Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density.

The aim of our study is the development of a method for calculating the interface of dimerization of protein-protein complexes based on simplified medium-resolution structures. In particular, we wished to evaluate if the existing concepts for the computation of the Solvent-Accessible Surface Area (SASA) of macromolecules could be applied to medium-resolution models. Therefore, we selected a set of 140 protein chains and computed their reduced representations by topological analysis of their electron density maps at 2.85 A crystallographic resolution. This procedure leads to a limited number of critical points (CPs) that can be identified and associated to backbone and side-chain parts. To evaluate the SASA and interfaces of dimerization of the reduced representations, we chose and modified two existing programs that calculate the SASA of atomic representations, and tested (1) several radii tables of amino acids, (2) the influence of the backbone and side-chain points, and (3) the radius of the solvent molecule, which rolls over the surface. The results are shown in terms of relative error compared to the values calculated on the corresponding atomic representations of the proteins.

Application of a Kohonen neural network to the analysis of data regarding the alkylation of toluene with methanol catalyzed by ZSM-5 type zeolites.

para-Xylene is widely used in chemical industry. It can be synthesized by alkylation of toluene with methanol using zeolite ZSM-5 as catalyst. The proportion of para-xylene, among its other isomers and other reaction byproducts, depends on the reaction conditions. As this process still remains largely empirical, we attempted to build a theoretical model able to predict the para-xylene yield under specific reaction conditions. We have consequently collected data regarding this reaction from the literature and exploited the potency of a particular artificial neural network (ANN), the counter-propagation ANN based on the Kohonen technique. The results show that such an approach is suitable to establish a predictive model of the yield in para-xylene on the basis of reaction parameters. The quality of the model could be further improved by considering a larger valuable data set, e.g. including experiments characterized by a low yield in para-xylene.

A new graph descriptor for molecules containing cycles. Application as screening criterion for searching molecular structures within large databases of organic compounds.

The search of molecular structures inside a large database of chemical compounds is a critical step for many computer programs used in several domains of chemistry. During the last years, the size of many chemical databases has dramatically increased, hence in the meantime, search engines needed to be more and more powerful. The speed and the efficiency of screening processes of the chemical compounds are thus essential. Looking forward for algorithms dedicated to structure and substructure search, we have developed a new graph descriptor for structures containing cycles in order to find efficient indexation and classification criteria of molecular structures. This graph descriptor can be used as a screening criteria for structure and substructure search in large databases of organic compounds.

Critical point representations of electron density maps for the comparison of benzodiazepine-type ligands.

A procedure for the comparison of three-dimensional electron density distributions is proposed for similarity searches between pharmacological ligands at various levels of crystallographic resolution. First, a graph representation of molecular electron density distributions is generated using a critical point analysis approach. Pairwise as well as multiple comparisons between the obtained graphs of critical points are then carried out using a Monte Carlo/simulated annealing technique, and results are compared with genetic algorithm solutions.

Comparison of benzodiazepine-like compounds using topological analysis and genetic algorithms.

Four compounds within a set of ligands for the benzodiazepine receptors are characterized by their electron density maps at different resolution levels and reconstructed from calculated structure factors. The resulting complex three-dimensional density maps are first simplified into connected graphs using topological analysis. Then, an original genetic algorithm method, GAGS (Genetic Algorithm for Graph Similarity search), is developed and implemented in order to compare the connected graphs. Finally, the analysis of the best solutions of the algorithm are expressed in terms of functional group superimpositions. The GAGS analysis is applied to different resolution levels of the electron density maps and the resulting models are compared in order to assess the influence of the resolution on the resulting pharmacophore models.

Protein model representation and construction.

Crystallographic studies play a major role in current efforts towards protein structure determination. However, despite recent advances in computational tools for molecular modeling and graphics, the task of constructing a protein model from crystallographic data remains complex and time-consuming, requiring extensive expert intervention. This paper describes an approach to automating the process of model construction, where a model is represented as an annotated trace (or partial trace) of the three-dimensional backbone of the structure. Potential models are generated using an evolutionary algorithm, which incorporates multiple fitness functions tailored to different structural levels in the protein. Preliminary experimental results, which demonstrate the viability of the approach, are reported.

Similarity and complementarity of molecular shapes: applicability of a topological analysis approach.

