Simplicial neighborhood analysis of protein packing (SNAPP): a computational geometry approach to studying proteins.
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Amino Acid Sequence↗
Biomedical subjects
Alexander Tropsha
Publications and source records attributed to Alexander Tropsha.
Quantitative structure-activity relationship analysis of functionalized amino acid anticonvulsant agents using k nearest neighbor and simulated annealing PLS methods.
We report the development of rigorously validated quantitative structure-activity relationship (QSAR) models for 48 chemically diverse functionalized amino acids with anticonvulsant activity. Two variable selection approaches, simulated annealing partial least squares (SA-PLS) and k nearest neighbor (kNN), were employed. Both methods utilize multiple descriptors such as molecular connectivity indices or atom pair descriptors, which are derived from two-dimensional molecular topology. QSAR models with high internal accuracy were generated, with leave-one-out cross-validated R(2) (q(2)) values ranging between 0.6 and 0.8. The q(2) values for the actual dataset were significantly higher than those obtained for the same dataset with randomly shuffled activity values, indicating that models were statistically significant. The original dataset was further divided into several training and test sets, with highly predictive models providing q(2) values greater than 0.5 for the training sets and R(2) values greater than 0.6 for the test sets. These models were capable of predicting with reasonable accuracy the activity of 13 novel compounds not included in the original dataset. The successful development of highly predictive QSAR models affords further design and discovery of novel anticonvulsant agents.
Amino Acids↗
Antitumor agents. 213. Modeling of epipodophyllotoxin derivatives using variable selection k nearest neighbor QSAR method.
We have applied a variable selection k nearest neighbor quantitative structure-activity relationship (kNN QSAR) method to develop predictive QSAR models for 157 epipodophyllotoxins synthesized previously in our ongoing effort to develop potential anticancer agents. QSAR models were generated using multiple topological descriptors of chemical structures, including molecular connectivity indices (MCI) and molecular operating environment descriptors. The 157 compounds were separated into several training and test sets. The robustness of QSAR models was characterized by the values of the internal leave one out cross-validated R2 (q2) for the training set and external predictive R2 for the test set. The significance of the training set models was confirmed by statistically higher values of q2 for the original data set as compared to q2 values for the same data set with randomly shuffled activities. kNN QSAR models were compared with those obtained with the comparative molecular field analysis method; the kNN QSAR approach afforded models with higher values of both q2 and predictive R2. One of the best models obtained from kNN analysis using MCI as descriptors provided q2 and predictive R2 values of 0.60 and 0.62, respectively. QSAR models developed in these studies shall aid in future design of novel potent epipodophyllotoxin derivatives.
Antineoplastic Agents↗
Beware of q2!
Validation is a crucial aspect of any quantitative structure-activity relationship (QSAR) modeling. This paper examines one of the most popular validation criteria, leave-one-out cross-validated R2 (LOO q2). Often, a high value of this statistical characteristic (q2 > 0.5) is considered as a proof of the high predictive ability of the model. In this paper, we show that this assumption is generally incorrect. In the case of 3D QSAR, the lack of the correlation between the high LOO q2 and the high predictive ability of a QSAR model has been established earlier [Pharm. Acta Helv. 70 (1995) 149; J. Chemomet. 10(1996)95; J. Med. Chem. 41 (1998) 2553]. In this paper, we use two-dimensional (2D) molecular descriptors and k nearest neighbors (kNN) QSAR method for the analysis of several datasets. No correlation between the values of q2 for the training set and predictive ability for the test set was found for any of the datasets. Thus, the high value of LOO q2 appears to be the necessary but not the sufficient condition for the model to have a high predictive power. We argue that this is the general property of QSAR models developed using LOO cross-validation. We emphasize that the external validation is the only way to establish a reliable QSAR model. We formulate a set of criteria for evaluation of predictive ability of QSAR models.
