Filopodial retraction force is generated by cortical actin dynamics and controlled by reversible tethering at the tip

Significance

Cells can sense their environment by using hair-like structures called filopodia that often exert pulling forces upon adhesive tip contact. We show, using optical tweezers and confocal microscopy, that the retraction force is generated by the dynamics of the cortical actin cytoskeleton, constantly pulling on the filopodial base. The weakest point of force transduction is at the tip between the actin shaft and the membrane. This allows tip-bound filopodia to apply controlled forces and to use a “load-and-fail” sensing process.

Abstract

Filopodia are dynamic, finger-like plasma membrane protrusions that sense the mechanical and chemical surroundings of the cell. Here, we show in epithelial cells that the dynamics of filopodial extension and retraction are determined by the difference between the actin polymerization rate at the tip and the retrograde flow at the base of the filopodium. Adhesion of a bead to the filopodial tip locally reduces actin polymerization and leads to retraction via retrograde flow, reminiscent of a process used by pathogens to invade cells. Using optical tweezers, we show that filopodial retraction occurs at a constant speed against counteracting forces up to 50 pN. Our measurements point toward retrograde flow in the cortex together with frictional coupling between the filopodial and cortical actin networks as the main retraction-force generator for filopodia. The force exerted by filopodial retraction, however, is limited by the connection between filopodial actin filaments and the membrane at the tip. Upon mechanical rupture of the tip connection, filopodia exert a passive retraction force of 15 pN via their plasma membrane. Transient reconnection at the tip allows filopodia to continuously probe their surroundings in a load-and-fail manner within a well-defined force range.

Filopodia are actin-rich cell membrane protrusions, involved in processes as diverse as cell migration, wound closure, and cell invasion by pathogens (1–3). During cell migration, filopodia can exert forces on the substrate (4, 5) and act as precursors of focal adhesions (6–8). Filopodia initiate contacts during wound closure and contribute to dorsal closure of the fruit fly embryo in a zipper-like fashion (9–12). Viruses can hijack filopodia and filopodia-like cell–cell bridges to surf toward the cell body (13, 14). Filopodia from macrophages and epithelial cells actively pull pathogens bound to their tips (15–18). In all these examples filopodial retraction and retrograde force production are crucial. However, although filopodia formation and growth have been well studied (1–3), the mechanisms underlying their retraction are poorly understood.

Filopodia show continuous rearward movement of their actin filaments in a process called “retrograde flow” (3, 19). In the lamellipodium, from which filopodia often emanate, the retrograde flow originates from actin treadmilling due to actin depolymerization at the rear and polymerization at the front of the lamellipodium. This retrograde flow is further amplified by the motor activity of myosins (20–23). In neurons, the filopodial shaft is deeply anchored in the growth cone and filopodial dynamics depends on the balance between actin polymerization at the filopodial tip and its retrograde flow (19). In other cell types actin depolymerization at the tip has been associated with retracting filopodia (24).

Different contributions to filopodial force production during retraction can be considered. A connection between the filopodial tip and retracting actin filaments through transmembrane receptors such as integrins could transduce cortical forces applied on the actin shaft. In macrophages, force measurements on retracting filopodia suggested a major role for cortical myosins pulling on filopodial actin bundles (16). These measurements showed that retraction could be slowed down for forces below 20 pN. Applied forces higher than 20 pN inverted filopodial retraction of macrophages (25).

Filopodial force production can also be due to membrane mechanics (26). Forces exerted by actin-free tubes extruded from the cell plasma membrane typically range between 5 pN and 30 pN (27). Membrane tension could drive filopodial retraction by exerting inward forces against the actin filaments. Moreover, filopodial actin filaments have been found disconnected from the membrane at the tip (28, 29), underlining the importance of membrane properties in filopodial mechanics. The contributions of membrane- and actin-based forces, as well as the mechanical links controlling force production during filopodial retraction, are still unclear.

