  We present a method to obtain numerically accurate values of configurational
free energies of semiflexible macromolecular systems, based on the technique of
thermodynamic integration combined with normal-mode analysis of a reference
system subject to harmonic constraints. Compared with previous free-energy
calculations that depend on a reference state, our approach introduces two
innovations, namely the use of internal coordinates to constrain the reference
states and the ability to freely select these reference states. As a
consequence, it is possible to explore systems that undergo substantially
larger fluctuations than those considered in previous calculations, including
semiflexible biopolymers having arbitrary ratios of contour length L to
persistence length P. To validate the method, high accuracy is demonstrated for
free energies of prime DNA knots with L/P=20 and L/P=40, corresponding to DNA
lengths of 3000 and 6000 base pairs, respectively. We then apply the method to
study the free-energy landscape for a model of a synaptic nucleoprotein complex
containing a pair of looped domains, revealing a bifurcation in the location of
optimal synapse (crossover) sites. This transition is relevant to target-site
selection by DNA-binding proteins that occupy multiple DNA sites separated by
large linear distances along the genome, a problem that arises naturally in
gene regulation, DNA recombination, and the action of type-II topoisomerases.
