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 in which it has been shown that the characteristic reversal times of the bidirectional motion are practically independent of the number of motors. This result is in a striking contradiction with existing theoretical models that predict an exponential growth of the reversal times with the size of the system. We argue that the solution to this puzzle may be the crosstalk between the motors which is mediated by the elastic tensile stress that develops in the cytoskeleton track. The crosstalk does not directly correlate the attachment and detachment of the motors, which work independently of each other. However, it highly accelerates their detachments by making the detachment rates system size dependent.
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…
Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumption…
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…
Myosin V was the first discovered processive motor from the myosin family. It has therefore been subject of a number of mechanical, kinetic, optical and structural studies and now belongs to the best characterised motor proteins. This effort has been accompanied by a number of different theoretical models. In this article we give an overview of them and discuss what they have in common and where the open questions are. The latter include the existence of sub-steps, the process that limits the run length, the nature of backward steps, the flexibility of the lever arm and the state of the lead h…
The study of motor protein dynamics within cytoskeletal networks is of high interest to physicists and biologists to understand how the dynamics and properties of individual motors lead to cooperative effects and control of overall network behaviour. Here, we report a method to detect and track muscular myosin II filaments within an actin network tethered to supported lipid bilayers. Based on the characteristic shape of myosin II filaments, this automated tracking routine allowed us to follow the position and orientation of myosin II filaments over time, and to reliably classify their dynamics…
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.
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…
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）
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…
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.
Myosin-V is a highly processive dimeric protein that walks with 36nm steps along actin tracks, powered by coordinated ATP hydrolysis reactions in the two myosin heads. No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run-length with [ADP], [ATP] and external forcing. In particular, a result that has eluded all theoretical studies based upon rigorous physical chemistry is that run length decreases with both increasing [ADP] and [ATP]. We systematically analyse which mechanisms in existing models reproduce which experimental trends and use thi…
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…
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 pot…
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…
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…
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…
Molecular motors are found throughout the cells of the human body, and have many different and important roles. These micro-machines move along filament tracks, and have the ability to convert chemical energy into mechanical work that powers cellular motility. Different types of motors are characterized by different duty-ratios, which is the fraction of time that a motor is attached to its filament. In the case of myosin II - a non-processive molecular machine with a low duty ratio - cooperativity between several motors is essential to induce motion along its actin filament track. In this work…
The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: a) traveling waves, b) moving patches, and c) random fluctuations. Increasing actin concentration causes a transition from patches to waves. The waves and patches move by a treadmilling mechanism which does not require myosin II. The effects of downregulation of key proteins on actin wave behavior are evaluated.
It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated…
Almost 60 years ago Andrew Huxley with his seminal paper \cite{Huxley1957} laid the foundation of modern muscle modeling, linking chemical events to mechanical performance. He described mechanics and energetics of muscle contraction through the cyclical attachment and detachment of myosin motors to the actin filament with ad hoc assumptions on the dependence of the rate constants on the strain of the myosin motors. That relatively simple hypothesis is still present in recent models, even though with several modifications to adapt the model to the different experimental constraints which became…
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…
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 …
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…
We present a simple model for the bidirectional dynamics of actin bundles with alternating polarities in gliding assays with non-processive myosin motors. In the model, the bundle is represented as an elastic chain consisting of monomers with positive and negative polarities. The motion of the bundle is induced by the pulling forces of the underlying motors which stochastically attach to the monomers and, depending on the polarity of the monomers, pull them in the right or left direction. We demonstrate that perfectly a-polar chains consisting of equal numbers of monomers with positive and neg…
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…
Self organization mechanisms are essential for the cytoskeleton to adapt to the requirements of living cells. They rely on the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors. Here we present an in vitro minimal model system consisting of actin filaments, fascin and myosin-II filaments exhibiting pulsative collective long range dynamics. The reorganizations in the highly dynamic steady state of the active gel are characterized by alternating periods of runs and stalls resulting in a superdiffusive dynamics of the network's constituents. They are domina…
Biological functions rely on ordered structures and intricately controlled collective dynamics. In contrast to systems in thermodynamic equilibrium, order is typically established and sustained in stationary states by continuous dissipation of energy. Non-equilibrium dynamics is a necessary condition to make the systems highly susceptible to signals that cause transitions between different states. How cellular processes self-organize under this general principle is not fully understood. Here, we find that model actomyosin cortices, in the presence of rapid turnover, display distinct steady sta…
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…
In this paper, we develop and analyze a minimal model for a 2D network of cross-linked actin filaments and myosin motors, representing the cortical cytoskeleton of eukaryotic cells. We implement coarse-grained representations of force production by myosin motors and stress dissipation through an effective cross-link friction and filament turnover. We use this model to characterize how the sustained production of active stress, and the steady dissipation of elastic stress, depend individually on motor activity, effective cross-link friction and filament turnover. Then we combine these results t…
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 …
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…
