32 research outputs found
Statistical mechanics of triangulated ribbons
We use computer simulations and scaling arguments to investigate statistical
and structural properties of a semiflexible ribbon composed of isosceles
triangles. We study two different models, one where the bending energy is
calculated from the angles between the normal vectors of adjacent triangles,
the second where the edges are viewed as semiflexible polymers so that the
bending energy is related to the angles between the tangent vectors of
next-nearest neighbor triangles. The first model can be solved exactly whereas
the second is more involved. It was recently introduced by Liverpool and
Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a
model for double-stranded biopolymers such as DNA. Comparing observables such
as the autocorrelation functions of the tangent vectors and the bond-director
field, the probability distribution functions of the end-to-end distance, and
the mean squared twist we confirm the existence of local twist correlation, but
find no indications for other predicted features such as twist-stretch
coupling, kinks, or oscillations in the autocorrelation function of the
bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio
Pulling a polymer out of a potential well and the mechanical unzipping of DNA
Motivated by the experiments on DNA under torsion, we consider the problem of
pulling a polymer out of a potential well by a force applied to one of its
ends. If the force is less than a critical value, then the process is activated
and has an activation energy proportinal to the length of the chain. Above this
critical value, the process is barrierless and will occur spontaneously. We use
the Rouse model for the description of the dynamics of the peeling out and
study the average behaviour of the chain, by replacing the random noise by its
mean. The resultant mean-field equation is a nonlinear diffusion equation and
hence rather difficult to analyze. We use physical arguments to convert this in
to a moving boundary value problem, which can then be solved exactly. The
result is that the time required to pull out a polymer of segments
scales like . For models other than the Rouse, we argue that Comment: 11 pages, 6 figures. To appear in PhysicalReview
Micromechanics of Single Supercoiled DNA Molecules
Abstract. The theory of the mechanical response of single DNA molecules un-der stretching and twisting stresses is reviewed. Using established results for the the semiflexible polymer including the effect of torsional stress, and for the free energy of plectonemic supercoils, a theory of coexisting plectonemic and extended DNA is con-structed and shown to produce phenomena observed experimentally. Analytical results for DNA extension and torque are presented, and effects of anharmonicities in the plec-tonemic free energy are described. An application of the theory to the problem of torsional-stress-induced cruciform extrusion is also discussed. Key words. DNA, molecular biology, statistical mechanics, polymer physics. AMS(MOS) subject classifications. 82D60, 92C05, 92C40
Conformations of Linear DNA
We examine the conformations of a model for under- and overwound DNA. The
molecule is represented as a cylindrically symmetric elastic string subjected
to a stretching force and to constraints corresponding to a specification of
the link number. We derive a fundamental relation between the Euler angles that
describe the curve and the topological linking number. Analytical expressions
for the spatial configurations of the molecule in the infinite- length limit
were obtained. A unique configuraion minimizes the energy for a given set of
physical conditions. An elastic model incorporating thermal fluctuations
provides excellent agreement with experimental results on the plectonemic
transition.Comment: 5 pages, RevTeX; 6 postscript 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
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
Tops and Writhing DNA
The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.Comment: 17 pages two figure
Statistical mechanics of RNA folding: a lattice approach
We propose a lattice model for RNA based on a self-interacting two-tolerant
trail. Self-avoidance and elements of tertiary structure are taken into
account. We investigate a simple version of the model in which the native state
of RNA consists of just one hairpin. Using exact arguments and Monte Carlo
simulations we determine the phase diagram for this case. We show that the
denaturation transition is first order and can either occur directly or through
an intermediate molten phase.Comment: 8 pages, 9 figure
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 . 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
The unstructured linker arms of MutL enable GATC site incision beyond roadblocks during initiation of DNA mismatch repair
DNA mismatch repair (MMR) maintains genome stability through repair of DNA replication errors. In Escherichia coli, initiation of MMR involves recognition of the mismatch by MutS, recruitment of MutL, activation of endonuclease MutH and DNA strand incision at a hemimethylated GATC site. Here, we studied the mechanism of communication that couples mismatch recognition to daughter strand incision. We investigated the effect of catalytically-deficient Cas9 as well as stalled RNA polymerase as roadblocks placed on DNA in between the mismatch and GATC site in ensemble and single molecule nanomanipulation incision assays. The MMR proteins were observed to incise GATC sites beyond a roadblock, albeit with reduced efficiency. This residual incision is completely abolished upon shortening the disordered linker regions of MutL. These results indicate that roadblock bypass can be fully attributed to the long, disordered linker regions in MutL and establish that communication during MMR initiation occurs along the DNA backbone