2D-RNA-coupling numbers: a new computational chemistry approach to link secondary structure topology with biological function.

Methods for prediction of proteins, DNA, or RNA function and mapping it onto sequence often rely on bioinformatics alignment approach instead of chemical structure. Consequently, it is interesting to develop computational chemistry approaches based on molecular descriptors. In this sense, many researchers used sequence-coupling numbers and our group extended them to 2D proteins representations. However, no coupling numbers have been reported for 2D-RNA topology graphs, which are highly branched and contain useful information. Here, we use a computational chemistry scheme: (a) transforming sequences into RNA secondary structures, (b) defining and calculating new 2D-RNA-coupling numbers, (c) seek a structure-function model, and (d) map biological function onto the folded RNA. We studied as example 1-aminocyclopropane-1-carboxylic acid (ACC) oxidases known as ACO, which control fruit ripening having importance for biotechnology industry. First, we calculated tau(k)(2D-RNA) values to a set of 90-folded RNAs, including 28 transcripts of ACO and control sequences. Afterwards, we compared the classification performance of 10 different classifiers implemented in the software WEKA. In particular, the logistic equation ACO = 23.8 . tau(1)(2D-RNA) + 41.4 predicts ACOs with 98.9%, 98.0%, and 97.8% of accuracy in training, leave-one-out and 10-fold cross-validation, respectively. Afterwards, with this equation we predict ACO function to a sequence isolated in this work from Coffea arabica (GenBank accession DQ218452). The tau(1)(2D-RNA) also favorably compare with other descriptors. This equation allows us to map the codification of ACO activity on different mRNA topology features. The present computational-chemistry approach is general and could be extended to connect RNA secondary structure topology to other functions.

Computational chemistry approach to protein kinase recognition using 3D stochastic van der Waals spectral moments.

Three-dimensional (3D) protein structures now frequently lack functional annotations because of the increase in the rate at which chemical structures are solved with respect to experimental knowledge of biological activity. As a result, predicting structure-function relationships for proteins is an active research field in computational chemistry and has implications in medicinal chemistry, biochemistry and proteomics. In previous studies stochastic spectral moments were used to predict protein stability or function (González-Díaz, H. et al. Bioorg Med Chem 2005, 13, 323; Biopolymers 2005, 77, 296). Nevertheless, these moments take into consideration only electrostatic interactions and ignore other important factors such as van der Waals interactions. The present study introduces a new class of 3D structure molecular descriptors for folded proteins named the stochastic van der Waals spectral moments ((o)beta(k)). Among many possible applications, recognition of kinases was selected due to the fact that previous computational chemistry studies in this area have not been reported, despite the widespread distribution of kinases. The best linear model found was Kact = -9.44 degrees beta(0)(c) +10.94 degrees beta(5)(c) -2.40 degrees beta(0)(i) + 2.45 degrees beta(5)(m) + 0.73, where core (c), inner (i) and middle (m) refer to specific spatial protein regions. The model with a high Matthew's regression coefficient (0.79) correctly classified 206 out of 230 proteins (89.6%) including both training and predicting series. An area under the ROC curve of 0.94 differentiates our model from a random classifier. A subsequent principal components analysis of 152 heterogeneous proteins demonstrated that beta(k) codifies information different to other descriptors used in protein computational chemistry studies. Finally, the model recognizes 110 out of 125 kinases (88.0%) in a virtual screening experiment and this can be considered as an additional validation study (these proteins were not used in training or predicting series).

A model for the recognition of protein kinases based on the entropy of 3D van der Waals interactions.

The study and prediction of kinase function (kinomics) is of major importance for proteome research due to the widespread distribution of kinases. However, the prediction of protein function based on the similarity between a functionally annotated 3D template and a query structure may fail, for instance, if a similar protein structure cannot be identified. Alternatively, function can be assigned using 3D-structural empirical parameters. In previous studies, we introduced parameters based on electrostatic entropy (Proteins 2004, 56, 715) and molecular vibration entropy (Bioinformatics 2003, 19, 2079) but ignored other important factors such as van der Waals (vdw) interactions. In the work described here, we define 3D-vdw entropies (degrees theta(k)) and use them for the first time to derive a classifier for protein kinases. The model classifies correctly 88.0% of proteins in training and more than 85.0% of proteins in validation studies. Principal components analysis of heterogeneous proteins demonstrated that degrees theta(k) codify information that is different to that described by other bulk or folding parameters. In additional validation experiments, the model recognized 129 out of 142 kinases (90.8%) and 592 out of 677 non-kinases (87.4%) not used above. This study provides a basis for further consideration of degrees theta(k) as parameters for the empirical search for structure-function relationships.

