Animal cells form contractile structures to promote various functions, from cell motility to cell division. Force generation in these structures is often due to molecular motors such as myosin that require polar substrates for their function. Here, we propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for polarity. This mechanism is based on active binding/unbinding of crosslinkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We find that these two ingredients can generate steady state contraction via a non-thermal, ratchet-like process. We calculate the resulting force-velocity relation using both coarse-grained and microscopic models.
Contractility in animal cells is often generated by molecular motors such as myosin, which require polar substrates for their function. Motivated by recent experimental evidence of motor-independent contractility, we propose a robust motor-free mechanism that can generate contraction in biopolymer networks without the need for substrate polarity. We show that contractility is a natural consequence of active binding/unbinding of crosslinkers that breaks the Principle of Detailed Balance, together with the asymmetric force-extension response of semiflexible biopolymers. We calculate the resultin…
Force fluctuations exhibited in focal adhesions (FAs) that connect a cell to its extracellular environment, point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space that the system goes from …
The mechanical properties of the cell depend crucially on the tension of its cytoskeleton, a biopolymer network that is put under stress by active motor proteins. While the fibrous nature of the network is known to strongly affect the transmission of these forces to the cellular scale, our understanding of this process remains incomplete. Here we investigate the transmission of forces through the network at the individual filament level, and show that active forces can be geometrically amplified as a transverse motor-generated force force "plucks" the fiber and induces a nonlinear tension. In …
Contractile forces are essential for many developmental processes involving cell shape change and tissue deformation. Recent experiments on reconstituted actomyosin networks, the major component of the contractile machinery, have shown that active contractility occurs above a threshold motor concentration and within a window of crosslink concentration. We present a microscopic dynamic model that incorporates two essential aspects of actomyosin self-organization: the asymmetric load response of individual actin filaments and the correlated motor-driven events mimicking myosin-induced filament s…
Movement within eukaryotic cells largely originates from localized forces exerted by myosin motors on scaffolds of actin filaments. Although individual motors locally exert both contractile and extensile forces, large actomyosin structures at the cellular scale are overwhelmingly contractile, suggesting that the scaffold serves to favor contraction over extension. While this mechanism is well understood in highly organized striated muscle, its origin in disordered networks such as the cell cortex is unknown. Here we develop a mathematical model of the actin scaffold's local two- or three-dimen…
Modeling approaches of suspended, rod-like particles and recent experimental data have shown that depletion forces display different signatures depending on the orientation of these particles. It has been shown that axial attraction of two rods yields contractile forces of 0.1pN that are independent of the relative axial shift of the two rods. Here, we measured depletion-caused interactions of actin bundles extending the phase space of single pairs of rods to a multi-particle system. In contrast to a filament pair, we found forces up to 3pN . Upon bundle relaxation forces decayed exponentially…
Current understanding of how contractility emerges in disordered actomyosin networks of non-muscle cells is still largely based on the intuition derived from earlier works on muscle contractility. This view, however, largely overlooks the free energy gain following passive cross-linker binding, which, even in the absence of active fluctuations, provides a thermodynamic drive towards highly overlapping filamentous states. In this work, we shed light on this phenomenon, showing that passive cross-linkers, when considered in the context of two anti-parallel filaments, generate noticeable contract…
Microscopic origin of macroscopic contractility in actin-myosin active gel models
Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院（EPFL）生命科学学院生物工程研究所）；SIB Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；Department of Genetics and Evolution, University of Geneva（日内瓦大学生物遗传与进化系）；Laboratoire Matière et Systèmes Complexes, Université de Paris Cité（巴黎 Cité 大学物质与复杂系统实验室）；Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Physique des Cellules et Cancer（居里研究所，巴黎文理研究大学，索邦大学，法国国家科学研究中心 UMR168，细胞物理与癌症实验室）；Université Paris Cité, CNRS, Institut Jacques Monod（巴黎 Cité 大学，法国国家科学研究中心，雅克·莫诺研究所）
Cells and tissues exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, which includes an active gel of actin filaments, crosslinks, and myosin molecular motors. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (order nN and greater) on cellular, tissue, and organismal length scales (order 10 $μ$m and greater). Experimental studies of reconstituted active-network model systems have long suggested …
The cytoskeleton protein actin assembles into large bundles when supporting stresses in the cell, but grows into a fine branched network to induce cell motion. Such self-organization processes are studied in artificial networks of cytoskeleton proteins with thick actin bundles and large motor protein aggregates to enable optical observation. The effect of motor aggregate size on the cytoskeleton mechanical properties is studied here in networks comprised of much smaller motor assemblies. Large motor protein clusters are known to increase the stiffness of actin based networks by introducing ten…
Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-…
Bundles of filaments and motors are central to contractility in cells. The classic example is striated muscle, where actomyosin contractility is mediated by highly organized sarcomeres which act as fundamental contractile units. However, many contractile bundles in vivo and in vitro lack sarcomeric organization. Here we propose a model for how contractility can arise in actomyosin bundles without sarcomeric organization and validate its predictions with experiments on a reconstituted system. In the model, internal stresses in frustrated arrangements of motors with diverse velocities cause fila…
The actin cytoskeleton in living cells generates forces in conjunction with myosin motor proteins to directly and indirectly drive essential cellular processes. The semiflexible filaments of the cytoskeleton can respond nonlinearly to the collective action of motors. We here investigate mechanics and force generation in a model actin cytoskeleton, reconstituted in vitro, by observing the response and fluctuations of embedded micron-scale probe particles. Myosin mini-filaments can be modelled as force dipoles and give rise to deformations in the surrounding network of cross-linked actin. Anomal…
