A Combination of Actin Treadmilling and Cross-Linking Drives Contraction of Random Actomyosin Arrays

A mathematical model for axonal transport of large cargo vesicles

In this study, we consider axonal transport of large cargo vesicles characterised by transient expansion of the axon shaft. Our goal is to formulate a mathematical model which captures the dynamic mechanical interaction of such cargo vesicles with the membrane associated periodic cytoskeletal structure (MPS). It consists of regularly spaced actin rings that are transversal to the longitudinal direction of the axon and involved in the radial contraction of the axon. A system of force balance equations is formulated by which we describe the transversal rings as visco-elastic Kelvin-Voigt elements. In a homogenisation limit, we reformulate the model as a free boundary problem for the interaction of the submembranous MPS with the large vesicle. We derive a non-linear force-velocity relation as a quasi-steady state solution. Computationally we analyse the vesicle size dependence of the transport speed and use an asymptotic approximation to formulate it as a power law that can be tested experimentally.

Contractile ring composition dictates kinetics of in silico contractility

Constriction kinetics of the cytokinetic ring are expected to depend on dynamic adjustment of contractile ring composition, but the impact of ring component abundance dynamics on ring constriction is understudied. Computational models generally assume that contractile networks maintain constant total amounts of components, which is not always true. To test how compositional dynamics affect constriction kinetics, we first measured F-actin, non-muscle myosin II, septin, and anillin during Caenorhabditis elegans zygotic mitosis. A custom microfluidic device that positioned the cell with the division plane parallel to a light sheet allowed even illumination of the cytokinetic ring. Measured component abundances were implemented in a three-dimensional agent-based model of a membrane-associated contractile ring. With constant network component amounts, constriction completed with biologically unrealistic kinetics. However, imposing the measured changes in component quantities allowed this model to elicit realistic constriction kinetics. Simulated networks were more sensitive to changes in motor and filament amounts than those of crosslinkers and tethers. Our findings highlight the importance of network composition for actomyosin contraction kinetics.

Constriction of Actin Rings by Passive Crosslinkers

In many organisms, cell division is driven by the constriction of a cytokinetic ring, which consists of actin filaments and crosslinking proteins. While it has long been believed that the constriction is driven by motor proteins, it has recently been discovered that passive crosslinkers that do not turn over fuel are able to generate enough force to constrict actin filament rings. To study the ring constriction dynamics, we develop a model that includes the driving force of crosslinker condensation and the opposing forces of friction and filament bending. We analyze the constriction force as a function of ring topology and crosslinker concentration, and predict forces that are sufficient to constrict an unadorned plasma membrane. Our model also predicts that actin-filament sliding arises from an interplay between filament rotation and crosslinker hopping, producing frictional forces that are low compared with those of crosslinker-mediated microtubule sliding.

Computational model of integrin adhesion elongation under an actin fiber

Cells create physical connections with the extracellular environment through adhesions. Nascent adhesions form at the leading edge of migrating cells and either undergo cycles of disassembly and reassembly, or elongate and stabilize at the end of actin fibers. How adhesions assemble has been addressed in several studies, but the exact role of actin fibers in the elongation and stabilization of nascent adhesions remains largely elusive. To address this question, here we extended our computational model of adhesion assembly by incorporating an actin fiber that locally promotes integrin activation. The model revealed that an actin fiber promotes adhesion stabilization and elongation. Actomyosin contractility from the fiber also promotes adhesion stabilization and elongation, by strengthening integrin-ligand interactions, but only up to a force threshold. Above this force threshold, most integrin-ligand bonds fail, and the adhesion disassembles. In the absence of contraction, actin fibers still support adhesions stabilization. Collectively, our results provide a picture in which myosin activity is dispensable for adhesion stabilization and elongation under an actin fiber, offering a framework for interpreting several previous experimental observations.

