Growth Velocities of Branched Actin Networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side vs. end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.Comment: 6 figure

Planar lamellae and onions: a spatially resolved rheo-NMR approach to the shear-induced structural transformations in a surfactant model system

The shear-induced transformations between oriented planar lamellae and a state of closely packed multilamellar vesicles (MLVs) in a lyotropic nonionic surfactant model system were studied by the combination of nuclear magnetic resonance (NMR) spectroscopy and diffusometry with magnetic resonance imaging (MRI). (2)H NMR imaging confirmed the discontinuous nature of the transition from onions to planar lamellae, revealing the spatial coexistence of both states within the gap of the cylindrical Couette geometry. On the other hand, NMR diffusion measurements in three principal directions and at various values of strain strongly suggest that a multi-lamellar cylindrical or undulated intermediate structure exists during the continuous and spatially homogeneous transition from planar lamellae to MLVs

Role of tensile stress in action gels and a symmetry-breaking instability

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a “comet” pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro

Role of tensile stress in actin gels and a symmetry-breaking instability

It has been observed experimentally that the actin gel grown from spherical beads coated with polymerization enzymes spontaneously breaks the symmetry of its spherical shape, and yields a “comet” pushing the bead forward. We propose a mechano-chemical coupling mechanism for the initialization of this symmetry breaking. Key assumptions are that the dissociation of the gel takes place mostly in the region of the external surface, and that the rates of the dissociation depend on the tensile stress in the gel. We analyze a simplified two-dimensional model with a circular substrate. Our analysis shows that the symmetric steady state is always unstable against the inhomogeneous modulation of the thickness of the gel layer, for any radius of the circular substrate. We argue that this model represents the essential feature of three-dimensional systems for a certain range of characteristic lengths of the modulation. The characteristic time of the symmetry-breaking process in our model depends linearly on the radius of curvature of the substrate surface, which is consistent with experimental results, using spherical latex beads as substrate. Our analysis of the symmetry-breaking phenomenon demonstrates aspects of mechano-chemical couplings that should be working in vivo as well as in vitro