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Ralf Metzler

Publications and source records attributed to Ralf Metzler.

At least 199 records · Page 11Linked to original sources
arXiv2006

Breathing dynamics in heteropolymer DNA

While the statistical mechanical description of DNA has a long tradition, renewed interest in DNA melting from a physics perspective is nourished by measurements of the fluctuation dynamics of local denaturation bubbles by single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA breathing) is supposedly crucial for biological functioning during, for instance, transcription initiation and DNA's interaction with selectively single-stranded DNA binding proteins. Motivated by this, we consider the bubble breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master equation and complementary stochastic Gillespie simulations, providing the bubble size and the position of the bubble along the sequence as a function of time. We utilize new experimental data that independently obtain stacking and hydrogen bonding contributions to DNA stability. We calculate the spectrum of relaxation times and the experimentally measurable autocorrelation function of a fluorophore-quencher tagged base-pair, and demonstrate good agreement with fluorescence correlation experiments. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a promoter sequence of the T7 phage. The strong dependence on sequence, temperature and salt concentration for the breathing dynamics of DNA found here points at a good potential for nanosensing applications by utilizing short fluorophore-quencher dressed DNA constructs.

q-bio.BM↗
arXiv2006

Single DNA conformations and biological function

From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications.

physics.bio-ph↗
arXiv2006

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.

cond-mat.stat-mech↗
arXiv2006

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.

cond-mat.stat-mech↗
arXiv2006

Diffusion mechanisms of localised knots along a polymer

We consider the diffusive motion of a localized knot along a linear polymer chain. In particular, we derive the mean diffusion time of the knot before it escapes from the chain once it gets close to one of the chain ends. Self-reptation of the entire chain between either end and the knot position, during which the knot is provided with free volume, leads to an L^3 scaling of diffusion time; for sufficiently long chains, subdiffusion will enhance this time even more. Conversely, we propose local ``breathing'', i.e., local conformational rearrangement inside the knot region (KR) and its immediate neighbourhood, as additional mechanism. The contribution of KR-breathing to the diffusion time scales only quadratically, L^2, speeding up the knot escape considerably and guaranteeing finite knot mobility even for very long chains.

cond-mat.soft↗
arXiv2006

Fractal Dimension and Localization of DNA Knots

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the gyration radius of the adsorbed DNA knot scales with the 3D Flory exponent $ν\approx 0.58$ within error. In (ii), we find $ν\approx 0.66$, a value between the 3D and 2D ($ν=3/4$) exponents, indicating an incomplete 2D relaxation or a different polymer universality class. Compelling evidence is also presented for the localization of the knot crossings in 2D.

cond-mat.soft↗
arXiv2006

Sequence sensitivity of breathing dynamics in heteropolymer DNA

We study the fluctuation dynamics of localized denaturation bubbles in heteropolymer DNA with a master equation and complementary stochastic simulation based on novel DNA stability data. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a biological sequence of the T7 bacteriophage. Quantitative agreement with data from fluorescence correlation spectroscopy (FCS) is demonstrated.

q-bio.BM↗
arXiv2006

DNA bubble dynamics as a quantum Coulomb problem

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We demonstrate that the associated Fokker-Planck equation is equivalent to a Coulomb problem. Below the melting temperature the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential, at the melting temperature the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail, above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

cond-mat.stat-mech↗
arXiv2006

Optimal target search on a fast folding polymer chain with volume exchange

We study the search process of a target on a rapidly folding polymer (`DNA') by an ensemble of particles (`proteins'), whose search combines 1D diffusion along the chain, Levy type diffusion mediated by chain looping, and volume exchange. A rich behavior of the search process is obtained with respect to the physical parameters, in particular, for the optimal search.

cond-mat.soft↗
arXiv2005

First passage time of N excluded volume particles on a line

Motivated by recent single molecule studies of proteins sliding on a DNA molecule, we explore the targeting dynamics of N particles ("proteins") sliding diffusively along a line ("DNA") in search of their target site (specific target sequence). At lower particle densities, one observes an expected reduction of the mean first passage time proportional to 1/N**2, with corrections at higher concentrations. We explicitly take adsorption and desorption effects, to and from the DNA, into account. For this general case, we also consider finite size effects, when the continuum approximation based on the number density of particles, breaks down. Moreover, we address the first passage time problem of a tagged particle diffusing among other particles.

