Free-energy calculations for semi-flexible macromolecules: applications to DNA knotting and looping.
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.
Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, Texas 75083, USA.
Stefan M
SM
Giovan
Hypnagogic Software, Vancouver, British Columbia V6K 1V6, Canada.
Robert G
RG
Scharein
Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, Texas 78520, USA.
Andreas
A
Hanke
Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, Texas 75083, USA.
Stephen D
SD
Levene
D004247:DNA / Q000737:chemistry* / Q000235:genetics / Q000378:metabolism; D004250:DNA Topoisomerases, Type II / Q000737:chemistry / Q000378:metabolism; D004268:DNA-Binding Proteins / Q000737:chemistry / Q000378:metabolism; D046911:Macromolecular Substances / Q000737:chemistry / Q000378:metabolism; D011789:Quantum Theory; D013816:Thermodynamics
D004268:DNA-Binding Proteins; D046911:Macromolecular Substances; D004247:DNA; D004250:DNA Topoisomerases, Type II