Abstract

: We present algorithms for 3-D manipulation and conformational analysis of molecular chains, when bond length, bond angles and related dihedral angles remain fixed. These algorithms are useful for local deformations of linear molecules, exact ring closure in cyclic molecules and molecular embedding for short chains. Other possible applications include structure prediction, protein folding, conformation energy analysis and 3D molecular matching and docking. The algorithms are applicable to all serial molecular chains and make no asssumptions about their geometry. We make use of results on direct and inverse kinematics from robotics and mechanics literature and show the correspondence between kinematics and conformational analysis of molecules. In particular, we pose these problems algebraically and compute all the solutions making use of the structure of these equations and matrix computations. The algorithms have been implemented and perform well in practice. In particular, they take ...

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