P. Duane Walker

A new computational microscope for molecules: High resolution MEDLA images of taxol and HIV-1 protease, using additive electron density fragmentation principles and fuzzy set methods

Based on the molecular electron density lego assembler (MEDLA) method, a “computational microscope” was developed that generates accurate images of bodies of large molecules at a resolution far exceeding current experimental techniques. The MEDLA “microscope” can be “tuned” to display the high electron density regions of formal chemical bonds; or to show the low density regions of hydrogen bonds and secondary interactions, or to display local shape requirements important in molecular recognition. The power of the method is illustrated by examples of detailed images of taxol, an important anti-cancer agent, and HIV-1 protease, a protein of 1564 atoms. A mathematical framework of the approach, based on fuzzy sets, and the fundamentals of several additional applications of the additive, fuzzy fragmentation principle are presented.

TOWARD SIMILARITY MEASURES FOR MACROMOLECULAR BODIES : MEDLA TEST CALCULATIONS FOR SUBSTITUTED BENZENE SYSTEMS

A new method is proposed for the evaluation of numerical similarity measures for large molecules, defined in terms of their electron density (ED) distributions. The technique is based on the Molecular Electron Density Lego Assembler (MEDLA) approach, proposed earlier for the generation of ab initio quality electron densities for proteins and other macromolecules. The reliability of the approach is tested using a family of 13 substituted aromatic systems for which both standard ab initio electron density computations and the MEDLA technique are applicable. These tests also provide additional examples for evaluating the accuracy of the MEDLA technique. Electron densities for a series of 13 substituted benzenes were calculated using the standard ab initio method with STO‐3G, 3‐21G, and 6‐31G** basis sets as well as the MEDLA approach with a 6‐31G** database of electron density fragments. For each type of calculation, pairwise similarity measures of these compounds were calculated using a point‐by‐point numerical comparison of the EDs. From these results, 2D similarity maps were constructed, serving as an aid for quick visual comparisons for the entire molecular family. The MEDLA approach is shown to give virtually equivalent numerical similarity measures and similarity maps as the standard ab initio method using a 6‐31G** basis set. By contrast, significant differences are found between the standard ab initio 6‐31G** results and the standard ab initio results obtained with smaller STO‐3G and 3‐21G basis sets. These tests indicate that the MEDLA‐based similarity measures faithfully mimic the actual, standard ab initio 6‐31G** similarity measures, suggesting the MEDLA method as a reliable technique to assess the shape similarities of proteins and other macromolecules. The speed of the MEDLA computations allows rapid, pairwise comparisons of the actual EDs for a series of molecules, requiring no more computer time than other simplified, less detailed representations of molecular shape. The MEDLA method also reduces the need to store large volumes of numerical density data on disk, as these densities can be quickly recomputed when needed. For these reasons, the proposed MEDLA similarity analysis technique is likely to become a useful tool in computational drug design.

Fuzzy molecular fragments in drug research

Pharmaceutical research, chemistry and biochemistry suffer from a special handicap — researchers are unable to see individual molecules directly. Current advanced experimental techniques can generate, at best, only blurry pictures of molecules. However, using a new ‘computational microscope’ method of quantum chemical, ab initio molecular imaging, based on an ‘additive fuzzy electron density fragment principle’ and a molecular electron density ‘Lego’ assembler density construction method, realistic detailed images of molecules can be generated. The authors describe how this method can be applied to both small and large molecules and indicate the features of the technique that are relevant to the process of drug discovery.

Application of the shape group method to conformational processes: Shape and conjugation changes in the conformers of 2‐phenyl pyrimidine

The shape group method (SGM) and the associated (a,b)‐parameter maps provide a detailed shape characterization of molecular charge distributions. This method is applied to the study of the variations of shape and conjugation of conformers of 2‐phenyl pyrimidine in their electronic ground state. Within the SGM framework, the method of (a,b)‐parameter maps provides a concise, nonvisual, algorithmic technique for shape characterization of molecules with fixed nuclear geometries. Moreover, shape codes derived from the (a,b)‐parameter maps afford a practical means for efficiently storing the shape properties of molecules in an electronic database. The shape codes of two or more charge distributions can be compared directly, and numerical measures of molecular shape similarity can be computed using a technique that is simple, fast, and inexpensive, especially in relation to direct, pairwise comparisons of electronic charge densities. The quantitative and automated nature of the method suggests applications in the field of computer‐aided molecular design. In this study, the method is used for the first time to determine detailed numerical shape codes and shape similarity measures for a nontrivial conformational problem involving changes in energy and in conjugation. Numerical shape similarity measures of eight conformers of 2‐phenyl pyrimidine are determined and correlated with variations in conformational energy and conjugation. The competing effects of steric repulsion and conjugation lead to important correlations between conformational energy and shape.

Shape groups of the electronic isodensity surfaces for small molecules: shapes of 10-electron hydrides

An algorithm for a detailed 3‐D characterization of the shapes of molecular charge distributions is implemented in the form of a comprehensive package of computer programs, GSHAPE, and applied to a series of 10‐electron hydrides to critically evaluate the methodology. Attention is paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend on two continuous parameters: a density value defining the density contour and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is calculated at the ab initio level using basis sets ranging from STO‐3G to 6‐31G**. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualization of the results is one option of our program using Application Visualization Software (AVS). For a given molecule, in a given nuclear geometry, the technique provides a 2‐D shape map, displaying the distribution of the shape gruops as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis automatically. This feature makes it potentially useful in the context of computer‐aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, a variety of 2‐D shape maps are discussed.