Actin Mechanics and Fragmentation

Abstract

Cell physiological processes require the regulation and coordination of both mechanical and dynamical properties of the actin cytoskeleton. Here we review recent advances in understanding the mechanical properties and stability of actin filaments and how these properties are manifested at larger (network) length scales. We discuss how forces can influence local biochemical interactions, resulting in the formation of mechanically sensitive dynamic steady states. Understanding the regulation of such force-activated chemistries and dynamic steady states reflects an important challenge for future work that will provide valuable insights as to how the actin cytoskeleton engenders mechanoresponsiveness of living cells.

Keywords: actin; biophysics; cell motility; cofilin; cytoskeleton; persistence length; rheology; severing; strain; stress.

FIGURE 1.

Actin filament organization and deformation in Aplysia neuronal growth cones. A, an example of a Filipodium actin filament bundle buckling (region of interest defined by a red box). Filaments are labeled with rhodamine phalloidin. B, high magnification rotary shadowed electron micrograph of a similar region. Images provided by Dr. Paul Forscher (Yale University).

FIGURE 2.

Actin filament structure and mechanics. A, the four actin subdomains are numbered accordingly, and the DNase I binding loop is labeled. Bound ADP is colored green. The two strands are colored violet or orange. B, two images of an Alexa Fluor 488-labeled actin filament undergoing thermally driven bending fluctuations. The filament length is ∼20 μm. C, top and side view of a buckled actin filament demonstrating out-of-plane deformation caused by twist-bend coupling elasticity (Reprinted from Ref. , De La Cruz, E. M., Roland, J., McCullough, B. R., Blanchoin, L., and Martiel, J.-L. (2010) Origin of twist-bend coupling in actin filaments. Biophys. J. 99, 1852–1860, with permission from Elsevier and the Biophysical Society). D, table of actin filament bending (L_B), torsional (L_T), and twist-bend (L_TB) persistence lengths under standard polymerizing conditions (50 mm KCl, 1–2 mm MgCl₂, pH 7.0, and without phalloidin or associated regulatory proteins) for filaments composed of subunits of the indicated nucleotide states. These persistence lengths are composite values representing weighted average of all populated filament conformations, as noted in the text, and the absolute persistence lengths of the various, individual filament structures are likely to vary. Values are from Ref. .

FIGURE 3.

Force extension of actin filaments. Shown is a linear log plot of the force required to achieve a given end-to-end length of an actin filament 1-μm in contour length. (Note that on a linear log plot, linear functions appear as exponentials instead of straight lines). At room temperature (300 K) and zero force, thermal bending fluctuations along the length of the filament reduce the end-to-end distance below the contour length to ∼983 nm (76), although the contour length is less than the persistence length of actin (10 μm). For small positive (or negative) forces, the filament behaves like a linear entropic spring, with an extension (compression) that is directly proportional to the force (dashed red line) (76). For forces larger than ∼0.1 pN, this entropic spring becomes non-linear, diverging as the end-to-end distance approaches the contour length in the case of an inextensible filament (dotted black line), just as for a worm-like chain (76, 81). Actin filaments are not inextensible, however, and the incorporation of a Young's Modulus of 2.3 gigapascals (26) and proper renormalization of the force (76) yields a more complete picture (solid black line), wherein filaments may be extended beyond their contour length. At forces larger than ∼100 pN, the end-to-end distance exceeds the contour length and asymptotically approaches the response of a purely enthalpic linear spring (dashed blue line). Experiments (82) suggest that filaments rupture at forces of ∼400 pN. Under compression, the critical Euler buckling force is ∼0.4 pN (76), allowing for a large range of end-to-end distances under nearly constant force (solid black line). Inset: the same curves plotted on a linear-linear plot. The complete response can barely be distinguished from the nonlinear entropic response over this range of forces. The equations used to generate these plots can be found in supplemental File S1.

FIGURE 4.

Mechanical response of actin networks. A, schematics indicating the bend-dominated deformations that occur in low density and sparsely cross-linked filament networks (top) and stretch-dominated deformations that occur in high density and densely cross-linked actin networks. B, a full state space of the types of network deformations that occur as a function of actin concentration and filament length (presuming that every filament overlap has a rigid cross-linker). C, the shear elastic modulus as a function of applied stress (x axis) for a network that is stretch dominated, which exhibits stress stiffening, and bending dominated, which exhibits stress weakening.