Here, we studied the retraction dynamics and the forces exerted by a single filopodium that is contacting an optically trapped bead at its tip. We found that filopodia retracted in association with a reduced actin polymerization at their tip at rates below those needed to compensate for the retrograde flow. The speed of filopodial retraction was only marginally affected by counteracting forces up to 50 pN, suggesting that the driving forces for retraction were not limiting within this range. We argue that actin treadmilling in the cell cortex, that functions far from its stall regime, transduces inward forces to the filopodial actin shaft at the base via high friction. In addition we found that filopodia can exert passive inward forces of 15 pN by using cell membrane-based forces. External counterforces that are only 5 pN higher than the membrane force can lead to rupture of connections between the actin shaft and the membrane at the filopodial tip. These weak contacts at the tip define the maximal pulling force of filopodia and allow cytoskeletal inward forces to operate only for short time intervals (<25 s). We found that the mechanical disconnection between membrane and actin filaments is only transient as actin dynamics at the tip are altered after disconnection. A continuous load-and-fail behavior allows thus tip-bound filopodia to probe the mechanics of their environment.

Results

Filopodial Retraction Abruptly Stalls at a Defined Transition Force.

Retraction of filopodia can be induced by attaching beads to their tips and counteracting mechanical forces can stall or even invert filopodial retraction (16, 25, 30). To better understand the mechanism and the dynamics of filopodial retraction against force we analyzed the dependency of retraction speed on counteracting forces, using the experimental setup shown in Fig. 1A.

Fig. 1.

Filopodial dynamics against mechanical force. (A) Experimental setup for the application of force to the tip of a filopodium via a bead trapped in an optical trap. Membrane and actin dynamics are monitored by confocal fluorescence microscopy. (B) Force (Upper) and substrate position (Lower) for a retracting filopodium. Position clamp: The filopodium pulls at velocity v_p and stalls at a transition force F_t. Force clamp: The filopodium pulls the bead toward the cell at velocity v_f. (Insets) Confocal images at marked times (blue circles). (Scale bar: 4 μm.) (C) Filopodial retraction speed v_p in position-clamp mode (red circles, 122 determinations, n = 29). Boxes include central 50% of data points in the corresponding force interval, and red lines denote median. Seventy percent of determinations were below the mean transition force <F_t>; in remaining cases stall occurred at higher F_t. (D) Filopodial retraction speed v_f in the force-clamp mode (green circles, 216 determinations, n = 129). Retraction can be observed above <F_t> for some time (26% of cases). (E) Transition forces F_t from indicated cell types. (F) Retraction speed of filopodia in force-clamp v_f and position-clamp v_p for different cell types, independently of applied forces. Retraction speeds as a function of applied force are shown in Fig. S2. All speeds are defined positive when pointing away from the cell body.

HeLa cells were fluorescently labeled with the lipophilic dye FM4-64 and observed by confocal microscopy. A filopodium that was not attached to the substrate was selected and its tip was approached to an optically trapped, carboxylated bead (COOH bead). After bead binding, most filopodia retracted (75%, n = 101, Fig. S1A), resulting in displacement of the bead relative to the trap center with velocity v_p. (Fig. 1B). For nonmigrating cells, if the positions of the trap and of the substrate are kept constant (“position-clamp” mode), v_p represents the filopodial retraction speed against the force F exerted by the optical trap. The force increases with the distance Δx between the bead and the trap center according to , where k_x is the trap stiffness (Fig. 1B). Only short pulling events of at most 400 nm could be observed because retraction stalled abruptly at a transition force F_t. This transition was followed by a force plateau (Fig. 1B), as reported previously (30). To study complete retraction of filopodia, we used a feedback system that adjusted the position of the nonmigrating cell by moving the microscope’s stage at a subsecond timescale, thus allowing the displacement of the bead within the trap to remain constant (“force-clamp” mode). In this mode, filopodia could be observed retracting against a controlled force in a linear fashion (Fig. 1B, Insets at t > 8 min). The stage position (Fig. 1B, Lower) is directly related to the filopodial length and the retraction speed v_f can be measured during the whole retraction process.

Retraction speeds measured in position-clamp mode v_p (Fig. 1C) and force-clamp mode v_f (Fig. 1D) of individual filopodia were plotted as a function of F. Filopodia abruptly stalled at an average force <F_t> of 21 ± 4 pN when probed in the position-clamp mode (Fig. 1E) and a minority of filopodia (30%, n = 29) retracted to higher individual transition forces (Fig. 1C). Consistently, most filopodia (74%) were observed to retract against counteracting forces below 21 pN in the force-clamp mode. For higher forces, retraction can be observed for some time (26% of cases, Fig. 1D), but they ultimately led to elongation of the filopodial structure (Fig. S1C and see Fig. 3).

Fig. 3.

