A viscous two-phase model for contractile actomyosin bundles

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.

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.

Balance between Force Generation and Relaxation Leads to Pulsed Contraction of Actomyosin Networks

Actomyosin contractility regulates various biological processes, including cell migration and cytokinesis. The cell cortex underlying the membrane of eukaryote cells exhibits dynamic contractile behaviors facilitated by actomyosin contractility. Interestingly, the cell cortex shows reversible aggregation of actin and myosin called "pulsed contraction" in diverse cellular phenomena, such as embryogenesis and tissue morphogenesis. Although contractile behaviors of actomyosin machinery have been studied extensively in several in vitro experiments and computational studies, none of them successfully reproduced the pulsed contraction observed in vivo. Recent experiments have suggested the pulsed contraction is dependent upon the spatiotemporal expression of a small GTPase protein called RhoA. This only indicates the significance of biochemical signaling pathways during the pulsed contraction. In this study, we reproduced the pulsed contraction with only the mechanical and dynamic behaviors of cytoskeletal elements. First, we observed that small pulsed clusters or clusters with fluctuating sizes may appear when there is subtle balance between force generation from motors and force relaxation induced by actin turnover. However, the size and duration of these clusters differ from those of clusters observed during the cellular phenomena. We found that clusters with physiologically relevant size and duration can appear only with both actin turnover and angle-dependent F-actin severing resulting from buckling induced by motor activities. We showed how parameters governing F-actin severing events regulate the size and duration of pulsed clusters. Our study sheds light on the underestimated significance of F-actin severing for the pulsed contraction observed in physiological processes.

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

We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive. The simulations reveal how contraction scales with mechanochemical parameters. For example, they show that the ring made of longer filaments generates greater force but contracts slower. The model predicts that the ring contracts with a constant rate proportional to the initial ring radius if either myosin is released from the ring during contraction and actin filaments shorten, or if myosin is retained in the ring, while the actin filament number decreases. We demonstrate that a balance of actin nucleation and compression-dependent disassembly can also sustain contraction. Finally, the model demonstrates that with time pattern formation takes place in the ring, worsening the contractile process. The more random the actin dynamics are, the higher the contractility will be.

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.

A mechanism of leading-edge protrusion in the absence of Arp2/3 complex

Cells employ protrusive leading edges to navigate and promote their migration in diverse physiological environments. Classical models of leading-edge protrusion rely on a treadmilling dendritic actin network that undergoes continuous assembly nucleated by the Arp2/3 complex, forming ruffling lamellipodia. Recent work demonstrated, however, that, in the absence of the Arp2/3 complex, fibroblast cells adopt a leading edge with filopodia-like protrusions (FLPs) and maintain an ability to move, albeit with altered responses to different environmental signals. We show that formin-family actin nucleators are required for the extension of FLPs but are insufficient to produce a continuous leading edge in fibroblasts lacking Arp2/3 complex. Myosin II is concentrated in arc-like regions of the leading edge in between FLPs, and its activity is required for coordinated advancement of these regions with formin-generated FLPs. We propose that actomyosin contraction acting against membrane tension advances the web of arcs between FLPs. Predictions of this model are verified experimentally. The dependence of myosin II in leading-edge advancement helps explain the previously reported defect in directional movement in the Arpc3-null fibroblasts. We provide further evidence that this defect is cell autonomous during chemotaxis.