  We present an elastic model of B-form DNA as a stack of thin, rigid plates or
base pairs that are not permitted to deform. The symmetry of DNA and the
constraint of plate rigidity limit the number of bulk elastic constants
contributing to a macroscopic elasticity theory of DNA to four. We derive an
effective twist-stretch energy in terms of the macroscopic stretch epsilon
along and relative excess twist sigma about the DNA molecular axis. In addition
to the bulk stretch and twist moduli found previously, we obtain a
twist-stretch modulus with the following remarkable properties: 1) it vanishes
when the radius of the helical curve following the geometric center of each
plate is zero, 2) it vanishes with the elastic constant K_{23} that couples
compression normal to the plates to a shear strain, if the plates are
perpendicular to the molecular axis, and 3) it is nonzero if the plates are
tilted relative to the molecular axis. This implies that a laminated helical
structure carved out of an isotropic elastic medium will not twist in response
to a stretching force, but an isotropic material will twist if it is bent into
the shape of a helix.