cond-mat.stat-mech↗
arXiv2005

Sensing DNA - DNA as nanosensor: a perspective towards nanobiotechnology

Based on modern single molecule techniques, we devise a number of possible experimental setups to probe local properties of DNA such as the presence of DNA-knots, loops or folds, or to obtain information on the DNA-sequence. Similarly, DNA may be used as a local sensor. Employing single molecule fluorescence methods, we propose to make use of the physics of DNA denaturation nanoregions to find out about the solvent conditions such as ionic strength, presence of binding proteins, etc. By measuring dynamical quantities in particular, rather sensitive nanoprobes may be constructed with contemporary instruments.

cond-mat.soft↗
arXiv2005

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.

cond-mat.soft↗
arXiv2005

Coupled dynamics of DNA-breathing and single-stranded DNA binding proteins

We study the size fluctuations of a local denaturation zone in a DNA molecule in the presence of proteins that selectively bind to single-stranded DNA, based on a (2+1)-dimensional master equation. By tuning the physical parameters we can drive the system from undisturbed bubble fluctuations to full, binding protein-induced denaturation. We determine the effective free energy landscape of the DNA-bubble and explore its relaxation modes.

q-bio.BM↗
arXiv2005

Stochastic approach to DNA breathing dynamics

We propose a stochastic Gillespie scheme to describe the temporal fluctuations of local denaturation zones in double-stranded DNA as a single molecule time series. It is demonstrated that the model recovers the equilibrium properties. We also study measurable dynamical quantities such as the bubble size autocorrelation function. This efficient computational approach will be useful to analyse in detail recent single molecule experiments on clamped homopolymer breathing domains, to probe the parameter values of the underlying Poland-Scheraga model, as well as to design experimental conditions for similar setups.

q-bio.BM↗
arXiv2004

Chaperone assisted translocation

We investigate the translocation of a stiff polymer through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind reversibly to the polymer on both sides of the membrane. A bound chaperone covers one (univalent binding) or many (multivalent binding) binding sites. Assuming that the diffusion of the chaperones is fast compared to the rate of translocation we describe the process by a one-dimensional master equation. We expand previous models by a detailed study of the effective force in the master equation, which is obtained by the appropriate statistical mechanical average over the chaperone states. The dependence of the force on the degree of valency (the number of binding sites occupied by a chaperone) is studied in detail. We obtain finite size corrections (to the thermodynamical expression for the force), which, for univalent binding, can be expressed analytically. We finally investigate the mean velocity for translocation as a function of chaperone binding strength and size. For both univalent and multivalent binding simple results are obtained for the case of a sufficiently long translocating polymer.

cond-mat.stat-mech↗
arXiv2003

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. (A. Mogilner et al., Phys. Lett. {\bf 237}, 297 (1998)), and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

cond-mat.stat-mech↗
arXiv2003

Sensitivity of Phage Lambda upon Variations of the Gibbs Free Energy

We investigate the sensitivity of production rates (activities) of the regulatory proteins CI (repressor) and Cro at the right operator (O_R}) of bacteriophage lambda. The DNA binding energies of CI, Cro, and RNA polymerase are perturbed to check the uncertainty of the activity, due to the experimental error, by means of a computational scattering method according to which the binding energies are simultaneously chosen at random around the literature values, with a width corresponding to the experimental error. In a grand canonical ensemble, with the randomly drawn protein-DNA binding energies as input, we calculate the corresponding activities of the promoters P_RM and P_R. By repeating this procedure we obtain a mean value of the activity that roughly corresponds to wild-type (unperturbed) activity. The standard deviation emerging from this scheme, a measure of the sensitivity due to experimental error, is significant (typically > 20% relative to wild-type activity), but still the promoter activities are sufficiently separated to make the switch feasible. We also suggest a new compact way of presenting repressor and Cro data.

cond-mat.stat-mech↗