Forced elongation of filopodia. (A) Force (Upper) and substrate position (Lower) for a retracting filopodium probed in force clamp. Before: Retraction against a force F_a with speed v_f. Stepwise increase to a probe force F_τ led to stretching Δx of the filopodium. After a time τ, fast elongation occurred (“release”) and the feedback was turned off (“after”). (B) Confocal images (average of three images taken during 15 s) of filopodia labeled with the indicated fluorescent markers immediately before and after release. (Scale bars: 2 μm.) (Lower) Ratios of average fluorescence intensity values for individual filopodia at areas A–D equivalent to those depicted in the Upper images. Determinations: Membrane marker, n = 40; LifeAct-RFP, n = 18; fascin-GFP, n = 10. Numbers denote the mean ratio in percentage ± SEM. (C) Probability that fast elongation for a single filopodium has occurred before a time τ for different probe forces F_τ. Determinations: F_τ = 45 pN (n = 60), 35 pN (n = 28), and 20 pN (n = 14). Dashed lines show fits of the data to Eq. S7 (SI Text).

The speed of single filopodia while retracting against forces between 0 pN and 50 pN did not show any explicit dependency on force, either in position- or in force-clamp mode until abrupt stall or forced elongation occurred. When averaged, the speeds recorded in different force intervals showed only a slight increase from <v_p> = −7 ± 1 nm/s to −10 ± 1 nm/s at forces of 5 pN and 15 pN, respectively, and no dependency of <v_f> = −14 ± 1 nm/s for forces between 0 and 20 pN (Fig. 1 C and D). For forces higher than 20 pN, <v_f> decreased to −8 ± 2 nm/s, which was similar to <v_p> = −10 ± 2 nm/s observed in this regime. This weak dependency can be explained by the viscoelastic properties of the filopodium (SI Text).

We tested whether similar results could be observed in two other cell lines. Consistent with results observed for HeLa cells, retraction of filopodia emanating from fibroblastic carassius auratus (CAR) cells and human embryonic kidney cells (HEK-293T) could also be observed following bead attachment to their tip. For the tested cell lines, retraction was abruptly stalled at transition forces F_t in the range of 20–40 pN (Fig. 1E). Additionally, the retraction speed did not significantly vary for different counteracting forces, either in force-clamp or in position-clamp mode (Fig. S2). Fig. 1F summarizes filopodial retraction speeds of all tested cell lines regardless of the counteracting force. The average retraction speed was lower when measured in the position-clamp mode compared with the force-clamp mode for all tested cell lines. Stretching of the viscoelastic filopodia against external elastic load can account for this difference (Discussion).

Together, this suggests that whereas the absolute values of F_t, v_p, and v_f may be cell-line specific, the mechanics underlying filopodial retraction are conserved.

Bead Adhesion Reduces Actin Polymerization at the Filopodial Tip, Leading to Retraction Driven by the Cortical Retrograde Flow.

To analyze the underlying actin dynamics, we performed photobleaching experiments on cells expressing actin-GFP. First, experiments were done in the absence of bead manipulation and by bleaching areas in the fluorescent filopodium and in the adjacent cortex (Fig. 2 A and B). The displacement of bleached areas (movement of positions b and a, Fig. 2A) as a function of time was analyzed using kymographs (Fig. 2B, Lower).

Fig. 2.

Actin dynamics of filopodia. (A) Schematic of a filopodium protruding from the cortex. Tracking of photobleached areas allows measuring the retrograde flow speeds in the filopodium (v_rf) and in the cortex (v_rc). The filopodial growth or retraction velocity v_filo is given by the movement of the tip (position c). Speeds are defined positive when pointing away from the cell body. (B) (Upper) Representative confocal microscopy time-lapse z-projections of HeLa cells transfected with actin-GFP. (Scale bar: 2 μm.) Marked areas were bleached (dashed white boxes). (Lower) Kymographs taken along the filopodium and in the cortex (boxed areas in Upper panel). (Lower Right) Speeds were measured as shown in the zoom. (Scale bars: horizontal, 30 s; vertical, 2 μm.) (C) Pairwise correlation between retrograde flow in the filopodium (v_rf) and in the adjacent cortex (v_rc) measured at the same time. Red dashed line denotes bisector. Points show a Pearson correlation of r = 0.48 (68 determinations, n = 26). (D) Distribution of actin polymerization speeds at the tip (v_poly) and reversed retrograde flow speed in the shaft, −v_rf, and in the cortex, −v_rc, grouped for stationary, growing, and retracting filopodia (68 determinations, n = 26). v_poly was determined using Eq. 1. (E) Distribution of actin polymerization speeds at the tip (v_poly) and retrograde flow in the shaft v_rf for bead-bound filopodia in force-clamp mode (n = 9).

