A combinatorial algorithm for calculating ligand binding

We consider the problem of predicting the mode of binding of a small molecule to a receptor site on a protein. One plausible approach, given a rigid molecule and its geometry, is to search directly for the orientation in space that maximizes the degree of contact. The computation time required for such a naive procedure is proportional to n³m³, where n is the number of points in the site where binding can occur, and m is the number of atoms in the ligand. We give an alternative, combinatorial approach, in which only “contact–no-contact” criteria are considered. We relate this problem to the well-known combinatorial problem of finding cliques in a graph and show that we can use a solution to the clique problem not only to solve our original problem, but also the problem of avoiding energetically unfavorable matches. Our experience with this method indicates that the computation time required is proportional to nm^2.8, with a lower constant of proportionality than that of the naive procedure.     

Voronoi binding site models

A frequently occurring problem in drug design and enzymology is that the binding constants for several compounds to the same site are known, but the geometry and energetic interactions of the site are not. This paper presents in detail a novel approach to the problem which accurately but compactly represents the allowed conformation space of each ligand, accurately depicts their three-dimensional structures, and realistically allows each ligand to adopt the conformation and positioning in the site which is most favorable energetically. The investigator supplies only the ligand structures and observed binding free energies, along with a proposed site geometry. With no further assumptions about how the ligands bind and what parts of the ligands are important in determining the binding, the algorithm fits the observed binding energies without leaving outliers, predicts exactly how each of the given ligands binds in the site, and predicts the strength and mode of binding of new compounds, regardless of chemical similarity to the original set of ligands. The method is illustrated by devising a simple site that accounts for the binding of five polychlorinated biphenyls to thyroxine binding prealbumin. This model then predicts the binding energies correctly for an additional six biphenyls, and fails on one compound.     

Chemical data mining of the NCI human tumor cell line database

The NCI Developmental Therapeutics Program Human Tumor cell line data set is a publicly available database that contains cellular assay screening data for over 40 000 compounds tested in 60 human tumor cell lines. The database also contains microarray assay gene expression data for the cell lines, and so it provides an excellent information resource particularly for testing data mining methods that bridge chemical, biological, and genomic information. In this paper we describe a formal knowledge discovery approach to characterizing and data mining this set and report the results of some of our initial experiments in mining the set from a chemoinformatics perspective.     

A statistical measure of association and a series expansion of chain conformations

A simple, easily calculated, nonparametric statistic is described that can detect the presence of a functional relationship in bivariate data. Given a sample of data points (x,y), the statistic's value is nearly 1 if y is a linear function of x with little noise; it is greater than 1 if y is a nonlinear function of x; and it is close to 2 if x and y are uniformly and independently distributed. The statistic can be used to rapidly screen through large data sets to identify the most functionally related variable pairs. As an illustration, the statistic is used to detect relations between polypeptide conformational energy and functions of a series expansion for chain conformations.     

Voronoi binding site models: Calculation of binding modes and influence of drug binding data accuracy

A new and accurate method for calculating the geometrically allowed modes of binding of a ligand molecule to a Voronoi site model is reported. It is shown that the feasibility of the binding of a group of atoms to a Voronoi site reduces to a simple set of linear and quadratic inequalities and quadratic equalities which can be solved by minimization of a simple function. Newton's numerical method of solution coupled to a line search proved to be successful. Moreover, we have developed efficient molecular and site data bases to discard quickly infeasible binding modes without time-consuming numerical calculation. The method is tested with a data set consisting of the binding constants for a series of biphenyls binding to prealbumin. After determination of the conformation space of the molecules and proposal of a Voronoi site geometry, the geometrically feasible modes are calculated and the energy interaction parameters determined to fit the observed binding energies to the site within experimental error ranges. We actually allowed these ranges to vary in order to study the influence of their broadness on the site geometry and found that as they increase, one can first model the receptor as a three-region site then as a single region site, but never as a two-region site.     

Cluster distance geometry of polypeptide chains

Distance geometry has been a broadly useful tool for dealing with conformational calculations. Customarily each atom is represented as a point, constraints on the distances between some atoms are obtained from experimental or theoretical sources, and then a random sampling of conformations can be calculated that are consistent with the constraints. Although these methods can be applied to small proteins having on the order of 1000 atoms, for some purposes it is advantageous to view the problem at lower resolution. Here distance geometry is generalized to deal with distances between sets of points. In the end, much of the same techniques produce a sampling of different configurations of these sets of points subject to distance constraints, but now the radii of gyration of the different sets play an important role. A simple example is given of how the packing constraints for polypeptide chains combine with loose distance constraints to give good calculated protein conformers at a very low resolution.     

The measurement of molecular diversity by receptor site interaction simulation

The assembly of large compound libraries for the purpose of screening against various receptor targets to identify chemical leads for drug discovery programs has created a need for methods to measure the molecular diversity of such libraries. The method described here, for which we propose the acronym RESIS (for Receptor Site Interaction Simulation), relates directly to this use. A database is built of three-dimensional representations of the compounds in the library and a set of three-point three-dimensional theoretical receptor sites is generated based on putative hydrophobic and polar interactions. A series of flexible, three-dimensional searches is then performed over the database, using each of the theoretical sites as the basis for one such search. The resulting pattern of hits across the grid of theoretical receptor sites provides a measure of the molecular diversity of the compound library. This can be conveniently displayed as a density map which provides a readily comprehensible visual impression of the library diversity characteristics. A library of 7500 drug compounds derived from the CIPSLINEPC databases was characterized with respect to molecular diversity using the RESIS method. Some specific uses for the information obtained from application of the method are discussed. A comparison was made of the results from the RESIS method with those from a recently published two-dimensional approach for assessing molecular diversity using sets of compounds from the Maybridge database (MAY).     

The Utility of Interaction Analysis for Generalizing Characteristics of Science Classrooms

Validating and generalizing from holistic observation protocols of classroom practice have proven difficult. These tools miss crucial classroom characteristics, like the type of instruction, the organization of learners, and the level of cognitive engagement that occur differentially in the time span of a lesson. As a result, this study examined the potential of interaction analysis for drawing detailed inferences about science classrooms. Holistic and interaction analysis techniques were applied to an existing set of observational data from a group of high school teachers (N = 21) who were participating in long‐term professional development. Results indicate that interaction analysis provides crucial details that are otherwise absent. Questions are raised about the overall benefit and use of holistic observation protocols without supplemental information.