Comparison of knowledge-based and distance geometry approaches for generation of molecular conformations.

A knowledge-based approach for generating conformations of molecules has been developed. The method described here provides a good sampling of the molecule's conformational space by restricting the generated conformations to those consistent with the reference database. The present approach, internally named et for enumerate torsions, differs from previous database-mining approaches by employing a library of much larger substructures while treating open chains, rings, and combinations of chains and rings in the same manner. In addition to knowledge in the form of observed torsion angles, some knowledge from the medicinal chemist is captured in the form of which substructures are identified. The knowledge-based approach is compared to Blaney et al.'s distance geometry (DG) algorithm for sampling the conformational space of molecules. The structures of 113 protein-bound molecules, determined by X-ray crystallography, were used to compare the methods. The present knowledge-based approach (i) generates conformations closer to the experimentally determined conformation, (ii) generates them sooner, and (iii) is significantly faster than the DG method.

Latent semantic structure indexing (LaSSI) for defining chemical similarity.

A novel method for computing chemical similarity from chemical substructure descriptors is described. This new method, called LaSSI, uses the singular value decomposition (SVD) of a chemical descriptor-molecule matrix to create a low-dimensional representation of the original descriptor space. Ranking molecules by similarity to a probe molecule in the reduced-dimensional space has several advantages over analogous ranking in the original descriptor space: matching latent structures is more robust than matching discrete descriptors, choosing the number of singular values provides a rational way to vary the "fuzziness" of the search, and the reduction in the dimensionality of the chemical space increases searching speed. LaSSI also allows the calculation of the similarity between two descriptors and between a descriptor and a molecule.

Chemical similarity searches using latent semantic structural indexing (LaSSI) and comparison to TOPOSIM.

Similarity searches based on chemical descriptors have proven extremely useful in aiding large-scale drug screening. Here we present results of similarity searching using Latent Semantic Structure Indexing (LaSSI). LaSSI uses a singular value decomposition on chemical descriptors to project molecules into a k-dimensional descriptor space, where k is the number of retained singular values. The effect of the projection is that certain descriptors are emphasized over others and some descriptors may count as partially equivalent to others. We compare LaSSI searches to searches done with TOPOSIM, our standard in-house method, which uses the Dice similarity definition. Standard descriptor-based methods such as TOPOSIM count all descriptors equally and treat all descriptors as independent. For this work we use atom pairs and topological torsions as examples of chemical descriptors. Using objective criteria to determine how effective one similarity method is versus another in selecting active compounds from a large database, we find for a series of 16 drug-like probes that LaSSI is as good as or better than TOPOSIM in selecting active compounds from the MDDR database, if the user is allowed to treat k as an adjustable parameter. Typically, LaSSI selects very different sets of actives than does TOPOSIM, so it can find classes of actives that TOPOSIM would miss.

Derivation of a 3D pharmacophore model for the angiotensin-II site one receptor.

A systematic search has been used to derive a hypothesis for the receptor-bound conformation of A-II antagonists at the AT1 receptor. The validity of the pharmacophore hypothesis has been tested using CoMFA, which included 50 diverse A-II antagonists, spanning four orders of magnitude in activity. The resulting cross-validated R2 of 0.64 (conventional R2 of 0.76) is indicative of a good predictive model of activity, and has been used to estimate potency for a variety of non-peptidyl antagonists. The structural model for the non-peptide has been compared with respect to the natural substrate, A-II, by generating peptide to non-peptide overlays.

Extending the trend vector: the trend matrix and sample-based partial least squares.

Trend vector analysis [Carhart, R.E. et al., J. Chem. Inf. Comput. Sci., 25 (1985) 64], in combination with topological descriptors such as atom pairs, has proved useful in drug discovery for ranking large collections of chemical compounds in order of predicted biological activity. The compounds with the highest predicted activities, upon being tested, often show a several-fold increase in the fraction of active compounds relative to a randomly selected set. A trend vector is simply the one-dimensional array of correlations between the biological activity of interest and a set of properties or 'descriptors' of compounds in a training set. This paper examines two methods for generalizing the trend vector to improve the predicted rank order. The trend matrix method finds the correlations between the residuals and the simultaneous occurrence of descriptors, which are stored in a two-dimensional analog of the trend vector. The SAMPLS method derives a linear model by partial least squares (PLS), using the 'sample-based' formulation of PLS [Bush, B.L. and Nachbar, R.B., J. Comput.-Aided Mol. Design, 7 (1993) 587] for efficiency in treating the large number of descriptors. PLS accumulates a predictive model as a sum of linear components. Expressed as a vector of prediction coefficients on properties, the first PLS component is proportional to the trend vector. Subsequent components adjust the model toward full least squares. For both methods the residuals decrease, while the risk of overfitting the training set increases. We therefore also describe statistical checks to prevent overfitting. These methods are applied to two data sets, a small homologous series of disubstituted piperidines, tested on the dopamine receptor, and a large set of diverse chemical structures, some of which are active at the muscarinic receptor. Each data set is split into a training set and a test set, and the activities in the test set are predicted from a fit on the training set. Both the trend matrix and the SAMPLS approach improve the predictions over the simple trend vector. The SAMPLS approach is superior to the trend matrix in that it requires much less storage and CPU time. It also provides a useful set of axes for visualizing properties of the compounds. We describe a randomization method to determine the optimum number of PLS components that is very much faster for large training sets than leave-one-out cross-validation.

Sample-distance partial least squares: PLS optimized for many variables, with application to CoMFA.

Three-dimensional molecular modeling can provide an unlimited number m of structural properties. Comparative Molecular Field Analysis (CoMFA), for example, may calculate thousands of field values for each model structure. When m is large, partial least squares (PLS) is the statistical method of choice for fitting and predicting biological responses. Yet PLS is usually implemented in a property-based fashion which is optimal only for small m. We describe here a sample-based formulation of PLS which can be used to fit any single response (bioactivity). SAMPLS reduces all explanatory data to the pairwise 'distances' among n samples (molecules), or equivalently to an n-by-n covariance matrix C. This matrix, unmodified, can be used to fit all PLS components. Furthermore, SAMPLS will validate the model by modern resampling techniques, at a cost independent of m. We have implemented SAMPLS as a Fortran program and have reproduced conventional and cross-validated PLS analyses of data from two published studies. Full (leave-each-out) cross-validation of a typical CoMFA takes 0.2 CPU s. SAMPLS is thus ideally suited to structure-activity analysis based on CoMFA fields or bonded topology. The sample-distance formulation also relates PLS to methods like cluster analysis and nonlinear mapping, and shows how drastically PLS simplifies the information in CoMFA fields.