Intrinsic cell rheology drives junction maturation

A fundamental property of higher eukaryotes that underpins their evolutionary success is stable cell-cell cohesion. Yet, how intrinsic cell rheology and stiffness contributes to junction stabilization and maturation is poorly understood. We demonstrate that localized modulation of cell rheology governs the transition of a slack, undulated cell-cell contact (weak adhesion) to a mature, straight junction (optimal adhesion). Cell pairs confined on different geometries have heterogeneous elasticity maps and control their own intrinsic rheology co-ordinately. More compliant cell pairs grown on circles have slack contacts, while stiffer triangular cell pairs favour straight junctions with flanking contractile thin bundles. Counter-intuitively, straighter cell-cell contacts have reduced receptor density and less dynamic junctional actin, suggesting an unusual adaptive mechano-response to stabilize cell-cell adhesion. Our modelling informs that slack junctions arise from failure of circular cell pairs to increase their own intrinsic stiffness and resist the pressures from the neighbouring cell. The inability to form a straight junction can be reversed by increasing mechanical stress artificially on stiffer substrates. Our data inform on the minimal intrinsic rheology to generate a mature junction and provide a springboard towards understanding elements governing tissue-level mechanics.

F-actin bending facilitates net actomyosin contraction By inhibiting expansion with plus-end-located myosin motors

Contraction of actomyosin networks underpins important cellular processes including motility and division. The mechanical origin of actomyosin contraction is not fully-understood. We investigate whether contraction arises on the scale of individual filaments, without needing to invoke network-scale interactions. We derive discrete force-balance and continuum partial differential equations for two symmetric, semi-flexible actin filaments with an attached myosin motor. Assuming the system exists within a homogeneous background material, our method enables computation of the stress tensor, providing a measure of contractility. After deriving the model, we use a combination of asymptotic analysis and numerical solutions to show how F-actin bending facilitates contraction on the scale of two filaments. Rigid filaments exhibit polarity-reversal symmetry as the motor travels from the minus to plus-ends, such that contractile and expansive components cancel. Filament bending induces a geometric asymmetry that brings the filaments closer to parallel as a myosin motor approaches their plus-ends, decreasing the effective spring force opposing motor motion. The reduced spring force enables the motor to move faster close to filament plus-ends, which reduces expansive stress and gives rise to net contraction. Bending-induced geometric asymmetry provides both new understanding of actomyosin contraction mechanics, and a hypothesis that can be tested in experiments.

A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.

The actin cytoskeleton is a complex dynamic system, regulated by multiple proteins that bind to actin filaments. Some actin-binding proteins are crosslinkers, which can bind pairs of actin filaments, forming actin networks. Actin crosslinkers can be passive linkers, providing only structural integrity, or can be active linkers such as myosin motors, which exert forces on the network. Experiments have shown that crosslinked actin networks can behave viscously when the number of passive crosslinkers is low, but become elastic, when there are many crosslinkers. Motors can only lead to contraction of the network when there is an intermediate concentration of passive crosslinkers. The behavior of networks in the cell depends on the concentration and activity of several distinct crosslinkers, which have different binding sites, geometries, affinities, and concentrations. In this work we propose a simple analytical model based on chemical kinetics and the Flory-Stockmayer theory that gives us insight into how different crosslinkers interact with the actin filaments so as to give rise to the emergent mechanical behavior. This theory also allows us to compute analytically several crucial aspects of the development of the mechanical properties during network assembly.

Protein friction and filament bending facilitate contraction of disordered actomyosin networks

We use mathematical modeling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semiflexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament systems to show that filament bending flexibility can facilitate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent filament aggregation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only arise because of additional regulatory mechanisms or more complex mechanical behavior.

Anillin propels myosin-independent constriction of actin rings

Constriction of the cytokinetic ring, a circular structure of actin filaments, is an essential step during cell division. Mechanical forces driving the constriction are attributed to myosin motor proteins, which slide actin filaments along each other. However, in multiple organisms, ring constriction has been reported to be myosin independent. How actin rings constrict in the absence of motor activity remains unclear. Here, we demonstrate that anillin, a non-motor actin crosslinker, indispensable during cytokinesis, autonomously propels the contractility of actin bundles. Anillin generates contractile forces of tens of pico-Newtons to maximise the lengths of overlaps between bundled actin filaments. The contractility is enhanced by actin disassembly. When multiple actin filaments are arranged into a ring, this contractility leads to ring constriction. Our results indicate that passive actin crosslinkers can substitute for the activity of molecular motors to generate contractile forces in a variety of actin networks, including the cytokinetic ring.