All analyzed filopodia showed retrograde flow in the actin shaft v_rf and in the adjacent cortex v_rc with identical mean velocities of −26 ± 1 nm/s and −27 ± 2 nm/s, respectively. In individual filopodia, the retrograde flow speed in the shaft correlated with that in the cortex (Fig. 2C). This points toward high friction between filopodial and cortical actin networks.

The speed of filopodial growth and retraction v_filo is determined by the balance between the retrograde flow in the filopodium and the actin polymerization rate of newly incorporated actin at the filopodial tip v_poly (19). The rate of actin polymerization corresponding to the assembly of monomers at the filopodial tip was determined from the kymographs as

for stationary, growing, or retracting filopodia (Fig. 2 A, B, and D). We additionally verified that actin was newly incorporated at the tip, using two independent fluorescence markers (Fig. S3 A and B).

Based on relation [1], in filopodia with a stationary length, the tip-polymerization rate v_poly has to exactly balance the speed of filopodial retrograde flow v_rf (19), which is similar to the retrograde flow in the cortex v_rc (Fig. 2D). When analyzing elongating and retracting filopodia, we found that the mean velocities of retrograde flow (v_rf and v_rc) remained constant (Fig. 2D). Consistently, the mean polymerization rate of actin at the tip v_poly was higher for growing filopodia and lower for retracting ones compared with filopodia with stationary length. Of note, we did not observe depolymerization at the tip (Fig. 2D, v_poly ≥ 0). This suggests that the cortical retrograde flow constantly pulls on the filopodial actin shaft and that filopodia grow or retract, depending on the actin polymerization rate at their tip.

Quantification of the dynamics of individual filopodia confirmed that the cortical retrograde flow did not correlate with filopodial dynamics, whereas the actin polymerization rate at the tip did (Fig. S3 C–E). Thus, the balance between the tip polymerization rate and the cortical retrograde flow accounts for filopodial dynamics (Fig. S3 F and G), because of high friction between the cortical and filopodial actin networks.

We next tested the effect of bead adhesion on filopodial actin dynamics. Beads were approached to the tip of a filopodium emanating from actin-GFP transfected cells, using optical tweezers. We observed filopodial retraction in the force-clamp mode, while simultaneously bleaching an area in the filopodial shaft. Kymograph analysis (Fig. S4A) showed that the actin polymerization rate at the tip was lower than the retrograde flow, with values similar to those for bead-free retracting filopodia (Fig. 2E). We obtained consistent results by analyzing occasionally occurring fluorescence speckles moving backward in the filopodial shaft (Fig. S4 C and D).

Based on these data, we argue that the cortical retrograde flow constantly drives retrograde flow in the filopodial actin shaft through high frictional coupling. Filopodia elongate or retract by controlling the actin polymerization rate at the tip that is reduced upon tip adhesion to a bead.

Actin Linkage to the Tip Membrane Limits Force Exertion.

To determine components involved in the mechanical stall and forced filopodial elongation that occurs at relatively small transition forces (<F_t> ∼ 20 pN, Fig. 1E), we applied forces higher than <F_t> while analyzing actin and membrane dynamics, using confocal fluorescence microscopy.

Fig. 3A shows a force and substrate-position trace for a bead-bound filopodium pulling against a constant force F_a = 7 pN in the force-clamp mode (“before”). The filopodium was retracting with a constant velocity v_f (Fig. 3A, Lower). After 160 s, the feedback force was abruptly increased to F_τ = 45 pN, a value larger than the average transition force <F_t>. The filopodium instantaneously stretched over a length Δx due to its viscoelastic properties, sustained the force during a time τ, and suddenly elongated (Fig. 3A, “release”). After an elongation of 2–5 μm, the force-clamp control was turned off (Fig. 3A, t = 4.1 min), leading to a force relaxation toward a plateau force F_b. A complete detachment of the filopodium from the bead was only rarely observed (8%, n = 163). This sudden elongation was reminiscent of the extension dynamics of pure membrane tubes (27), indicating disconnection between the cell’s actin cytoskeleton and the membrane (Fig. S1C). To localize where this disconnection occurred, filopodia were imaged immediately before and after filopodial elongation, using different fluorescent markers (Fig. 3B). Staining with the lipophilic dye FM4-64 confirmed that the filopodial membrane remained attached to the bead and elongated after rupture. In contrast, F-actin labeling with LifeAct-RFP and Fascin-GFP showed a discontinuous distribution after the force release. A quantitative analysis of the fluorescence intensity ratios at the filopodial tip and at its base before (A/B) or following rupture (C/D) revealed a depletion of F-actin at the ruptured tip region (Fig. 3B). These observations are consistent with rupture of the linkage between the membrane and actin filaments at the filopodial tip, suggesting this linkage as the limiting factor for filopodial force application.

