Abstract
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.
Highlights
Free-energy changes govern the direction of all chemical and biophysical processes in biological systems
It is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations
Our results for the free energies of DNA knots obtained by thermodynamic integration (TI)-normal mode analysis (NMA) are compared directly to the knots’ probabilities of occurrence in ensembles of chains generated by random segment passage during successive deformations of the chain (Equilibrium Segment Passage, ESP) (Fig. 5)
Summary
Free-energy changes govern the direction of all chemical and biophysical processes in biological systems. For macromolecular systems, obtaining accurate estimates of the free energy is one of the most challenging problems in computational biology and chemistry.. Systems involving intermediate length scales such as semiflexible DNA-protein structures are abundant in living cells; this class of problems has generally eluded standard computational free-energy methods because the inherent flexibility of molecules on these elevated length scales results in large conformational fluctuations in rugged potential energy landscapes.. The free energy, F, of a system in the canonical ensemble, i.e., at constant number of particles N, volume V , and temperature T, is defined as. Assuming that the kinetic energy of the system is independent of the particle positions,
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