ELASTICITY THEORY OF A TWISTED STACK OF PLATES

We present an elastic model of B-form DNA as a stack of thin, rigid pl ates or base pairs that are not permitted to deform. The symmetry of D NA and the constraint of plate rigidity limit the number of bulk elast ic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the mac roscopic stretch epsilon along and relative excess twist sigma about t he DNA molecular asis. In addition to the bulk stretch and twist modul i found previously, we obtain a twist-stretch modulus with the followi ng remarkable properties: 1) it vanishes when the radius of the helica l curve following the geometric center of each plate is zero, 2) it va nishes with the elastic constant K-23 that couples compression normal to the plates to a shear strain, if the plates are perpendicular to th e molecular axis, and 3) it is nonzero if the plates are tilted relati ve to the molecular axis. This implies that a laminated helical struct ure carved out of an isotropic elastic medium will not twist in respon se to a stretching force, but an isotropic material will twist if it i s be ni into the shape of a helix.