The Cre-recombination system has become an important tool for genetic manipulation of higher organisms and a model for site-specific DNA-recombination mechanisms employed by the λ-Int superfamily of recombinases. We report a novel quantitative approach for characterizing the probability of DNA-loop formation in solution using time-dependent ensemble Förster resonance energy transfer measurements of intra- and inter-molecular Cre-recombination kinetics. Our method uses an innovative technique for incorporating multiple covalent modifications at specific sites in covalently closed DNA. Because the mechanism of Cre recombinase does not conform to a simple kinetic scheme, we employ numerical methods to extract rate constants for fundamental steps that pertain to Cre-mediated loop closure. Cre recombination does not require accessory proteins, DNA supercoiling or particular metal-ion cofactors and is thus a highly flexible system for quantitatively analyzing DNA-loop formation in vitro and in vivo.

The formation of DNA loops is a ubiquitous theme in biological processes, including DNA replication, recombination and repair, and gene regulation. These loops are mediated by proteins bound at specific sites along the contour of a single DNA molecule, in some cases many thousands of base pairs apart. Loop formation incurs a thermodynamic cost that is a sensitive function of the length of looped DNA as well as the geometry and elastic properties of the DNA-bound protein. The free energy of DNA looping is logarithmically related to a generalization of the Jacobson-Stockmayer factor for DNA cyclization, termed the J factor. In the present article, we review the thermodynamic origins of this quantity, discuss how it is measured experimentally and connect the macroscopic interpretation of the J factor with a statistical-mechanical description of DNA looping and cyclization.

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.

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 20 L P = and 40 L P = , 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.

For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequencedependent bends or inhomogeneous bending flexibility. Within the last ten years, however, approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum.However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, k B T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.

In Cre site-specific recombination, the synaptic intermediate is a recombinase homotetramer containing a pair of loxP DNA target sites. The enzyme system's strand-exchange mechanism proceeds via a Holliday-junction (HJ) intermediate; however, the geometry of DNA segments in the synapse has remained highly controversial. In particular, all crystallographic structures are consistent with an achiral, planar Holliday-junction (HJ) structure, whereas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-handed chiral junction. We use the kinetics of loop closure involving closely spaced (131–151 bp) loxP sites to investigate the in-aqueo ensemble of conformations for the longest-lived looped DNA intermediate. Fitting the experimental site-spacing dependence of the loop-closure probability, J, to a statistical-mechanical theory of DNA looping provides evidence for substantial out-of-plane HJ distortion, which unequivocally stands in contrast to the square-planar intermediate geometry from Cre-loxP crystal structures and those of other int-superfamily recombinases. J measurements for an HJ-isomerization-deficient Cre mutant suggest that the apparent geometry of the wild-type complex is consistent with temporal averaging of right-handed and achiral structures. Our approach connects the static pictures provided by crystal structures and the natural dynamics of macromolecules in solution, thus advancing a more comprehensive dynamic analysis of large nucleoprotein structures and their mechanisms.

Multiscale modeling has become a major focus in computational chemistry and biology in order to simulate systems of ever-increasing complexity. To properly treat such systems on multiple length scales, it is necessary to rigorously treat the momenta and coordinates of the individual entities that make up the system of interest. We use principles of polymer physics to model DNA on two different length scales: individual DNA base pairs and rigid cylinders composed of many base pairs. Our results yield rigorous expressions for the partition functions of these systems, from which equilibrium thermodynamic properties can be obtained. * )

In Cre site-specific recombination, the synaptic intermediate is a recombinase homotetramer containing a pair of DNA target sites. The strand-exchange mechanism proceeds via a Holliday-junction (HJ) intermediate; however, the geometry of the DNA segments in the synapse has remained highly controversial. In particular, all crystallographic structures are consistent with an achiral planar Holliday-junction (HJ) structure, whereas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-handed chiral junction. Here we use the kinetics of loop closure involving closely spaced (131-151 bp), directly repeated loxP sites to investigate the in-aqueo ensemble of conformations for the longest-lived looped DNA intermediate. Fitting the experimental site-spacing dependence of the loop-closure probability, J, to a statistical-mechanical theory of DNA looping provides evidence for substantial out-ofplane HJ distortion. This result unequivocally stands in contrast to the square-planar intermediate geometry determined from crystallographic data for the Cre-loxP system and other int-superfamily recombinases. J measurements carried out with an isomerization-deficient Cre mutant suggest that the apparent geometry of the wild-type complex may result from the temporal averaging of diverse right-handed and achiral structures. Applied to Cre recombinase, and other biological systems, our approach bridges the static pictures provided by crystal structures and the natural dynamics of macromolecules in vivo. This approach thus advances a more comprehensive dynamic analysis of large nucleoprotein structures and their mechanisms.