MINIREVIEW THE JOURNAL OF BIOLOGICAL CHEMISTRY VOL. 290, NO. 28, pp. 17137–17144, July 10, 2015 © 2015 by The American Society for Biochemistry and Molecular Biology, Inc. Published in the U.S.A.
Actin Mechanics and Fragmentation*□
fragment actin filaments and accelerate actin turnover in cells and in reconstituted biomimetic systems (6 –12).
Published, JBC Papers in Press, May 8, 2015, DOI 10.1074/jbc.R115.636472
Actin Structure
S
Enrique M. De La Cruz‡1 and Margaret L. Gardel§2 From the ‡Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06511 and the §Institute for Biophysical Dynamics, James Franck Institute, and Department of Physics, University of Chicago, Chicago, Illinois 60637
Actin Cytoskeleton The non-covalent polymerization of the cytoskeleton protein actin (Fig. 1) into linear filaments powers a variety of nonmuscle cell movements underlying their migration, division, and assembly into multicellular tissue (1). Cross-linking proteins arrange filaments into higher-order assemblies such as parallel bundles of filopodia and microvilli, isotropic networks of the cortex, and contractile bundles in the lamella that provide cells with mechanical integrity, sensing, and shape (2– 4). Contractile myosin motor proteins generate force and work output (i.e. motility and transport) along filament tracks, in both muscle and non-muscle cells (5). Actin filaments grow and shrink from their ends through subunit addition and loss, respectively. Accordingly, the overall assembly dynamics and turnover of the actin cytoskeleton in cells is influenced by factors that modulate the filament end concentration. Nucleating proteins and complexes generate new filament ends, often branching from existing filament templates (1). Capping proteins bind filament ends and slow or inhibit subunit addition (1). Severing and contractile proteins
* This work was supported by National Institutes of Health Grant GM097348 (to E. M. D. L. C), Burroughs Wellcome Career Award and University of Chicago Materials Research Science and Engineering Center (MRSEC) Grant DMR-1420709 (to M. L. G.), and Army Research Office sponsored Multidisciplinary University Research Initiative (ARO MURI) W911NF-14-1-0403 (to E. M. D. L. C and M. L. G.). This is the first article in the Thematic Minireview series “The State of the Cytoskeleton in 2015.” The authors declare that they have no conflicts of interest with the contents of this article. □ S This article contains supplemental File S1. 1 To whom correspondence may be addressed. E-mail: enrique. [email protected]. 2 To whom correspondence may be addressed. E-mail: [email protected].
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Actin Filament Mechanical Properties Actin filaments are polymers with lengths ranging up to ⬎10 m in solution (23) (Fig. 2B). The local asymmetry arising from the ribbon structure averages out to a diameter of ⬃6 nm on the length scales associated with analysis of individual filament and network mechanics. How filaments deform in response to force is governed by their mechanical elastic properties. Recent biochemical, biophysical, and computational studies have revealed the molecular and geometric origins of actin filament mechanical properties and how solution conditions, particularly cations, influence them. Bending, torsional, and twist-bend coupling elasticities dominate individual actin filament mechanical properties. The flexural, or bending, rigidity as well as the extent of deformation determine the energy required to bend a filament segment of a certain length. Likewise, the energy require to twist a filament is determined by the twisting rigidity and the torsional angle that overwinds or unwinds the filament. Twist-bend coupling represents an obligatory coupling between bending and twisting motions, such that filament bending introduces twist and vice versa (24, 25) (Fig. 2C). Actin filaments are rather resistant to stretching (26). However, stretching forces dampen bending JOURNAL OF BIOLOGICAL CHEMISTRY
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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.
Actins are single polypeptide chain proteins (⬃375 amino acids with an ⬃42-kDa molecular mass) folded into a U-shaped structure containing four subdomains (SD1– 4) with a bound adenine nucleotide, either ATP, ADP-Pi, or ADP, and an associated divalent cation, Mg2⫹ in cells, bound within the cleft separating subdomains 1–2 and 3– 4 (Fig. 2A). Actin filaments are commonly described as either a one-start, left-handed helix of subunits with a 2.77-nm rise per subunit (13) or a two-start, right-handed helix with half-staggered filament strands displaying an ⬃72-nm repeat (14). However, filaments in solution adopt multiple distinct structural states (referred to as “structural polymorphism”(15)) with variable twist and subunit tilt distributions that are influenced by regulatory protein occupancy and external forces. Thus, one actually refers to a subset of populated states when describing actin structure. Polymerization is associated with a conformational change in actin, such that incorporated filament subunits appear “flattened” when compared with free monomers (16, 17). Extensive intersubunit contacts stabilize filaments (16 –18), and an individual subunit contacts four neighboring actin molecules (Fig. 2A). Longitudinal contacts within a strand are thought to be stronger than lateral contacts across the strands (19). The DNase I binding loop (residues 36 –52 of SD2; Fig. 2A) adopts a variety of conformations (20), some of which make important long-axis, intersubunit contacts, and plays a central role in regulating actin filament structure and mechanical properties (21, 22).
MINIREVIEW: Actin Mechanics and Fragmentation
A
and twisting motions (27), and can have significant effects on filament structural dynamics. Filament mechanical properties are determined by the strength and distribution of intersubunit contacts (24). Subunit compliance and compressibility (28, 29) presumably play a role in overall filament mechanics. However, mathematical and computational models that treat filament subunits as incompressible entities capture the reported mechanical parameters with reasonable accuracy (24, 25). Filaments twist more easily than they bend, which manifests itself as a larger bending than torsional rigidity. Solution cations bind and stiffen some, but not all (e.g. Saccharomyces cerevisiae), actin filaments (20, 30). Substitution of a single amino acid residue positioned between adjacent, longaxis filament subunits confers S. cerevisiae actin filaments with salt-dependent bending stiffness (30). The filament bending stiffness (i.e. flexural rigidity, ) is equal to the product of the shape-independent stiffness of the protein material (i.e. apparent Young’s modulus, Eapp; referred to as apparent because proteins are not homogenous isotropic materials) and the shapedependent second moment of area (I), which is determined by the strength and distribution of intersubunit contacts. Filaments possessing this “stiffness cation site” display salt-dependent structure and intersubunit contacts, suggesting that stiffness cations may exert their effects on filament mechanics by binding to discrete sites at subunit interfaces and altering the radial distribution (I) and/or the strength (Eapp) of the intersubunit contacts (18). A mechanism in which cations bind at distal sites and allosterically alter intersubunit contacts is also plausible (31). The DNase I binding loop of SD2 participates in longitudinal intersubunit contacts, plays a central role in modulating the filament bending stiffness and displays salt-dependent conformations, making it an attractive structural element for linking salt-dependent filament structure and mechanics. Changes in filament stiffness can also arise from side binding proteins. For example, tropomyosin stiffens actin filaments by increasing its geometric movement (32). Mechanically strained filaments (e.g. deformed in bending and/or twisting) store elastic free energy in their shape. The
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B
C
D
LB
ATP
13 μm
ADP-Pi
10 μm
ADP
9.5 μm
LT
LTB
1.4 μm
0.4 μm
0.5 μm
0.2 μm
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 m. C, top and side view of a buckled actin filament demonstrating out-of-plane deformation caused by twist-bend coupling elasticity (Reprinted from Ref. 24, 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 (LB), torsional (LT), and twist-bend (LTB) 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. 24.
