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Biomedical subjects

Ralf Metzler

Publications and source records attributed to Ralf Metzler.

At least 19 recordsLinked to original sources
PubMed2006

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 is demonstrated.

Bacteriophage T7↗
PubMed2005

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, Lévy 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.

Journal Article↗
PubMed2005

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 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 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.

Binding Sites↗
PubMed2005

Coupled dynamics of DNA breathing and of proteins that selectively bind to single-stranded DNA.

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.

Binding Sites↗
PubMed2005

Natural cutoff in Lévy flights caused by dissipative nonlinearity.

Lévy flight models are often used to describe stochastic processes in complex systems. However, due to the occurrence of diverging position and/or velocity fluctuations Lévy flights are physically problematic if describing the dynamics of a particle of finite mass. Here we show that the velocity distribution of a random walker subject to Lévy noise can be regularized by nonlinear friction, leading to a natural cutoff in the velocity distribution and finite velocity variance.

Journal Article↗
PubMed2005

Target search of N sliding proteins on a DNA.

At low to moderate ambient salt concentrations, DNA-binding proteins bind relatively tightly to DNA, and only very rarely detach. Intersegmental transfer due to DNA-looping can be excluded by applying an external pulling force to the DNA molecule. Under such conditions, we explore the targeting dynamics of N proteins sliding diffusively along DNA in search of their specific target sequence. At lower densities of binding proteins, we find a reduction of the characteristic search time proportional to N(-2), with corrections at higher concentrations. Rates for detachment and attachment of binding proteins are incorporated in the model. Our findings are in agreement with recent single molecule studies in the presence of bacteriophage T4 gene 32 protein for which the unbinding rate is much lower than the specific binding rate.

Binding Sites↗
PubMed2004

Nonspecific binding of the OR repressors CI and Cro of bacteriophage lambda.

We estimate the Gibbs free energy for nonspecific binding (DeltaGNSB) to the Escherichia coli DNA for two regulatory proteins of the lambda phage, CI and Cro. By means of a statistical-mechanical approach, we calculate the cI and cro activities associated with the operator OR of an introduced lambda phage genome (prophage). In this statistical model we apply in vitro-measured binding free energies to fit in vivo experimental data for cI and cro activities, respectively, where DeltaGNSB is introduced as a free (fitting) parameter. Without nonspecific binding included in the model, the quality of the description is fairly poor, whereas data are nicely correlating with our model with nonspecific binding included over the entire data range. The obtained values of DeltaGNSB are -4.1+/-0.9 kcal/mol, for CI, and -4.2+/-0.8 kcal/mol, for Cro. In particular, in a lysogen (approximately 250 CI monomers per cell) we conclude that 86% of the total CI in the cell is nonspecifically bound, leaving on average around 10 CI dimers freely available in the E. coli cytoplasma. These findings corroborate the view that due to low free cellular particle numbers a dynamical analysis of genetic regulation at OR and comparable systems should include a stochastic component. In addition, we perform a stability analysis of the OR system in the presence of nonspecific binding.

Bacteriophage lambda↗
PubMed2004

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. [Phys. Lett. A 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.

Adenosine Triphosphate↗
PubMed2004

In vivo non-specific binding of lambda CI and Cro repressors is significant.

We propose a thermodynamic model that includes the non-specific binding of the lambda phage regulatory proteins CI and Cro. By fitting the model to experimental in vivo data on activities of the two promoters P(RM) and P(R) versus concentration, we estimate the free energy upon non-specific binding to be -4.1+/-0.9 kcal/mol for CI and -4.2+/-0.8 kcal/mol for Cro. For concentrations >100 nM of CI or Cro, we find that >50% of these proteins are non-specifically bound. In particular, in a lysogen (approximately 250 CI monomeric equivalents per cell) nearly 90% of CI is non-specifically bound.

Bacteriophage lambda↗
PubMed2004

Helical packaging of semiflexible polymers in bacteriophages.

We investigate multilayered helical packaging of double-stranded DNA, or of a general polymer chain with persistence length lb, into an ideal, inert cylindrical container, reaching densities slightly below close packaging. We calculate the free energy as a function of the packaged length, based on the energies for bending, twisting, the suffered entropy loss, and the electrostatic energy in a Debye-Hückel model. In the absence of charges on the packaged polymer, a critical packaging force can be determined, similar to the mechanism involved in DNA unzipping models. When charges are taken into consideration, in the final packaging state the charges which are chemically distant become geometrically close, and therefore a steep rise is seen in the free energy. We argue that due to the extremely ordered and almost closely packaged final state the actual packaging geometry does not influence the behaviour of the free energy, pointing towards a certain universality of this state of the polymer. Our findings are compared to a recent simulations study, showing that the model is sensitive to the screening length.

Bacteriophage lambda↗
PubMed2004

Sensitivity of OR in phage lambda.

We investigate the sensitivity of the right operator in bacteriophage lambda. In particular, the system is probed in the three different regulatory protein concentration-regimes: 1), lysogen (CI dominates); 2), during induction (CI and Cro at comparable concentrations); and 3), after induction (Cro dominates). Systematic perturbations of the protein-operator binding energies show in a lysogen that the activity (production rate) at promoter PRM is robust to variations, in contrast to PR, where the sensitivity is high. Both promoters, however, show large sensitivity in regimes 2 and 3. In all regimes we identify several suppressors, meaning that for a given large perturbation (+/-2 kcal/mol) of one binding energy, there exist compensating perturbation(s) that restore the wild-type activity.

Bacteriophage lambda↗
PubMed2004

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.

Binding Sites↗
PubMed2003

Bifurcation, bimodality, and finite variance in confined Lévy flights.

We investigate the statistical behavior of Lévy flights confined in a symmetric, quartic potential well U(x) proportional, variant x(4). At stationarity, the probability density function features a distinct bimodal shape and decays with power-law tails which are steep enough to give rise to a finite variance, in contrast to free Lévy flights. From a delta-initial condition, a bifurcation of the unimodal state is observed at t(c)>0. The nonlinear oscillator with potential U(x)=ax(2)/2+bx(4)/4, a,b>0, shows a crossover from unimodal to bimodal behavior at stationarity, depending on the ratio a/b.

Journal Article↗
PubMed2003

Towards deterministic equations for Lévy walks: the fractional material derivative.

Lévy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Lévy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Lévy walks, in which the fractional equivalent of the material derivative occurs. Our approach is expected to be useful for the dynamical formulation of Lévy walks in an external force field or in phase space, for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited.

Journal Article↗
PubMed2003

Entropy loss in long-distance DNA looping.

The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow us to obtain a fast estimate for the entropy loss for a given configuration. Numerical values obtained for some examples suggest that the entropy loss encountered in loop closure in typical genetic switches may become a relevant factor in comparison to both k(B)T and typical bond energies in biopolymers, which has to be overcome by the released bond energy between the looping contact sites.

Binding Sites↗