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.

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.

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.

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.

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.

Denaturation transition of stretched DNA.

In the last two decades, single-molecule force measurements using optical and magnetic tweezers and atomic force spectroscopy have dramatically expanded our knowledge of nucleic acids and proteins. These techniques characterize the force on a biomolecule required to produce a given molecular extension. When stretching long DNA molecules, the observed force-extension relationship exhibits a characteristic plateau at approximately 65 pN where the DNA may be extended to almost twice its B-DNA length with almost no increase in force.

The thermodynamics of DNA loop formation, from J to Z.

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.

Non-equilibrium Casimir force between vibrating plates.

We study the fluctuation-induced, time-dependent force between two plates confining a correlated fluid which is driven out of equilibrium mechanically by harmonic vibrations of one of the plates. For a purely relaxational dynamics of the fluid we calculate the fluctuation-induced force generated by the vibrating plate on the plate at rest. The time-dependence of this force is characterized by a positive lag time with respect to the driving.

Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity.

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight.

Single DNA denaturation and bubble dynamics.

While the Watson-Crick double-strand is the thermodynamically stable state of DNA in a wide range of temperature and salt conditions, even at physiological conditions local denaturation bubbles may open up spontaneously due to thermal activation. By raising the ambient temperature, titration, or by external forces in single molecule setups bubbles proliferate until full denaturation of the DNA occurs. Based on the Poland-Scheraga model we investigate both the equilibrium transition of DNA denaturation and the dynamics of the denaturation bubbles with respect to recent single DNA chain experiments for situations below, at, and above the denaturation transition.

Kinetics and thermodynamics of salt-dependent T7 gene 2.5 protein binding to single- and double-stranded DNA.

Bacteriophage T7 gene 2.5 protein (gp2.5) is a single-stranded DNA (ssDNA)-binding protein that has essential roles in DNA replication, recombination and repair.

Denaturation transition of stretched DNA.

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent c, for which we find the new value c = 4 nu-1/2 such that the transition is second order with c = 1.

Probing molecular free energy landscapes by periodic loading.

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular, for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's relation for obtaining equilibrium quantities from nonequilibrium data.

Entropy loss in long-distance DNA looping.

The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow us to obtain a fast estimate for the entropy loss for a given configuration. Numerical values obtained for some examples suggest that the entropy loss encountered in loop closure in typical genetic switches may become a relevant factor in comparison to both k(B)T and typical bond energies in biopolymers, which has to be overcome by the released bond energy between the looping contact sites.

Tightness of slip-linked polymer chains.

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot).

Correlation functions near modulated and rough surfaces.

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near surface correlations can be measured by scattering probes.

Equilibrium shapes of flat knots.

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop.