Asymmetric cell divisions are essential for the development of multicellular organisms. To proceed, they require an initially symmetric cell to polarize. In Caenorhabditis elegans zygotes, anteroposterior polarization is facilitated by a large-scale flow of the actomyosin cortex, which directs the asymmetry of the first mitotic division. Cortical flows appear in many contexts of development, but their underlying forces and physical principles remain poorly understood. How actomyosin contractility and cortical tension interact to generate large-scale flow is unclear. Here we report on the subcellular distribution of cortical tension in the polarizing C. elegans zygote, which we determined using position- and direction-sensitive laser ablation. We demonstrate that cortical flow is associated with anisotropies in cortical tension and is not driven by gradients in cortical tension, which contradicts previous proposals. These experiments, in conjunction with a theoretical description of active cortical mechanics, identify two prerequisites for large-scale cortical flow: a gradient in actomyosin contractility to drive flow and a sufficiently large viscosity of the cortex to allow flow to be long-ranged. We thus reveal the physical requirements of large-scale intracellular cortical flow that ensure the efficient polarization of the C. elegans zygote.

Networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic timescale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G ∼ ω 1/2 for low frequencies ω. This model quantitatively describes the measured rheology of actin networks cross-linked with α-Actinin-4 over more than four decades in frequency.PACS numbers: 87.16. Ka,83.80.Lz,87.15.La,Reconstituted biopolymers such as actin are excellent models for semi-flexible polymers, with network mechanics and dynamics that are strikingly different from flexible polymer networks [1][2][3][4][5][6][7][8]. One essential feature setting biopolymer networks apart from rubber-like materials is the intrinsic dynamics of their cross-links. Such systems represent a distinct class of polymeric materials whose long-time dynamics are not governed by viscosity or reptation [9], but rather, by the transient nature of their cross-links. This can give rise to a complex mechanical response, particularly at long times, where the network is expected to flow. Such flow can have important implications for cells, where their internal networks are constantly remodeling, reflecting the transient nature of their cross-links [10]. The simplest possible description of a material that is elastic on short timescales while flowing on long timescales is that of a Maxwell fluid; this exhibits a single relaxation time τ , as depicted in Fig. 1. Indeed, some recent experiments on transient networks have suggested the existence of a single relaxation time [11]; by contrast, other experiments-probing longer time-scales-evince a more complex viscoelastic behavior [12,13], indicative of multiple relaxation times. Thus, the basic physical principles governing such transient networks remain a mystery. A predictive theoretical model is essential to elucidate the effect of dynamic cross-linking, and to help explain the complex viscoelastic behavior observed experimentally.Here, we develop a microscopic model for long-time network relaxation that is controlled by cross-link dynamics. This cross-link governed dynamics (CGD) model describes the structural relaxation that results from many independent unbinding and rebinding events. Using a combination of Monte Carlo simulations and an analytic approach, we demonstrate that this type of cross-link dynamics yields power-law network rheology arising from a broad spectrum of relaxation rates. Our predictions are The CGD model can be qualitatively understood in simple physical terms. We assume each filament to be cross-linked to the network, with an average spacing c . Only filament bending modes between cross-links can relax (Fig. 1, lower inset), and the thermalization of these modes results in an entropic, spring-like response. To account for transient cross-linking, we assume that the linkers unbind at a rate 1/τ o...

In cells, many vital processes involve myosin-driven motility that actively remodels the actin cytoskeleton and changes cell shape. Here we study how the collective action of myosin motors organizes actin filaments into contractile structures in a simplified model system devoid of biochemical regulation. We show that this self-organization occurs through an active multistage coarsening process. First, motors form dense foci by moving along the actin network structure followed by coalescence. Then the foci accumulate actin filaments in a shell around them. These actomyosin condensates eventually cluster due to motor-driven coalescence. We propose that the physical origin of this multistage aggregation is the highly asymmetric load response of actin filaments: they can support large tensions but buckle easily under piconewton compressive loads. Because the motor-generated forces well exceed this threshold, buckling is induced on the connected actin network that resists motor-driven filament sliding. We show how this buckling can give rise to the accumulation of actin shells around myosin foci and subsequent coalescence of foci into superaggregates. This new physical mechanism provides an explanation for the formation and contractile dynamics of disordered condensed actomyosin states observed in vivo.active gels | molecular motors | nonequilibrium | soft condensed matter C ells undergo dramatic changes in shape and internal organization during vital processes such as migration and division. These changes involve remodeling of the cytoskeleton partly driven by collective physical interactions between molecular motors and cytoskeletal filaments. The motors use adenosine triphosphate (ATP) as fuel and hydrolyze it to actively generate forces and move along filaments (1). Multiheaded motors or complexes of motors may cross-link neighboring filaments and generate relative motion between them. Kinesin and dynein motors interact with microtubules to form the mitotic spindle, which is responsible for chromosome segregation (2). Myosin motors interact with filamentous actin (F-actin) to form complex arrays such as the contractile ring driving cell division (3, 4) and contractile networks that drive cell migration (4) and polarizing cortical flows (5, 6).To identify the biophysical processes underlying cytoskeletal organization, many in vitro model systems of purified motors and filaments that lack biochemical regulation have been recently developed. It is known that kinesins can organize microtubules into polarity sorted asters, as well as vortex or bundle states (7-10). These structures resemble physiological arrays such as the mitotic spindle (11). In contrast to microtubules, purified F-actin does not form well-defined structures when motors are added. Actin-myosin II solutions remain disordered at high levels of ATP (12-14) and generate dense condensates that appear internally unstructured if the ATP level is lowered or when the actin filaments are cross-linked (15-18). Interestingly, similar dense condensates appear in...