The flexibility of the nucleic acids: (I). "SIR", a novel approach to the variation of polymer geometry in constrained systems.

A novel and powerful methodology is developed which allows the alteration of molecular structures subjected to constraints and its application to polynucleotides with mononucleotide repeat symmetry, including the treatment of the flexible sugar rings is described. In contrast to procedures proposed by other authors, the constraints are formulated as differential equations which are linear with respect to the differentials of the geometrical variables. These equations can be solved easily by stepwise numerical integration involving sucessive infinitesimal rotations (SIR). Moreover, these equations define a set of independent curvilinear coordinates which can be used directly as the parameters of the energy functional in an energy minimisation procedure. This methodology allows the scanning of the full configurational space of a complex macromolecule, with direct access to the helicoidal variables in the case of periodic systems. Through this approach many problems involving biomacromolecular conformation, which would otherwise be intractable, may be studied with considerable ease.