Novel 2D maps and coupling numbers for protein sequences. The first QSAR study of polygalacturonases; isolation and prediction of a novel sequence from Psidium guajava L.

The development of 2D graph-theoretic representations for DNA sequences was very important for qualitative and quantitative comparison of sequences. Calculation of numeric features for these representations is useful for DNA-QSAR studies. Most of all graph-theoretic representations identify each one of the four bases with a unitary walk in one axe direction in the 2D space. In the case of proteins, twenty amino acids instead of four bases have to be considered. This fact has limited the introduction of useful 2D Cartesian representations and the corresponding sequences descriptors to encode protein sequence information. In this study, we overcome this problem grouping amino acids into four groups: acid, basic, polar and non-polar amino acids. The identification of each group with one of the four axis directions determines a novel 2D representation and numeric descriptors for proteins sequences. Afterwards, a Markov model has been used to calculate new numeric descriptors of the protein sequence. These descriptors are called herein the sequence 2D coupling numbers (zeta(k)). In this work, we calculated the zeta(k) values for 108 sequences of different polygalacturonases (PGs) and for 100 sequences of other proteins. A Linear Discriminant Analysis model derived here (PG=5.36.zeta1-3.98.zeta3-42.21) successfully discriminates between PGs and other proteins. The model correctly classified 100% of a subset of 81 PGs and 75 non-PG proteins sequences used to train the model. The model also correctly classified 51 out of 52 (98.07%) of proteins sequences used as external validation series. The uses of different group of amino acids and/or axes orientation give different results, so it is suggested to be explored for other databases. Finally, to illustrates the use of the model we report the isolation and prediction of the PG action for a novel sequence (AY908988) isolated by our group from Psidium guajava L. This prediction coincides very well with sequence alignment results found by the BLAST methodology. These findings illustrate the possibilities of the sequence descriptors derived for this novel 2D sequence representation in proteins sequence QSAR studies.

Recognition of stable protein mutants with 3D stochastic average electrostatic potentials.

As more and more proteins are applied to biochemical research there is increasing interest in studying their stability. In this study, a Markov model has been used to calculate molecular descriptors of the protein structure and these are called the average electrostatic potentials (xi(k)). These descriptors were intended to encode indirect electrostatic pair-wise interactions between amino acids located at Euclidean distance k within a given 3D protein backbone. The different xi(k) values could be calculated for the protein as a whole or for specific protein regions (orbits), which include amino acids that lie within a given range of distances from the center of charge of the protein. In this work we calculated the xi(k) values for 657 mutants of different proteins. A Linear Discriminant Analysis model correctly classified a subset of 435 out of 493 proteins according to their thermal stability - a level of predictability of 88.2%. This experiment was repeated with three additional subsets of proteins selected at random from the initial series of 657. More specifically, the model predicted 314/356 (88.2%) of mutants with higher stability than the corresponding wild-type protein and 264/301 (86.7%) of proteins with near wild-type stability. These results illustrate the possibilities for the average stochastic potentials xi(k) in the study of 3D-structure/property relationships for biochemically relevant proteins.

2D RNA-QSAR: assigning ACC oxidase family membership with stochastic molecular descriptors; isolation and prediction of a sequence from Psidium guajava L.

Quantitative structure-activity relationship (QSAR) techniques for small molecules could be applied to nucleic acids. Unfortunately, almost all molecular descriptors are more successful at encoding branching information than sequences and/or cannot be back-projected. A solution for scaling the QSAR problem up to RNA may be to transform sequences into secondary structures first. Our group has used Markovian negentropies as molecular descriptors for drug design with preliminary results in bioinformatics [Bioinformatics 2003, 19, 2079]. However, RNA-QSAR studies on RNA molecules have not been described to date. Novel Markovian negentropies have been introduced here as molecular descriptors for 2D-RNA structures. An RNA-QSAR study of the ACC proteins from different plants has been carried out. The QSAR recognizes 19/20 sequences (95.0%) within the ACC family and 12/17 (70.6%) of the control group sequences. The model has a high Matthews' regression coefficient (C = 0.68). Overall cross-validation average accuracies were 14 out of 15 for ACC sequences (93.3%) and 10 out of 13 for control sequences (76.9%). Finally, ACC oxidase family membership was assigned to a new sequence isolated for the first time in this work from Psidium guajava L. A backprojection map for this sequence identifies the left stem (40%) and the main stem (45%) as highly important substructures. Results of an nBLAST experiment are consistent with this finding and indicate a high conservation score (>70) for left stem and main stem; whereas major loop, right stem, cap and major loop right half were hardly conserved.

