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

DNA-Topology Simplification by Topoisomerases

The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.

Loop-closure kinetics reveal a stable, right-handed DNA intermediate in Cre recombination

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.

Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA

The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.

Protein/DNA interactions in complex DNA topologies: expect the unexpected

DNA supercoiling results in compacted DNA structures that can bring distal sites into close proximity. It also changes the local structure of the DNA, which can in turn influence the way it is recognised by drugs, other nucleic acids and proteins. Here, we discuss how DNA supercoiling and the formation of complex DNA topologies can affect the thermodynamics of DNA recognition. We then speculate on the implications for transcriptional control and the three-dimensional organisation of the genetic material, using examples from our own simulations and from the literature. We introduce and discuss the concept of coupling between the multiple length-scales associated with hierarchical nuclear structural organisation through DNA supercoiling and topology.

Protein/DNA interactions in complex DNA topologies: expect the unexpected

DNA supercoiling results in compacted DNA structures that can bring distal sites into close proximity. It also changes the local structure of the DNA, which can in turn influence the way it is recognised by drugs, other nucleic acids and proteins. Here, we discuss how DNA supercoiling and the formation of complex DNA topologies can affect the thermodynamics of DNA recognition. We then speculate on the implications for transcriptional control and the three-dimensional organisation of the genetic material, using examples from our own simulations and from the literature. We introduce and discuss the concept of coupling between the multiple length-scales associated with hierarchical nuclear structural organisation through DNA supercoiling and topology.

DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

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 sequence-dependent bends or inhomogeneous bending flexibility. Within the last 10 years 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, kB T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.