Ventral stress fibers induce plasma membrane deformation in human fibroblasts

Interactions between the actin cytoskeleton and the plasma membrane are important in many eukaryotic cellular processes. During these processes, actin structures deform the cell membrane outward by applying forces parallel to the fiber’s major axis (as in migration) or they deform the membrane inward by applying forces perpendicular to the fiber’s major axis (as in the contractile ring during cytokinesis). Here we describe a novel actin–membrane interaction in human dermal myofibroblasts. When labeled with a cytosolic fluorophore, the myofibroblasts displayed prominent fluorescent structures on the ventral side of the cell. These structures are present in the cell membrane and colocalize with ventral actin stress fibers, suggesting that the stress fibers bend the membrane to form a “cytosolic pocket” that the fluorophores diffuse into, creating the observed structures. The existence of this pocket was confirmed by transmission electron microscopy. While dissolving the stress fibers, inhibiting fiber protein binding, or inhibiting myosin II binding of actin removed the observed pockets, modulating cellular contractility did not remove them. Taken together, our results illustrate a novel actin–membrane bending topology where the membrane is deformed outward rather than being pinched inward, resembling the topological inverse of the contractile ring found in cytokinesis.

The Ringleaders: Understanding the Apicomplexan Basal Complex Through Comparison to Established Contractile Ring Systems

The actomyosin contractile ring is a key feature of eukaryotic cytokinesis, conserved across many eukaryotic kingdoms. Recent research into the cell biology of the divergent eukaryotic clade Apicomplexa has revealed a contractile ring structure required for asexual division in the medically relevant genera Toxoplasma and Plasmodium; however, the structure of the contractile ring, known as the basal complex in these parasites, remains poorly characterized and in the absence of a myosin II homolog, it is unclear how the force required of a cytokinetic contractile ring is generated. Here, we review the literature on the basal complex in Apicomplexans, summarizing what is known about its formation and function, and attempt to provide possible answers to this question and suggest new avenues of study by comparing the Apicomplexan basal complex to well-studied, established cytokinetic contractile rings and their mechanisms in organisms such as S. cerevisiae and D. melanogaster. We also compare the basal complex to structures formed during mitochondrial and plastid division and cytokinetic mechanisms of organisms beyond the Opisthokonts, considering Apicomplexan diversity and divergence.

Comparative Analysis of the Roles of Non-muscle Myosin-IIs in Cytokinesis in Budding Yeast, Fission Yeast, and Mammalian Cells

The contractile ring, which plays critical roles in cytokinesis in fungal and animal cells, has fascinated biologists for decades. However, the basic question of how the non-muscle myosin-II and actin filaments are assembled into a ring structure to drive cytokinesis remains poorly understood. It is even more mysterious why and how the budding yeast Saccharomyces cerevisiae, the fission yeast Schizosaccharomyces pombe, and humans construct the ring structure with one, two, and three myosin-II isoforms, respectively. Here, we provide a comparative analysis of the roles of the non-muscle myosin-IIs in cytokinesis in these three model systems, with the goal of defining the common and unique features and highlighting the major questions regarding this family of proteins.

Bond Type and Discretization of Nonmuscle Myosin II Are Critical for Simulated Contractile Dynamics

Molecular motors drive cytoskeletal rearrangements to change cell shape. Myosins are the motors that move, cross-link, and modify the actin cytoskeleton. The primary force generator in contractile actomyosin networks is nonmuscle myosin II (NMMII), a molecular motor that assembles into ensembles that bind, slide, and cross-link actin filaments (F-actin). The multivalence of NMMII ensembles and their multiple roles have confounded the resolution of crucial questions, including how the number of NMMII subunits affects dynamics and what affects the relative contribution of ensembles' cross-linking versus motoring activities. Because biophysical measurements of ensembles are sparse, modeling of actomyosin networks has aided in discovering the complex behaviors of NMMII ensembles. Myosin ensembles have been modeled via several strategies with variable discretization or coarse graining and unbinding dynamics, and although general assumptions that simplify motor ensembles result in global contractile behaviors, it remains unclear which strategies most accurately depict cellular activity. Here, we used an agent-based platform, Cytosim, to implement several models of NMMII ensembles. Comparing the effects of bond type, we found that ensembles of catch-slip and catch motors were the best force generators and binders of filaments. Slip motor ensembles were capable of generating force but unbound frequently, resulting in slower contractile rates of contractile networks. Coarse graining of these ensemble types from two sets of 16 motors on opposite ends of a stiff rod to two binders, each representing 16 motors, reduced force generation, contractility, and the total connectivity of filament networks for all ensemble types. A parallel cluster model, previously used to describe ensemble dynamics via statistical mechanics, allowed better contractility with coarse graining, though connectivity was still markedly reduced for this ensemble type with coarse graining. Together, our results reveal substantial tradeoffs associated with the process of coarse graining NMMII ensembles and highlight the robustness of discretized catch-slip ensembles in modeling actomyosin networks.