Many cell membrane proteins that bind to actin form dynamic clusters driven by contractile flows generated by the actomyosin machinery at the cell cortex. Recent evidence suggests that a necessary condition for the generation of these protein clusters on the membrane is the stratified organization of the active agents -formin-nucleated actin, myosin-II minifilaments, and ARP2/3-nucleated actin mesh -within the cortex. Further, the observation that these clusters dynamically remodel, requires that the components of this active machinery undergo turnover. Here we develop a coarse-grained agent-b…
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 intracellular environment is a dynamic space filled with various organelles moving in all directions. Included in this diverse group of organelles are vesicles, which are involved in transport of molecular cargo throughout the cell. Vesicles move in either a directed or non-directed fashion, often depending on interactions with cytoskeletal proteins such as microtubules, actin filaments, and molecular motors. How these proteins affect the local fluctuations of vesicles in the cytoplasm is not clear since they have the potential to both facilitate and impede movement. Here we show that vesi…
Living cells adapt and respond actively to the mechanical properties of their environment. In addition to biochemical mechanotransduction, evidence exists for a myosin-dependent, purely mechanical sensitivity to the stiffness of the surroundings at the scale of the whole cell. Using a minimal model of the dynamics of actomyosin cortex, we show that the interplay of myosin power strokes with the rapidly remodelling actin network results in a regulation of force and cell shape that adapts to the stiffness of the environment. Instantaneous changes of the environment stiffness are found to trigger…
The composite cytoskeleton, comprising interacting networks of semiflexible actin and rigid microtubules, actively generates forces and restructures using motor proteins such as myosins to enable key mechanical processes including cell motility and mitosis. Yet, how motor-driven activity alters the mechanics of cytoskeleton composites remains an open challenge. Here, we perform optical tweezers microrheology on actin-microtubule composites driven by myosin II motors to show that motor activity increases the linear viscoelasticity and elastic storage of the composite by active restructuring to …
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…
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…
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…
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…
Biological systems are among the most challenging subjects for theoretical physicists, as well as experimentalists or simulationists. Physical principles should have been both constraints and guide-lines for the evolution of living systems over billions of years. One generally aims at clarifying what physical principles, possibly new ones, are behind the phenomena of biological interest and at understanding how they work within the entire biological world. In the present talk we describe an example of such an effort. Since the discovery of `superprecipitation' by Szent-Gyorgyi's group in 1940'…
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…
Molecular motors belonging to the kinesin and myosin super family hydrolyze ATP by cycling through a sequence of chemical states. These cytoplasmic motors are dimers made up of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, the motors walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. Thus, the one motor head must regulate chemical state of the other, referred to as "gating", a concept that is not fully und…
Filopodia are actin-rich structures, present on the surface of practically every known eukaryotic cell. These structures play a pivotal role in specific cell-cell and cell-matrix interactions by allowing cells to explore their environment, generate mechanical forces, perform chemical signaling, or convey signals via intercellular tunneling nano-bridges. The dynamics of filopodia appear quite complex as they exhibit a rich behavior of buckling, pulling, length and shape changes. Here, we show that filopodia additionally explore their 3D extracellular space by combining growth and shrinking with…
Active force generation by actin-myosin cortex coupled to the cell membrane allows the cell to deform, respond to the environment, and mediate cell motility and division. Several membrane-bound activator proteins move along it and couple to the membrane curvature. Besides, they can act as nucleating sites for the growth of filamentous actin. Actin polymerization can generate a local outward push on the membrane. Inward pull from the contractile actomyosin cortex can propagate along the membrane via actin filaments. We use coupled evolution of fields to perform linear stability analysis and num…
Intracellular transport of large cargoes, such as organelles, vesicles or large proteins, is a complex dynamical process that involves the interplay of ATP-consuming molecular motors, cytoskeleton filaments and the viscoelastic cytoplasm. The displacements of particles or probes in the cell cytoplasm as a function of time are characterized by different (anomalous) diffusion regimes. We investigate here the motion of pigment organelles (melanosomes) driven by myosin-V motors in \emph{Xenopus laevis} melanocytes using a high spatio-temporal resolution tracking technique. By analyzing the mean sq…
Substrate-based cell motility is essential for fundamental biological processes, such as tissue growth, wound healing and immune response. Even if a comprehensive understanding of this motility mode remains elusive, progress has been achieved in its modeling using a whole cell physical model. The model takes into account the main mechanisms of cell motility - actin polymerization, substrate mediated adhesion and actin-myosin dynamics and combines it with steric cell-cell and hydrodynamic interactions. The model predicts the onset of collective cell migration, which emerges spontaneously as a r…
Contraction of the cytokinetic ring during cell division leads to physical partitioning of a eukaryotic cell into two daughter cells. This involves flows of actin filaments and myosin motors in the growing membrane interface at the mid-plane of the dividing cell. Assuming boundary driven alignment of the acto-myosin filaments at the inner edge of the iterface we explore how the resulting active stresses influence the flow. Using the continuum gel theory framework, we obtain exact axisymmetric solutions of the dynamical equations. These solutions are consistent with experimental observations on…
Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively generate in actin filaments. Here, we use a statistical mechanical analysis to investigate the influence of the EMC effect on the sarcomere - the basic contractile unit of skeletal muscles. We demonstrate that the EMC effect leads to an increase in the attachment probability of motors located near the end of the sarcomere while, simultan…
Many cells exhibit large-scale active circulation of their entire fluid contents, a process termed cytoplasmic streaming. This phenomenon is particularly prevalent in plant cells, often presenting strikingly regimented flow patterns. The driving mechanism in such cells is known: myosin-coated organelles entrain cytoplasm as they process along actin filament bundles fixed at the periphery. Still unknown, however, is the developmental process which constructs the well-ordered actin configurations required for coherent cell-scale flow. Previous experimental works on streaming regeneration in cell…
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…