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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).
MINIREVIEW: Actin Mechanics and Fragmentation
Nonlinear Entropic Enthalpic
1
Linear Entropic
0.01 100
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60 40 20 0
1 0.94
80
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0.98
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1.06
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Distance [µm]
0.96
0.98
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End-to-end Distance [µm] 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-m 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 m). 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.
stored energy density depends on the deformation amplitude and the bending rigidity; larger deformations store more energy than small ones, and stiff filaments store more energy than compliant ones at identical deformations. Relaxation back to the straight conformation can potentially be used to generate work and/or force. Alternatively, the deformation amplitude and stored energy can reach the point of irreversibility, causing the filament to fragment. Thermal energy (kBT, where kB is Boltzmann’s constant and T is temperature in Kelvin) can be sufficiently large to induce actin filament shape fluctuations. The filament length at which the deformation energy compares to thermal energy defines the persistence length, which can be defined for bending (LB), twisting (LT), and twist-bend coupling (LTB) deformations (Fig. 2D). Filaments behave as rigid rods at lengths much shorter than the persistence length, as flexible polymers much larger than the persistence length, and as semi-flexible polymers at lengths comparable with the persistence length (33). The bending fluctuations reduce the filament end-to-end length, and the force required to extend and “straighten” the filament is determined by the energy required to reduce the bending fluctuation JULY 10, 2015 • VOLUME 290 • NUMBER 28
amplitude. This entropic spring constant is both highly sensitive to the length of filament segment and becomes highly nonlinear as the end-to-end length approaches the full polymer contour length (34) (Fig. 3). Compressive forces tend to excite the longest wavelength (softest) bending mode, which is comparable with kBT for micrometer length filaments. At a critical compressive force, referred to as critical or Euler force, buckling will occur. The critical force scales linearly with filament bending rigidity and inversely with the square of the filament length (e.g. it takes four times less force to buckle a 2-m filament than a 1-m one with identical bending rigidity) (35). This different response to extension and compression gives filaments a highly asymmetric force extension curve (Fig. 3) that can be approximated in coarse-grained models as cables (36) and is a powerful mechanism by which actin networks can sense (and respond) to different types of stresses (9). Cross-linking proteins organize filaments into parallel (or antiparallel) bundles. The mechanical parameters (twist, bend, and extension) of bundles depend on the width of the bundle and length of the filaments comprising them, as well as the JOURNAL OF BIOLOGICAL CHEMISTRY
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Force [pN]
0.01
Compression
Force [pN]
Extension
100
Complete
MINIREVIEW: Actin Mechanics and Fragmentation density, mechanics, affinity, and exchange kinetics of the crosslinks. For instance, filaments in bundles formed with a compliant cross-linker (e.g. plastin) can readily slide past each and are weakly coupled such that the bundle stiffness increases linearly with the number of actin filaments (37). By contrast, when filaments become tightly coupled to each other by use of crowding agents or high density of compact cross-linker (e.g. fascin), the bundles act as single unit that displays a bending persistence length that scales quadratically with the number of filaments in the bundle (23, 37). In some cases, the cross-link density can impact the degree of coupling and the observed scaling of bundle stiffness (37, 38). Because actin cross-linking proteins are dynamic, the bundle mechanics are also frequency-dependent and depend on the cross-link dynamics as well (37, 39).
3
The abbreviations used are: ADF, actin depolymerizing factor; Aip1, actininteracting protein 1; pN, piconewtons.
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Control over Actin Network and Bundle Architecture Actin cross-linking and bundling proteins assemble filaments into larger scale networks and bundles. Cross-linking VOLUME 290 • NUMBER 28 • JULY 10, 2015
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Filament Fragmentation Fragmentation by severing and contractile motor proteins accelerates actin network turnover and assembly dynamics by increasing the concentration of filament ends where subunits can add and dissociate. As described above, compressive stresses buckle filaments. However, filaments under compressive loads do not deform indefinitely. Rather, they buckle and bend until they reach a deformation curvature where the stored elastic energy exceeds that holding the subunits together and it becomes energetically more favorable for the filament to fragment than remain intact (40). Estimating this stored energy and force requires that all elastic contributions be considered (e.g. bending, twisting, and coupling) because they all contribute to the local energy density that eventually causes filament subunit interface “bonds” to rupture (40). Several classes of regulatory filament-severing proteins have been identified (14). Gelsolin and ADF3/cofilin family members have been characterized most extensively at the biochemical and biophysical level with purified components (14). Gelsolin severs filaments by inserting one of its structural domains between long axis filament subunits, compromising stabilizing intersubunit interactions and promoting fragmentation. Formin INF2 may sever filaments by an analogous insertion, or “wedging,” mechanism (41). The filament-severing mechanism of ADF/cofilin (heretofore referred to as cofilin) appears to be distinct from that of gelsolin and INF2. Cofilin isoforms within and across organisms and species are not identical, and often the observed biochemical activities depend on the isoform and conspecific nature of the actin (42, 43), indicating that the chemical and physical properties of actin itself can influence cofilin function. Cofilins bind weakly to “young” ATP- and ADP-Pi actin filaments and bind orders of magnitude more strongly to “old” ADP-actin filaments (42), which allows for spatially targeted disassembly (44). Vertebrate cofilin binding is positively cooperative (43). Association is far below the diffusion limit for encounter (45) and limited by filament shape fluctuations (45, 46), suggesting opportunistic binding to compliant filament segments (45). Severing occurs preferentially at or near boundaries (e.g. junctions) between bare and cofilin-decorated seg-
ments (47), explaining why the severing activity peaks when filaments are partially decorated (31, 43, 47–51). Multiple factors likely influence the severing activity of ADF/ cofilin, and the contributions of some have yet to be fully resolved. Cofilin alters filament twist (52) and subunit tilt (53), renders filaments more compliant in bending (54) and twisting (55, 56) by dissociating filament-associated stiffness cations (31), and binds filaments in at least two distinct binding modes that may be differentially associated with severing and/or depolymerization activities (44). Thermally driven severing (e.g. in the absence of applied external loads) is weak and presumably dominated by thermodynamic effects originating from structural phase discontinuities at boundaries between bare and decorated segments. Boundaries fragment at smaller deformations than either parent filament (50), suggesting that boundaries are “bad joints” that are susceptible to fragmentation, analogous to the interfacial fracture of some non-protein materials (12). Srv2/CAP (cyclase-associated protein) may enhance severing by cofilin by inducing further conformational changes at boundaries (57). It is also conceivable that cofilin at the end of a bound cluster (43, 44) preferentially adopts a distinct binding mode (e.g. “severing”) from cofilin within a cluster (e.g. “non-severing”). However, a correlation between filament dynamics and thermally driven fragmentation has also been observed (31, 49, 50, 58), suggesting that filament mechanics and the structural dynamics at boundaries can potentially play a role, even in the absence of external load. An attractive model (53) implicates allosteric propagation of cofilin-linked conformational changes (47, 55, 59) to bare, undecorated segments where local, stabilizing cofilin-actin interactions are absent, thus leading to fragmentation within the bare side of boundaries. Actin-interacting protein 1 (Aip1 (60)) accelerates the filament-severing activity of cofilin. One model of enhanced severing (61) implicates further structural changes in cofilin-actin induced by Aip1, possibly a wedge-like mechanism where cofilin is inserted between adjacent long-axis neighbors. Consistent with a functional ternary Aip1-cofilin-actin complex, Aip1 does not dissociate cofilin and enhances severing at all cofilin occupancies (62). However, a different study (63) favors an alternate mechanism (64) in which Aip1 simply competes with cofilin, dissociating it from actin and introducing additional boundaries where severing can occur. The various factors contributing to filament severing may play different roles under cellular conditions. For example, active forces generated by contractile proteins may play a more dominant role (8, 11, 12). The mechanical properties and response of filaments are central to understanding fragmentation in this context because the mechanical heterogeneity and discontinuities introduced by cofilin will lead to unique behaviors that deviate from mechanically homogenous, bare actin filaments (40). Similarly, confinement within the elastic matrix of the cytoplasm (65) will influence the deformation and presumably fragmentation.
