Biomedical subjects

Erwin Frey

Publications and source records attributed to Erwin Frey.

At least 19 recordsLinked to original sources

PubMed2006

Dynamics of semiflexible polymers in a flow field.

We present a method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments, we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.

Biopolymers↗

PubMed2006

Entropic forces generated by grafted semiflexible polymers.

The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, where the persistence length of the polymer is larger than its contour length, we find that the entropic force shows scaling behavior. We identify the characteristic length scales and the explicit form of the scaling functions. In certain asymptotic regimes, we give simple analytical expressions which describe the full results to a very high numerical accuracy. Depending on the constraints imposed on the transverse fluctuations of the filament, there are characteristic differences in the functional form of the entropic forces. In a two-dimensional geometry, the entropic force exhibits a marked peak.

Journal Article↗

PubMed2006

Driven lattice gas of dimers coupled to a bulk reservoir.

We investigate the nonequilibrium steady state of a one-dimensional (1D) lattice gas of dimers. The dynamics is described by a totally asymmetric exclusion process (TASEP) supplemented by attachment and detachment processes, mimicking chemical equilibrium of the 1D driven transport with the bulk reservoir. The steady-state phase diagram and current and density profiles are calculated using both a refined mean-field theory and extensive stochastic simulations. As a consequence of the on-off kinetics, a phase coexistence region arises intervening between low and high density phases such that the discontinuous transition line of the TASEP splits into two continuous ones. The results of the mean-field theory and simulations are found to coincide. We show that the physical picture obtained in the corresponding lattice gas model with monomers is robust, in the sense that the phase diagram changes quantitatively, but the topology remains unaltered. The mechanism for phase separation is identified as generic for a wide class of driven 1D lattice gases.

Computer Simulation↗

PubMed2006

Bottleneck-induced transitions in a minimal model for intracellular transport.

We consider the influence of disorder on the nonequilibrium steady state of a minimal model for intracellular transport. In this model particles move unidirectionally according to the totally asymmetric exclusion process (TASEP) and are coupled to a bulk reservoir by Langmuir kinetics. Our discussion focuses on localized point defects acting as a bottleneck for the particle transport. Combining analytic methods and numerical simulations, we identify a rich phase behavior as a function of the defect strength. Our analytical approach relies on an effective mean-field theory obtained by splitting the lattice into two subsystems, which are effectively connected exploiting the local current conservation. Introducing the key concept of a carrying capacity, the maximal current that can flow through the bulk of the system (including the defect), we discriminate between the cases where the defect is irrelevant and those where it acts as a bottleneck and induces various novel phases (called bottleneck phases). Contrary to the simple TASEP in the presence of inhomogeneities, many scenarios emerge and translate into rich underlying phase diagrams, the topological properties of which are discussed.

Biological Transport↗

PubMed2006

Floppy modes and nonaffine deformations in random fiber networks.

We study the elasticity of random fiber networks. Starting from a microscopic picture of the nonaffine deformation fields, we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory. By relating nonaffinity to the low-energy excitations of the network ("floppy modes"), we achieve a detailed characterization of the nonaffine deformations present in fibrous networks.

Journal Article↗

PubMed2006

Bulk-driven nonequilibrium phase transitions in a mesoscopic ring.

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte Carlo simulations to characterize the emerging nonequilibrium steady states. Monte Carlo simulations reveal interesting correlation effects that we explain phenomenologically.

Journal Article↗

PubMed2006

Actin-binding proteins sensitively mediate F-actin bundle stiffness.

Bundles of filamentous actin (F-actin) form primary structural components of a broad range of cytoskeletal processes including filopodia, sensory hair cell bristles and microvilli. Actin-binding proteins (ABPs) allow the cell to tailor the dimensions and mechanical properties of the bundles to suit specific biological functions. Therefore, it is important to obtain quantitative knowledge on the effect of ABPs on the mechanical properties of F-actin bundles. Here we measure the bending stiffness of F-actin bundles crosslinked by three ABPs that are ubiquitous in eukaryotes. We observe distinct regimes of bundle bending stiffness that differ by orders of magnitude depending on ABP type, concentration and bundle size. The behaviour observed experimentally is reproduced quantitatively by a molecular-based mechanical model in which ABP shearing competes with F-actin extension/compression. Our results shed new light on the biomechanical function of ABPs and demonstrate how single-molecule properties determine mesoscopic behaviour. The bending mechanics of F-actin fibre bundles are general and have implications for cytoskeletal mechanics and for the rational design of functional materials.

Actins↗

PubMed2006

Exclusion processes with internal states.

We introduce driven exclusion processes with internal states that serve as generic transport models in various contexts, ranging from molecular or vehicular traffic on parallel lanes to spintronics. The ensuing nonequilibrium steady states are controllable by boundary as well as bulk rates. A striking polarization phenomenon accompanied by domain wall motion and delocalization is discovered within a mesoscopic scaling. We quantify this observation within an analytic description providing exact phase diagrams. Our results are confirmed by stochastic simulations.

Journal Article↗

PubMed2006

Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length.

