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.