MINIREVIEW: Actin Mechanics and Fragmentation
Entropic Spring Extension
Enthalpic Stretch
101
G’ (Pa)
Extension/Stretch dominated
F-acn length
Bend dominated
100
Concentraon
10-2
10-1
100 σ (Pa)
101
102
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.
Actin Network Mechanics The mechanical properties of the actin networks will determine the extent and pattern of deformation in response to JULY 10, 2015 • VOLUME 290 • NUMBER 28
mechanical stress. The type of response will depend on the spatial scale, direction, duration, and magnitude of the applied stress. For example, at the scale of a single bundle or filament, the mechanics can be dominated by the local compressional, stretching, or bending rigidity of the filament/bundle depending on the direction of the applied force. At longer length scales, the mechanical response is dominated both by the mechanics of individual elements as well as by how the filaments/bundles are connected together. Thus, actin network architecture determines the mechanical properties of the elements as well as which types of microscopic deformations occur in response to a macroscopic stress. Below, we describe two regimes that dominate actin network mechanics. In filament networks or bundles that are densely crosslinked, the deformations are self-similar, or affine, from microscopic to macroscopic length scales. For shear or extensional stress, this results in a mechanical response that is dominated by stretching of filaments or bundles (Fig. 4A). The relationship between the stress (force per unit area) and strain (relative deformation) provides a measure of elastic modulus. The elastic modulus has units of energy per volume and can be thought of as the amount of energy required to deform the medium. The elastic modulus of filament networks is determined both by the actin filament/bundle concentration and the stretching and/or by the bending modulus of the filament/bundle itself. Thus, factors that affect the stretching/bending modulus of the filament or bundle (e.g. time scales and applied stress) will directly impact the macroscopic mechanical response. Indeed, the nonlinearity of the extensional spring constant of actin filaments can directly manifest into a nonlinear stiffening of cross-linked networks in response to stresses applied externally (72, 73) or generated internally (e.g. by myosin motors) (74). Strain stiffening in networks composed of linearly elastic filaments/bundles can also arise from geometric effects (75, 76). As the cross-link or filament density is reduced, the sparse connectivity within the network results in deformations that are not self-similar (non-affine) from microscopic to macroscopic length scales. For instance, shear deformation at the macroscopic length scale generates filament bending, with a small fraction of filaments/bundles bearing the majority of the stress. Here the bending-dominated response at the microscopic scale results in softening of the network at macroscopic scale. JOURNAL OF BIOLOGICAL CHEMISTRY
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proteins are monomeric or homodimeric proteins that contain two filament binding sites. Cross-linking proteins can vary considerably in their affinity, compliance, and distance between actin binding sites. Smaller cross-linkers (e.g. fascin and fimbrin) form compact bundles, whereas larger, more compliant cross-linkers (e.g. filamin and ␣-actinin) form loose bundles or “mesh-like” networks. Most cross-linkers exhibit both behaviors with the tendency to form at high cross-linker concentrations. When a stress is applied to an actin network or bundle, the deformations and dynamics of filaments and actin crosslinking proteins determine the mechanical response. In general, this mechanical response will, in some circumstances, behave like an elastic solid, and in others, it will behave like a viscous fluid. Thus, actin networks can be considered viscoelastic in their mechanical response. The architecture of cross-linked actin networks is determined both by filament assembly dynamics (rate of nucleation, growth, and severing) and by factors controlling cross-linking (cross-link kinetics and concentration) and actin filament concentration and length (66, 67). In the absence of cross-linkers, assembled filaments display a homogeneous distribution with a relatively uniform average distance between filaments (termed the “mesh size”). Filaments longer than the mesh size are sterically entangled in the network. Steric entanglements constrain filament motions and, consequently, give rise to viscoelastic behavior (68, 69). Steric entanglements also prevent realignment of filaments into bundles (66). Thus, the architecture of cross-linked networks is determined by competing timescales of bundle formation and the arrested mobility that occurs with entanglement. For a given cross-link type and density, fast growing filaments form fine meshworks, whereas slowly elongating filaments form networks of dense bundles (70). Thus, architecture of cross-linked actin network is kinetically determined, reflecting an arrested or kinetically “trapped” state rather than the lowest energy state defined by true thermodynamic equilibrium (66, 71). As a result, the actin cytoskeletal architectures found within living cells will exist in a dynamic steady state determined by a balance of filament assembly and disassembly dynamics and regulatory protein interactions. These microscopic rates, as discussed above, may also be force-regulated.
MINIREVIEW: Actin Mechanics and Fragmentation
Mechanochemical Feedback in Dynamic Steady States The response of actin filaments and associated binding proteins to applied stress provides a natural mechanism to modify the large-scale network architecture in response to externally applied or internally generated stresses. For actin networks that are in a dynamic steady state with polymer disassembly/assembly, forces that alter the local rate of filament stability (disassembly), assembly, or binding of actin-binding proteins will induce a transition to a new dynamic steady state. Although the experimental characterization of such mechanochemically responsive actin networks is still in its nascent stages, recent data suggest that distinct modules may differentiate branched versus contractile networks in response to stress. The filament binding affinity of the Arp2/3 complex depends on the filament curvature (79), raising the possibility that a branched network exhibiting a compressive load could respond both by modulating the branch density and possibly by cofilinmediated severing and filament subunit exchange. Together, this will increase the branch density and decrease average filament length, resulting in increased force generation network stiffness as a result of the applied load. In contractile networks containing actin and myosin II filaments, network contraction arises from filament bending and buckling (9). This results in a preferential severing of compressed, buckled filaments, thereby altering the local filament end density. In the presence of barbed end capping proteins, this could result in local disassembly from the pointed end, whereby in the presence of barbed end elongation factors, this would result in enhanced assembly. Unraveling how these mechanochemical feedbacks can be used to achieve the dynamic steady states observed in cells and enable cell mechanosensing will be an exciting area of future study. Acknowledgments—We thank Drs. Paul Forscher (Yale University) for providing images in Fig. 1, Austin Elam (Yale University) for preparation of Fig. 2A, Hyeran Kang (Yale University) for images in Fig. 2B, and Patrick McCall for preparing Fig. 3. The data in Fig. 4C were previously published in Ref. 80. We thank Moumita Das for useful suggestions.
