Sequence Effects on DNA Entropic Elasticity

DNA stretching experiments are usually interpreted using the worm-like chain model; the persistence length A appearing in the model is then interpreted as the elastic stiffness of the double helix. In fact the persistence length obtained by this method is a combination of bend stiffness and intrinsic bend effects reflecting sequence information, just as at zero stretching force. This observation resolves the discrepancy between the value of A measured in these experiments and the larger ``dynamic persistence length'' measured by other means. On the other hand, the twist persistence length deduced from torsionally-constrained stretching experiments suffers no such correction. Our calculation is very simple and analytic; it applies to DNA and other polymers with weak intrinsic disorder.Comment: LaTeX; postscript available at http://dept.physics.upenn.edu/~nelson/index.shtm

Constraints, Histones, and the 30 Nanometer Spiral

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin.Comment: ReVTeX, 15 pages, 18 figure

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Chromatin: a tunable spring at work inside chromosomes

This paper focuses on mechanical aspects of chromatin biological functioning. Within a basic geometric modeling of the chromatin assembly, we give for the first time the complete set of elastic constants (twist and bend persistence lengths, stretch modulus and twist-stretch coupling constant) of the so-called 30-nm chromatin fiber, in terms of DNA elastic properties and geometric properties of the fiber assembly. The computation naturally embeds the fiber within a current analytical model known as the ``extensible worm-like rope'', allowing a straightforward prediction of the force-extension curves. We show that these elastic constants are strongly sensitive to the linker length, up to 1 bp, or equivalently to its twist, and might locally reach very low values, yielding a highly flexible and extensible domain in the fiber. In particular, the twist-stretch coupling constant, reflecting the chirality of the chromatin fiber, exhibits steep variations and sign changes when the linker length is varied. We argue that this tunable elasticity might be a key feature for chromatin function, for instance in the initiation and regulation of transcription.Comment: 38 pages 15 figure

Conformations of closed DNA

We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structure. The stability of the distorted configurations is assessed, along with the effects of fluctuations on the free energy of the various configurations.Comment: 39 pages in REVTEX with 14 eps figures. Submitted to Phys. Rev. E. This manuscript updates, expands and revises, to a considerable extent, a previously posted manuscript, entitled "Conformations of Circular DNA," which appeared as cond-mat/970104

Modeling DNA Structure, Elasticity and Deformations at the Base-pair Level

We present a generic model for DNA at the base-pair level. We use a variant of the Gay-Berne potential to represent the stacking energy between neighboring base-pairs. The sugar-phosphate backbones are taken into account by semi-rigid harmonic springs with a non-zero spring length. The competition of these two interactions and the introduction of a simple geometrical constraint leads to a stacked right-handed B-DNA-like conformation. The mapping of the presented model to the Marko-Siggia and the Stack-of-Plates model enables us to optimize the free model parameters so as to reproduce the experimentally known observables such as persistence lengths, mean and mean squared base-pair step parameters. For the optimized model parameters we measured the critical force where the transition from B- to S-DNA occurs to be approximately $140{pN}$. We observe an overstretched S-DNA conformation with highly inclined bases that partially preserves the stacking of successive base-pairs.Comment: 15 pages, 25 figures. submitted to PR