A Coupled Base-Rotator Model for Structure and Dynamics of DNA: Local Fluctuations in Helical Twist Angles and Topological Solitons

Structure and dynamics of DNA are studied by using a model dynamical system in which each base in the system, coupled with its complementary base and nearest neighbores in the same strand by the bydrogen-bonding and the stacking energy, respectively, is allowed to rotate in a plane perpendicular to the helical axis. The potential energy of the base system is taken to be composed of two parts, intra-strand base-base interaction energy and inter-strand one, in which base-sequence variation of interaction constants is neglected. When the intra-strand interactions are much larger than the inter-strand ones, a continuum approximation can be used, and the model system admits various topological solitons propagating along the helical axis. By studying numerically nonlinear difference equations determined from the extrema of a potential function of the model system in its simplified yet nontrivial case, it is shown that there exist fairly large local fluctuations in helical twist angles from one base pair to the next characterized by commensurate, incommensurate and chaotic phases, in addition to the conventional, idealized B-form.