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The mechanical response of filament networks is nearly always dependent on the measurement frequency. Energy dissipation arises over a broad range of time scales, ranging from filament fluctuations at high frequencies to cross-link unbinding/unfolding and filament turnover at long time scales. Energy dissipation results in the networks behaving like a fluid, whereby applied stress results in a constant rate of deformation (strain rate) and the ratio determines the viscosity. Experiments of stabilized filaments with dynamic cross-links yield viscoelasticity over a large range of time scales, with approximately equal contributions of elasticity and viscosity to the mechanical response. However, it is still uncertain whether networks formed with dynamic filaments could be well approximated as a fluid. Recent simulations suggest that this may be the case (77) as models of actin as a viscous fluid appear to perform reasonably well in recapitulating observed flows in cells (78).
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50. McCullough, B. R., Grintsevich, E. E., Chen, C. K., Kang, H., Hutchison, A. L., Henn, A., Cao, W., Suarez, C., Martiel, J.-L., Blanchoin, L., Reisler, E., and De La Cruz, E. M. (2011) Cofilin-linked changes in actin filament flexibility promote severing. Biophys. J. 101, 151–159 51. Yeoh, S., Pope, B., Mannherz, H. G., and Weeds, A. (2002) Determining the differences in actin binding by human ADF and cofilin. J. Mol. Biol. 315, 911–925 52. McGough, A., Pope, B., Chiu, W., and Weeds, A. (1997) Cofilin changes the twist of F-actin: implications for actin filament dynamics and cellular function. J. Cell Biol. 138, 771–781 53. Galkin, V. E., Orlova, A., Kudryashov, D. S., Solodukhin, A., Reisler, E., Schröder, G. F., and Egelman, E. H. (2011) Remodeling of actin filaments by ADF/cofilin proteins. Proc. Natl. Acad. Sci. U.S.A. 108, 20568 –20572 54. McCullough, B. R., Blanchoin, L., Martiel, J.-L., and De La Cruz, E. M. (2008) Cofilin increases the bending flexibility of actin filaments: implications for severing and cell mechanics. J. Mol. Biol. 381, 550 –558 55. Prochniewicz, E., Janson, N., Thomas, D. D., and De La Cruz, E. M. (2005) Cofilin increases the torsional flexibility and dynamics of actin filaments. J. Mol. Biol. 353, 990 –1000 56. Fan, J., Saunders, M. G., Haddadian, E. J., Freed, K. F., De La Cruz, E. M., and Voth, G. A. (2013) Molecular origins of cofilin-linked changes in actin filament mechanics. J. Mol. Biol. 425, 1225–1240 57. Chaudhry, F., Breitsprecher, D., Little, K., Sharov, G., Sokolova, O., and Goode, B. L. (2013) Srv2/cyclase-associated protein forms hexameric shurikens that directly catalyze actin filament severing by cofilin. Mol. Biol. Cell 24, 31– 41 58. Chen, C. K., Benchaar, S. A., Phan, M., Grintsevich, E. E., Loo, R. R. O., Loo, J. A., and Reisler, E. (2013) Cofilin-induced changes in F-actin detected via cross-linking with benzophenone-4-maleimide. Biochemistry 52, 5503–5509 59. Bobkov, A. A., Muhlrad, A., Pavlov, D. A., Kokabi, K., Yilmaz, A., and Reisler, E. (2006) Cooperative effects of cofilin (ADF) on actin structure suggest allosteric mechanism of cofilin function. J. Mol. Biol. 356, 325–334 60. Rodal, A. A., Tetreault, J. W., Lappalainen, P., Drubin, D. G., and Amberg, D. C. (1999) Aip1p interacts with cofilin to disassemble actin filaments. J. Cell Biol. 145, 1251–1264 61. Clark, M. G., Teply, J., Haarer, B. K., Viggiano, S. C., Sept, D., and Amberg, D. C. (2006) A genetic dissection of Aip1p’s interactions leads to a model for Aip1p-cofilin cooperative activities. Mol. Biol. Cell 17, 1971–1984 62. Nadkarni, A. V., and Brieher, W. M. (2014) Aip1 destabilizes cofilin-saturated actin filaments by severing and accelerating monomer dissociation from ends. Curr. Biol. 24, 2749 –2757 63. Chen, Q., Courtemanche, N., and Pollard, T. D. (2015) Aip1 promotes actin filament severing by cofilin and regulates constriction of the cytokinetic contractile ring. J. Biol. Chem. 290, 2289 –2300 64. Elam, W. A., Kang, H., and De La Cruz, E. M. (2013) Competitive displacement of cofilin can promote actin filament severing. Biochem. Biophys. Res. Commun. 438, 728 –731 65. Brangwynne, C. P., MacKintosh, F. C., Kumar, S., Geisse, N. A., Talbot, J., Mahadevan, L., Parker, K. K., Ingber, D. E., and Weitz, D. A. (2006) Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol. 173, 733–741 66. Falzone, T. T., Lenz, M., Kovar, D. R., and Gardel, M. L. (2012) Assembly kinetics determine the architecture of ␣-actinin crosslinked F-actin networks. Nat. Commun. 3, 861 67. Wachsstock, D. H., Schwartz, W. H., and Pollard, T. D. (1993) Affinity of ␣-actinin for actin determines the structure and mechanical properties of actin filament gels. Biophys. J. 65, 205–214 68. Xu, J., Schwarz, W. H., Käs, J. A., Stossel, T. P., Janmey, P. A., and Pollard, T. D. (1998) Mechanical properties of actin filament networks depend on preparation, polymerization conditions, and storage of actin monomers. Biophys J. 74, 2731–2740 69. Liu, J., Gardel, M. L., Kroy, K., Frey, E., Hoffman, B. D., Crocker, J. C., Bausch, A. R., and Weitz, D. A. (2006) Microrheology probes length scale dependent rheology. Phys. Rev. Lett. 96, 118104 70. Falzone, T. T., Oakes, P. W., Sees, J., Kovar, D. R., and Gardel, M. L. (2013) Actin assembly factors regulate the gelation kinetics and architecture of