Reversal of contractility as a signature of self-organization in cytoskeletal bundles

Bundles of cytoskeletal filaments and molecular motors generate motion in living cells, and have internal structures ranging from very organized to apparently disordered. The mechanisms powering the disordered structures are debated, and existing models predominantly predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay between three well-characterized internal dynamical processes in cytoskeletal bundles: filament assembly and disassembly, the attachement-detachment dynamics of motors and that of crosslinking proteins. The resulting self-organization is easily understood in terms of motor and crosslink localization, and allows for an extensive control of the active bundle mechanics, including reversals of the filaments’ apparent velocities and the possibility of generating extension instead of contraction. This reversal mirrors some recent experimental observations, and provides a robust criterion to experimentally elucidate the underpinnings of both actomyosin activity and the dynamics of microtubule/motor assemblies in vitro as well as in diverse intracellular structures ranging from contractile bundles to the mitotic spindle.

The Actin Cytoskeleton as an Active Adaptive Material

Actin is the main protein used by biological cells to adapt their structure and mechanics to their needs. Cellular adaptation is made possible by molecular processes that strongly depend on mechanics. The actin cytoskeleton is also an active material that continuously consumes energy. This allows for dynamical processes that are possible only out of equilibrium and opens up the possibility for multiple layers of control that have evolved around this single protein.Here we discuss the actin cytoskeleton from the viewpoint of physics as an active adaptive material that can build structures superior to man-made soft matter systems. Not only can actin be used to build different network architectures on demand and in an adaptive manner, but it also exhibits the dynamical properties of feedback systems, like excitability, bistability, or oscillations. Therefore, it is a prime example of how biology couples physical structure and information flow and a role model for biology-inspired metamaterials.

Crosslinking activity of non-muscle myosin II is not sufficient for embryonic cytokinesis in C. elegans

Cytokinesis in animal cells requires the assembly and constriction of a contractile actomyosin ring. Non-muscle myosin II is essential for cytokinesis, but the role of its motor activity remains unclear. Here, we examine cytokinesis in C. elegans embryos expressing non-muscle myosin motor mutants generated by genome editing. Two non-muscle motor-dead myosins capable of binding F-actin do not support cytokinesis in the one-cell embryo, and two partially motor-impaired myosins delay cytokinesis and render rings more sensitive to reduced myosin levels. Further analysis of myosin mutants suggests that it is myosin motor activity, and not the ability of myosin to crosslink F-actin, that drives the alignment and compaction of F-actin bundles during contractile ring assembly, and that myosin motor activity sets the pace of contractile ring constriction. We conclude that myosin motor activity is required at all stages of cytokinesis. Finally, characterization of the corresponding motor mutations in C. elegans major muscle myosin shows that motor activity is required for muscle contraction but is dispensable for F-actin organization in adult muscles.

This article has an associated ‘The people behind the papers’ interview.

Highlighted Article: The motor activity of non-muscle myosin II is essential for cytokinesis and contributes to all stages of the process in C. elegans embryos.

Uncovering the dynamic precursors to motor-driven contraction of active gels

Cells and tissues have the remarkable ability to actively generate the forces required to change their shape. This active mechanical behavior is largely mediated by the actin cytoskeleton, a crosslinked network of actin filaments that is contracted by myosin motors. Experiments and active gel theories have established that the length scale over which gel contraction occurs is governed by a balance between molecular motor activity and crosslink density. By contrast, the dynamics that govern the contractile activity of the cytoskeleton remain poorly understood. Here we investigate the microscopic dynamics of reconstituted actin-myosin networks using simultaneous real-space video microscopy and Fourier-space dynamic light scattering. Light scattering reveals different regimes of microscopic dynamics as a function of sample age. We uncover two dynamical precursors that precede macroscopic gel contraction. One is characterized by a progressive acceleration of stress-induced rearrangements, while the other consists of sudden, heterogeneous rearrangements. Intriguingly, our findings suggest a qualitative analogy between self-driven rupture and collapse of active gels and the delayed rupture of passive gels observed in earlier studies of colloidal gels under external loads.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Molecular Mechanism of Cytokinesis

