arXiv subjects

Ulrich S. Schwarz

Publications and source records attributed to Ulrich S. Schwarz.

47 records · Page 3Linked to original sources

arXiv2013

Unifying autocatalytic and zeroth order branching models for growing actin networks

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions.

q-bio.SC↗

arXiv2012

Stochastic force generation by small ensembles of myosin II motors

Forces in the actin cytoskeleton are generated by small groups of non-processive myosin II motors for which stochastic effects are highly relevant. Using a crossbridge model with the assumptions of fast powerstroke kinetics and equal load sharing between equivalent states, we derive a one-step master equation for the activity of a finite-sized ensemble of mechanically coupled myosin II motors. For constant external load, this approach yields analytical results for duty ratio and force-velocity relation as a function of ensemble size. We find that stochastic effects cannot be neglected for ensemble sizes below 15. The one-step master equation can be used also for efficient computer simulations with linear elastic external load and reveals the sequence of build-up of force and ensemble rupture that is characteristic for reconstituted actomyosin contractility.

q-bio.SC↗

arXiv2012

Force localization in contracting cell layers

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions, although the edge itself still retracts. We also show that anisotropic extracellular stiffness leads to force localization in the stiffer direction, as observed experimentally.

q-bio.TO↗

arXiv2011

Viscoelastic response of contractile filament bundles

The actin cytoskeleton of adherent tissue cells often condenses into filament bundles contracted by myosin motors, so-called stress fibers, which play a crucial role in the mechanical interaction of cells with their environment. Stress fibers are usually attached to their environment at the endpoints, but possibly also along their whole length. We introduce a theoretical model for such contractile filament bundles which combines passive viscoelasticity with active contractility. The model equations are solved analytically for two different types of boundary conditions. A free boundary corresponds to stress fiber contraction dynamics after laser surgery and results in good agreement with experimental data. Imposing cyclic varying boundary forces allows us to calculate the complex modulus of a single stress fiber.

q-bio.SC↗

arXiv2010

Role of anisotropy for protein-protein encounter

Protein-protein interactions comprise both transport and reaction steps. During the transport step, anisotropy of proteins and their complexes is important both for hydrodynamic diffusion and accessibility of the binding site. Using a Brownian dynamics approach and extensive computer simulations, we quantify the effect of anisotropy on the encounter rate of ellipsoidal particles covered with spherical encounter patches. We show that the encounter rate $k$ depends on the aspect ratios $ξ$ mainly through steric effects, while anisotropic diffusion has only a little effect. Calculating analytically the crossover times from anisotropic to isotropic diffusion in three dimensions, we find that they are much smaller than typical protein encounter times, in agreement with our numerical results.

q-bio.BM↗

arXiv2009

Stochastic simulations of cargo transport by processive molecular motors

We use stochastic computer simulations to study the transport of a spherical cargo particle along a microtubule-like track on a planar substrate by several kinesin-like processive motors. Our newly developed adhesive motor dynamics algorithm combines the numerical integration of a Langevin equation for the motion of a sphere with kinetic rules for the molecular motors. The Langevin part includes diffusive motion, the action of the pulling motors, and hydrodynamic interactions between sphere and wall. The kinetic rules for the motors include binding to and unbinding from the filament as well as active motor steps. We find that the simulated mean transport length increases exponentially with the number of bound motors, in good agreement with earlier results. The number of motors in binding range to the motor track fluctuates in time with a Poissonian distribution, both for springs and cables being used as models for the linker mechanics. Cooperativity in the sense of equal load sharing only occurs for high values for viscosity and attachment time.

q-bio.SC↗

arXiv2009

Effect of adhesion geometry and rigidity on cellular force distributions

The behaviour and fate of tissue cells is controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force distributions for cells adhering to adhesive patterns with different geometries and rigidities. For continuous adhesion along a closed contour, forces are predicted to be localized to the corners. For discrete sites of adhesion, the model predicts the forces to be mainly determined by the lateral pull of the cell contour. With increasing distance between two neighboring sites of adhesion, the adhesion force increases because cell shape results in steeper pulling directions. Softer substrates result in smaller forces. Our predictions agree well with experimental force patterns measured on pillar assays.

q-bio.CB↗

arXiv2008

Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches

We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20-9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5-95 percent. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modelling of the dynamics of large protein complexes.

q-bio.BM↗

arXiv2006

Focal adhesions as mechanosensors: the two-spring model

Adhesion-dependent cells actively sense the mechanical properties of their environment through mechanotransductory processes at focal adhesions, which are integrin-based contacts connecting the extracellular matrix to the cytoskeleton. Here we present first steps towards a quantitative understanding of focal adhesions as mechanosensors. It has been shown experimentally that high levels of force are related to growth of and signaling at focal adhesions. In particular, activation of the small GTPase Rho through focal adhesions leads to the formation of stress fibers. Here we discuss one way in which force might regulate the internal state of focal adhesions, namely by modulating the internal rupture dynamics of focal adhesions. A simple two-spring model shows that the stiffer the environment, the more efficient cellular force is built up at focal adhesions by molecular motors interacting with the actin filaments.

q-bio.SC↗

arXiv2005

L-selectin mediated leukocyte tethering in shear flow is controlled by multiple contacts and cytoskeletal anchorage facilitating fast rebinding events

L-selectin mediated tethers result in leukocyte rolling only above a threshold in shear. Here we present biophysical modeling based on recently published data from flow chamber experiments (Dwir et al., J. Cell Biol. 163: 649-659, 2003) which supports the interpretation that L-selectin mediated tethers below the shear threshold correspond to single L-selectin carbohydrate bonds dissociating on the time scale of milliseconds, whereas L-selectin mediated tethers above the shear threshold are stabilized by multiple bonds and fast rebinding of broken bonds, resulting in tether lifetimes on the timescale of $10^{-1}$ seconds. Our calculations for cluster dissociation suggest that the single molecule rebinding rate is of the order of $10^4$ Hz. A similar estimate results if increased tether dissociation for tail-truncated L-selectin mutants above the shear threshold is modeled as diffusive escape of single receptors from the rebinding region due to increased mobility. Using computer simulations, we show that our model yields first order dissociation kinetics and exponential dependence of tether dissociation rates on shear stress. Our results suggest that multiple contacts, cytoskeletal anchorage of L-selectin and local rebinding of ligand play important roles in L-selectin tether stabilization and progression of tethers into persistent rolling on endothelial surfaces.

q-bio.SC↗

arXiv2005

Effect of Poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.

cond-mat.soft↗