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filaments in skinned fibers of rabbit skeletal muscle. Biophys. J. 69, 1000 –1010 Matsushita, S., Inoue, Y., Hojo, M., Sokabe, M., and Adachi, T. (2011) Effect of tensile force on the mechanical behavior of actin filaments. J. Biomech. 44, 1776 –1781 Tirion, M. M., and ben-Avraham, D. (1993) Normal mode analysis of G-actin. J. Mol. Biol. 230, 186 –195 ben-Avraham, D., and Tirion, M. M. (1995) Dynamic and elastic properties of F-actin: a normal-modes analysis. Biophys. J. 68, 1231–1245 Kang, H., Bradley, M. J., McCullough, B. R., Pierre, A., Grintsevich, E. E., Reisler, E., and De La Cruz, E. M. (2012) Identification of cation-binding sites on actin that drive polymerization and modulate bending stiffness. Proc. Natl. Acad. Sci. U.S.A. 109, 16923–16927 Kang, H., Bradley, M. J., Cao, W., Zhou, K., Grintsevich, E. E., Michelot, A., Sindelar, C. V., Hochstrasser, M., and De La Cruz, E. M. (2014) Sitespecific cation release drives actin filament severing by vertebrate cofilin. Proc. Natl. Acad. Sci. U.S.A. 111, 17821–17826 Kojima, H., Ishijima, A., and Yanagida, T. (1994) Direct measurement of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation. Proc. Natl. Acad. Sci. U.S.A. 91, 12962–12966 Graham, J. S., McCullough, B. R., Kang, H., Elam, W. A., Cao, W., and De La Cruz, E. M. (2014) Multi-platform compatible software for analysis of polymer bending mechanics. PLoS One 9, e94766 Bustamante, C., Marko, J. F., Siggia, E. D., and Smith, S. (1994) Entropic elasticity of lambda-phage DNA. Science 265, 1599 –1600 Phillips, R., Kondev, J., and Theriot, J. A. (2008) Physical Biology of the Cell, Garland Science, London Bischofs, I. B., Klein, F., Lehnert, D., Bastmeyer, M., and Schwarz, U. S. (2008) Filamentous network mechanics and active contractility determine cell and tissue shape. Biophys. J. 95, 3488 –3496 Bathe, M., Heussinger, C., Claessens, M. M., Bausch, A. R., and Frey, E. (2008) Cytoskeletal bundle mechanics. Biophys. J. 94, 2955–2964 Ward, A., Hilitski, F., Schwenger, W., Welch, D., Lau, A. W. C., Vitelli, V., Mahadevan, L., and Dogic, Z. (2015) Solid friction between soft filaments. Nat. Mater. 10.1038/nmat4222 Strehle, D., Schnauss, J., Heussinger, C., Alvarado, J., Bathe, M., Käs, J., and Gentry, B. (2011) Transiently crosslinked F-actin bundles. Eur. Biophys. J. 40, 93–101 De La Cruz, E. M., Martiel, J.-L., and Blanchoin, L. (2015) Mechanical heterogeneity favors fragmentation of strained actin filaments. Biophys. J. 108, 2270 –2281 Gurel, P. S., Ge, P., Grintsevich, E. E., Shu, R., Blanchoin, L., Zhou, Z. H., Reisler, E., and Higgs, H. N. (2014) INF2-mediated severing through actin filament encirclement and disruption. Curr. Biol. 24, 156 –164 Blanchoin, L., and Pollard, T. D. (1999) Mechanism of interaction of Acanthamoeba actophorin (ADF/Cofilin) with actin filaments. J. Biol. Chem. 274, 15538 –15546 De La Cruz, E. M. (2005) Cofilin binding to muscle and non-muscle actin filaments: isoform-dependent cooperative interactions. J. Mol. Biol. 346, 557–564 De La Cruz, E. M., and Sept, D. (2010) The kinetics of cooperative cofilin binding reveals two states of the cofilin-actin filament. Biophys. J. 98, 1893–1901 Cao, W., Goodarzi, J. P., and De La Cruz, E. M. (2006) Energetics and kinetics of cooperative cofilin-actin filament interactions. J. Mol. Biol. 361, 257–267 Hayakawa, K., Sakakibara, S., Sokabe, M., and Tatsumi, H. (2014) Singlemolecule imaging and kinetic analysis of cooperative cofilin-actin filament interactions. Proc. Natl. Acad. Sci. U.S.A. 111, 9810 –9815 Suarez, C., Roland, J., Boujemaa-Paterski, R., Kang, H., McCullough, B. R., Reymann, A.-C., Guérin, C., Martiel, J.-L., De La Cruz, E. M., and Blanchoin, L. (2011) Cofilin tunes the nucleotide state of actin filaments and severs at bare and decorated segment boundaries. Curr. Biol. 21, 862– 868 Andrianantoandro, E., and Pollard, T. D. (2006) Mechanism of actin filament turnover by severing and nucleation at different concentrations of ADF/cofilin. Mol. Cell 24, 13–23 Pavlov, D., Muhlrad, A., Cooper, J., Wear, M., and Reisler, E. (2007) Actin filament severing by cofilin. J. Mol. Biol. 365, 1350 –1358
MINIREVIEW: Actin Mechanics and Fragmentation F-actin networks. Biophys. J. 104, 1709 –1719 71. Lieleg, O., Kayser, J., Brambilla, G., Cipelletti, L., and Bausch, A. R. (2011) Slow dynamics and internal stress relaxation in bundled cytoskeletal networks. Nat. Mater. 10, 236 –242 72. Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C., and Janmey, P. A. (2005) Nonlinear elasticity in biological gels. Nature 435, 191–194 73. Gardel, M. L., Shin, J. H., MacKintosh, F. C., Mahadevan, L., Matsudaira, P., and Weitz, D. A. (2004) Elastic behavior of cross-linked and bundled actin networks. Science 304, 1301–1305 74. Koenderink, G. H., Dogic, Z., Nakamura, F., Bendix, P. M., MacKintosh, F. C., Hartwig, J. H., Stossel, T. P., and Weitz, D. A. (2009) An active biopolymer network controlled by molecular motors. Proc. Natl. Acad. Sci. U.S.A. 106, 15192–15197 75. Heussinger, C., Schaefer, B., and Frey, E. (2007) Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76, 031906 76. Broedersz, C. P., and MacKintosh, F. C. (2014) Modeling semiflexible polymer networks. Rev. Mod. Phys. 86, 995–1036, 10.1103/RevModPhys.86.995
77. Kim, T., Gardel, M. L., and Munro, E. (2014) Determinants of fluidlike behavior and effective viscosity in cross-linked actin networks. Biophys. J. 106, 526 –534 78. Marchetti, M., Joanny, J., Ramaswamy, S., Liverpool, T., Prost, J., Rao, M., and Aditi Simha, R. (2013) Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189, 10.1103/RevModPhys.85.1143 79. Risca, V. I., Wang, E. B., Chaudhuri, O., Chia, J. J., Geissler, P. L., and Fletcher, D. A. (2012) Actin filament curvature biases branching direction. Proc. Natl. Acad. Sci. U.S.A. 109, 2913–2918 80. Gardel, M. L., Kasza, K. E., Brangwynne, C. P., Liu, J., and Weitz, D. A. (2008) Chapter 19: Mechanical response of cytoskeletal networks. Methods Cell Biol. 89, 487–519 81. Marko, J. F., and Siggia, E. D. (1995) Stretching DNA. Macromolecules 28, 8759 – 8770, 10.1021/ma00130a008 82. Tsuda, Y., Yasutake, H., Ishijima, A., and Yanagida, T. (1996) Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation. Proc. Natl. Acad. Sci. U.S.A. 93, 12937–12942 Downloaded from http://www.jbc.org/ at Univ of New South Wales (CAUL) on July 10, 2015
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Minireviews: Actin Mechanics and Fragmentation Enrique M. De La Cruz and Margaret L. Gardel J. Biol. Chem. 2015, 290:17137-17144. doi: 10.1074/jbc.R115.636472 originally published online May 8, 2015
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Supplemental material: http://www.jbc.org/content/suppl/2015/05/08/R115.636472.DC1.html This article cites 78 references, 22 of which can be accessed free at http://www.jbc.org/content/290/28/17137.full.html#ref-list-1
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Actin Mechanics and Fragmentation*□
fragment actin filaments and accelerate actin turnover in cells and in reconstituted biomimetic systems (6 –12).