To quantify the strength of these links, we determined the time τ until rupture and rapid elongation occurred for multiple filopodia and for different applied forces F_τ. Fig. 3C shows the probability distribution P_u(τ) that rupture occurred when a force F_τ was exerted for a time τ. When applying forces F_τ of 20 pN, 35 pN, and 45 pN, most filopodia (∼60%) immediately elongated within less than 2 s. In the remaining cases, filopodia continued pulling and showed rupture only after several seconds, as shown in the example in Fig. 3A. For these latter filopodia, the probability of having observed rupture increased with time (Fig. 3C). In addition, the probability for inducing rupture after a defined time increases with increasing forces F_τ. A Bell–Evans model for the rupture of multiple links explains the observed dependency of tip link stability on force and time (SI Text).

We have shown that filopodia can withstand and pull against high forces up to 50 pN for short times. Our measurements point toward the strength of the connection between actin filaments and the membrane at the tip as the limiting factor for force production.

Ruptured Filopodia Pull with Passive Membrane Forces and with an Active Load-and-Fail Mechanism.

The relative weakness of membrane–actin links at the filopodial tip highlights the importance of the plasma membrane for filopodial force exertion during retraction. In intact filopodia, where the actin cytoskeleton is connected to the bead-bound tip, discrimination between membrane- and actin-based force production is difficult because they are closely related (31). We thus analyzed ruptured filopodia to determine their relative force contributions.

After rupture and fast elongation (Fig. 3A, “after”), the remaining structures showed different force dynamics; two distinct examples are shown in Fig. 4A. In all cases, we observed a force relaxation toward an average plateau force F_b = 13.2 ± 0.5 pN (Fig. 4B). In most cases (75%, n = 131) the force remained constant, with force fluctuations lower than 5 pN within 3 min after rupture, reminiscent of actin-free membrane tethers pulled from cells (Fig. 4A, Upper) (27). In the remaining cases, distinct load-and-fail events were observed superimposed on the force plateau (Fig. 4A, Lower).

Fig. 4.

Filopodial dynamics and mechanics after forced elongation. (A) Force traces observed in the position-clamp mode after forced elongation. (Upper) Seventy-five percent of observed cases (n = 131) show a plateau (“const-f”) with fluctuations lower than 5 pN. (Lower) Occasional force rises were observed in the remaining cases. (B) Distribution of plateau forces after forced elongation for individual filopodia. F_b, all determinations; F_b(k ∼ 0), filopodia with stiffness smaller than 7 pN/μm (n = 39); F_mem, membrane tubes directly pulled from the lamellipodium (n = 15). Rare control tethers showing load-and-fail behavior (37) were excluded. (C) Stiffness measurements: Step displacements (gray) lasting 2–3 s were imposed to filopodia in different states (see Fig. S5 A–C for protocol). Blue traces: Averaged responses of four filopodia, where the stiffness is deduced from fitting Eq. S3 (red). (D) Stiffnesses measured during the plateau state (const-f, n = 100) and during force rises (rise, n = 11). Values beyond the limit of our fits (>200 pN/μm) have been grouped. (E) LifeAct-RFP images of a filopodium immediately before and after rupture and more than 3 min later. (F) Relative intensity values measured at positions N, C, E, and F showing that the filopodial actin shaft stops retracting after rupture (n = 17).