Microtubules are hollow cylindrical structures that constitute one of the three major classes of cytoskeletal filaments. On the mesoscopic length scale of a cell, their material properties are characterized by a single stiffness parameter, the persistence length l(p). Its value, in general, depends on the microscopic interactions between the constituent tubulin dimers and the architecture of the microtubule. Here, we use single-particle tracking methods combined with a fluctuation analysis to systematically study the dependence of l(p) on the total filament length L. Microtubules are grafted to a substrate with one end free to fluctuate in three dimensions. A fluorescent bead is attached proximally to the free tip and is used to record the thermal fluctuations of the microtubule's end. The position distribution functions obtained with this assay allow the precise measurement of l(p) for microtubules of different contour length L. Upon varying L between 2.6 and 47.5 mum, we find a systematic increase of l(p) from 110 to 5,035 mum. At the same time we verify that, for a given filament length, the persistence length is constant over the filament within the experimental accuracy. We interpret this length dependence as a consequence of a nonnegligible shear deflection determined by subnanometer relative displacement of adjacent protofilaments. Our results may shine new light on the function of microtubules as sophisticated nanometer-sized molecular machines and give a unified explanation of seemingly uncorrelated spreading of microtubules' stiffness previously reported in literature.

Animals↗

PubMed2006

Localization transition of the three-dimensional lorentz model and continuum percolation.

The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation theory and obtain an excellent matching of the critical density and exponents. Within a dynamic scaling ansatz incorporating two divergent length scales we achieve data collapse for the mean-square displacements and identify the leading corrections to scaling. We provide evidence for a divergent non-Gaussian parameter close to the transition.

Journal Article↗

PubMed2006

Stiff polymers, foams, and fiber networks.

We study the elasticity of fibrous materials composed of generalized stiff polymers. It is shown that, in contrast to cellular foam-like structures, affine strain fields are generically unstable. Instead, a subtle interplay between the architecture of the network and the elastic properties of its building blocks leads to intriguing mechanical properties with intermediate asymptotic scaling regimes. We present exhaustive numerical studies based on a finite element method complemented by scaling arguments.

Journal Article↗

PubMed2005

Renewal processes and fluctuation analysis of molecular motor stepping.

We present a systematic method of analysis of experiments performed with single motor proteins. The use of such a method should allow a more detailed description of the motor's chemical cycle through the precise fitting of the experimental data. We model the dynamics of a processive or rotary molecular motor using a renewal process, in line with the work initiated by Svoboda, Mitra and Block. We apply a functional technique to compute different types of multiple-time correlation function of the renewal process, which have applications to bead-assay experiments performed both with processive molecular motors, such as myosin V and kinesin, and rotary motors, such as F1-ATPase.

Kinesins↗

PubMed2005

Dynamic correlation functions and Boltzmann-Langevin approach for driven one-dimensional lattice gas.

We study the dynamics of the totally asymmetric exclusion process with open boundaries by phenomenological theories complemented by extensive Monte Carlo simulations. Upon combining domain wall theory with a kinetic approach known as Boltzmann-Langevin theory we are able to give a complete qualitative picture of the dynamics in the low- and high-density regimes and at the corresponding phase boundary. At the coexistence line between high- and low-density phases we observe a time scale separation between local density fluctuations and collective domain wall motion, which are well accounted for by the Boltzmann-Langevin and domain wall theory, respectively. We present Monte Carlo data for the correlation functions and power spectra in the full parameter range of the model.

Journal Article↗

PubMed2005

Statics and dynamics of single DNA molecules confined in nanochannels.

The successful design of nanofluidic devices for the manipulation of biopolymers requires an understanding of how the predictions of soft condensed matter physics scale with device dimensions. Here we present measurements of DNA extended in nanochannels and show that below a critical width roughly twice the persistence length there is a crossover in the polymer physics.

Bacteriophage lambda↗

PubMed2005

Propagation and relaxation of tension in stiff polymers.

We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches, etc.) that can be represented as sudden changes of ambient/boundary conditions. The theory relies on a comprehensive analysis of the nonequilibrium propagation and relaxation of backbone stresses in a wormlike chain. We recover and substantially extend previous results based on heuristic arguments. New experimental implications are pointed out.

Journal Article↗

PubMed2004

Internal motility in stiffening actin-myosin networks.

We present a study on filamentous actin solutions containing heavy meromyosin subfragments of myosin II motor molecules. We focus on the viscoelastic phase behavior and internal dynamics of such networks during adenosine-triphosphate depletion. By combining microrheology and fluorescence microscopy, we observed a sol-gel transition accompanied by a sudden onset of directed filament motion. We interpret the sol-gel transition in terms of myosin II enzymology, and suggest a "zipping" mechanism to explain the filament motion in the vicinity of the sol-gel transition.

Actins↗

PubMed2004

Linear response of a grafted semiflexible polymer to a uniform force field.

We use the wormlike chain model to analytically calculate the linear response of a grafted semiflexible polymer to a uniform force field. The result is a function of the bending stiffness, the temperature, the total contour length, and the orientation of the field with respect to that of the grafted end. We also study the linear response of a wormlike chain with a periodic alternating sequence of positive and negative charges. This can be considered as a model for a polyampholyte with intrinsic bending stiffness and negligible intramolecular interactions. We show how the finite intrinsic persistence length affects the linear response to the external field.

Journal Article↗

PubMed2004

Overdamped stress relaxation in buckled rods.

We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. For the bulk, two interesting parameter regimes of generic self-similar intermediate asymptotics are distinguished, which give rise to approximate and exact power-law solutions, respectively. For the case of open boundary conditions the corresponding nontrivial boundary-layer scenarios are derived by a multiple-scale perturbation ("adiabatic") method. Our results compare well with--and provide the theoretical explanation for--previous results from numerical simulations, and they suggest directions for further fruitful numerical and experimental investigations.

Journal Article↗