Developments based on a topological analysis approach of electron density maps are presented and applied to two different fields: the interpretation of electron density maps of proteins and the description of shape complementarity between a cyclodextrin host and a guest molecule. A global representation of the electron density distribution, through the location, identification and linkage of its critical points (points where the gradient of the density vanishes, i.e., peaks and passes), is generated using the program ORCRIT. On one hand, the interpretation of protein electron density maps is based on similarity evaluations between graphs of critical points and known structures. So far, the method has been applied to 3 A resolution maps for the recognition of secondary structure motifs using a procedure relevant to expert systems in artificial intelligence. Satisfying matches between critical point graphs and their corresponding protein structure depict the ability of the topological analysis to catch the essential secondary structural features in electron density maps. On the other hand, mapping the accessible volume of a host molecule is achieved by representing the peaks as ellipsoids with axes related to local curvature of the electron density function. Related energies of the interacting species can also be estimated. A qualitative comparison is made between the results generated by the topological analysis and energy values obtained by conventional molecular mechanics calculations. A positive comparison and a close complementarity between cyclodextrin and ligands shows that the topological analysis method gives a good representation of the electron density function.

Shape information from a critical point analysis of calculated electron density maps: application to DNA-drug systems.

A computational method is described for mapping the volume within the DNA double helix accessible to the groove-binding antibiotic netropsin. Topological critical point analysis is used to locate maxima in electron density maps reconstructed from crystallographically determined atomic coordinates. The peaks obtained in this way are represented as ellipsoids with axes related to local curvature of the electron density function. Combining the ellipsoids produces a single electron density function which can be probed to estimate effective volumes of the interacting species. Close complementarity between host and ligand in this example shows the method to give a good representation of the electron density function at various resolutions. At the atomic level, the ellipsoid method gives results which are in close agreement with those from the conventional spherical van der Waals approach.

Molecular scene analysis: application of a topological approach to the automated interpretation of protein electron-density maps.

Methods to assist in the spatial and visual analysis of electron-density maps have been investigated as part of a project in molecular scene analysis [Fortier, Castleden, Glasgow, Conklin, Walmsley, Leherte & Allen (1993). Acta Cryst. D49, 168-178]. In particular, the usefulness of the topological approach for the segmentation of medium-resolution (3 A) maps of proteins and their interpretation in terms of structural motifs has been assessed. The approach followed is that proposed by Johnson [Johnson (1977). ORCRIT. The Oak Ridge Critical Point Network Program. Chemistry Division, Oak Ridge National Laboratory, USA] which provides a global representation of the electron-density distribution through the location, identification and linkage of its critical points. In the first part of the study, the topological approach was applied to calculated maps of three proteins of small to medium size so as to develop a methodology that could then be used for analyzing maps of medium resolution. The methodology was then applied to both calculated and experimental maps of penicillopepsin at 3 A resolution. The study shows that the networks of critical points can provide a useful segmentation of the maps, tracing the protein main chains and capturing their conformation. In addition, these networks can be parsed in terms of secondary-structure motifs, through a geometrical analysis of the critical points. The procedure adopted for secondary-structure recognition, which was phrased in terms of geometry-based rules, provides a basis for a further automated implementation of a more complete set of recognition operations through the use of artificial-intelligence techniques.

Segmentation and interpretation of 3D protein images.

The segmentation and interpretation of three-dimensional images of proteins is considered. A topological approach is used to represent a protein structure as a spanning tree of critical points, where each critical point corresponds to a residue or the connectivity between residues. The critical points are subsequently analyzed to recognize secondary structure motifs within the protein. Results of applying the approach to ideal and experimental images of proteins at medium resolution are presented.

Molecular scene analysis: the integration of direct-methods and artificial-intelligence strategies for solving protein crystal structure.

A knowledge-based approach to crystal structure determination is presented. The approach integrates direct-methods and artificial-intelligence strategies to rephrase the structure determination process as an exercise in scene analysis. A general joint probability distribution framework, which allows the incorporation of isomorphous replacement, anomalous scattering and a priori structural information, forms the basis of the direct-methods strategies. The accumulated knowledge on crystal and molecular structures is exploited through the use of artificial-intelligence strategies, which include techniques of knowledge representation, search and machine learning.