Before revision:  Here, we construct a simple explicit two-parameter variational solution, referred to as harmonic loop, which reproduces the exact loop energy up to the fourth significant digit . The harmonic-loop solution is easier to handle than the exact one, simplifying the analytical calculation of several quantities. We generalize this solution to a twistable DNA model with anisotropic bending and twist-bend coupling, and show that the loop shape thus derived is in excellent agreement with simulations of two different coarse-grained DNA models.
After revision:  Here, we construct a simple explicit two-parameter variational solution, referred to as harmonic loop, which reproduces the exact loop energy up to the fourth significant digit , and is in very good agreement with shapes obtained from coarse-grained DNA models.