Free-energy calculations for semi-flexible macromolecules: Applications to DNA knotting and looping

We present a method to obtain numerically accurate values of configurationalfree energies of semiflexible macromolecular systems, based on the technique ofthermodynamic integration combined with normal-mode analysis of a referencesystem subject to harmonic constraints. Compared with previous free-energycalculations that depend on a reference state, our approach introduces twoinnovations, namely the use of internal coordinates to constrain the referencestates and the ability to freely select these reference states. As aconsequence, it is possible to explore systems that undergo substantiallylarger fluctuations than those considered in previous calculations, includingsemiflexible biopolymers having arbitrary ratios of contour length L topersistence length P. To validate the method, high accuracy is demonstrated forfree energies of prime DNA knots with L/P=20 and L/P=40, corresponding to DNAlengths of 3000 and 6000 base pairs, respectively. We then apply the method tostudy the free-energy landscape for a model of a synaptic nucleoprotein complexcontaining a pair of looped domains, revealing a bifurcation in the location ofoptimal synapse (crossover) sites. This transition is relevant to target-siteselection by DNA-binding proteins that occupy multiple DNA sites separated bylarge linear distances along the genome, a problem that arises naturally ingene regulation, DNA recombination, and the action of type-II topoisomerases.Comment: Main article: 24 pages, 8 figures; Supplemental Material: 21 pages, 6 figures. Typos correcte