Division of amoebas, fungi, and animal cells into two daughter cells at the end of the cell cycle depends on a common set of ancient proteins, principally actin filaments and myosin-II motors. Anillin, formins, IQGAPs, and many other proteins regulate the assembly of the actin filaments into a contractile ring positioned between the daughter nuclei by different mechanisms in fungi and animal cells. Interactions of myosin-II with actin filaments produce force to assemble and then constrict the contractile ring to form a cleavage furrow. Contractile rings disassemble as they constrict. In some cases, knowledge about the numbers of participating proteins and their biochemical mechanisms has made it possible to formulate molecularly explicit mathematical models that reproduce the observed physical events during cytokinesis by computer simulations.

Network Contractility During Cytokinesis-from Molecular to Global Views

Cytokinesis is the last stage of cell division, which partitions the mother cell into two daughter cells. It requires the assembly and constriction of a contractile ring that consists of a filamentous contractile network of actin and myosin. Network contractility depends on network architecture, level of connectivity and myosin motor activity, but how exactly is the contractile ring network organized or interconnected and how much it depends on motor activity remains unclear. Moreover, the contractile ring is not an isolated entity; rather, it is integrated into the surrounding cortex. Therefore, the mechanical properties of the cell cortex and cortical behaviors are expected to impact contractile ring functioning. Due to the complexity of the process, experimental approaches have been coupled to theoretical modeling in order to advance its global understanding. While earlier coarse-grained descriptions attempted to provide an integrated view of the process, recent models have mostly focused on understanding the behavior of an isolated contractile ring. Here we provide an overview of the organization and dynamics of the actomyosin network during cytokinesis and discuss existing theoretical models in light of cortical behaviors and experimental evidence from several systems. Our view on what is missing in current models and should be tested in the future is provided.

Actin turnover ensures uniform tension distribution during cytokinetic actomyosin ring contraction

In many eukaryotes, cytokinesis is facilitated by the contraction of an actomyosin ring (AMR). The exact mechanisms that lead to this contractility are unknown, although some models posit that actin turnover in the AMR is essential. The effect of reduced actin dynamics during AMR formation has been well studied in Schizosaccharomyces pombe; however, the corresponding effects on AMR contraction are not well understood. By using mutants of the fission yeast actin severing protein Adf1, we observed that contracting AMRs display a "peeling" phenotype, where bundles of actin and myosin peel off from one side of the AMR, and are pulled across to the opposite side. This occurs multiple times during cytokinesis and is dependent on the activity of myosins Myo2, Myp2, and Myo51. We found that the distribution of Myo2 in the AMR anticorrelates with the location of peeling events, suggesting that peeling is caused by a nonuniform tension distribution around the AMR, and that one of the roles of actin turnover is to maintain a uniform tension distribution around the AMR.

Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis

Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to 'modeling for biologists', and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.

Molecular mechanisms of contractile-ring constriction and membrane trafficking in cytokinesis

In this review, we discuss the molecular mechanisms of cytokinesis from plants to humans, with a focus on contribution of membrane trafficking to cytokinesis. Selection of the division site in fungi, metazoans, and plants is reviewed, as well as the assembly and constriction of a contractile ring in fungi and metazoans. We also provide an introduction to exocytosis and endocytosis, and discuss how they contribute to successful cytokinesis in eukaryotic cells. The conservation in the coordination of membrane deposition and cytoskeleton during cytokinesis in fungi, metazoans, and plants is highlighted.

Cell-cell adhesion interface: orthogonal and parallel forces from contraction, protrusion, and retraction

The epithelial lateral membrane plays a central role in the integration of intercellular signals and, by doing so, is a principal determinant in the emerging properties of epithelial tissues. Mechanical force, when applied to the lateral cell-cell interface, can modulate the strength of adhesion and influence intercellular dynamics. Yet the relationship between mechanical force and epithelial cell behavior is complex and not completely understood. This commentary aims to provide an investigative look at the usage of cellular forces at the epithelial cell-cell adhesion interface.

