Force amplification response of actin filaments under confined compression

Abstract

Actin protein is a major component of the cell cytoskeleton, and its ability to respond to external forces and generate propulsive forces through the polymerization of filaments is central to many cellular processes. The mechanisms governing actin's abilities are still not fully understood because of the difficulty in observing these processes at a molecular level. Here, we describe a technique for studying actin–surface interactions by using a surface forces apparatus that is able to directly visualize and quantify the collective forces generated when layers of noninterconnected, end-tethered actin filaments are confined between 2 (mica) surfaces. We also identify a force-response mechanism in which filaments not only stiffen under compression, which increases the bending modulus, but more importantly generates opposing forces that are larger than the compressive force. This elastic stiffening mechanism appears to require the presence of confining surfaces, enabling actin filaments to both sense and respond to compressive forces without additional mediating proteins, providing insight into the potential role compressive forces play in many actin and other motor protein-based phenomena.

The ability of actin networks to generate vectorial forces through the growth of individual filaments at an opposing surface (1–3) is central to cellular processes such as phagocytosis (4), lamellapodia (5) and filopodia (6) locomotion, and intracellular transport of endocytic vesicles (7). However, a fundamental understanding of the molecular-level mechanisms and dynamics of polymerizing actin during force generation is still lacking, due in part to the experimentally inaccessible molecular length and time scales associated with these processes.

We describe a technique using the surface forces apparatus (SFA) to study the dynamic behavior and forces generated by a “hairy array” of randomly oriented, actively polymerizing F-actin filaments end-tethered to and confined between 2 mica surfaces. Under appropriate solution conditions, when the surfaces are brought together, the confined filaments generate a monotonically repulsive elastic reaction force between them modulated by temporal spatial/force fluctuations resulting from the dynamic growth and collapse of polymerizing filaments. These fluctuations can be stopped by adding capping agents but continue indefinitely so long as the solution is not depleted of ATP. The preparation of the surfaces for the force and visualization measurements are described in Materials and Methods.

Results and Discussion

After the initial nucleation stage (Fig. 1 A–C), the filaments become strongly bound to the mica surfaces at a single end, allowing the other, unbound end to polymerize freely and grow radially in the direction of the opposing surface, generating repulsive forces capable of forcing the confining surfaces apart (Fig. 1D). The attachment of the filaments to the surfaces prevents them from diffusing away from the contact region, even after the surfaces have been separated (Fig. 1E) and enables the filaments to generate repulsive polymerization forces. The end-tethering to the surface also appears to have a stabilizing effect on the filaments that prevents their total depolymerization, keeping the number and surface coverage density of filaments in the contact region essentially constant over the duration of a typical experiment (≈2–4 h). We were thus able to investigate the mechanical properties of and forces produced by the filament layers while also visualizing, in real time, their growth and fluctuation dynamics with angstrom-level resolution.

Fig. 1.

Schematics of the stages of filament nucleation into a growing, force generating “hairy layer” of end-tethered actin filaments on each mica surface. (A) Simple illustration of the experimental setup consisting of 2 crossed-cylinder mica surfaces with a droplet of actin solution (monomers, ATP, Tris-buffer) held in between by capillary force. The 2 surfaces are moved normally toward or away from each other by moving the motor-driven translational stage attached to the double cantilever force-measuring spring that supports the lower surface. The separations, D, and local geometry are measured by using an optical interference method, and forces, F, are measured from the deflection of the force-measuring spring of stiffness, K. (B) As the surfaces are brought together for the first time, a concentrated layer of actin monomers is trapped and compressed within the confined contact area. (C) Over time, the pressure and confinement induces the nucleation of actin filaments that become strongly adhered, at one end only, to either the upper or lower surface. (D) As the surfaces are again separated, the filaments polymerize and grow radially in the direction of the opposing surface, generating a repulsive force that drives the surfaces apart. (E) When well-separated, the end-tethered filaments remain stable and firmly bound to the mica surfaces.

After filaments have been nucleated during the initial confinement, subsequent “approaches” and “separations” of the surfaces are invariably met with a repulsive force that is found to be significantly larger on separation (decompression) than on the prior approach (compression)—the opposite effect of typical hysteretic and viscous forces. A typical force–distance curve is shown in Fig. 2A for 2 surfaces approaching at a rate of 15 nm/s and then separated at the same rate. The increased intensity in the mean “background” repulsive (elastic) force on decompression than on approach is clearly seen.

Fig. 2.