Data Interpretation, Statistical↗
Predictive QSAR modeling based on diversity sampling of experimental datasets for the training and test set selection.
One of the most important characteristics of Quantitative Structure Activity Relashionships (QSAR) models is their predictive power. The latter can be defined as the ability of a model to predict accurately the target property (e.g., biological activity) of compounds that were not used for model development. We suggest that this goal can be achieved by rational division of an experimental SAR dataset into the training and test set, which are used for model development and validation, respectively. Given that all compounds are represented by points in multidimensional descriptor space, we argue that training and test sets must satisfy the following criteria: (i) Representative points of the test set must be close to those of the training set; (ii) Representative points of the training set must be close to representative points of the test set; (iii) Training set must be diverse. For quantitative description of these criteria, we use molecular dataset diversity indices introduced recently (Golbraikh, A., J. Chem. Inf. Comput. Sci., 40 (2000) 414-425). For rational division of a dataset into the training and test sets, we use three closely related sphere-exclusion algorithms. Using several experimental datasets, we demonstrate that QSAR models built and validated with our approach have statistically better predictive power than models generated with either random or activity ranking based selection of the training and test sets. We suggest that rational approaches to the selection of training and test sets based on diversity principles should be used routinely in all QSAR modeling research.
Algorithms↗
Rational principles of compound selection for combinatorial library design.
It is practically impossible in a short period of time to synthesize and test all compounds in any large exhaustive chemical library. We discuss rational approaches to selecting representative subsets of virtual libraries that help direct experimental synthetic efforts for both targeted and diverse library design. For targeted library design, we consider principles based on the similarity to lead molecules. In the case of diverse library design, we discuss algorithms aimed at the selection of both diverse and representative subsets of the entire chemical library space. We illustrate methodologies with several practical examples.
Chemistry, Pharmaceutical↗
Novel ZE-isomerism descriptors derived from molecular topology and their application to QSAR analysis.
We introduce several series of novel ZE-isomerism descriptors derived directly from two-dimensional molecular topology. These descriptors make use of a quantity named ZE-isomerism correction, which is added to the vertex degrees of atoms connected by double bonds in Z and E configurations. This approach is similar to the one described previously for topological chirality descriptors (Golbraikh, A., et al. J. Chem. Inf. Comput. Sci. 2001, 41, 147-158). The ZE-isomerism descriptors include modified molecular connectivity indices, overall Zagreb indices, extended connectivity, overall connectivity, and topological charge indices. They can be either real or complex numbers. Mathematical properties of different subgroups of ZE-isomerism descriptors are discussed. These descriptors circumvent the inability of conventional topological indices to distinguish between Z and E isomers. The applicability of ZE-isomerism descriptors to QSAR analysis is demonstrated in the studies of a series of 131 anticancer agents inhibiting tubulin polymerization.
Antineoplastic Agents↗
QSAR modeling using chirality descriptors derived from molecular topology.
Topological descriptors of chemical structures (such as molecular connectivity indices) are widely used in Quantitative Structure-Activity Relationships (QSAR) studies. Unfortunately, these descriptors lack the ability to discriminate between stereoisomers, which limits their application in QSAR. To circumvent this problem, we recently introduced chirality descriptors derived from molecular graphs and applied them in QSAR studies of ecdysteroids (Golbraikh A.; Bonchev, D.; Tropsha, A. J. Chem. Inf. Comput. Sci. 2001,41, 147-158). In this paper, we extend our earlier work by applying chirality descriptors to four data sets containing chiral compounds. All models were derived with the k-nearest neighbors (kNN) QSAR method developed in our laboratory (Zheng, W.; Tropsha, A. J. Chem. Inf. Comput. Sci. 2000, 40, 185-194). They were validated using the same training and test sets that were employed in various, mostly 3D-QSAR, investigations published by other authors. We show that for all data sets 2D-QSAR models that use a combination of chirality descriptors with conventional (chirality insensitive) topological descriptors afford better or similar predictive ability as compared to models generated with 3D-QSAR approaches. The results presented in this paper reassure that 2D-QSAR modeling provides a powerful alternative to 3D-QSAR.
