The writhe distribution in DNA plasmids as derived from the free energy of supercoiling

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.

A symplectic integration method for elastic filaments

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint-free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin.

Effects of the nucleoid protein HU on the structure, flexibility, and ring-closure properties of DNA deduced from Monte Carlo simulations

The histone-like HU (heat unstable) protein plays a key role in the organization and regulation of the Escherichia coli genome. The nonspecific nature of HU binding to DNA complicates analysis of the mechanism by which the protein contributes to the looping of DNA. Conventional models of the looping of HU-bound duplexes attribute the changes in biophysical properties of DNA brought about by the random binding of protein to changes in the effective parameters of an ideal helical wormlike chain. Here, we introduce a novel Monte Carlo approach to study the effects of nonspecific HU binding on the configurational properties of DNA directly. We randomly decorated segments of an ideal double-helical DNA with HU molecules that induce the bends and other structural distortions of the double helix find in currently available X-ray structures. We find that the presence of HU at levels approximating those found in the cell reduces the persistence length by roughly threefold compared with that of naked DNA. The binding of protein has particularly striking effects on the cyclization properties of short duplexes, altering the dependence of ring closure on chain length in a way that cannot be mimicked by a simple wormlike model and accumulating at higher-than-expected levels on successfully closed chains. Moreover, the uptake of protein on small minicircles depends on chain length, taking advantage of the HU-induced deformations of DNA structure to facilitate ligation. Circular duplexes with bound HU show much greater propensity than protein-free DNA to exist as negatively supercoiled topoisomers, suggesting a potential role of HU in organizing the bacterial nucleoid. The local bending and undertwisting of DNA by HU, in combination with the number of bound proteins, provide a structural rationale for the condensation of DNA and the observed expression levels of reporter genes in vivo.

Thermal fluctuations of small rings of intrinsically helical DNA treated like an elastic rod

It is shown that the writhe distribution in a collection of thermally fluctuating rings formed from intrinsically helical DNA treated like an elastic rod can be determined completely from a knowledge of the dependence of the configuration integral on the intrinsic geometric torsion of the rods. When the length of the rods is of the order of the persistence length or less, the configuration integral can be expressed in terms of the frequencies of the normal modes of the rings, and so these torsion-dependent frequencies then become the quantities of interest. The nature of the normal modes of rings formed from intrinsically helical elastic rods, as deduced from the equations of motion in the Kirchhoff-Clebsch theory of the dynamics of elastic rods, is described. Examples of computed writhe distributions are given. The observed broadening of the writhe distribution as the intrinsic curvature of the rods is increased is shown to be related to the stability properties of the circular equilibrium configuration of the elastic rods. These results thus imply that thermal fluctuations in small rings of intrinsically curved DNA will be more pronounced than in rings of the same size formed from intrinsically straight DNA.

Fluctuating elastic rings: statics and dynamics

We study the effects of thermal fluctuations on elastic rings. Analytical expressions are derived for correlation functions of Euler angles, mean-square distance between points on the ring contour, radius of gyration, and probability distribution of writhe fluctuations. Since fluctuation amplitudes diverge in the limit of vanishing twist rigidity, twist elasticity is essential for the description of fluctuating rings. We discover a crossover from a small scale regime in which the filament behaves as a straight rod, to a large scale regime in which spontaneous curvature is important and twist rigidity affects the spatial configurations of the ring. The fluctuation-dissipation relation between correlation functions of Euler angles and response functions, is used to study the deformation of the ring by external forces. The effects of inertia and dissipation on the relaxation of temporal correlations of writhe fluctuations, are analyzed using Langevin dynamics.