In the presence of ATP, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modelling can help to quantify the relationship between individual motors plus filaments to organisation and dynamics on molecular and supra-molecular length scales. Here we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between fil…
The cytoskeleton is a model active matter system that controls diverse cellular processes from division to motility. While both active actomyosin dynamics and actin-microtubule interactions are key to the cytoskeleton's versatility and adaptability, an understanding of their interplay is lacking. Here, we couple microscale experiments with mechanistic modeling to elucidate how connectivity, rigidity, and force-generation affect emergent material properties in in vitro composites of actin, tubulin, and myosin. We use time-resolved differential dynamic microscopy and spatial image autocorrelatio…
Actomyosin contractility is essential for biological force generation, and is well understood in highly organized structures such as striated muscle. Additionally, actomyosin bundles devoid of this organization are known to contract both in vivo and in vitro, which cannot be described by standard muscle models. To narrow down the search for possible contraction mechanisms in these systems, we investigate their microscopic symmetries. We show that contractile behavior requires non-identical motors that generate large enough forces to probe the nonlinear elastic behavior of F-actin. This suggest…
Motility initiation in crawling cells requires transformation of a symmetric state into a polarized state. In contrast, motility arrest is associated with re-symmetrization of the internal configuration of a cell. Experiments on keratocytes suggest that polarization is triggered by the increased contractility of motor proteins but the conditions of re-symmetrization remain unknown. In this paper we show that if adhesion with the extra-cellular substrate is sufficiently low, the progressive intensification of motor-induced contraction may be responsible for both transitions: from static (symmet…
Pinned Boundaries Delay Contraction and Shape Stress Relaxation in Active Gels
School of Physics and Astronomy, Rochester Institute of Technology（罗切斯特理工学院物理与天文学学院）；Department of Physics and Biophysics, University of San Diego（圣地亚哥大学物理与生物物理系）
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 ense…
Reconstituted filamentous actin networks with myosin motor proteins form active gels, in which motor proteins generate forces that drive the network far from equilibrium. This motor activity can also strongly affect the network elasticity; experiments have shown a dramatic stiffening in in vitro networks with molecular motors. Here we study the effects of motor generated forces on the mechanics of simulated 2D networks of athermal stiff filaments. We show how heterogeneous internal motor stresses can lead to stiffening in networks that are governed by filament bending modes. The motors are mod…
Cell motility and tissue morphogenesis depend crucially on the dynamic remodelling of actomyosin networks. An actomyosin network consists of an actin polymer network connected by crosslinker proteins and motor protein myosins that generate internal stresses on the network. A recent discovery shows that for a range of experimental parameters, actomyosin networks contract to clusters with a power-law size distribution [Alvarado J. et al. (2013) Nature Physics 9 591]. Here, we argue that actomyosin networks can exhibit robust critical signature without fine-tuning because the dynamics of the syst…
The structural reorganization of the actin cytoskeleton is facilitated through the action of motor proteins that crosslink the actin filaments and transport them relative to each other. Here, we present a combined experimental-computational study that probes the dynamic evolution of mixtures of actin filaments and clusters of myosin motors. While on small spatial and temporal scales the system behaves in a very noisy manner, on larger scales it evolves into several well distinct patterns such as bundles, asters, and networks. These patterns are characterized by junctions with high connectivity…
The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles nat…
We have developed several distinct model systems of microtubule-based 3D active isotropic fluids and have compared their dynamical and structural properties. The non-equilibrium dynamics of these fluids is powered by three different types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. The fourth modification uses specific microtubule crosslinkers to induce bundle formation instead of a non-specific depletant. In comparison to the formerly developed systems, each new active fluid formulation has certain enhanced …
Active gels made of cytoskeletal proteins are valuable materials with attractive non-equilibrium properties such as spatial self-organization and self-propulsion. At least four typical routes to spatial patterning have been reported to date in different types of cytoskeletal active gels: bending and buckling instabilities in extensile systems, and global and local contraction instabilities in contractile gels. Here we report the observation of these four instabilities in a single type of active gel and we show that they are controlled by two parameters: the concentrations of ATP and depletion …
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and heavily crosslinked. Relating their large-scale dynamics to properties of their constituents remains an unsolved problem. Here we study an in vitro system made from microtubules and XCTK2 kinesin motors, which forms an aligned and active gel. Using photobleaching we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local polarity. This phenomenon is also obse…
The actin cortex is a thin layer of actin filaments and myosin motors beneath the outer membrane of animal cells. It determines the cells' mechanical properties and forms important morphological structures. Physical descriptions of the cortex as a contractile active gel suggest that these structures can result from dynamic instabilities. However, in these analyses the cortex is described as a two-dimensional layer. Here, we show that the dynamics of the cortex is qualitatively different when gel fluxes in the direction perpendicular to the membrane are taken into account. In particular, an iso…
Computer simulations can aid in understanding how collective materials properties emerge from interactions between simple constituents. Here, we introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and crosslinking proteins at biologically relevant time and length scales. We demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, mechanical responses to shear, motor motilities, and network rearrangements. We use the simulation to predict …
Spatially localised defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar 'actin' filaments and 'myosin' motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent defect structures are characterized by distinct textures and can be either static or mobile - we derive effective equations of motion for these 'extended particles' and analyse their shape, kinetics, interactions and scattering. Depending on the impact parameter and propulsion speed, these active defects undergo elastic scattering or merger…