Databases, Factual↗
Combinatorial QSAR of ambergris fragrance compounds.
A combinatorial quantitative structure-activity relationships (Combi-QSAR) approach has been developed and applied to a data set of 98 ambergris fragrance compounds with complex stereochemistry. The Combi-QSAR approach explores all possible combinations of different independent descriptor collections and various individual correlation methods to obtain statistically significant models with high internal (for the training set) and external (for the test set) accuracy. Seven different descriptor collections were generated with commercially available MOE, CoMFA, CoMMA, Dragon, VolSurf, and MolconnZ programs; we also included chirality topological descriptors recently developed in our laboratory (Golbraikh, A.; Bonchev, D.; Tropsha, A. J. Chem. Inf. Comput. Sci. 2001, 41, 147-158). CoMMA descriptors were used in combination with MOE descriptors. MolconnZ descriptors were used in combination with chirality descriptors. Each descriptor collection was combined individually with four correlation methods, including k-nearest neighbors (kNN) classification, Support Vector Machines (SVM), decision trees, and binary QSAR, giving rise to 28 different types of QSAR models. Multiple diverse and representative training and test sets were generated by the divisions of the original data set in two. Each model with high values of leave-one-out cross-validated correct classification rate for the training set was subjected to extensive internal and external validation to avoid overfitting and achieve reliable predictive power. Two validation techniques were employed, i.e., the randomization of the target property (in this case, odor intensity) also known as the Y-randomization test and the assessment of external prediction accuracy using test sets. We demonstrate that not every combination of the data modeling technique and the descriptor collection yields a validated and predictive QSAR model. kNN classification in combination with CoMFA descriptors was found to be the best QSAR approach overall since predictive models with correct classification rates for both training and test sets of 0.7 and higher were obtained for all divisions of the ambergris data set into the training and test sets. Many predictive QSAR models were also found using a combination of kNN classification method with other collections of descriptors. The combinatorial QSAR affords automation, computational efficiency, and higher probability of identifying significant QSAR models for experimental data sets than the traditional approaches that rely on a single QSAR method.
Algorithms↗
kappa Nearest neighbors QSAR modeling as a variational problem: theory and applications.
Variable selection k Nearest Neighbor (kNN) QSAR is a popular nonlinear methodology for building correlation models between chemical descriptors of compounds and biological activities. The models are built by finding a subspace of the original descriptor space where activity of each compound in the data set is most accurately predicted as the averaged activity of its k nearest neighbors in this subspace. We have formulated the problem of searching for the optimized kNN QSAR models with the highest predictive power as a variational problem. We have investigated the relative contribution of several model parameters such as the selection of variables, the number (k) of nearest neighbors, and the shape of the weighting function used to evaluate the contributions of k nearest neighbor compound activities to the predicted activity of each compound. We have derived the expression for the weighting function which maximizes the model performance. This optimization methodology was applied to several experimental data sets divided into the training and test sets. We report a significant improvement of both the leave-one-out cross-validated R(2) (q(2)) for the training sets and predictive R(2) of the test sets in all cases. Depending on the data set, the average improvements in the prediction accuracy (prediction R(2)) for the test sets ranged between 1.1% and 94% and for the training sets (q(2)) between 3.5% and 118%. We also describe a modified computational procedure for model building based on the use of relational databases to store descriptors and calculate compounds' similarities, which simplifies calculations and increases their efficiency.
Models, Molecular↗
Chemometric analysis of ligand receptor complementarity: identifying Complementary Ligands Based on Receptor Information (CoLiBRI).