Stochastic-based descriptors studying biopolymers biological properties: extended MARCH-INSIDE methodology describing antibacterial activity of lactoferricin derivatives.

Lactoferricin are a number of related peptides derived from the enzymatic cleavage of lactoferrin, an iron-binding protein. These peptides, and other peptides derived from them by simple amino acid substitutions, have shown interesting antibacterial activity. In this paper we applied the MARCH-INSIDE methodology extended to peptide and proteins, to a QSAR study related to antibacterial activity of 31 derivatives of lactoffericin against E. Coli and S. Aureus by means of Linear Discriminant (LDA) and Multiple Linear Regression Analysis (MLR). In the case of LDA we obtained models that classify correctly more than 80% of all cases (85.7% for E. Coli antibacterial activity and 83.9 for S. Aureus). With the application of a Leave-One-Out Cross Validation Procedure, the percentage of good classification of both classification models remained near the above reported values (87.1% for E. Coli antibacterial activity and 83.9 for S. Aureus). We obtained several linear regression models taking into account total and local descriptors. The inclusion of those local descriptors improved the correlation parameters, the statistical quality, and the predictive power of the former model obtained only with total descriptors. The best models explained more than 80% of the experimental variance in the antimicrobial activity of those compounds. These results are comparable with those reported previously by Strom (Strom, M. B.; Rekdal, O.; Svendesen, J. S. J Peptide Res 2001, 57, 127-139.) and Tore-Lejon (Lejon, T.; Strom, M.; Svendsen, S. J Protein Sci 2001, 7, 74-78.; Lejon, T.; Svendsen J. S.; Haug, B. E. J Peptide Sci 2002, 8, 302-306.) in a smaller dataset applying Z-scales and volume-based descriptors and PLS as statistical techniques.

Markovian chemicals "in silico" design (MARCH-INSIDE), a promising approach for computer-aided molecular design III: 2.5D indices for the discovery of antibacterials.

The present work continues our series on the use of MARCH-INSIDE molecular descriptors (parts I and II: J Mol Mod 8:237-245, [2002] and 9:395-407, [2003]). These descriptors encode information pertaining to the distribution of electrons in the molecule based on a simple stochastic approach to the idea of electronegativity equalization (Sanderson's principle). Here, 3D-MARCH-INSIDE molecular descriptors for 667 organic compounds are used as input for a linear discriminant analysis. This 2.5D-QSAR model discriminates between antibacterial compounds and non-antibacterial ones with 92.9% accuracy in training sets. On the other hand, the model classifies 94.0% of the compounds in test set correctly. Additionally, the present QSAR performs similar-to-better than other methods reported elsewhere. Finally, the discovery of a novel compound illustrates the use of the method. This compound, 2-bromo-3-(furan-2-yl)-3-oxo-propionamide has MIC50 of 6.25 and 12.50 microg/mL against Pseudomonas aeruginosa ATCC 27853 and Escherichia coli ATCC 27853, respectively while ampicillin, amoxicillin, clindamycin, and metronidazole have, for instance, MIC50 values higher than 250 mug/mL against E. coli. Consequently, the present method may becomes a useful tool for the in silico discovery of antibacterials.

Predicting multiple drugs side effects with a general drug-target interaction thermodynamic Markov model.

Most of present molecular descriptors just consider the molecular structure. In the present article we pretend extending the use of Markov chain models to define novel molecular descriptors, which consider in addition to molecular structure other parameters like target site or toxic effect. Specifically, this molecular descriptor takes into consideration not only the molecular structure but the specific system the drug affects too. Herein, it is developed a general Markov model that describes 39 different drugs side effects grouped in 11 affected systems for 301 drugs, being 686 cases finally. The data was processed by linear discriminant analysis (LDA) classifying drugs according to their specific side effects, forward stepwise was fixed as strategy for variables selection. The average percentage of good classification and number of compounds used in the training/predicting sets were 100/100% for systemic phenomena (47 out of 47)/(12 out of 12) and metabolic (18 out of 18)/(5 out of 5), muscular-skeletal (23 out of 23)/(6 out of 6) and neurological manifestations (33 out of 33)/(8 out of 8); 97.6/96.7% for cardiovascular manifestation (122 out of 125)/(30 out of 31); 97.1/97.5% for breathing manifestations (34 out of 35)/(8 out of 9); 97/99.4% for gastrointestinal manifestations (159 out of 164)/(40 out of 41); 97/95% for endocrine manifestations (32 out of 33)/(7 out of 8); 96.4/94.6% for psychiatric manifestations (53 out of 55)/(13 out of 14); 95.1/99.1% for hematological manifestations (98 out of 103)/(25 out of 26) and 88/92.3% for dermal manifestations (44 out of 50)/(12 out of 13). In addition, we report preliminary experimental reversible decrease of lymphocytes differential count after administration of the antibacterial drug G-1 in mice, which coincide with a posterior probability (P%=74.91) predicted by the model. This article develops a model that encompasses a large number of side effects grouped in specific organ systems in a single stochastic framework for the first time.