Published, JBC Papers in Press, May 8, 2015, DOI 10.1074/jbc.R115.636472
Actin Structure
S
Enrique M. De La Cruz‡1 and Margaret L. Gardel§2 From the ‡Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06511 and the §Institute for Biophysical Dynamics, James Franck Institute, and Department of Physics, University of Chicago, Chicago, Illinois 60637
Actin Cytoskeleton The non-covalent polymerization of the cytoskeleton protein actin (Fig. 1) into linear filaments powers a variety of nonmuscle cell movements underlying their migration, division, and assembly into multicellular tissue (1). Cross-linking proteins arrange filaments into higher-order assemblies such as parallel bundles of filopodia and microvilli, isotropic networks of the cortex, and contractile bundles in the lamella that provide cells with mechanical integrity, sensing, and shape (2– 4). Contractile myosin motor proteins generate force and work output (i.e. motility and transport) along filament tracks, in both muscle and non-muscle cells (5). Actin filaments grow and shrink from their ends through subunit addition and loss, respectively. Accordingly, the overall assembly dynamics and turnover of the actin cytoskeleton in cells is influenced by factors that modulate the filament end concentration. Nucleating proteins and complexes generate new filament ends, often branching from existing filament templates (1). Capping proteins bind filament ends and slow or inhibit subunit addition (1). Severing and contractile proteins
* This work was supported by National Institutes of Health Grant GM097348 (to E. M. D. L. C), Burroughs Wellcome Career Award and University of Chicago Materials Research Science and Engineering Center (MRSEC) Grant DMR-1420709 (to M. L. G.), and Army Research Office sponsored Multidisciplinary University Research Initiative (ARO MURI) W911NF-14-1-0403 (to E. M. D. L. C and M. L. G.). This is the first article in the Thematic Minireview series “The State of the Cytoskeleton in 2015.” The authors declare that they have no conflicts of interest with the contents of this article. □ S This article contains supplemental File S1. 1 To whom correspondence may be addressed. E-mail: enrique. [email protected]. 2 To whom correspondence may be addressed. E-mail: [email protected].
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Actin Filament Mechanical Properties Actin filaments are polymers with lengths ranging up to ⬎10 m in solution (23) (Fig. 2B). The local asymmetry arising from the ribbon structure averages out to a diameter of ⬃6 nm on the length scales associated with analysis of individual filament and network mechanics. How filaments deform in response to force is governed by their mechanical elastic properties. Recent biochemical, biophysical, and computational studies have revealed the molecular and geometric origins of actin filament mechanical properties and how solution conditions, particularly cations, influence them. Bending, torsional, and twist-bend coupling elasticities dominate individual actin filament mechanical properties. The flexural, or bending, rigidity as well as the extent of deformation determine the energy required to bend a filament segment of a certain length. Likewise, the energy require to twist a filament is determined by the twisting rigidity and the torsional angle that overwinds or unwinds the filament. Twist-bend coupling represents an obligatory coupling between bending and twisting motions, such that filament bending introduces twist and vice versa (24, 25) (Fig. 2C). Actin filaments are rather resistant to stretching (26). However, stretching forces dampen bending JOURNAL OF BIOLOGICAL CHEMISTRY
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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.
Actins are single polypeptide chain proteins (⬃375 amino acids with an ⬃42-kDa molecular mass) folded into a U-shaped structure containing four subdomains (SD1– 4) with a bound adenine nucleotide, either ATP, ADP-Pi, or ADP, and an associated divalent cation, Mg2⫹ in cells, bound within the cleft separating subdomains 1–2 and 3– 4 (Fig. 2A). Actin filaments are commonly described as either a one-start, left-handed helix of subunits with a 2.77-nm rise per subunit (13) or a two-start, right-handed helix with half-staggered filament strands displaying an ⬃72-nm repeat (14). However, filaments in solution adopt multiple distinct structural states (referred to as “structural polymorphism”(15)) with variable twist and subunit tilt distributions that are influenced by regulatory protein occupancy and external forces. Thus, one actually refers to a subset of populated states when describing actin structure. Polymerization is associated with a conformational change in actin, such that incorporated filament subunits appear “flattened” when compared with free monomers (16, 17). Extensive intersubunit contacts stabilize filaments (16 –18), and an individual subunit contacts four neighboring actin molecules (Fig. 2A). Longitudinal contacts within a strand are thought to be stronger than lateral contacts across the strands (19). The DNase I binding loop (residues 36 –52 of SD2; Fig. 2A) adopts a variety of conformations (20), some of which make important long-axis, intersubunit contacts, and plays a central role in regulating actin filament structure and mechanical properties (21, 22).
MINIREVIEW: Actin Mechanics and Fragmentation
A
and twisting motions (27), and can have significant effects on filament structural dynamics. Filament mechanical properties are determined by the strength and distribution of intersubunit contacts (24). Subunit compliance and compressibility (28, 29) presumably play a role in overall filament mechanics. However, mathematical and computational models that treat filament subunits as incompressible entities capture the reported mechanical parameters with reasonable accuracy (24, 25). Filaments twist more easily than they bend, which manifests itself as a larger bending than torsional rigidity. Solution cations bind and stiffen some, but not all (e.g. Saccharomyces cerevisiae), actin filaments (20, 30). Substitution of a single amino acid residue positioned between adjacent, longaxis filament subunits confers S. cerevisiae actin filaments with salt-dependent bending stiffness (30). The filament bending stiffness (i.e. flexural rigidity, ) is equal to the product of the shape-independent stiffness of the protein material (i.e. apparent Young’s modulus, Eapp; referred to as apparent because proteins are not homogenous isotropic materials) and the shapedependent second moment of area (I), which is determined by the strength and distribution of intersubunit contacts. Filaments possessing this “stiffness cation site” display salt-dependent structure and intersubunit contacts, suggesting that stiffness cations may exert their effects on filament mechanics by binding to discrete sites at subunit interfaces and altering the radial distribution (I) and/or the strength (Eapp) of the intersubunit contacts (18). A mechanism in which cations bind at distal sites and allosterically alter intersubunit contacts is also plausible (31). The DNase I binding loop of SD2 participates in longitudinal intersubunit contacts, plays a central role in modulating the filament bending stiffness and displays salt-dependent conformations, making it an attractive structural element for linking salt-dependent filament structure and mechanics. Changes in filament stiffness can also arise from side binding proteins. For example, tropomyosin stiffens actin filaments by increasing its geometric movement (32). Mechanically strained filaments (e.g. deformed in bending and/or twisting) store elastic free energy in their shape. The
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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 m. C, top and side view of a buckled actin filament demonstrating out-of-plane deformation caused by twist-bend coupling elasticity (Reprinted from Ref. 24, 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 (LB), torsional (LT), and twist-bend (LTB) 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. 24.
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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).
