Configurational statistics of the DNA duplex: Extended generator matrices to treat the rotations and translations of adjacent residues

The base‐to‐base virtual bond treatment of nucleic acids used in statistical mechanical calculations of polynucleotide chain properties has been refined by incorporating the six parameters that relate the positions and orientations of sequential rigid bodies. The scheme allows for the sequence‐dependent bending, twisting, and displacement of base pairs as well as for asymmetry in the angular and translational fluctuations of individual residues. Expressions are developed for the generator matrices required for the computation, as a function of chain length, of various parameters measuring the overall mean extension and shape of the DNA. Quantities of interest include the end‐to‐end vector r, the square of the end‐to‐end distance r², the square radius of gyration s², the center‐of‐gravity vector g, the second moments of inertia S^×2, and the higher moments of r and g. The matrix expressions introduced in the 1960s by Flory and co‐workers for the determination of configuration‐dependent polymer chain averages are decomposed into their translational and orientational contributions so that the methods can be extended to the rigid body analysis of chemical moieties. The new expressions permit, for the first time, examination of the effects of sequence‐dependent translations, such as the lateral sliding of residues in A‐ and B‐helices and the vertical opening of base pairs in drug–DNA complexes, on the average extension and shape of the long flexible double helix. The approach is illustrated in the following paper using conformational energy estimates of the base sequence‐dependent flexibility of successive B‐DNA base pairs. © 1994 John Wiley & Sons, Inc.