Near Helical Conformations of an Elastic dsDNA Ribbon

Abstract

We find analytically the conditions to form a nearly helical conformation for a model of double-stranded DNA under external force and torque. For such conformations, the tilting angle can be either oscillatory or decaying with increasing arclength, depending on the relationship among the force, torque and initial tilting angle. Both conformations are possible for a small initial tilting angle while only the oscillatory solution is possible for a large initial tilting angle. Phase diagram that depicts the oscillatory and decaying solutions is calculated. The corresponding linking number, twist, writhe number, relative extension and the locus of the chain are also calculated analytically.