We have developed a novel structure-based chemoinformatics approach to search for Complimentary Ligands Based on Receptor Information (CoLiBRI). CoLiBRI is based on the representation of both receptor binding sites and their respective ligands in a space of universal chemical descriptors. The binding site atoms involved in the interaction with ligands are identified by the means of a computational geometry technique known as Delaunay tessellation as applied to X-ray characterized ligand-receptor complexes. TAE/RECON multiple chemical descriptors are calculated independently for each ligand as well as for its active site atoms. The representation of both ligands and active sites using chemical descriptors allows the application of well-known chemometric techniques in order to correlate chemical similarities between active sites and their respective ligands. We have established a protocol to map patterns of nearest neighbor active site vectors in a multidimensional TAE/RECON space onto those of their complementary ligands and vice versa. This protocol affords the prediction of a virtual complementary ligand vector in the ligand chemical space from the position of a known active site vector. This prediction is followed by chemical similarity calculations between this virtual ligand vector and those calculated for molecules in a chemical database to identify real compounds most similar to the virtual ligand. Consequently, the knowledge of the receptor active site structure affords straightforward and efficient identification of its complementary ligands in large databases of chemical compounds using rapid chemical similarity searches. Conversely, starting from the ligand chemical structure, one may identify possible complementary receptor cavities as well. We have applied the CoLiBRI approach to a data set of 800 X-ray characterized ligand-receptor complexes in the PDBbind database. Using a k nearest neighbor (kNN) pattern recognition approach and variable selection, we have shown that knowledge of the active site structure affords identification of its complimentary ligand among the top 1% of a large chemical database in over 90% of all test active sites when a binding site of the same protein family was present in the training set. In the case where test receptors are highly dissimilar and not present among the receptor families in the training set, the prediction accuracy is decreased; however, CoLiBRI was still able to quickly eliminate 75% of the chemical database as improbable ligands. CoLiBRI affords rapid prefiltering of a large chemical database to eliminate compounds that have little chance of binding to a receptor active site.
Algorithms↗
Combinatorial QSAR modeling of P-glycoprotein substrates.
Quantitative structure-activity (property) relationship (QSAR/QSPR) models are typically generated with a single modeling technique using one type of molecular descriptors. Recently, we have begun to explore a combinatorial QSAR approach which employs various combinations of optimization methods and descriptor types and includes rigorous and consistent model validation (Kovatcheva, A.; Golbraikh, A.; Oloff, S.; Xiao, Y.; Zheng, W.; Wolschann, P.; Buchbauer, G.; Tropsha, A. Combinatorial QSAR of Ambergris Fragrance Compounds. J. Chem. Inf. Comput. Sci. 2004, 44, 582-95). Herein, we have applied this approach to a data set of 195 diverse substrates and nonsubstrates of P-glycoprotein (P-gp) that plays a crucial role in drug resistance. Modeling methods included k-nearest neighbors classification, decision tree, binary QSAR, and support vector machines (SVM). Descriptor sets included molecular connectivity indices, atom pair (AP) descriptors, VolSurf descriptors, and molecular operation environment descriptors. Each descriptor type was used with every QSAR modeling technique; so, in total, 16 combinations of techniques and descriptor types have been considered. Although all combinations resulted in models with a high correct classification rate for the training set (CCR(train)), not all of them had high classification accuracy for the test set (CCR(test)). Thus, predictive models have been generated only for some combinations of the methods and descriptor types, and the best models were obtained using SVM classification with either AP or VolSurf descriptors; they were characterized by CCR(train) = 0.94 and 0.88 and CCR(test) = 0.81 and 0.81, respectively. The combinatorial QSAR approach identified models with higher predictive accuracy than those reported previously for the same data set. We suggest that, in the absence of any universally applicable "one-for-all" QSAR methodology, the combinatorial QSAR approach should become the standard practice in QSPR/QSAR modeling.
ATP Binding Cassette Transporter, Subfamily B, Mem↗
A novel automated lazy learning QSAR (ALL-QSAR) approach: method development, applications, and virtual screening of chemical databases using validated ALL-QSAR models.