Unified Markov thermodynamics based on stochastic forms to classify drugs considering molecular structure, partition system, and biological species: distribution of the antimicrobial G1 on rat tissues.

To date, molecular descriptors do not commonly account for important information beyond chemical structure. The present work, attempts to extend, in this sense, the stochastic molecular descriptors, incorporating information about the specific biphasic partition system, the biological species, and chemical structure inside the molecular descriptors. Consequently, MARCH-INSIDE molecular descriptors may be identified with time-dependent thermodynamic parameters (entropy and mean free energy) of partition process. A classification function was developed to classify data of 423 drugs and up to 14 different partition systems at the same time. The model has shown a high overall accuracy of 92.1% (293 out of 318 cases) in training series and 90% (36 out of 40 cases) in predicting ones. Finally, we illustrate the use of the model by predicting a high probability (%) for G1 (a novel antibacterial drug) to undergo partition on different biotic systems (rat organs): liver (97.7), spleen (97.5), lung (97.4), and adipose tissue (97.6). These theoretical results coincide with herein reported steady state plasma concentrations (c) and partition coefficients (P) in liver (c=42.25+/-7.86/P=4.75), spleen (11.47+/-4.43/P=1.29), lung (17.04+/-3.58/P=1.91), and adipose tissue (28.19+/-11.82/P=3.17). All values were relative to (14)C-labeled-radioactive-G1 in plasma (c=8.9+/-3.05) after 3h of oral administration. In closing, the present stochastic forms derive average thermodynamic parameters fitting on a more clearly physicochemical framework with respect to classic vector-matrix-vector forms, which include, as particular cases, quadratic forms such as Wiener index, Randic invariants, Zagreb descriptors, Harary index, Balaban index, and Marrero-Ponce quadratic molecular indices.

Stochastic-based descriptors studying peptides biological properties: modeling the bitter tasting threshold of dipeptides.

MARCH-INSIDE methodology was applied to the prediction of the bitter tasting threshold of 48 dipeptides by means of pattern recognition techniques, in this case linear discriminant analysis (LDA), and regression methods. The LDA models yielded a percentage of good classification higher than 80% with the two main families of descriptor generated by this methodology (95.8% for self return probability and 83.3% using electronic delocalization entropy). The regression models can explain more than 80% of the experimental variance of the independent variable. Two regression models were obtained with R(2) values of 0.82 and 0.88 for the whole data and the data without two outliers, respectively; having a standard deviation of 0.27 and 0.23. The predictive power of the obtained equations was assessed by the Leave-One-Out cross validation procedures, giving the same percentages of good classification as in the training set, in the LDA models, and yielding values of q(2) of 0.78 and 0.86 in the regression model, respectively. The validation of this methodology was also carried out by comparison with previous reports modeling this data with other well-known methodologies, even 3-D molecular descriptors.

Markov entropy backbone electrostatic descriptors for predicting proteins biological activity.

The spherical truncation of electrostatic interactions between aminoacids makes it possible to break down long-range spatial electrostatic interactions, resulting in short-range interactions. As a result, a Markov Chain model may be used to calculate the probabilities with which the effect of a given interaction reaches aminoacids at different distances within the backbone. The entropies of a Markov Chain model of this type may then be used to codify information about the spatial distribution of charges in the protein used in this study exploring the structure-activity relationship. In this paper, a linear discriminant analysis is reported, which correctly classified 92.3% of 26 under investigation in training and leave-one-out cross validation, purely for illustrative purposes. Classification was carried out for three possible activities: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. The discriminant analysis equations were contracted into two canonical roots. These simple canonical roots have high regression coefficients (R(c1)=0.903 and R(c2)=0.70). Root1 explains the biological activity of alcohol dehydrogenases while Root2 discriminates between lysozymes and dihydrofolate reductases. It was possible to profile the effect of core, middle, and surface aminoacids on biological activity. In contrast, a model considering classic physicochemical parameters such as: polarizability, refractivity, and partition coefficient classify correctly only the 80.8% of the proteins.

Markovian Backbone Negentropies: Molecular descriptors for protein research. I. Predicting protein stability in Arc repressor mutants.

