CONFORMATIONAL-ANALYSIS OF MOLECULAR CHAINS USING NANO-KINEMATICS

We present algorithms for 3-D manipulation and conformational analysis of molecular chains, when bond lengths, bond angles and related dihed ral angles remain fixed. These algorithms are useful for local deforma tions of linear molecules, exact ring closure in cyclic molecules and molecular embedding for short chains. Other possible applications incl ude structure prediction, protein folding, conformation energy analysi s and 3D molecular matching and docking. The algorithms are applicable to all serial molecular chains and make no assumptions about their ge ometry. We make use of results on direct and inverse kinematics from r obotics and mechanics literature and show the correspondence between k inematics 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 part icular, they take tens of milliseconds an current workstations for loc al deformations and chain closures on molecular chains consisting of s ix or fewer rotatable dihedral angles.