A novel automated lazy learning quantitative structure-activity relationship (ALL-QSAR) modeling approach has been developed on the basis of the lazy learning theory. The activity of a test compound is predicted from a locally weighted linear regression model using chemical descriptors and the biological activity of the training set compounds most chemically similar to this test compound. The weights with which training set compounds are included in the regression depend on the similarity of those compounds to a test compound. We have applied the ALL-QSAR method to several experimental chemical data sets including 48 anticonvulsant agents with known ED50 values, 48 dopamine D1-receptor antagonists with known competitive binding affinities (Ki), and a Tetrahymena pyriformis data set containing 250 phenolic compounds with toxicity IGC50 values. When applied to database screening, models developed for anticonvulsant agents identified several known anticonvulsant compounds that were not only absent in the training set but highly chemically dissimilar to the training set compounds. This initial success indicates that ALL-QSAR can be further exploited as a general tool for accurate bioactivity prediction and database screening in drug design and discovery. Because of its local nature, the ALL-QSAR approach appears to be especially well-suited for the development of highly predictive models for the sparse or unevenly distributed data sets.
Database Management Systems↗
Predictive QSAR modeling based on diversity sampling of experimental datasets for the training and test set selection.
One of the most important characteristics of Quantitative Structure Activity Relashionships (QSAR) models is their predictive power. The latter can be defined as the ability of a model to predict accurately the target property (e.g., biological activity) of compounds that were not used for model development. We suggest that this goal can be achieved by rational division of an experimental SAR dataset into the training and test set, which are used for model development and validation, respectively. Given that all compounds are represented by points in multidimensional descriptor space, we argue that training and test sets must satisfy the following criteria: (i) Representative points of the test set must be close to those of the training set; (ii) Representative points of the training set must be close to representative points of the test set; (iii) Training set must be diverse. For quantitative description of these criteria, we use molecular dataset diversity indices introduced recently (Golbraikh, A., J. Chem. Inf. Comput. Sci., 40 (2000) 414-425). For rational division of a dataset into the training and test sets, we use three closely related sphere-exclusion algorithms. Using several experimental datasets, we demonstrate that QSAR models built and validated with our approach have statistically better predictive power than models generated with either random or activity ranking based selection of the training and test sets. We suggest that rational approaches to the selection of training and test sets based on diversity principles should be used routinely in all QSAR modeling research.
Algorithms↗
Rational selection of training and test sets for the development of validated QSAR models.
Quantitative Structure-Activity Relationship (QSAR) models are used increasingly to screen chemical databases and/or virtual chemical libraries for potentially bioactive molecules. These developments emphasize the importance of rigorous model validation to ensure that the models have acceptable predictive power. Using k nearest neighbors (kNN) variable selection QSAR method for the analysis of several datasets, we have demonstrated recently that the widely accepted leave-one-out (LOO) cross-validated R2 (q2) is an inadequate characteristic to assess the predictive ability of the models [Golbraikh, A., Tropsha, A. Beware of q2! J. Mol. Graphics Mod. 20, 269-276, (2002)]. Herein, we provide additional evidence that there exists no correlation between the values of q2 for the training set and accuracy of prediction (R2) for the test set and argue that this observation is a general property of any QSAR model developed with LOO cross-validation. We suggest that external validation using rationally selected training and test sets provides a means to establish a reliable QSAR model. We propose several approaches to the division of experimental datasets into training and test sets and apply them in QSAR studies of 48 functionalized amino acid anticonvulsants and a series of 157 epipodophyllotoxin derivatives with antitumor activity. We formulate a set of general criteria for the evaluation of predictive power of QSAR models.
Algorithms↗
Comparing graph representations of protein structure for mining family-specific residue-based packing motifs.
We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almost-Delaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almost-Delaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs.
Algorithms↗