Transient Binding and Dissipation in Cross-Linked Actin Networks

In contrast with entangled actin solutions, transiently cross-linked actin networks can provide highly elastic properties while still allowing for local rearrangements in the microstructure-on biological relevant time scales. Here, we show that thermal unbinding of transient cross-links entails local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the viscoelastic response of an isotropically cross-linked actin network by experimentally tuning the off rate of the transiently cross-linking molecules, their density, and the solvent viscosity. We reproduce the measured frequency response by a semiphenomenological model that is predicated on microscopic unbinding events

Cytoskeletal Polymer Networks: Viscoelastic Properties are Determined by the Microscopic Interaction Potential of Cross-links

AbstractAlthough the structure of cross-linking molecules mainly determines the structural organization of actin filaments and with that the static elastic properties of the cytoskeleton, it is largely unknown how the biochemical characteristics of transiently cross-linking proteins (actin-binding proteins (ABPs)) affect the viscoelasticity of actin networks. In this study, we show that the macroscopic network response of reconstituted actin networks can be traced back to the microscopic interaction potential of an individual actin/ABP bond. The viscoelastic response of cross-linked actin networks is set by the cross-linker off-rate, the binding energy, and the characteristic bond length of individual actin/ABP interactions

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.Comment: 11 pages, 12 figure

The response function of a sphere in a viscoelastic two-fluid medium

In order to address basic questions of importance to microrheology, we study the dynamics of a rigid sphere embedded in a model viscoelastic medium consisting of an elastic network permeated by a viscous fluid. We calculate the complete response of a single bead in this medium to an external force and compare the result to the commonly-accepted, generalized Stokes-Einstein relation (GSER). We find that our response function is well approximated by the GSER only within a particular frequency range determined by the material parameters of both the bead and the network. We then discuss the relevance of this result to recent experiments. Finally we discuss the approximations made in our solution of the response function by comparing our results to the exact solution for the response function of a bead in a viscous (Newtonian) fluid.Comment: 12 pages, 2 figure

Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

Curved Tails in Polymerization-Based Bacterial Motility

The curved actin ``comet-tail'' of the bacterium Listeria monocytogenes is a visually striking signature of actin polymerization-based motility. Similar actin tails are associated with Shigella flexneri, spotted-fever Rickettsiae, the Vaccinia virus, and vesicles and microspheres in related in vitro systems. We show that the torque required to produce the curvature in the tail can arise from randomly placed actin filaments pushing the bacterium or particle. We find that the curvature magnitude determines the number of actively pushing filaments, independent of viscosity and of the molecular details of force generation. The variation of the curvature with time can be used to infer the dynamics of actin filaments at the bacterial surface.Comment: 8 pages, 2 figures, Latex2

Microstructure and viscoelasticity of confined semiflexible polymer networks

The rapidly decreasing dimensions of many technological devices have spurred interest in confinement effects1. Long before, living organisms invented ingenious ways to cope with the requirement of space saving designs down to the cellular level. Typical length scales in cells range from nanometres to micrometres so that the polymeric constituents of the cytoskeleton are often geometrically confined. Hence, the mechanical response of polymers to external confinement has potential implications both for technology and for our understanding of biological systems alike. Here we report a study of in vitro polymerized filamentous actin confined to emulsion droplets. We correlate observations of the microstructure, local rheological properties and single filament fluctuations. Enforcing progressively narrower confinement is found to induce a reduction of polymer fluctuations, network stiffening, structural heterogeneities and eventually cortex formation. We argue that the structural and mechanical effects can be consistently explained by a gradual suppression of single polymer eigenmodes

Structure and Dynamics of Crosslinked Actin Networks

The actin cytoskeleton, a network of protein-polymers, is responsible for the mechanical stability of cells. This biopolymer network is also crucial for processes that require spatial and temporal variations in the network structure such as cell migration, division and intracellular transport. The cytoskeleton therefore has to combine structural integrity and mechanical stability with the possibility of fast and efficient network reorganization and restructuring. Cells meet this challenge by using proteins to link filamentous actin (F-actin) and construct complex networks. The molecular properties of the cross-linking proteins determine to a large extent the (micro)structure, viscoelastic properties and dynamics of the resulting networks. This review focuses on the structural polymorphism that can be induced by cross-linking proteins in reconstituted F-actin networks and summarizes recent results on how the molecular properties of cross-linking proteins dictate the ensuing viscoelastic properties

Mechanical plasticity of collagen directs branch elongation in human mammary gland organoids.

Epithelial branch elongation is a central developmental process during branching morphogenesis in diverse organs. This fundamental growth process into large arborized epithelial networks is accompanied by structural reorganization of the surrounding extracellular matrix (ECM), well beyond its mechanical linear response regime. Here, we report that epithelial ductal elongation within human mammary organoid branches relies on the non-linear and plastic mechanical response of the surrounding collagen. Specifically, we demonstrate that collective back-and-forth motion of cells within the branches generates tension that is strong enough to induce a plastic reorganization of the surrounding collagen network which results in the formation of mechanically stable collagen cages. Such matrix encasing in turn directs further tension generation, branch outgrowth and plastic deformation of the matrix. The identified mechanical tension equilibrium sets a framework to understand how mechanical cues can direct ductal branch elongation