Representative plots of the normal force profile and spatial/force fluctuations. (A) Typical normal force-distance profile on approach (compression) and separation (decompression) of a 2 mg/ml actin solution measured by using a spring of stiffness K = 200 N/m at a constant approach/retraction velocity (of the translational stage) of 15 nm/s (see Fig. 1A). The force, F, has been normalized by the local radius of curvature, R, to allow for comparison with theory and between experiments. Dynamic fluctuations due to actin polymerization appear as sawtooth-like spikes superimposed on a smooth exponential (elastic) background repulsion. A significant increase (hysteresis) in both the fluctuation's amplitude (ΔD, ΔF_f) and background repulsive force is observed on decompression relative to compression. The black lines are exponential fits to the background force. (B) Representative plots showing the dynamic fluctuations in the gap distance (ΔD, left axis) and force (ΔF_f, right axis) produced by the growth and collapse of actin filaments after the surfaces were moved to and then held at a static mean separation position measured in separate experiments using 2 different force-measuring springs of different stiffness: K = 200 N/m and 1,000 N/m. The measured normal force profiles for both of these experiments are shown in A and in Fig. 3A, respectively.

The polymerization-driven fluctuations in the forces, ΔF_f, lead to fluctuations in the distance, ΔD, between the surfaces as they deflect the force-measuring spring (Fig. 1A) by ΔD = (ΔF_f + ΔF_b)/K, where ΔF_b is the amount the background repulsive force decreases over ΔD. These give rise to the spikes with a characteristic sawtooth-like waveform superimposed on the monotonic background force profile in Fig. 2A; the fluctuating spikes are the manifestation of the additional, internally generated, repulsive force produced by the rapid growth and collapse of confined filaments. At large separations (D > 500 nm) the fluctuations in the force ΔF_f and distance ΔD are small, whereas at small separations (D < 50 nm) both appear to decrease, but the force fluctuations ΔF_f are actually still quite large—the steep background repulsion, on which the force fluctuations are superimposed, causes them to appear small. Given the area of the confined region and the magnitude of ΔF_f, we estimate the filament number density to be between 0.5 × 10⁴ and 1 × 10⁴ per μm² and the force generated per filament to be between 5 and 11 pN, which is in good agreement with values reported by others (1, 8).

If the surfaces are held in a “static position,” i.e., if the base of the spring in Fig. 1A is not moved, the fluctuations continue indefinitely without any apparent decrease in amplitude (ΔD, ΔF_f) or frequency (typically 0.2–1.0 Hz). Conversely, if the static position is held at a small separation distance, where the compressive forces on the filaments are large, a gradual increase in the mean distance and fluctuation amplitude is often observed that eventually plateaus with time, after which no further change is observed. This effect is not observed at large separations where the compressive forces are small. Fig. 2B shows recordings of the distance and force fluctuations with time for surfaces brought to, then left at, initial mean separations of ≈110 nm and ≈65 nm. The lower trace in Fig. 2B shows a recording made with a 5-times stiffer spring where the distance–force fluctuations are smaller, but the frequency of the fluctuations is approximately the same. In both cases, a gradual increase in mean separation distance and fluctuation amplitude is observed over a time period of ≈1 min. ATP is the source of energy for these fluctuations that persist as long as ATP is present in the solution. The fluctuations eventually disappear as all of the ATP is consumed; however, addition of ATP to the depleted solution regenerates the fluctuations.

Although the fluctuations may appear to be random or chaotic, spatial-frequency analysis by fast Fourier transform (FFT) reveals the presence of 3 characteristic frequencies that are unaffected by variations in the mean separation distance (background compressive force). This is in contrast to the exponential decay in frequencies characteristic of a purely stochastic process, like Brownian motion, governed by a random probability of events. This apparent built-in periodicity to the fluctuation motion hints at an additional mechanism governing the dynamics of the force-generation process at molecular length and time scales operating in tandem with, but independent from, the polymerization/depolymerization reactions whose kinetics are expected to be influenced by the presence of external forces (1–3). The nonrandomness and unchanging dynamics of the fluctuation motion is indicative of coupled behavior in which filaments operate collectively and cooperatively in the generation of forces (9, 10).

The measured monotonic background force profiles shown in Figs. 2A and 3A both exhibit a significant amplification in the strength of the near-exponential forces on decompressions relative to the compressions observed over the entire range of the force fields (defined as the region over which the measured forces are nonzero). The increase in the strength but not the range of the force implies an upward, rather than outward, shift of the force curve, i.e., along the vertical force axis rather than the horizontal distance axis. In other words, the amount of mechanical work, ∫FdD, released by the decompressing filaments is greater than the amount of externally applied mechanical work used initially to compress the filaments, demonstrating an ability of filaments to “respond” to a compressive force by generating an even larger opposing force.