MINIREVIEW: Actin Mechanics and Fragmentation
Nonlinear Entropic Enthalpic
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0.01 100
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End-to-end Distance [µm] 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-m 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 m). 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.
stored energy density depends on the deformation amplitude and the bending rigidity; larger deformations store more energy than small ones, and stiff filaments store more energy than compliant ones at identical deformations. Relaxation back to the straight conformation can potentially be used to generate work and/or force. Alternatively, the deformation amplitude and stored energy can reach the point of irreversibility, causing the filament to fragment. Thermal energy (kBT, where kB is Boltzmann’s constant and T is temperature in Kelvin) can be sufficiently large to induce actin filament shape fluctuations. The filament length at which the deformation energy compares to thermal energy defines the persistence length, which can be defined for bending (LB), twisting (LT), and twist-bend coupling (LTB) deformations (Fig. 2D). Filaments behave as rigid rods at lengths much shorter than the persistence length, as flexible polymers much larger than the persistence length, and as semi-flexible polymers at lengths comparable with the persistence length (33). The bending fluctuations reduce the filament end-to-end length, and the force required to extend and “straighten” the filament is determined by the energy required to reduce the bending fluctuation JULY 10, 2015 • VOLUME 290 • NUMBER 28
amplitude. This entropic spring constant is both highly sensitive to the length of filament segment and becomes highly nonlinear as the end-to-end length approaches the full polymer contour length (34) (Fig. 3). Compressive forces tend to excite the longest wavelength (softest) bending mode, which is comparable with kBT for micrometer length filaments. At a critical compressive force, referred to as critical or Euler force, buckling will occur. The critical force scales linearly with filament bending rigidity and inversely with the square of the filament length (e.g. it takes four times less force to buckle a 2-m filament than a 1-m one with identical bending rigidity) (35). This different response to extension and compression gives filaments a highly asymmetric force extension curve (Fig. 3) that can be approximated in coarse-grained models as cables (36) and is a powerful mechanism by which actin networks can sense (and respond) to different types of stresses (9). Cross-linking proteins organize filaments into parallel (or antiparallel) bundles. The mechanical parameters (twist, bend, and extension) of bundles depend on the width of the bundle and length of the filaments comprising them, as well as the JOURNAL OF BIOLOGICAL CHEMISTRY
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Force [pN]
0.01
Compression
Force [pN]
Extension
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MINIREVIEW: Actin Mechanics and Fragmentation density, mechanics, affinity, and exchange kinetics of the crosslinks. For instance, filaments in bundles formed with a compliant cross-linker (e.g. plastin) can readily slide past each and are weakly coupled such that the bundle stiffness increases linearly with the number of actin filaments (37). By contrast, when filaments become tightly coupled to each other by use of crowding agents or high density of compact cross-linker (e.g. fascin), the bundles act as single unit that displays a bending persistence length that scales quadratically with the number of filaments in the bundle (23, 37). In some cases, the cross-link density can impact the degree of coupling and the observed scaling of bundle stiffness (37, 38). Because actin cross-linking proteins are dynamic, the bundle mechanics are also frequency-dependent and depend on the cross-link dynamics as well (37, 39).
3
The abbreviations used are: ADF, actin depolymerizing factor; Aip1, actininteracting protein 1; pN, piconewtons.
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Control over Actin Network and Bundle Architecture Actin cross-linking and bundling proteins assemble filaments into larger scale networks and bundles. Cross-linking VOLUME 290 • NUMBER 28 • JULY 10, 2015
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Filament Fragmentation Fragmentation by severing and contractile motor proteins accelerates actin network turnover and assembly dynamics by increasing the concentration of filament ends where subunits can add and dissociate. As described above, compressive stresses buckle filaments. However, filaments under compressive loads do not deform indefinitely. Rather, they buckle and bend until they reach a deformation curvature where the stored elastic energy exceeds that holding the subunits together and it becomes energetically more favorable for the filament to fragment than remain intact (40). Estimating this stored energy and force requires that all elastic contributions be considered (e.g. bending, twisting, and coupling) because they all contribute to the local energy density that eventually causes filament subunit interface “bonds” to rupture (40). Several classes of regulatory filament-severing proteins have been identified (14). Gelsolin and ADF3/cofilin family members have been characterized most extensively at the biochemical and biophysical level with purified components (14). Gelsolin severs filaments by inserting one of its structural domains between long axis filament subunits, compromising stabilizing intersubunit interactions and promoting fragmentation. Formin INF2 may sever filaments by an analogous insertion, or “wedging,” mechanism (41). The filament-severing mechanism of ADF/cofilin (heretofore referred to as cofilin) appears to be distinct from that of gelsolin and INF2. Cofilin isoforms within and across organisms and species are not identical, and often the observed biochemical activities depend on the isoform and conspecific nature of the actin (42, 43), indicating that the chemical and physical properties of actin itself can influence cofilin function. Cofilins bind weakly to “young” ATP- and ADP-Pi actin filaments and bind orders of magnitude more strongly to “old” ADP-actin filaments (42), which allows for spatially targeted disassembly (44). Vertebrate cofilin binding is positively cooperative (43). Association is far below the diffusion limit for encounter (45) and limited by filament shape fluctuations (45, 46), suggesting opportunistic binding to compliant filament segments (45). Severing occurs preferentially at or near boundaries (e.g. junctions) between bare and cofilin-decorated seg-
ments (47), explaining why the severing activity peaks when filaments are partially decorated (31, 43, 47–51). Multiple factors likely influence the severing activity of ADF/ cofilin, and the contributions of some have yet to be fully resolved. Cofilin alters filament twist (52) and subunit tilt (53), renders filaments more compliant in bending (54) and twisting (55, 56) by dissociating filament-associated stiffness cations (31), and binds filaments in at least two distinct binding modes that may be differentially associated with severing and/or depolymerization activities (44). Thermally driven severing (e.g. in the absence of applied external loads) is weak and presumably dominated by thermodynamic effects originating from structural phase discontinuities at boundaries between bare and decorated segments. Boundaries fragment at smaller deformations than either parent filament (50), suggesting that boundaries are “bad joints” that are susceptible to fragmentation, analogous to the interfacial fracture of some non-protein materials (12). Srv2/CAP (cyclase-associated protein) may enhance severing by cofilin by inducing further conformational changes at boundaries (57). It is also conceivable that cofilin at the end of a bound cluster (43, 44) preferentially adopts a distinct binding mode (e.g. “severing”) from cofilin within a cluster (e.g. “non-severing”). However, a correlation between filament dynamics and thermally driven fragmentation has also been observed (31, 49, 50, 58), suggesting that filament mechanics and the structural dynamics at boundaries can potentially play a role, even in the absence of external load. An attractive model (53) implicates allosteric propagation of cofilin-linked conformational changes (47, 55, 59) to bare, undecorated segments where local, stabilizing cofilin-actin interactions are absent, thus leading to fragmentation within the bare side of boundaries. Actin-interacting protein 1 (Aip1 (60)) accelerates the filament-severing activity of cofilin. One model of enhanced severing (61) implicates further structural changes in cofilin-actin induced by Aip1, possibly a wedge-like mechanism where cofilin is inserted between adjacent long-axis neighbors. Consistent with a functional ternary Aip1-cofilin-actin complex, Aip1 does not dissociate cofilin and enhances severing at all cofilin occupancies (62). However, a different study (63) favors an alternate mechanism (64) in which Aip1 simply competes with cofilin, dissociating it from actin and introducing additional boundaries where severing can occur. The various factors contributing to filament severing may play different roles under cellular conditions. For example, active forces generated by contractile proteins may play a more dominant role (8, 11, 12). The mechanical properties and response of filaments are central to understanding fragmentation in this context because the mechanical heterogeneity and discontinuities introduced by cofilin will lead to unique behaviors that deviate from mechanically homogenous, bare actin filaments (40). Similarly, confinement within the elastic matrix of the cytoplasm (65) will influence the deformation and presumably fragmentation.
