📝 Original Info
- Title: Branching actin network remodeling governs the force-velocity relationship
- ArXiv ID: 1111.6611
- Date: 2023-06-15
- Authors: : John Doe, Jane Smith, Michael Brown
📝 Abstract
Actin networks, acting as an engine pushing against an external load, are fundamentally important to cell motility. A measure of the effectiveness of an engine is the velocity the engine is able to produce at a given force, the force-velocity curve. One type of force-velocity curve, consisting of a concave region where velocity is insensitive to increasing force followed by a decrease in velocity, is indicative of an adaptive response. In contrast, an engine whose velocity rapidly decays as a convex curve in response to increasing force would indicate a lack of adaptive response. Even taken outside of a cellular context, branching actin networks have been observed to exhibit both concave and convex force-velocity curves. The exact mechanism that can explain both force-velocity curves is not yet known. We carried out an agent-based stochastic simulation to explore such a mechanism. Our results suggest that upon loading, branching actin networks are capable of remodeling by increasing the number filaments growing against the load. Our model provides a mechanism that can account for both convex and concave force-velocity relationships observed in branching actin networks. Finally, our model gives a potential explanation to the experimentally observed force history dependence for actin network velocity.
💡 Deep Analysis
Deep Dive into Branching actin network remodeling governs the force-velocity relationship.
Actin networks, acting as an engine pushing against an external load, are fundamentally important to cell motility. A measure of the effectiveness of an engine is the velocity the engine is able to produce at a given force, the force-velocity curve. One type of force-velocity curve, consisting of a concave region where velocity is insensitive to increasing force followed by a decrease in velocity, is indicative of an adaptive response. In contrast, an engine whose velocity rapidly decays as a convex curve in response to increasing force would indicate a lack of adaptive response. Even taken outside of a cellular context, branching actin networks have been observed to exhibit both concave and convex force-velocity curves. The exact mechanism that can explain both force-velocity curves is not yet known. We carried out an agent-based stochastic simulation to explore such a mechanism. Our results suggest that upon loading, branching actin networks are capable of remodeling by increasing th
📄 Full Content
Branching actin networks are the principle engine that drives cell motility ranging from cell migration (1,2) to endomembrane trafficking (3). In the lamellipodium of migrating cells, actin filaments grow from their barbedends, pushing against the plasma membrane in the direction of cell movement. New filaments branch off of existing filaments through the actin related protein (Arp2/3) complex, activated by WASP at the membrane. Filaments branch at a characteristic angle of ∼ 70 • . Capping proteins limit the growth of filaments by binding to the barbed-end of the filament. At the back of the network, actin filaments depolymerize and are severed, providing a fresh actin monomer supply to the front (1,2). Understanding the basic process by which an actin network is able to exert force against a load is a fundamental step to understanding a number of cellular processes (4).
Both in vitro and in vivo experiments have been performed to probe the force-velocity relationship of growing actin networks (5)(6)(7)(8)(9)(10). Migrating cells show an adaptive response exhibiting a concave force-velocity relationship (6,7). However, the concave force-velocity relationship is preceded by a large reduction in velocity to small forces (6). The mechanism controlling the concave force-velocity relationship and the initial response to small forces in cells is complicated by other cellular components such as focal adhesions. To study the exact mechanism that determines the force-velocity relationship of a branching actin network, in vitro experiments with more controllable conditions have been performed. One study measured the velocity of an actin network growing against a constant load force set by an atomic force microscope, and the resulting force-velocity relationship was convex (10). In a different in vitro experiment, the actin network grew against the flexible cantilever. The load force thus progressively increased as actin polymerization deflected the cantilever, and the network showed a concave force-velocity relationship (9). That experiment also showed a hysteresis effect where the velocity of the network was dependent upon the past forces applied to the network.
Experiments done in vitro have demonstrated both convex and concave force-velocity relationships in branching actin networks. This suggests that actin networks can respond to external forces in both an adaptive and a non-adaptive manner outside of cellular context. Even within the simplified in vitro setting, it is still unclear how the individual factors that govern branching actin network dynamics generate both the convex and the concave curves. It has previously been proposed that the actin network remodels itself in response to force (9), but the nature of such remodeling is largely unknown.
Evidence suggests that actin filaments utilize thermodynamic free energy to add additional monomers to exert force towards the leading edge of the network (11). The proposed model for that behavior has been termed the Brownian ratchet (12)(13)(14). The Brownian ratchet mechanism takes advantage of the asymmetry in the on and off rates of actin monomer binding to an existing filament. Small gaps arise between the actin filaments and the leading edge due to thermodynamic fluctuations. Monomers are able to bind during such fluctuations and push the leading edge forward. The predicted force-velocity curve for a single filament is a convex negative exponential function. When many filaments grow against the same load, they are able to share the load. A simple force-sharing mechanism predicted that the force-velocity curve is nonetheless convex (15), even though its slope is shallower than that for single filament. A model that tries to explain the force-insensitive region of the concave force-velocity curve ( 16) is largely incapable of accounting for the convex curve.
Our theoretical model was built to study both types of force-velocity relationships for branching actin networks. We used an agent-based stochastic simulation method inspired by Weichsel et al. (17) and Schaus and Borisy (18). Our results show that the balance between growth, branching and capping events controls the ability of a branching actin network to reinforce itself against a load. The model can explain both convex and concave force-velocity relationships.
To discern the physical mechanism governing the force-velocity relationships of branching actin networks, we aimed to construct the simplest model able to reproduce the observed effects without compromising the physical essence of actin networks. The model therefore only includes the four essential processes of branching actin networks in in vitro conditions. Below, we describe the qualitative features of our model.
- Filaments grow by adding new monomers to the barbed end of the filaments. When the filament is not in contact with the load, it does not feel the load and, hence, it could grow at its free rate V 0 . When a filament is in conta
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