Fig. 3.

Normal force and shear viscosity profiles showing the stiffening response of actin to compression. (A) Normal force profiles on compression and decompression of a 3 mg/ml actin solution before and 30 min after addition of 1 μg/mL gelsolin, measured at the same contact location by using a force measuring spring of stiffness K = 1,000 N/m and a constant approach/separation velocity (of the translational stage) of 12 nm/s. (B) Shear viscosity, η, of a confined film in a 3 mg/ml actin solution measured on compression (approach) and decompression (separation) of the surfaces by using the shearing method described in ref. 9. The viscous forces are measured by using a lateral force strain gauge as the surfaces are sheared laterally back and forth by using a piezoelectric bimorph “slider” (shearing rate ≈10.3 mm/s, peak-to-peak shearing amplitude ≈26 mm). Errors in the measured viscosity, denoted by vertical bars, are due in part to the fluctuations of the polymerizing actin filaments that were also observed in the lateral (viscous) forces and that were similar in character to the normal fluctuations.

To obtain further insights into the mechanism of this compression-induced force-amplification response, forces were measured before and after the addition of gelsolin—a protein that both severs and caps actin filaments. The results (Fig. 3A) show that even after the actin polymerization and fluctuations are halted, an amplification of the repulsive forces is still observed. The force amplification, therefore, is not an effect of the polymerization reaction or its kinetics, for example, one that can be attributed to the hydrolysis of ATP or differences in the monomer diffusion rates during compression and decompression that may alter the polymerization rates of the filaments.

Refractive index measurements (11) did not show any detectable difference in the density of actin between the surfaces on compression and decompression, indicating that the enhanced repulsion is not caused by the increase in the local number or surface density of filaments within the contact region. Additionally, multiple compression–decompression measurements performed at the same contact location yielded highly reproducible (but hysteretic) curves, suggesting that the amplification in the repulsive forces is due to some intrinsic, yet transient, compression-induced change in the elastomechanical properties of the filaments.

Fig. 3B shows that the viscosity of the confined actin layer also exhibits different values on approach and separation. For the geometry of Fig. 1A, the theoretical lateral (shear or friction) force, F_‖, is related to the viscosity, η, of the liquid between the surfaces by F_‖ ≈ (16π/5) RηV_‖ ln(2R/D) for R ≫ D, where V_‖ is the shearing velocity (12). In a first approximation, the characteristic elastic modulus of the materials, G, which is proportional to the average bending elastic modulus of the filaments, κ, in our experimental geometry, is related to η by G ∝ τη, where τ is a characteristic relaxation time (12, 13). After a compression, the effective viscosity measured on decompression was typically 1.7 ± 0.4 times the value measured on compression, signifying an equal or higher increase in G, which converges with the value on approach (compression) at larger separations. The range of this effect was similar to the range of the force amplification. We note that, in addition to normal fluctuations, large lateral force fluctuations were also observed during the viscosity measurements, demonstrating that the filaments are polymerizing and generating forces in all directions and not only normally to the surfaces. The normal and lateral fluctuations appear to be correlated and are thus different aspects of the same process. Again, refractive index measurements taken during viscosity measurements on compression and decompression showed no measurable difference in actin density, nor was any shear-induced filament aggregation or bundling observed (which typically appear as “bumps” in the smooth fringes). We therefore conclude that the increase in the shear viscosity, η, and, likewise, the amplification in the background forces, arise from an increase in the filaments' elastic bending stiffness (enthalpic elasticity) under compression.

Because our system consists of many short, unconnected filaments that deform more or less freely, the enthalpic elasticity of the filaments becomes the more dominant component in the overall elastic response of the system to compression. Consequently, our observations are not explicable in terms of existing models of bulk cross-linked or entangled networks. Although such models do predict an increased stiffness on compression, they apply to entropic stiffening mechanisms associated with the interconnectivity of a polymer network. Most importantly, these models do not predict the crucial reaction force enhancement that we observe under thin-film confinement. We therefore propose that the observed compression-stiffening response is a physicochemical mechanism, where enthalpic stiffening of the filament backbone arises from a reversible, compression-induced transition of individual monomer–monomer bonds from a more flexible primary binding state into a stiffer secondary state. Consequently, a shift in the distribution of monomer–monomer bond state occupancy occurs causing the number of bonds occupying the secondary state to increase as the compressive force rises resulting in an enhancement in the filament backbone stiffness as illustrated schematically in Fig. 4. In many ways, this response may be analogous to the “catch bond” response exhibited by P-selectins in which the strength of ligand–selectin bonds (reaction forces) increase under tensile forces (14).