Architecture shapes contractility in actomyosin networks

Myosin-driven contraction of the actin cytoskeleton is at the base of cell and tissue morphogenesis. At the molecular level, myosin motors drive contraction by sliding actin filaments past one another using energy produced by ATP hydrolysis. How this microscopic sliding activity gives rise to cell-scale contractions has been an active research question first in muscle cells, and over the last few decades in non-muscle cells. While many early investigations focused on myosin motor activity, increasingly, the nanoscale architecture of the actin network emerges as a key regulator of contractility. Here we review theoretical and in vitro reconstitution studies that have uncovered some of the key mechanisms by which actin network organization controls contractile tension generation. We then discuss recent findings indicating that similar principles apply in cells.

Cross-linkers both drive and brake cytoskeletal remodeling and furrowing in cytokinesis

Cell shape changes such as cytokinesis are driven by the actomyosin contractile cytoskeleton. The molecular rearrangements that bring about contractility in nonmuscle cells are currently debated. Specifically, both filament sliding by myosin motors, as well as cytoskeletal cross-linking by myosins and nonmotor cross-linkers, are thought to promote contractility. Here we examined how the abundance of motor and nonmotor cross-linkers affects the speed of cytokinetic furrowing. We built a minimal model to simulate contractile dynamics in the Caenorhabditis elegans zygote cytokinetic ring. This model predicted that intermediate levels of nonmotor cross-linkers are ideal for contractility; in vivo, intermediate levels of the scaffold protein anillin allowed maximal contraction speed. Our model also demonstrated a nonlinear relationship between the abundance of motor ensembles and contraction speed. In vivo, thorough depletion of nonmuscle myosin II delayed furrow initiation, slowed F-actin alignment, and reduced maximum contraction speed, but partial depletion allowed faster-than-expected kinetics. Thus, cytokinetic ring closure is promoted by moderate levels of both motor and nonmotor cross-linkers but attenuated by an over-abundance of motor and nonmotor cross-linkers. Together, our findings extend the growing appreciation for the roles of cross-linkers in cytokinesis and reveal that they not only drive but also brake cytoskeletal remodeling.

A theory that predicts behaviors of disordered cytoskeletal networks

Morphogenesis in animal tissues is largely driven by actomyosin networks, through tensions generated by an active contractile process. Although the network components and their properties are known, and networks can be reconstituted in vitro, the requirements for contractility are still poorly understood. Here, we describe a theory that predicts whether an isotropic network will contract, expand, or conserve its dimensions. This analytical theory correctly predicts the behavior of simulated networks, consisting of filaments with varying combinations of connectors, and reveals conditions under which networks of rigid filaments are either contractile or expansile. Our results suggest that pulsatility is an intrinsic behavior of contractile networks if the filaments are not stable but turn over. The theory offers a unifying framework to think about mechanisms of contractions or expansion. It provides the foundation for studying a broad range of processes involving cytoskeletal networks and a basis for designing synthetic networks.

Myosin Clusters of Finite Size Develop Contractile Stress in 1D Random Actin Arrays

Myosin-powered force generation and contraction in nonmuscle cells underlies many cell biological processes and is based on contractility of random actin arrays. This contractility must rely on a microscopic asymmetry, the precise mechanism of which is not completely clear. A number of models of mechanical and structural asymmetries in actomyosin contraction have been posited. Here, we examine a contraction mechanism based on a finite size of myosin clusters and anisotropy of force generation by myosin heads at the ends of the myosin clusters. We use agent-based numerical simulations to demonstrate that if average lengths of actin filaments and myosin clusters are similar, then the proposed microscopic asymmetry leads to effective contraction of random 1D actomyosin arrays. We discuss the model's implication for mechanics of contractile rings and stress fibers.

Actin turnover maintains actin filament homeostasis during cytokinetic ring contraction

Many cytokinetic actomyosin ring components undergo dynamic turnover, but its function is unclear. Chew et al. show that continuous actin polymerization ensures crucial F-actin homeostasis during ring contraction, without which ring proteins organize into noncontractile clusters.

