Coupling of twist and writhe in short DNA loops

WASP: a software package for correctly characterizing the topological development of ribbon structures

We introduce the Writhe Application Software Package (WASP) which can be used to characterisze the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterization is achieved by the general twist–writhe decomposition of both open and closed ribbons, in particular through a quantity termed the polar writhe. We demonstrate how this decomposition is far more natural and straightforward than artificial closure methods commonly utilized in DNA modelling. In particular, we demonstrate how the decomposition of the polar writhe into local and non-local components distinctly characterizes the local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As example applications, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations, and it is shown that the decomponsition into local and non-local components is particularly important for the detection of plectonemes. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.

Effect of sequence-dependent rigidity on plectoneme localization in dsDNA

We use Monte-Carlo simulations to study the effect of variable rigidity on plectoneme formation and localization in supercoiled double-stranded DNA. We show that the presence of soft sequences increases the number of plectoneme branches and that the edges of the branches tend to be localized at these sequences. We propose an experimental approach to test our results in vitro, and discuss the possible role played by plectoneme localization in the search process of transcription factors for their targets (promoter regions) on the bacterial genome.

On binding of DNA-bending proteins to DNA minicircles

We present a theoretical study of binding of DNA-bending proteins to circular DNA, using computer simulations of the wormlike chain model of DNA. We find that the binding affinity is affected by the bending elasticity and the conformational entropy of the polymer and that while protein adsorption is identical on open and closed long DNA molecules, there is significant enhancement of binding on DNA minicircles, compared to their linear counterparts. We also find that the ratio of the radii of gyration of open and closed chains depends on protein concentration for short DNA molecules. Experimental tests of our predictions are proposed.

Force-free measurements of the conformations of DNA molecules tethered to a wall

Using an optimized combination of tethered particle motion method, total internal reflection, and a gold nanobead, we measured the three-dimensional distribution of the free end of a tethered DNA molecule. The distribution along the axial z direction (perpendicular to the surface) is found to be Rayleigh-like, in agreement with wormlike chain and freely jointed chain simulations. Using these simulations, we show that the presence of the wall increases the correlations between the orientations of neighboring chain segments compared to free DNA. While the measured and the simulated planar (xy) distributions always agree with that of a Gaussian-random-walk (GRW) model, for short DNA lengths (1 μm) studied in our experiment, the corresponding axial (z) distributions deviate from those predicted for a GRW confined to half-space.

Effect of spontaneous twist on DNA minicircles

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.

Entropic elasticity of dilated and contorted idealized circular chains

Thermal energy provides random motion to particles that leads to the well-known entropic force, which favors the clumping of linear and circular molecules. We evaluate the entropic force which resists the radial dilation and subsequent twisting out of plane of circular polymers by developing mechanical models and performing molecular dynamics simulations. We find that dilating a circular chain is analogous to stretching its linear counterpart. We also find that the torque applied to an already dilated ring and the resulting twist out of plane are related by a linear relationship for a wide range of deformed configurations and, using this result, we are able to predict the angular fluctuations of such a macromolecule.

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. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.