Our goal is to develop a set of computational methods for the analysis of molecular kinematics and molecular conformations that are relevant to receptor-ligand interactions. We are also interested in studying geometric and matching problems arising when the three-dimensional structure of molecules is considered in the analysis of receptor ligand interactions. Our target application is computer-assisted drug design, which is a significant component of rational drug design. Computer assisted drug design is becoming more relevant as the understanding of molecular activity improves and the amount of available experimental data that requires processing increases.
A fundamental assumption for rational drug design is that drug activity is obtained through the molecular binding of one molecule (the ligand) to the pocket of another, usually larger, molecule (the receptor, commonly a protein). In their active, or bound, conformations, the molecules exhibit geometric and chemical complementarity, both of which are essential for successful drug activity. An example is shown in the figure below. The left side shows the protease thermolysin and one of its inhibitors. Thermolysin is the large molecule shown in the picture (PDB code 1TMN), while the inhibitor (a carboxymethyl dipeptide, CDP) is drawn in green near the center of the molecule. The right half of the figure below shows the folding of the polymer chain of thermolysin as a ribbon, and the inhibitor.
The modeling of molecular structure is a complex task, in particular because most molecules are flexible, being able to adopt a number of different conformations that are of similar energy. The modeling of the binding process is also a difficult task, as the characteristics of the receptor, the ligand, and the solvent in which these are found have to be taken into account. Although chemists strive to obtain models that are as accurate as possible, several approximations have to be made in practice. The figure below shows the hard sphere model and the stick models (all atom centers and bonds) for 1TMN. In general, bond lengths, bond angles and torsional angles are considered the degrees of freedom of the molecule.
It is clear that the more accurate the model used, the better the chances chemists stand in predicting molecular interactions. Nevertheless, a large number of predictions made with approximate models have been confirmed with experimental observations. This has encouraged researchers to build tools that use approximate models and investigate the extent to which these tools can be useful. These approximate models pose difficult algorithmic questions. More accurate molecular modeling, gained through better theoretical understanding or increased computational power, can only improve the techniques developed with simpler models.
The problems that arise can be classified into two broad categories:
The techniques that we are using in computer-aided drug design include robotics (kinematics and planning), graphics algorithms (visualization of molecules), geometric calculations (surface computation), numerical methods (energy minimization), graph theoretic methods (invariant identification), randomized algorithms (conformational search), dimension reduction methods (analysis of motion), computer vision methods (docking), and a variety of other techniques including AI methods.