Amplification of actin polymerization forces

Abstract

The actin cytoskeleton drives many essential processes in vivo, using molecular motors and actin assembly as force generators. We discuss here the propagation of forces caused by actin polymerization, highlighting simple configurations where the force developed by the network can exceed the sum of the polymerization forces from all filaments.

Figure 1.

Different actin networks. Networks of actin filaments are essential for many biological processes at the cellular level, and the organization of the filaments in space must be adapted to the task. Here, polymerization force (orange) of actin filaments (red) occurs near the plasma membrane (blue). Linear filopodia bundles with fascin (black) can produce high speeds, but represent a weak configuration for force generation. Lamellipodia are thin cellular extensions in which filaments are nearly parallel to the substrate on which the cell is crawling. The 2D branched network, created by Arp2/3 actin-nucleating complexes (black), can produce higher forces at the expense of displacement. During endocytosis in yeast, actin forms a 3D network at the site of the invagination that appears roughly spherical, but the organization of actin filaments in space is not known. The coat structure (yellow) enables actin to pull the membrane inward and actin polymerizes near the base of the structure, where Arp2/3 nucleators are shown in black (Picco et al., 2015). Endocytosis requires strong force amplification to pull the invagination against the turgor pressure.

Figure 2.

Polymerization mechanics. (A) During polymerization, the addition of one actin monomer (orange) corresponds to an elongation (δ) at the barbed end of an actin filament (red) and is associated with a change of free energy (ΔG_p = −k_b T ln(C/C*)). (B) The work required to push a load over a distance (h) with a force (f) is f × h, and thus assembly remains favorable as long as ΔG_p + f × h < 0. In the case where polymerization occurs straight against a load (h = δ), the maximal force (f_a) is f_a = k_b T ln(C/C*)/δ (Hill, 1981). (C) If the filament encounters the load with an angle (θ), then h = δ sinθ and the maximal force is consequently increased: f_θ = f_a/sinθ. (D) In the branched network of a lamellipod, actin grows against the leading membrane at an angle (θ = ∼54°). In the absence of friction, the force between the polymerizing tip (orange) of the actin and the membrane (blue) is perpendicular to the membrane. It can then reach a maximum magnitude of f_a/sinθ. The sum of the forces produced by the two filaments is then ∼2.5 f_a. (E) Higher forces arise by polymerizing with shallow angles. The device illustrated here is composed of a growing actin filament with a “leg” on its side. By elongating, the filament will induce rotation around the pivot point, where the leg is contacting the membrane. High forces can be exerted on a load supported at the branch point, as a result of the amplification achieved by the lever arm and contact angle. (F) The highest forces are generated if a filament polymerizes parallel to the surface. In the illustrated configuration, elongation of the filament will cause a load (green dome) to separate from the membrane. The maximal force is calculated as in E, except that anchoring has to be assumed at the pivot point to balance forces horizontally. The device can sustain high forces applied on the top of the dome because the upward movement is small compared with the elongation of the filament.