DNA bending energy ($G_b=\frac{k_{B}T{l}_p}{2}\int {\kappa }^{2}d\ell$)

The curvature-dependent elastic energy of a semiflexible DNA polymer in the isotropic worm-like chain model. Here $l_p$ is the persistence length, $\kappa$ the curvature and $\ell$ the polymer contour length. A complete circular loop of radius $R$ costs $\pi k_{B}T{l}_p/R$, obtained by integrating constant curvature $1/R$ over length $2\pi R$.