Optimization Model And Algorithms For Drug Molecular Docking

Drug molecular design began in the 1960s, and has been applied successfully to innovative drug discovery and optimization. The main driving forces are the development of structural biology and molecular biology, which may identify the functions of some biological macromolecules and determine their three-dimensional structures. Furthermore, the development of computer science has greatly enhanced both speed and accuracy of the computation and data analysis, and promoted the research of drug molecular design methods and applications. Novel theories and approaches have become a major avenue for drug discovery efforts at the post-genomic era. Molecular docking, as a main method of computer-aided drug design, has been successfully used in the drug discovery process. It can greatly reduce the costs and speed up the pace of drug research and development. According to statistics, due to the use of computer-aided drug design, the direct costs of drug research and development have been decreased by 1.3 billion dollars and the cycles of the process have been shortened by 0.9 years (equivalent to more than 10-100 million in sales).Molecular docking is fundamentally an optimization problem of predicting the interaction energy between small organic molecules and biological receptors. With the development of molecular biology and structural biology, the interaction energy between organic molecules and biological macromolecules has been understood profoundly. The optimization model has been developed from lock and key -based rigid one to induced-fit -based flexible one. However, even the simplest structure of small organic molecules have a high degree of freedom, for the receptor, considering its degree of freedom will increase the computational complexity dramatically.In this paper, drug molecular docking problem has been studied from the perspective of mathematical programming. An optimization model of molecular docking is proposed, in which the ligand is flexible and the receptor is rigid. Furthermore, the author considers the conformation changes of the receptor by introducing the concepts of residue groups and key residues. The receptor would be divided into several groups, and .the motions for each group would reflect the movement of the receptor; the partial flexibility of the receptor would be described by the sidechain dihedral angles of the key residues. Thus two different flexbile-flexible optimization models for molecular docking have been built. The models may consider the flexibility of receptor in the conformation space with continuous changes. Besides, the author adopts hierarchical optimization to divide the optimization process into two parts: one is rigid-flexible phase, the other is flexible-rigid phase, and establishes a hierarchical optimization model.As for the optimization algorithm, an evolvement-based genetic algorithm is developed, in which the species dynamics model is introduced into the algorithm to reflect the true state of evolution. In the algorithm, the steady-state solution is regarded as the arithmetic crossover operator, an adaptive strategy is used to overcome the difficulty of confirming the crossover and mutation probabilities, and small population strategy and elitist maintaining strategy ensure the diversity of the populations. These strategies would speed up the optimizing process and ensure rapid and steady convergence.Combined with the aforementioned optimization models and algorithm, the author developed a flexible-rigid molecular docking program, two flexible-flexible programs and a hierarchical one. Docking results show these programs can be applied in drug molecular design efficiently.The author gratefully acknowledges financial support for this work from the National Natural Science Foundation (No. 10772042), the Subsidized by the Special Funds for Major State Basic Research Project (No. 2004CB518901) and High Science and Technology Project (No. 2006AA01A124) of China.