Pharmacophore Perception by Molecule Alignment
Enzymes take a key role in the research of the pharmaceutical industry, because they represent targets for the specific development of drugs. Within the scope of rational drug design computational methods gain more and more importance to design workflows that are faster, more efficient and cheaper. A main principle in drug discovery and development is the interaction between receptors and enzymes with their ligands. A problematic situation arises from the fact, the number of enzymes where the 3D structure is known is still small compared to the actual number of pharmaceutic relevant enzymes. It is quite clear that many proteins can never be crystallized or their structure will dramatically change when taken out of their natural environment such as for membrane proteins. Nevertheless, to gain knowledge of the binding mode of a ligand inside the enzymes' active site without information about the proteins' 3D structure, methods have to be developed to acquire information on the geometry of the binding pocket. Because similar molecular compounds have related biological effects a reverse technique can be applied to compare the geometry of ligands and therefrom derive a complementary mapping of the spatial and physical properties of the active site. For this purpose, a systematic superimposition of a series of ligands, that bind to the same receptor, is carried out, to calculate the 3D maximum common substructure (3D-MCSS).
Figure 1: Superimposition of four angiotensin-II
antagonists which play a role in blood pressure
regulation and the treatment of cardiac insufficiency.
Dashed circles mark pharmacophoric points. The model
of the pharmacophore is shown at the bottom.
Extracting the largest 3D substructure common to a set of molecules or ligands, much in the same way as the comparison of a set of keys, will give us the essential features necessary for a key to fit into a lock. Through a pharmacophore pattern similarities are defined between ligands binding to the same receptor. A pharmacophore defines the three-dimensional arrangement of substructural units such as hydrogen bonding or hydrogen accepting sites or hydrophobic areas in a molecule. It provides indications of substructures relevant for the receptor affinity of the different substrates and leads to indirect mapping of the receptor site. This pharmacophore pattern can be derived from the 3D maximum common substructure (3D-MCSS) that these compounds have in common and it can help finding new lead structures necessary for drug design in medicinal chemistry (Figure 1). In addition to the structural similarity, which is calculated through the MCSS, there is also a necessity for similarity in physicochemical properties of the molecules for the estimation of molecular recognition.
Figure 2: Flowchart of the hybrid algorithm
that combines a genetic algorithm with the numerical
optimization method directed tweak. Additionally, two
new operators called creep and crunch are implemented.
The determination of the MCSS out of the superimposition of flexible 3D structures is a computationally expensive task. Therefore, a method has been developed that is based on a combination of a genetic algorithm with a numerical optimization method. A major goal of this hybrid procedure is to adequately address the conformational flexibility of ligand molecules. The genetic algorithm optimizes in a nondeterministic process the size and the geometric fit of the overlay. The geometric fit is further improved by changing torsional angles combining the genetic algorithm and the directed tweak method. The 3D substructure search starts with one conformation for each structure and investigates the conformational flexibility during the optimization process. The starting points correspond to the chromosomes or individuals of a population representing potential solutions to the search problem. The genetic operators selection, mutation, and crossover are iteratively applied to the population. Also two additional operators that are tailored to the specific problem have been implemented, called creep and crunch (Figure 2).
Figure 3: Results of the Pareto optimization of the superposition of vinylcyclobutane and propylcyclobutane. The plot shows the rms value of the superpositions versus the size N of the substructures. The dashed line marks the set of the Pareto solutions which cannot be improved further.
The MCSS search is a multi-criteria optimization problem, where the notion of optimality is difficult to define. Two contradictory main principal parameters contribute to the fitness of a superimposition and have to be optimized: the size of the substructure and its geometric fit. The substructure size has to be as large as possible whereas the deviation in the positions of the superimposed atoms should be as low as possible. An optimization concept taking both criteria into account was developed by Vilfredo Pareto. Pareto optimization means that an optimized state is reached if none of the parameters can be improved further without making another one worse (Figure 3). Selection drives the optimization and causes evolutionary pressure: The selection operator moves individuals from one generation into the next one based on their relative fitness. A special selection type to prevent premature loss of genetic information that might occur is called restricted tournament selection (RTS). The genetic operators are applied to the chromosomes after the selection process and a new population forms the offspring generation.
GAMMA (Genetic Algorithm for Multiple Molecule Alignment) is the program that provides the possibility for computing the 3D maximum common substructure (MCSS) of a data set of several compounds. The program has been extended to the simultaneous superimposition of a set of conformationally flexible molecules. As matching criteria physico-chemical atom properties, like electronegativity or atomic charges can be chosen.
M. Wagener, J. Gasteiger: "The Determination of Maximum Common Substructures by a Genetic Algorithm: Application in Synthesis Design and for the Structural Analysis of Biological Activity", Angew. Chem. 1994, 106, 1245-1248. Angew. Chem. Int. Ed. Engl. 1994, 33, 1189-1192.
S. Handschuh, M. Wagener, J. Gasteiger: "Superposition of Three-Dimensional Structures Allowing for Conformational Flexibility by a Hybrid Method", J. Chem. Inf. Sci. 1998, 38, 220-232.
S. Handschuh, J. Gasteiger: "Pharmacophores Derived from 3D Substructure Perception" in: "Pharmacophore: Perception, Development and Use in Drug Design", O. GŁner (Editor). La Jolla, CA: International University Line, 1999, pp. 430-453
S. Handschuh, J. Gasteiger: "The Search for the Spatial and Electronic Requirements of a Drug", J. Mol. Model. 2000, 6, 358-378.
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Last modified: 9. Jan. 2003, A. Schunk