Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids

Dynamics of elastic rods in perfect friction contact

One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range potentials. We study the dynamics of elastic rods with perfect rolling contact which is physically relevant for rods with a rough surface. Such dynamics cannot be described by the introduction of any kind of potential. We show that, surprisingly, the presence of rolling contact in rod dynamics leads to highly complex behavior even for the evolution of small disturbances.

Elasticity and electrostatics of plectonemic DNA

We present a self-contained theory for the mechanical response of DNA in single molecule experiments. Our model is based on a one-dimensional continuum description of the DNA molecule and accounts both for its elasticity and for DNA-DNA electrostatic interactions. We consider the classical loading geometry used in experiments where one end of the molecule is attached to a substrate and the other one is pulled by a tensile force and twisted by a given number of turns. We focus on configurations relevant to the limit of a large number of turns, which are made up of two phases, one with linear DNA and the other one with superhelical DNA. The model takes into account thermal fluctuations in the linear phase and electrostatic interactions in the superhelical phase. The values of the torsional stress, of the supercoiling radius and angle, and key features of the experimental extension-rotation curves, namely the slope of the linear region and thermal buckling threshold, are predicted. They are found in good agreement with experimental data.

Modeling DNA loops using the theory of elasticity

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

Implications of the dependence of the elastic properties of DNA on nucleotide sequence

Recent advances in structural biochemistry have provided evidence that not only the geometric properties but also the elastic moduli of duplex DNA are strongly dependent on nucleotide sequence in a way that is not accounted for by classical rod models of the Kirchhoff type. A theory of sequence-dependent DNA elasticity is employed here to calculate the dependence of the equilibrium configurations of circular DNA on the binding of ligands that can induce changes in intrinsic twist at a single base-pair step. Calculations are presented of the influence on configurations of the assumed values and distribution along the DNA of intrinsic roll and twist and a modulus coupling roll to twist. Among the results obtained are the following. For minicircles formed from intrinsically straight DNA, the distribution of roll-twist coupling strongly affects the dependence of the total elastic energy Psi on the amount alpha of imposed untwisting, and that dependence can be far from quadratic. (In fact, for a periodic distribution of roll-twist coupling with a period equal to the intrinsic helical repeat length, Psi can be essentially independent of alpha for -90 degrees < alpha <90 degrees.) When the minicircle is homogeneous and without roll-twist coupling, but with uniform positive intrinsic roll, the point at which Psi attains its minimum value shifts towards negative values of alpha. It is remarked that there are cases in which one can relate graphs of Psi versus alpha to the 'effective values' of bending and twisting moduli and helical repeat length obtained from measurements of equilibrium distributions of topoisomers and probabilities of ring closure. For a minicircle formed from DNA that has an 'S' shape when stress-free, the graphs of Psi versus alpha have maxima at alpha = 0. As the binding of a twisting agent to such a minicircle results in a net decrease in Psi, the affinity of the twisting agent for binding to the minicircle is greater than its affinity for binding to unconstrained DNA with the same sequence.

Nucleosome conformational flexibility and implications for chromatin dynamics

The active role of chromatin in the regulation of gene activity seems to imply a conformational flexibility of the basic chromatin structural unit, the nucleosome. This review is devoted to our recent results pertaining to this subject, using an original approach based on the topology of single particles reconstituted on DNA minicircles, combined with their theoretical simulation. Three types of chromatin particles have been studied so far: a subnucleosome, that is, the (H3-H4)(2) histone tetramer-containing particle, now known as the tetrasome; the nucleosome; and the linker histone H5/H1-bearing nucleosome (the chromatosome). All the particles were found to exist in two to three conformational states, which differ by their topological and mechanical properties. Our approach unveiled the molecular mechanisms of nucleosome conformational dynamics and will help to understand its functional relevance. A most surprising conclusion of the work was perhaps that DNA overall flexibility increases considerably upon particle formation, which might indeed be a requirement of genome function.

An introduction to the mechanics of DNA

This article gives an overview of recent research on the mechanical properties and spatial deformations of the DNA molecule. Globally the molecule behaves like a uniform elastic rod, and its twisting and writhing govern its compaction and packaging within a cell. Meanwhile high mechanical stresses can induce structural transitions of DNA giving, for example, a phase diagram in the space of the applied tension and torque. Locally, the mechanical properties vary according to the local sequence organization. These variations play a vital role in the biological functioning of the molecule.