Based on the Stochastic Inclined Rods Model (SIRM) proposed by H. Matsuura and M. Nakano, we study the microscopic motion of actin myosin system including the motion of the G-actin. Our model is composed of an inclined spring (rod), a myosin head, a myosin filament and G-actins. We discuss the stochastic resonance between the myosin head and random noise. The results of calculation show that the model can convert the random motion to one directional motion, and the myosin head works as a resonator of random noise which absorbs the energy through the stochastic resonance. The intermolecular potential between the myosin head and G-actin and the inclined rod play a key role for the muscle's motion. The energy consumed by the motor is directly supplied from the surroundings (i.e., the thermal motions of water molecules).
We present a study on filamentous actin solutions containing heavy meromyosin subfragments of myosin II motor molecules. We focus on the viscoelastic phase behavior and internal dynamics of such networks during ATP depletion. Upon simultaneously using micro-rheology and fluorescence microscopy as complementary experimental tools, we find a sol-gel transition accompanied by a sudden onset of directed filament motion. We interpret the sol-gel transition in terms of myosin II enzymology, and suggest a "zipping" mechanism to explain the filament motion in the vicinity of the sol-gel transition.
We study the influence of disorder in the helical actin structure on the myosin V step size, predicted from the elastic lever arm model. We show that fluctuations of +-5 degrees per actin subunit, as proposed by Egelman et al., significantly alter the distribution of step sizes and improve the agreement with experimental data.
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）
We present a model study of gliding assays in which actin filaments are moved by non-processive myosin motors. We show that even if the power stroke of the motor protein has no lateral component, the filaments will rotate around their axis while moving over the surface. Notably, the handedness of this twirling motion is opposite from that of the actin filament structure. It stems from the fact that the gliding actin filament has "target zones" where its subunits point towards the surface and are therefore more accessible for myosin heads. Each myosin head has a higher binding probability befor…
The cooperative action of many molecular motors is essential for dynamic processes such as cell motility and mitosis. This action can be studied by using motility assays in which the motion of cytoskeletal filaments over a surface coated with motor proteins is tracked. In previous studies of actin-myosin II systems, fast directional motion was observed, reflecting the tendency of myosin II motors to propagate unidirectionally along actin filaments. Here, we present a motility assay with actin bundles consisting of short filamentous segments with randomly alternating polarities. These actin tra…
Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geome- tries and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as non-perturbing multi-scale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in non-equilibrium bending dynamics, which we analyze in terms of …
Myosin V is a two-headed processive motor protein that walks in a hand-over-hand fashion along actin filaments. When it encounters a filament branch, formed by the Arp2/3 complex, it can either stay on the straight mother filament, or switch to the daughter filament. We study both probabilities using the elastic lever arm model for myosin V. We calculate the shapes and bending energies of all relevant configurations in which the trail head is bound to the actin filament before Arp2/3 and the lead head is bound either to the mother or to the daughter filament. Based on the assumption that the p…
Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This antenna m…
We present a numerical simulation study of the dynamics of filopodial growth in the presence of active transport by myosin X motors. We employ both a microscopic agent-based model, which captures the stochasticity of the growth process, and a continuum mean-field theory which neglects fluctuations. We show that in the absence of motors, filopodia growth is overestimated by the continuum mean-field theory. Thus fluctuations slow down the growth, especially when the protrusions are driven by a small number (10 or less) of F-actin fibres, and when the force opposing growth (coming from membrane e…
Many biological processes involve the action of molecular motors that interact with the cell cytoskeleton. Some processes, such as the transport of cargoes is achieved mainly by the action of individual motors. Other, such as cell motility and division, require the cooperative work of many motors. Collective motor dynamics can be quite complex and unexpected. One beautiful example is the bidirectional ("back and forth") motion of filaments which is induced when the motors within a group exert forces in opposite directions. This review tackles the puzzle emerging from a recent experimental work…
The actin cytoskeleton is an active semi-flexible polymer network whose non-equilibrium properties coordinate both stable and contractile behaviors to maintain or change cell shape. While myosin motors drive the actin cytoskeleton out-of-equilibrium, the role of myosin-driven active stresses in the accumulation and dissipation of mechanical energy is unclear. To investigate this, we synthesize an actomyosin material in vitro whose active stress content can tune the network from stable to contractile. Each increment in activity determines a characteristic spectrum of actin filament fluctuations…
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 …
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…
Tissue cells are in a state of permanent mechanical tension that is maintained mainly by myosin II minifilaments, which are bipolar assemblies of tens of myosin II molecular motors contracting actin networks and bundles. Here we introduce a stochastic model for myosin II minifilaments as two small myosin II motor ensembles engaging in a stochastic tug-of-war. Each of the two ensembles is described by the parallel cluster model that allows us to use exact stochastic simulations and at the same time to keep important molecular details of the myosin II cross-bridge cycle. Our simulation and analy…
We present a mechanochemical model for myosin V, a two-headed processive motor protein. We derive the properties of a dimer from those of an individual head, which we model both with a 4-state cycle (detached, attached with ADP.Pi, attached with ADP and attached without nucleotide) and alternatively with a 5-state cycle (where the power stroke is not tightly coupled to the phosphate release). In each state the lever arm leaves the head at a different, but fixed, angle. The lever arm itself is described as an elastic rod. The chemical cycles of both heads are coordinated exclusively by the mech…
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…
We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with a Helfrich-type model to account for membrane properties. The overall model allows to consider motility without the necessity for local adhesion. Besides a detailed numerical approach together with convergence studies for the highly nonlinear free boundary problem, we also compare the induced flow field of the motile cell with that of classical squirmer mode…
Living cells move thanks to assemblies of actin filaments and myosin motors that range from very organized striated muscle tissue to disordered intracellular bundles. The mechanisms powering these disordered structures are debated, and all models studied so far predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay of three well-characterized internal dynamical processes in actomyosin bundles: actin treadmilling, the attachement-detachment dynamics of myosin and that of crosslinking proteins. We show that these processes enable an exten…
The SIRM (Stochastic Inclined Rods Model) proposed by H. Matsuura and M. Nakano can explain the muscle's motion perfectly, but the intermolecular potential between myosin head and G-actin is too simple and only repulsive potential is considered. In this paper we study the SIRM with different complex potential and discuss the effect of the spring on the system. The calculation results show that the spring, the effective radius of the G-actin and the intermolecular potential play key roles in the motion. The sliding speed is about $4.7\times10^{-6}m/s$ calculated from the model which well agrees…
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 molecular motor myosin V exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is hand-over-hand stepping by a swinging lever arm movement toward the plus-end of actin filaments, essential to its role as a cellular transporter. However, single-molecule experiments have also shown that the motor "foot stomps", with one hand detaching and rebinding to the same site, and backsteps under sufficient load. Explaining the complete taxonomy of myosin V's load-dependent stepping pathways, and the ex…
We present a computer simulation study, via lattice Boltzmann simulations, of a microscopic model for cytoplasmic streaming in algal cells such as those of Chara corallina. We modelled myosin motors tracking along actin lanes as spheres undergoing directed motion along fixed lines. The sphere dimension takes into account the fact that motors drag vesicles or other organelles, and, unlike previous work, we model the boundary close to which the motors move as walls with a finite slip layer. By using realistic parameter values for actin lane and myosin density, as well as for endoplasmic and vacu…
Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantl…
Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the f…
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…