Fig. 4.

Proposed 2-state binding model describing the mechanism for the compression-induced elastic stiffening and force-amplification response of actin filaments. In this model, the bonds between monomers may occupy one of 2 binding states, E1 and E2, separated by a low-energy barrier. (A) A plot of the bond energy landscape (solid lines) and bond occupancy population densities (dashed lines) for the monomer–monomer bonds within a single filament as it stiffens under compression. As the compressive forces on the bond increases (a → e), the shape of the bond energy landscape is altered, decreasing the barrier of E₁ → E₂ transitions while increasing the barrier of E₂ → E₁ transitions, resulting in the shift in the bond occupancy population density in favor of the stiffer E₂ bond state. (B) Hypothetical force–distance curve as a single filament is compressed between 2 surfaces as the monomer–monomer bonds are increasingly forced from the flexible E₁ (red monomers) to the stiff E₂ (blue monomers) binding states. The dashed curves (a–e) represent the elastic force profiles for filaments of a given bond occupancy population density shown in A, also labeled (a–e). The solid blue line shows how the force profile might appear upon compression of a filament as it stiffens because of the shift in the bond occupancy population density. The solid red line shows the force profile on decompression. The transition of the bond occupancy population density back to the E₁ states occurs at larger separations (and lower compressive forces) than on compression leading to the larger repulsive force. The shape of the monomers is intended to clarify the 2-binding-state mechanism and is not based on the actual physical shape of actin monomers.

The proposed mechanism appears to explain the elastic stiffening and force amplification response we observe and may potentially be relevant to other biological systems. In its simplest form, our model assumes that actin monomers in a filament are distributed between 2 binding states with energies E₁ and E₂ that are separated by a repulsive barrier, where E₂ is the stiffer (although not necessarily energetically deeper) of the 2 states (Fig. 4A).* The existence of 2 distinct binding states having characteristically different bond stiffnesses have been reported by others both experimentally (15) and theoretically (16). The difference in the bond stiffness between these 2 states is associated with a conformational change in the DNase I-binding loop (DB loop) in ATP-bound actin from a random coil to an α-helix upon the release of inorganic phosphate and conversion to ADP-bound actin, which causes the bonds to become both weaker and more flexible (16). Molecular dynamics simulations performed by Chu and Voth (16) report that the computed persistence length, l_p, of filaments of (only) ATP-bound actin is ≈1.9 times longer than filaments of ADP-bound actin (16 and 8.5 μm, respectively)—a result that is in good agreement with experimental measurements (15).

This change in l_p, which is related to the elastic bending modulus, κ, by κ = l_pk_bT (17), is essentially identical to the amount (≈1.7) we measure for the increase in the shear viscosity, η (assumed to be proportional to κ), shown in Fig. 3B. Although the polymerization of filaments involves the addition of ATP-bound actin monomers, once incorporated, rapid hydrolysis of ATP transforms the bulk of monomers in the filament into the more flexible ADP-bound binding state. Therefore, one plausible origin of the observed enthalpic stiffening of actin filaments under compression is a transition from α-helix to random coil conformational state in the DB loop of ADP-bound monomers that transforms the conventionally flexible state of the intermonomer bonds into a stiffer state that mimics the bonds formed between ATP-bound monomers, equivalent to the E₁ → E₂ transition in Fig. 4A.

In the 2-state model (Fig. 4) as the compression force increases (a → e), the shape of the free-energy landscape (FEL) profile is altered progressively lowering the energy barrier for the E₁ → E₂ transition while simultaneously increasing the barrier for the E₂ → E₁ transition, resulting in a gradual shift in the equilibrium distribution or “population densities” of states, which obeys Boltzmann statistics, toward the stiffer E₂ binding state. This shift in distribution leads to an elastic stiffening of the filaments, which, in turn, enhances the enthalpic component of the elastic repulsive forces opposing the compressive force.

Fig. 4B illustrates how the stiffening of compressed filaments alters the measured elastic force–distance profiles. The curves in Fig. 4B labeled a–e correspond to the FEL profiles and bond distributions illustrated in Fig. 4A (also labeled a–e) and represent the elastic force profiles associated with 5 different configurations of the actin filament. As the increasing compression force shifts the distribution of bond states progressively toward E₂, the stiffened filaments “jump” from one force profile to the next, effectively shifting the measured mean elastic force profile upward.

