THE WRITHING OF CIRCULAR CROSS-SECTION RODS - UNDERSEA CABLES TO DNA SUPERCOILS

The large deflection theory of circular cross-section elastic rods is used to consider the writhing of long straight rods subjected to tensi on and torque, such as undersea cables, and to closed loops with inser ted twist, such as DNA supercoils. The writhed shape of the long strai ght rod under tension and torque is easily generated by twisting a pie ce of string with the fingers and consists of three separate parts: a balanced-ply region, a free end loop, and two tail regions. The soluti on for the rod shape in each of the regions is found. The results are then joined together to ensure continuity of the position and tangent vectors of the strand centreline through the introduction of point for ces and moments at the points where the strands enter and exit the bal anced ply. The results of the model are consistent with simple experim ents on long braided rope. The writhed shape of the closed loop with t wist inserted between the ends prior to closure is modelled as a balan ced ply joined to two end loops. The analysis combines the mechanics s olution with the conservation of topological link to provide a simple formula which quantitatively predicts the approximate shape and helix angle of the supercoil. The results are in good agreement with simple experiments on rope and with available data on DNA supercoils.