Before revision:  Here, we start from a more realistic 3D description and work out several approximations to arrive at a form that can be handled by the transfer-integral technique. We show that this new approach naturally results very sharpopening transition .
After revision:  Here, we start from a more realistic 3D description and work out several approximations to arrive at a new non-linear 1D Hamiltonian with a twist angle dependence. Our approximations were numerically compared to full 3D calculations, and established its validity in the regime of small angles. For long DNA sequences we obtain sharp, first-order-like melting, transitions .