such as DHFR synthase, play a significant role in drug resistance in both Malaria and Human Cancer. However, there are no general models to predict pPPCs using indices of PPC biopolymer structure. Therefore, we introduced herein new Markov Chain numerical descriptors of protein–protein Interactions (PPIs) based on electrostatic entropy measures and calculated these parameters for 5257 pairs of proteins (774 pPPCs and 4483 non-pPPCs) from more than 20 organisms, including parasite and human hosts. We found a simple Classification Tree with high Accuracy, Sensitivity, and Specificity (90.2–98.5%) both in training and independent test sub-sets and implemented this predictor in the user-friendly web server PlasmodPPI freely available at http://miaja.tic.udc.es/Bio-AIMS/PlasmodPPI.php.
Multi-target spectral moment: QSAR for antiviral drugs vs. different viral species
2009, Analytica Chimica Acta
The antiviral QSAR models have an important limitation today. They predict the biological activity of drugs against only one viral species. This is determined by the fact that most of the current reported molecular descriptors encode only information about the molecular structure. As a result, predicting the probability with which a drug is active against different viral species with a single unifying model is a goal of major importance. In this work, we use Markov Chain theory to calculate new multi-target spectral moments to fit a QSAR model for drugs active against 40 viral species. The model is based on 500 drugs (including active and non-active compounds) tested as antiviral agents in the recent literature; not all drugs were predicted against all viruses, but only those with experimental values. The database also contains 207 well-known compounds (not as recent as the previous ones) reported in the Merck Index with other activities that do not include antiviral action against any virus species. We used Linear Discriminant Analysis (LDA) to classify all these drugs into two classes as active or non-active against the different viral species tested, whose data we processed. The model correctly classifies 5129 out of 5594 non-active compounds (91.69%) and 412 out of 422 active compounds (97.63%). Overall training predictability was 92.34%. The validation of the model was carried out by means of external predicting series, the model classifying, thus, 2568 out of 2779 non-active compounds and 224 out of 229 active compounds. Overall training predictability was 92.82%. The present work reports the first attempts to calculate within a unified framework the probabilities of antiviral drugs against different virus species based on a spectral moment analysis.
Multi-target spectral moment: QSAR for antifungal drugs vs. different fungi species
2009, European Journal of Medicinal Chemistry
The most important limitation of antifungal QSAR models is that they predict the biological activity of drugs against only one fungal species. This is determined due the fact that most of the up-to-date reported molecular descriptors encode only information about the molecular structure. Consequently, predicting the probability with which a drug is active against different fungal species with a single unifying model is a goal of major importance. Herein, we use the Markov Chain theory to calculate new multi-target spectral moments to fit a QSAR model that predicts the antifungal activity of more than 280 drugs against 90 fungi species. Linear discriminant analysis (LDA) was used to classify drugs into two classes as active or non-active against the different tested fungal species whose data we processed. The model correctly classifies 12 434 out of 12 566 non-active compounds (98.95%) and 421 out of 468 active compounds (89.96%). Overall training predictability was 98.63%. Validation of the model was carried out by means of external predicting series, the model classifying, thus, 6216 out of 6277 non-active compounds and 215 out of 239 active compounds. Overall training predictability was 98.7%. The present is the first attempt to calculate, within a unifying framework, the probabilities of antifungal action of drugs against many different species based on spectral moment’s analysis.
Nucleotide's bilinear indices: Novel bio-macromolecular descriptors for bioinformatics studies of nucleic acids. I. Prediction of paromomycin's affinity constant with HIV-1 Ψ-RNA packaging region
2009, Journal of Theoretical Biology
A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on $ℜ^{n} [b_{mk} ({\bar{x}}_{m}, {\bar{y}}_{m}) : ℜ^{n} \times ℜ^{n} \to ℜ]$ in canonical basis. Nucleic acid's bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide's graph-theoretic electronic-contact matrices, $M_{m}^{k}$ and $^{s} M_{m}^{k}$ , respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using $M_{m}^{k}$ and $^{s} M_{m}^{k}$ as matrix operators of bilinear transformations. Moreover, biochemical information is codified by using different pair combinations of nucleotide-base properties as weightings (experimental molar absorption coefficient $ε_{260}$ at 260 nm and pH=7.0, first $(Δ E_{1})$ and second $(Δ E_{2})$ single excitation energies in eV, and first (f₁) and second (f₂) oscillator strength values (of the first singlet excitation energies) of the nucleotide DNA–RNA bases. As example of this approach, an interaction study of the antibiotic paromomycin with the packaging region of the HIV-1 Ψ-RNA have been performed and it have been obtained several linear models in order to predict the interaction strength. The best linear model obtained by using non-stochastic bilinear indices explains about 91% of the variance of the experimental Log K (R=0.95 and s=0.08×10⁻⁴ M⁻¹) as long as the best stochastic bilinear indices-based equation account for 93% of the Log K variance (R=0.97 and s=0.07×10⁻⁴ M⁻¹). The leave-one-out (LOO) press statistics, evidenced high predictive ability of both models (q²=0.86 and s_cv=0.09×10⁻⁴ M⁻¹ for non-stochastic and q²=0.91 and s_cv=0.08×10⁻⁴ M⁻¹ for stochastic bilinear indices). The nucleic acid's bilinear indices-based models compared favorably with other nucleic acid's indices-based approaches reported nowadays. These models also permit the interpretation of the driving forces of the interaction process. In this sense, developed equations involve short-reaching (k⩽3), middle-reaching (4<k<9), and far-reaching (k=10 or greater) nucleotide's bilinear indices. This situation points to electronic and topologic nucleotide's backbone interactions control of the stability profile of paromomycin–RNA complexes. Consequently, the present approach represents a novel and rather promising way to theoretical-biology studies.

View all citing articles on Scopus

View full text

Linear indices of the ‘macromolecular graph’s nucleotides adjacency matrix’ as a promising approach for bioinformatics studies. Part 1: Prediction of paromomycin’s affinity constant with HIV-1 Ψ-RNA packaging region

Abstract

Graphical abstract

Introduction

Section snippets

Computational methods

Results and discussion

Conclusions

Footprinting data

Acknowledgements

FEBS Lett.

Methods Enzymol.

Bioorg. Med. Chem. Lett.

Methods Enzymol.

Bioorg. Med. Chem.

Bioorg. Med. Chem.

Bioorg. Med. Chem.

Bioorg. Med. Chem.

J. Mol. Graphics Modell.

Nucleic Acids Res.

Nucleic Acids Res.

Nucleic Acids Res.

Annu. Rev. Biophys. Biophys. Chem.

Nucleic Acids Res.

Nucleic Acid Res.

Nucleic Acids Res.

The Molecular Basis of Antibiotic Action

Molecules

J. Chem. Inf. Comput. Sci.