Cytokinesis in many eukaryotes involves a tension-generating actomyosin-based contractile ring. Many components of actomyosin rings turn over during contraction, although the significance of this turnover has remained enigmatic. Here, using Schizosaccharomyces japonicus, we investigate the role of turnover of actin and myosin II in its contraction. Actomyosin ring components self-organize into ∼1-µm-spaced clusters instead of undergoing full-ring contraction in the absence of continuous actin polymerization. This effect is reversed when actin filaments are stabilized. We tested the idea that the function of turnover is to ensure actin filament homeostasis in a synthetic system, in which we abolished turnover by fixing rings in cell ghosts with formaldehyde. We found that these rings contracted fully upon exogenous addition of a vertebrate myosin. We conclude that actin turnover is required to maintain actin filament homeostasis during ring contraction and that the requirement for turnover can be bypassed if homeostasis is achieved artificially.

Morphological Transformation and Force Generation of Active Cytoskeletal Networks

Cells assemble numerous types of actomyosin bundles that generate contractile forces for biological processes, such as cytokinesis and cell migration. One example of contractile bundles is a transverse arc that forms via actomyosin-driven condensation of actin filaments in the lamellipodia of migrating cells and exerts significant forces on the surrounding environments. Structural reorganization of a network into a bundle facilitated by actomyosin contractility is a physiologically relevant and biophysically interesting process. Nevertheless, it remains elusive how actin filaments are reoriented, buckled, and bundled as well as undergo tension buildup during the structural reorganization. In this study, using an agent-based computational model, we demonstrated how the interplay between the density of myosin motors and cross-linking proteins and the rigidity, initial orientation, and turnover of actin filaments regulates the morphological transformation of a cross-linked actomyosin network into a bundle and the buildup of tension occurring during the transformation.

Role of Turnover in Active Stress Generation in a Filament Network

We study the effect of turnover of cross-linkers, motors, and filaments on the generation of a contractile stress in a network of filaments connected by passive cross-linkers and subjected to the forces exerted by molecular motors. We perform numerical simulations where filaments are treated as rigid rods and molecular motors move fast compared to the time scale of an exchange of cross-linkers. We show that molecular motors create a contractile stress above a critical number of cross-linkers. When passive cross-linkers are allowed to turn over, the stress exerted by the network vanishes due to the formation of clusters. When both filaments and passive cross-linkers turn over, clustering is prevented and the network reaches a dynamic contractile steady state. A maximum stress is reached for an optimum ratio of the filament and cross-linker turnover rates. Taken together, our work reveals conditions for stress generation by molecular motors in a fluid isotropic network of rearranging filaments.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array

We use perturbation theory to derive a continuum model for the dynamic actomyosin bundle/ring in the regime of very strong crosslinking. Actin treadmilling is essential for contraction. Linear stability analysis and numerical solutions of the model equations reveal that when the actin treadmilling is very slow, actin and myosin aggregate into equidistantly spaced peaks. When treadmilling is significant, actin filament of one polarity are distributed evenly, while filaments of the opposite polarity develop a shock wave moving with the treadmilling velocity. Myosin aggregates into a sharp peak surfing the crest of the actin wave. Any actomyosin aggregation diminishes contractile stress. The easiest way to maintain higher contraction is to upregulate the actomyosin turnover which destabilizes nontrivial patterns and stabilizes the homogeneous actomyosin distributions. We discuss the model's implications for the experiment.

Architecture and Connectivity Govern Actin Network Contractility

Actomyosin contractility plays a central role in a wide range of cellular processes, including the establishment of cell polarity, cell migration, tissue integrity, and morphogenesis during development. The contractile response is variable and depends on actomyosin network architecture and biochemical composition. To determine how this coupling regulates actomyosin-driven contraction, we used a micropatterning method that enables the spatial control of actin assembly. We generated a variety of actin templates and measured how defined actin structures respond to myosin-induced forces. We found that the same actin filament crosslinkers either enhance or inhibit the contractility of a network, depending on the organization of actin within the network. Numerical simulations unified the roles of actin filament branching and crosslinking during actomyosin contraction. Specifically, we introduce the concept of "network connectivity" and show that the contractions of distinct actin architectures are described by the same master curve when considering their degree of connectivity. This makes it possible to predict the dynamic response of defined actin structures to transient changes in connectivity. We propose that, depending on the connectivity and the architecture, network contraction is dominated by either sarcomeric-like or buckling mechanisms. More generally, this study reveals how actin network contractility depends on its architecture under a defined set of biochemical conditions.