Blinking statistics of a molecular beacon triggered by end-denaturation of DNA

We use a master equation approach based on the Poland-Scheraga free energy for DNA denaturation to investigate the (un)zipping dynamics of a denaturation wedge in a stretch of DNA, that is clamped at one end. In particular, we quantify the blinking dynamics of a fluorophore-quencher pair mounted within the denaturation wedge. We also study the behavioural changes in the presence of proteins, that selectively bind to single-stranded DNA. We show that such a setup could be well-suited as an easy-to-implement nanodevice for sensing environmental conditions in small volumes.Comment: 14 pages, 5 figures, LaTeX, IOP style. Accepted to J Phys Cond Mat special issue on diffusio

A model for melting of confined DNA

When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this "melting" transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte-Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behaviour and that the effect of confinement is stronger than in the ideal case.Comment: 5 pages, 4 figures, supplementary materia

Electromagnetic response of a dipole-coupled ellipsoidal bilayer

©2006 The American Physical Society. This paper was selected for the April 1, 2004 issue of Virtual Journal of Biological Physics Research, available at http://www.vjbio.org .We derive an expression for the polarizability of an ellipsoidally shaped cell-like structure at field frequencies where membrane molecular resonances ~vibrational and electronic! are important. We first present analytical results for the dielectric function of a flat, dipole coupled, bilayer consisting of molecules with one prominent resonance frequency. Due to the nature of the dipole coupling the dielectric function is different for the field being parallel or perpendicular to the bilayer normal with two new resonance frequencies v5v ˜ 0i and v5v ˜ 0' . We then combine this anisotropic bilayer dielectric function with the analytical solution of Gauss equation for an ellipsoid with an anisotropic coating ~the coating dielectric function being different parallel and perpendicular to the coating normal! in order to find the polarizability of an ellipsoidal bilayer membrane. In particular, we find that for a thin-walled ~compared to the size of the cell! membrane the resonance frequencies of the polarizability are the same as for a flat bilayer ~independent of the cell shape!. However, our analytic result for the geometric weights for the oscillator strengths is sensitive to the shape; the geometric weight for the v5v ˜ 0' (v5v ˜ 0i) peak is largest when the external field is along the largest ~smallest! axis. The geometric weights are shown to be constrained by three sum rules

Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate q kappa for binding (with a binding strength kappa); except for the case of no binding kappa=0 the presence of the chaperones give rise to an effective force that drives the translocation process. Based on a (2+1) variate master equation, we study in detail the coupled dynamics of diffusive translocation and (partial) rectification by the binding proteins. In particular, we calculate the mean translocation time as a function of the various physical parameters.Comment: 22 pages, 5 figures, IOP styl

Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vicious walkers in opposite potentials.Comment: 7 pages, 4 figure

Fluctuations in Polymer Translocation

We investigate a model of chaperone-assisted polymer translocation through a nanopore in a membrane. Translocation is driven by irreversible random sequential absorption of chaperone proteins that bind to the polymer on one side of the membrane. The proteins are larger than the pore and hence the backward motion of the polymer is inhibited. This mechanism rectifies Brownian fluctuations and results in an effective force that drags the polymer in a preferred direction. The translocated polymer undergoes an effective biased random walk and we compute the corresponding diffusion constant. Our methods allow us to determine the large deviation function which, in addition to velocity and diffusion constant, contains the entire statistics of the translocated length.Comment: 20 pages, 6 figure

Fluctuations of a driven membrane in an electrolyte

We develop a model for a driven cell- or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific ion-conducting units (representing pumps, channels or natural pores). We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain the membrane equation of motion within Stokes hydrodynamics. At steady state, the applied field causes an accumulation of charges close to the membrane, which, similarly to the equilibrium case, can be described with renormalized membrane tension and bending modulus. However, as opposed to the equilibrium situation, we find new terms in the membrane equation of motion, which arise specifically in the out-of-equilibrium case. We show that these terms lead in certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let

Exact steady-state velocity of ratchets driven by random sequential adsorption

We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratcheted motion. We also define and compare the relative efficiencies of ratcheting by deposition of particles with different sizes and we describe an associated "zone-refinement" process.Comment: 11 pages, 4 figures New asymptotic result for low chaperone density added. Exact translocation velocity is proportional to (chaperone density)^(1/3

Extension of nano-confined DNA: quantitative comparison between experiment and theory

The extension of DNA confined to nanochannels has been studied intensively and in detail. Yet quantitative comparisons between experiments and model calculations are difficult because most theoretical predictions involve undetermined prefactors, and because the model parameters (contour length, Kuhn length, effective width) are difficult to compute reliably, leading to substantial uncertainties. Here we use a recent asymptotically exact theory for the DNA extension in the "extended de Gennes regime" that allows us to compare experimental results with theory. For this purpose we performed new experiments, measuring the mean DNA extension and its standard deviation while varying the channel geometry, dye intercalation ratio, and ionic buffer strength. The experimental results agree very well with theory at high ionic strengths, indicating that the model parameters are reliable. At low ionic strengths the agreement is less good. We discuss possible reasons. Our approach allows, in principle, to measure the Kuhn length and effective width of a single DNA molecule and more generally of semiflexible polymers in solution.Comment: Revised version, 6 pages, 2 figures, 1 table, supplementary materia

The prolate-to-oblate shape transition of phospholipid vesicles in response to frequency variation of an AC electric field can be explained by the dielectric anisotropy of a phospholipid bilayer

The external electric field deforms flaccid phospholipid vesicles into spheroidal bodies, with the rotational axis aligned with its direction. Deformation is frequency dependent: in the low frequency range (~ 1 kHz), the deformation is typically prolate, while increasing the frequency to the 10 kHz range changes the deformation to oblate. We attempt to explain this behaviour with a theoretical model, based on the minimization of the total free energy of the vesicle. The energy terms taken into account include the membrane bending energy and the energy of the electric field. The latter is calculated from the electric field via the Maxwell stress tensor, where the membrane is modelled as anisotropic lossy dielectric. Vesicle deformation in response to varying frequency is calculated numerically. Using a series expansion, we also derive a simplified expression for the deformation, which retains the frequency dependence of the exact expression and may provide a better substitute for the series expansion used by Winterhalter and Helfrich, which was found to be valid only in the limit of low frequencies. The model with the anisotropic membrane permittivity imposes two constraints on the values of material constants: tangential component of dielectric permittivity tensor of the phospholipid membrane must exceed its radial component by approximately a factor of 3; and the membrane conductivity has to be relatively high, approximately one tenth of the conductivity of the external aqueous medium.Comment: 17 pages, 6 figures; accepted for publication in J. Phys.: Condens. Matte