MINIREVIEW: Actin Mechanics and Fragmentation
Entropic Spring Extension
Enthalpic Stretch
101
G’ (Pa)
Extension/Stretch dominated
F-acn length
Bend dominated
100
Concentraon
10-2
10-1
100 σ (Pa)
101
102
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.
Actin Network Mechanics The mechanical properties of the actin networks will determine the extent and pattern of deformation in response to JULY 10, 2015 • VOLUME 290 • NUMBER 28
mechanical stress. The type of response will depend on the spatial scale, direction, duration, and magnitude of the applied stress. For example, at the scale of a single bundle or filament, the mechanics can be dominated by the local compressional, stretching, or bending rigidity of the filament/bundle depending on the direction of the applied force. At longer length scales, the mechanical response is dominated both by the mechanics of individual elements as well as by how the filaments/bundles are connected together. Thus, actin network architecture determines the mechanical properties of the elements as well as which types of microscopic deformations occur in response to a macroscopic stress. Below, we describe two regimes that dominate actin network mechanics. In filament networks or bundles that are densely crosslinked, the deformations are self-similar, or affine, from microscopic to macroscopic length scales. For shear or extensional stress, this results in a mechanical response that is dominated by stretching of filaments or bundles (Fig. 4A). The relationship between the stress (force per unit area) and strain (relative deformation) provides a measure of elastic modulus. The elastic modulus has units of energy per volume and can be thought of as the amount of energy required to deform the medium. The elastic modulus of filament networks is determined both by the actin filament/bundle concentration and the stretching and/or by the bending modulus of the filament/bundle itself. Thus, factors that affect the stretching/bending modulus of the filament or bundle (e.g. time scales and applied stress) will directly impact the macroscopic mechanical response. Indeed, the nonlinearity of the extensional spring constant of actin filaments can directly manifest into a nonlinear stiffening of cross-linked networks in response to stresses applied externally (72, 73) or generated internally (e.g. by myosin motors) (74). Strain stiffening in networks composed of linearly elastic filaments/bundles can also arise from geometric effects (75, 76). As the cross-link or filament density is reduced, the sparse connectivity within the network results in deformations that are not self-similar (non-affine) from microscopic to macroscopic length scales. For instance, shear deformation at the macroscopic length scale generates filament bending, with a small fraction of filaments/bundles bearing the majority of the stress. Here the bending-dominated response at the microscopic scale results in softening of the network at macroscopic scale. JOURNAL OF BIOLOGICAL CHEMISTRY
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proteins are monomeric or homodimeric proteins that contain two filament binding sites. Cross-linking proteins can vary considerably in their affinity, compliance, and distance between actin binding sites. Smaller cross-linkers (e.g. fascin and fimbrin) form compact bundles, whereas larger, more compliant cross-linkers (e.g. filamin and ␣-actinin) form loose bundles or “mesh-like” networks. Most cross-linkers exhibit both behaviors with the tendency to form at high cross-linker concentrations. When a stress is applied to an actin network or bundle, the deformations and dynamics of filaments and actin crosslinking proteins determine the mechanical response. In general, this mechanical response will, in some circumstances, behave like an elastic solid, and in others, it will behave like a viscous fluid. Thus, actin networks can be considered viscoelastic in their mechanical response. The architecture of cross-linked actin networks is determined both by filament assembly dynamics (rate of nucleation, growth, and severing) and by factors controlling cross-linking (cross-link kinetics and concentration) and actin filament concentration and length (66, 67). In the absence of cross-linkers, assembled filaments display a homogeneous distribution with a relatively uniform average distance between filaments (termed the “mesh size”). Filaments longer than the mesh size are sterically entangled in the network. Steric entanglements constrain filament motions and, consequently, give rise to viscoelastic behavior (68, 69). Steric entanglements also prevent realignment of filaments into bundles (66). Thus, the architecture of cross-linked networks is determined by competing timescales of bundle formation and the arrested mobility that occurs with entanglement. For a given cross-link type and density, fast growing filaments form fine meshworks, whereas slowly elongating filaments form networks of dense bundles (70). Thus, architecture of cross-linked actin network is kinetically determined, reflecting an arrested or kinetically “trapped” state rather than the lowest energy state defined by true thermodynamic equilibrium (66, 71). As a result, the actin cytoskeletal architectures found within living cells will exist in a dynamic steady state determined by a balance of filament assembly and disassembly dynamics and regulatory protein interactions. These microscopic rates, as discussed above, may also be force-regulated.
MINIREVIEW: Actin Mechanics and Fragmentation
Mechanochemical Feedback in Dynamic Steady States The response of actin filaments and associated binding proteins to applied stress provides a natural mechanism to modify the large-scale network architecture in response to externally applied or internally generated stresses. For actin networks that are in a dynamic steady state with polymer disassembly/assembly, forces that alter the local rate of filament stability (disassembly), assembly, or binding of actin-binding proteins will induce a transition to a new dynamic steady state. Although the experimental characterization of such mechanochemically responsive actin networks is still in its nascent stages, recent data suggest that distinct modules may differentiate branched versus contractile networks in response to stress. The filament binding affinity of the Arp2/3 complex depends on the filament curvature (79), raising the possibility that a branched network exhibiting a compressive load could respond both by modulating the branch density and possibly by cofilinmediated severing and filament subunit exchange. Together, this will increase the branch density and decrease average filament length, resulting in increased force generation network stiffness as a result of the applied load. In contractile networks containing actin and myosin II filaments, network contraction arises from filament bending and buckling (9). This results in a preferential severing of compressed, buckled filaments, thereby altering the local filament end density. In the presence of barbed end capping proteins, this could result in local disassembly from the pointed end, whereby in the presence of barbed end elongation factors, this would result in enhanced assembly. Unraveling how these mechanochemical feedbacks can be used to achieve the dynamic steady states observed in cells and enable cell mechanosensing will be an exciting area of future study. Acknowledgments—We thank Drs. Paul Forscher (Yale University) for providing images in Fig. 1, Austin Elam (Yale University) for preparation of Fig. 2A, Hyeran Kang (Yale University) for images in Fig. 2B, and Patrick McCall for preparing Fig. 3. The data in Fig. 4C were previously published in Ref. 80. We thank Moumita Das for useful suggestions.
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17144 JOURNAL OF BIOLOGICAL CHEMISTRY
VOLUME 290 • NUMBER 28 • JULY 10, 2015
Minireviews: Actin Mechanics and Fragmentation Enrique M. De La Cruz and Margaret L. Gardel J. Biol. Chem. 2015, 290:17137-17144. doi: 10.1074/jbc.R115.636472 originally published online May 8, 2015
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