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The docking problem can be described informally as follows: given a receptor (normally a protein) with its specific binding site and a ligand (a small molecule), does the ligand bind to the receptor, and if yes, what are the binding's strength and geometry? The problem has a geometric as well as a combinatorial character. It is a geometric problem because the relative orientation of two objects in three dimensions must be determined. But restricting the attention to geometry is only sufficient if both binding partners, are regarded as rigid. In general, both molecules are subject to more or less significant structural changes during the docking process (induced fit) depending on their conformational flexibility. Thus, if we want to find the energetically most favorable placements of the ligand into the active site of the receptor, we must take molecular flexibility and different patterns of receptor ligand interactions into account. Both of these aspects can be modeled discretely. Thus the docking problem turns into a combinatorial optimization problem. We apply algorithms for computational geometry, combinatorial optimization and computer vision to this problem.
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