Although only 5 discrete jumps are shown in Fig. 4B, in systems involving many filaments, the jumps are more numerous and more closely spaced, making the measured force profile appear continuous. Upon decompression, hysteresis will occur because the filaments are now stiffer than on compression, thereby raising the path to higher F values because of the amplification in the elastic repulsion at any value of D, punctuated by the return transitions back to the original ground state that occur at larger D values as D → ∞. As a consequence of this hysteresis in the stiffening response, the amplification in the opposing elastic forces generated by filaments in compression will persist for some time, especially as long as the compressive force is present.

Stress-stiffening behavior has been observed before in actin filament networks and gels and arises from the interconnectivity of the network structure causing filaments to be pulled into tension and their entropic elasticity to increase as the network deforms (17–19). The role that the enthalpic elasticity of filaments may play in the stress-stiffening response has largely been ignored although recent experiments suggest that the enthalpic component may, in fact, be significant (17); however, any subtle contributions of the enthalpic component in the elastic response remains obscured by the more dominant entropic contribution and by dynamic rearrangements in network architecture and filament density induced by compressive forces. Perhaps for these reasons, the enthalpic stiffening response of actin filaments to compression has eluded detection despite intensive experimental study.

The ability of actin filaments to alter their elastic properties under compression constitutes a mechanism of actin-based mechanotransduction that arises from the intrinsic physicochemical properties of the intermonomer bonds, which enables filaments to both sense and respond directly to external forces without the assistance of ancillary mediating proteins or chemical signals. This previously unknown stiffening response of individual actin filaments may shed light on a number of reported phenomena such as (i) the apparent acceleration in growth velocity observed in actin networks that were previously subjected to large compressive loads (20) and (ii) the counterintuitive adhesion-controlled propulsion of actin (21). In addition, the compression-induced stiffening response of actin may potentially play a critical function in a number of cellular processes that govern cell locomotion, phagocytosis, and cytoskeletal rearrangements triggered by external forces.

Finally, the capacity of individual actin filaments to reversibly alternate between stiff (high-stress) states, flexible (low-stress) states, and free (unbound) states may determine the complex dynamics of force production in which compression generates autoexcitation feedback that reinforces and intensifies the stiffening response (and thus propulsive forces), where the opposing forces are highest. In light of our results, models describing the forces produced by polymerizing actin should take into account the variable and dynamically changing nature of actin filament elasticity, filament conformation (length and curvature) and the role of the external compressive forces in stimulating and directing their force generation processes.

Materials and Methods

The SFA technique used in these studies employs an optical interference method to directly measure the shapes and distances D between 2 curved surfaces to ±0.1 nm (Fig. 1A) (11). The forces, F, between the surfaces are obtained from the measured deflection of a force-measuring spring of stiffness K. The basic techniques for performing and analyzing static and dynamic normal and lateral (friction) forces have been described by Israelachvili and coworkers (11, 12).

The experimental system used in these SFA experiments is markedly different from traditional systems used to study actin, which usually involve motility assays of dendritic networks of reconstituted actin filaments in solution. The structure and dynamics of these networks are sensitive to the kinetic balance between numerous synergistic reactions (22). Our experiments were performed with the minimum number of components necessary for actin to nucleate, polymerize, and generate forces: G-actin monomers (2–3 mg/ml, 99% purity obtained from Cytoskeleton) in Tris buffer solution [5 mM Tris (pH 8), 0.2 mM dithiolthreitol] containing 0.2 mM ATP.

To induce the nucleation, 2 crossed cylindrical mica sheets of radius R ≈ 2 cm were slowly brought together, with a small droplet (50–75 μL) of actin solution between them (Fig. 1 A and B). The surfaces trap a 40- to 50-nm-thick layer of actin monomers, corresponding to 7–9 monomer diameters, under a moderate pressure of P = 5–10 atm within a well-defined flattened contact region of area 1,000–5,000 μm². Within 10–20 min under pressure, the compressed monomers undergo nucleation and growth, forming stable actin filaments (Fig. 1 B and C). We note the absence of Mg²⁺, K⁺, and proteins such as WASP and ActA that are typically required to induce the nucleation of actin (22). Without these nucleating agents, essentially no homonucleation of filaments occurs in the bulk solution, limiting the filaments in our experimental system to only those nucleated within the contact region. The confining (negatively charged) mica surfaces in buffer containing ATP and pressure is, apparently, sufficient to trigger nucleation.