Empty cell-membrane tubes behave as viscous fluids at low frequencies, exhibiting low elasticity as long as the cell membrane reservoir is not depleted (27, 32, 33). To determine the contribution of inward forces that are only due to the plasma membrane, we probed the elasticity of filopodial structures after forced elongation and selected those with low elastic moduli. The viscoelastic properties of ruptured filopodia were measured by imposing a series of step movements to the substrate during 2–3 s and by averaging between 5 and 50 corresponding response traces (Fig. S5 A–C). Fig. 4C shows the averaged response traces (blue) from four filopodia. Fitting the response functions gives the elasticity of the probed structure (dashed red traces in Fig. 4C and Fig. S5C). When they were measured during a force plateau (Fig. 4A, “const-f”), we observed elasticity values widely spread between zero and more than 200 pN/μm (Fig. 4D). These values varied among filopodia and variation could also be observed for a single filopodium over time (Fig. S5D). We postulate that filopodia with a low stiffness (<7 pN/μm) corresponded to ruptured filopodia with actin filaments completely disconnected from the membrane at the tip. The corresponding plateau forces F_b(k ∼ 0) for those filopodia are shown in Fig. 4B. The mean force <F_b(k ∼ 0)> = 15.3 ± 0.7 pN matches the mean force of control tethers pulled directly from the plasma membrane, <F_mem> = 13.6 ± 1.4 pN. This demonstrates that the filopodial plasma membrane itself exerts forces of 15 pN after detachment from the actin shaft.

During the plateau phase, the time-averaged stiffness of these structures showed a low median value of 19 pN/μm (Fig. 4D, const-f), and thus membrane mechanics dominated. In contrast, when measuring the stiffness during active force rise events, high median values around 100 pN/μm were observed (Fig. 4D, “rise”). The pulling speed during these rise phases, v_p = 10 ± 2 nm/s (n = 28), was similar to the pulling speed observed for nonruptured retracting filopodia (Fig. 1C), suggesting that active pulling via the retrograde flow resumed, and thus reconnection between membrane and filopodial actin filaments allowed cytoskeletal force transduction.

To elucidate how actin reconnection at the filopodial tip occurred after rupture, LifeAct-RFP fluorescence was quantified at different positions within the filopodium after extended time periods (>3 min) (Fig. 4 E and F). More than 3 min after rupture, the relative fluorescence intensity at the former tip position (“F/G”) was equivalent to that immediately after rupture (“N/D”), showing that the filopodial actin shaft did not further retract. In contrast, the relative fluorescence intensity next to the bead increased in some cases (6 of 16, “E/G”). This indicates that following rupture, increased actin polymerization rates at the tip may allow the reestablishment of the actin–membrane connection for some filopodia.

Taken together, we show that an actin-based inward force can act concomitantly with a passive and constant inward force due to the plasma membrane. The transient aspect of the active rise phases suggests that connection of the actin filaments is reestablished for short periods, until rupture occurs again, leading to a load-and-fail behavior.

Discussion–Conclusion

We propose a mechanical model that explains how a single filopodium exerts a pulling force via its tip (Fig. 5). We have shown that two inward forces are exerted by filopodia: a passive force via the membrane and an active cytoskeletal force produced by the retrograde flow in the cortex that is transduced via high frictional coupling to the filopodial actin shaft at its base. Such frictional coupling might also drive retrograde flow in filopodia of other cell types (19, 34), where it could account for high pulling forces up to 1 nN (4, 5). It also allows the filopodial actin filaments to exert pulling and pushing forces against the membrane at the tip, depending on the polymerization rate v_poly. The filopodial actin shaft can be seen as a viscoelastic Kelvin–Voigt material (25) with a stiffness k_filo. If the filopodium pulls against an elastic substrate, such as the bead held in the optical trap in the position-clamp mode, stretching of the actin shaft will lead to a reduced apparent pulling speed (SI Text, Eqs. S1 and S2). In this case, k_eff is given by the trap stiffness k_trap that was between 60 pN/μm and 100 pN/μm in our experiments (SI Text). In the force-clamp mode the effective trap stiffness k_eff is zero and the pulling speed reflects the balance between the negative speed of retrograde flow and the polymerization speed at the tip. Consistently we observe smaller pulling speeds v_p in position-clamp mode compared with the force-clamp mode v_f for all tested cell lines (Fig. 1F). We also determined the stiffness k_filo of intact filopodia from HeLa cells by applying strain fluctuations (Fig. S5E). The measured value k_filo = 73 ± 22 pN/μm (n = 13, Fig. S5F) accounts well for the dependency of the retraction speed on trap stiffness (SI Text).

Fig. 5.