As more and more protein structures are determined and applied to drug manufacture, there is increasing interest in studying their stability. In this sense, developing novel computational methods to predict and study protein stability in relation to their amino acid sequences has become a significant goal in applied Proteomics. In the study described here, Markovian Backbone Negentropies (MBN) have been introduced in order to model the effect on protein stability of a complete set of alanine substitutions in the Arc repressor. A total of 53 proteins were studied by means of Linear Discriminant Analysis using MBN as molecular descriptors. MBN are molecular descriptors based on a Markov chain model of electron delocalization throughout the protein backbone. The model correctly classified 43 out of 53 (81.13%) proteins according to their thermal stability. More specifically, the model classified 20/28 (71.4%) proteins with near wild-type stability and 23/25 (92%) proteins with reduced stability. Moreover, the model presented a good Mathew's regression coefficient of 0.643. Validation of the model was carried out by several Jackknife procedures. The method compares favorably with surface-dependent and thermodynamic parameter stability scoring functions. For instance, the D-FIRE potential classification function shows a level of good classification of 76.9%. On the other hand, surface, volume, logP, and molar refractivity show accuracies of 70.7, 62.3, 59.0, and 60.0%, respectively.

Vibrational Markovian modelling of footprints after the interaction of antibiotics with the packaging region of HIV type 1.

The design of novel anti-HIV compounds has now become a crucial area for scientists working in numerous interrelated fields of science such as molecular biology, medicinal chemistry, mathematical biology, molecular modelling and bioinformatics. In this context, the development of simple but physically meaningful mathematical models to represent the interaction between anti-HIV drugs and their biological targets is of major interest. One such area currently under investigation involves the targets in the HIV-RNA-packaging region. In the work described here, we applied Markov chain theory in an attempt to describe the interaction between the antibiotic paromomycin and the packaging region of the RNA in Type-1 HIV. In this model, a nucleic acid squeezed graph is used. The vertices of the graph represent the nucleotides while the edges are the phosphodiester bonds. A stochastic (Markovian) matrix was subsequently defined on this graph, an operation that codifies the probabilities of interaction between specific nucleotides of HIV-RNA and the antibiotic. The strength of these local interactions can be calculated through an inelastic vibrational model. The successive power of this matrix codifies the probabilities with which the vibrations after drug-RNA interactions vanish along the polynucleotide main chain. The sums of self-return probabilities in the k-vicinity of each nucleotide represent physically meaningful descriptors. A linear discriminant function was developed and gave rise to excellent discrimination in 80.8% of interacting and footprinted nucleotides. The Jackknife method was employed to assess the stability and predictability of the model. On the other hand, a linear regression model predicted the local binding affinity constants between a specific nucleotide and the antibiotic (R(2)=0.91, Q(2)=0.86). These kinds of models could play an important role either in the discovery of new anti-HIV compounds or the study of their mode of action.

Markovian negentropies in bioinformatics. 1. A picture of footprints after the interaction of the HIV-1 Psi-RNA packaging region with drugs.

MOTIVATION: Many experts worldwide have highlighted the potential of RNA molecules as drug targets for the chemotherapeutic treatment of a range of diseases. In particular, the molecular pockets of RNA in the HIV-1 packaging region have been postulated as promising sites for antiviral action. The discovery of simpler methods to accurately represent drug-RNA interactions could therefore become an interesting and rapid way to generate models that are complementary to docking-based systems. RESULTS: The entropies of a vibrational Markov chain have been introduced here as physically meaningful descriptors for the local drug-nucleic acid complexes. A study of the interaction of the antibiotic Paromomycin with the packaging region of the RNA present in type-1 HIV has been carried out as an illustrative example of this approach. A linear discriminant function gave rise to excellent discrimination among 80.13% of interacting/non-interacting sites. More specifically, the model classified 36/45 nucleotides (80.0%) that interacted with paromomycin and, in addition, 85/106 (80.2%) footprinted (non-interacting) sites from the RNA viral sequence were recognized. The model showed a high Matthews' regression coefficient (C = 0.64). The Jackknife method was also used to assess the stability and predictability of the model by leaving out adenines, C, G, or U. Matthews' coefficients and overall accuracies for these approaches were between 0.55 and 0.68 and 75.8 and 82.7, respectively. On the other hand, a linear regression model predicted the local binding affinity constants between a specific nucleotide and the aforementioned antibiotic (R2 = 0.83,Q2 = 0.825). These kinds of models may play an important role either in the discovery of new anti-HIV compounds or in the elucidation of their mode of action. AVAILABILITY: On request from the corresponding author (humbertogd@cbq.uclv.edu.cu or humbertogd@navegalia.com).