Kavraki, Lydia E.Zhang, Ming2017-08-022017-08-022002-01-25Kavraki, Lydia E. and Zhang, Ming. "Finding Solutions of the Inverse Kinematics Problems in Computer-aided Drug Design." (2002) https://hdl.handle.net/1911/96292.https://hdl.handle.net/1911/96292The efficient computation of low-energy molecular conformations is of critical importance to problems ranging from protein folding to computer-assisted drug design. Despite the growing number of papers on three-dimensional conformational search, several questions remain open. In this paper we investigate one such question relating to molecular inverse kinematics problems. In these problems we are given an initial conformation of a molecule and the target positions of some feature atoms of the molecule. We wish to automatically compute a new conformation of the molecule that brings the feature atoms to their target positions. We first show how to derive a system of polynomial equations from the geometric constraints of the feature atoms. In contrast with previous work, we do not attempt to solve the system of equations directly, which is computationally expensive. Instead, we adopt a technique based on the Groebner basis from algebraic geometry and develop a novel subdivision algorithm to approximate the real solutions. The approximated solutions can then be used as the starting conformations for existing(heuristic) energy minimization procedures that try to satisfy the target positions of feature atoms and reduce the overall energy of the conformation. To our knowledge, this is the first time that a rigorous algebraic methodology has been used to approximate molecular inverse kinematics solutions and the first time that a subdivision algorithm has been developed to efficiently locate the solutions.15 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR02-385