Mechanical model for filopodia. Force production via the tip arises from the parallel action of membrane forces (F_mem) and from actin dynamics. Cortical retrograde flow (v_rc) couples with high friction to the filopodial actin shaft, modeled as a Kevin–Voigt body with an elastic modulus k_filo and a viscosity c_filo. Polymerization at the tip (v_poly) slower than the cortical retrograde flow leads to retraction. Cytoskeletal force transduction can fail due to weak actin–membrane linkage at the tip (b_int). An elastic force with stiffness k_eff controlled by the optical trap is exerted on the bead.

We have shown that most filopodia cannot withstand forces higher than 20 pN because of weak connections between the actin shaft and the membrane at the tip (corresponding to b_int, Fig. 5). After disruption of these links the membrane alone can exert forces of 15 pN. This value could be an underestimation for membrane forces in intact filopodia, if the actin shaft alters the radius of the filopodium compared with the equilibrium radius of an empty membrane tube (31, 35). Relative tube radii can be deduced by analyzing the fluorescence signal of the membrane dye (36). Intact filopodia show a quasi-cylindrical shape (Fig. 3B, Left, “A/B”) in agreement with EM images (30). Actin-depleted tubes pulled from filopodia kept the cylindrical shape after rupture (Fig. 3B, Left, “C/D”), with similar radii to those of the actin-filled filopodia (Fig. 3B, Left, “D/B”), suggesting also membrane forces of 15 pN in intact filopodia. This implies that pulling forces higher than 15 pN are solely due to the retrograde flow of actin filaments.

Our measurements show that upon binding to a bead, filopodia retract in association with a reduction of the actin polymerization speed at the tip. Surprisingly, although mechanically stalled filopodia still show retrograde flow (Fig. S4C), we did not observe further retraction of the actin shaft after forced rupture (Fig. 4F, F/G ≈ N/D). Following mechanical rupture, the rate of actin polymerization at the tip could increase to compensate or even overcome the retrograde flow. Such behavior would point toward a control mechanism at the tip that senses rupture and adjusts the actin polymerization rate, ensuring contact between the actin shaft and the membrane.

Our paper provides evidence that actin–membrane links at the tip control the extent of cytoskeletal forces transduced to the substrate by filopodia. The nature and strength of these links may depend on the specific type of external tip adhesion to the substrate. Previously measured average stall forces for filopodia of HeLa cells varied with the type and density of adhesive links to differently coated beads, but stayed below 15 pN (30). In addition, when probing filopodial dynamics and mechanics using fibronectin-coated beads that specifically bind integrins (Fig. S6 A–C), we observed no drastic changes compared with COOH beads. In sharp contrast, filopodia from professional phagocytes such as macrophages can resist mechanical rupture against high forces up to 600 pN (25), arguing for strong tip connections. These filopodia can be mechanically forced to stall (16) and to slowly elongate (25), which may be due to enhanced actin polymerization at the tip (25) or due to weak frictional coupling at the filopodial base mediated, e.g., via molecular motors (16).

Our experiments point toward a sensing mechanism at the filopodial tip that allows the cell to quickly react to external mechano-chemical signals by controlling the actin polymerization rate. A future challenge will be to identify implicated molecular players and to reveal how they help in translating chemical and mechanical signals to coordinate filopodial actin dynamics.

Materials and Methods

Cell Culture.

Human cervical adenocarcinoma cells (HeLa), human embryonic kidney cells (HEK-293T), and goldfish fin fibroblast cells (CAR) were cultured as described in SI Text. Cells were plated on glass coverslips and, if mentioned, transfected using the Fugene HD (Roche) or jetPEI (Polyplus) reagents (SI Text). Before experiments, cells were rinsed three times in EM buffer (120 mM NaCl, 7 mM KCl, 1.8 mM CaCl₂, 0.8 mM MgCl₂, 5 mM glucose, and 25 mM Hepes, pH 7.3) and mounted on a microscope chamber.

Experimental Setup.

Fluorescence recovery after photobleaching (FRAP) experiments without bead manipulation were performed on an Eclipse Ti confocal microscope (Nikon) equipped with a 100× objective (NA 1.4) in a 37 °C controlled environment (SI Text). Experiments with bead manipulation were performed on a Nikon TE2000 confocal microscope with a temperature-controlled objective (100×, NA 1.3) and a custom-build optical trap. The force detection and the calibration of the optical trap via the bead’s power spectrum are detailed in SI Text.