Phase boundaries with discontinuous stretch and twist in DNA

The DNA molecule has been modeled for long as an elastic rod capable of resisting stretching, bending and torsion. Experiments over the last two decades have revealed that DNA undergoes several structural transitions depending on the tension, torque and temperature. At fixed temperature the phase diagram of DNA consists of several regions on the tension-torque plane which are separated by coexistence lines. Along these lines two phases of DNA can co-exist by occupying different regions separated by phase boundaries along the molecule. The stretch and twisting curvature are discontinuous across these phase boundaries and the structural transition proceeds by the motion of these boundaries along the length of the molecule. Here we describe a continuum framework to study the propagation of phase boundaries across which the stretch and twisting curvature are discontinuous. We derive an expression for the driving force and assume a kinetic relation for the mobility of these phase boundaries as a function of this driving force. We also develop a finite difference method to integrate the equations of motion for our DNA including the phase boundary. We use it to study the B-DNA to L-DNA transition and the B-DNA to Z-DNA transition at equilibrium and away from it. Our computations match the experiments very well and suggest falsifiable hypotheses that can be tested by new experiments.