Filopodial retraction force is generated by cortical actin dynamics … · Filopodial retraction force is generated by cortical actin dynamics and controlled by reversible tethering

Filopodial retraction force is generated by corticalactin dynamics and controlled by reversibletethering at the tipThomas Bornschlögla,b,c,d, Stéphane Romeroe,f,g, Christian L. Vestergaarda,b,c,d,h, Jean-François Joannya,b,c,d,Guy Tran Van Nhieue,f,g,1, and Patricia Bassereaua,b,c,d,1,2

aInstitut Curie, Centre de Recherche, 75248 Paris, France; bCentre National de la Recherche Scientifique, Unité Mixte de Recherche 168, 75248 Paris, France;cUniversité Pierre et Marie Curie, 75252 Paris, France; eCollège de France, Equipe Communication Intercellulaire et Infections Microbiennes, Centre deRecherche Interdisciplinaire en Biologie, 75005 Paris, France; fInstitut National de la Santé et de la Recherche Médicale, U1050, 75005 Paris, France;dCelTisPhyBio and gMEMOLIFE Laboratory of Excellence and Paris Sciences et Lettres, 75005 Paris, France; and hDepartment of Micro- and Nanotechnology,Technical University of Denmark, Kongens Lyngby, 2450, Denmark

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 8, 2013 (received for review September 2, 2013)

Filopodia are dynamic,finger-like plasmamembrane protrusions thatsense themechanical and chemical surroundings of the cell. Here, weshow in epithelial cells that the dynamics of filopodial extension andretraction are determined by the difference between the actinpolymerization rate at the tip and the retrogradeflowat the base ofthe filopodium. Adhesion of a bead to the filopodial tip locallyreduces actin polymerization and leads to retraction via retrogradeflow, reminiscent of a process used by pathogens to invade cells.Using optical tweezers, we show that filopodial retraction occurs ata constant speed against counteracting forces up to 50 pN. Ourmeasurements point toward retrograde flow in the cortex togetherwith frictional coupling between the filopodial and cortical actinnetworks as the main retraction-force generator for filopodia. Theforce exerted by filopodial retraction, however, is limited by theconnection betweenfilopodial actinfilaments and themembrane atthe tip. Upon mechanical rupture of the tip connection, filopodiaexert a passive retraction force of 15 pN via their plasmamembrane.Transient reconnection at the tip allows filopodia to continuouslyprobe their surroundings in a load-and-fail manner within a well-defined force range.

cytoskeleton | mechanics | membrane-tension | pulling | lamellipodium

Filopodia are actin-rich cell membrane protrusions, involved inprocesses as diverse as cell migration, wound closure, and cell

invasion by pathogens (1–3). During cell migration, filopodia canexert forces on the substrate (4, 5) and act as precursors of focaladhesions (6–8). Filopodia initiate contacts during wound clo-sure and contribute to dorsal closure of the fruit fly embryo ina zipper-like fashion (9–12). Viruses can hijack filopodia andfilopodia-like cell–cell bridges to surf toward the cell body (13,14). Filopodia from macrophages and epithelial cells activelypull pathogens bound to their tips (15–18). In all these examplesfilopodial retraction and retrograde force production are crucial.However, although filopodia formation and growth have beenwell studied (1–3), the mechanisms underlying their retractionare poorly understood.Filopodia show continuous rearward movement of their actin

filaments in a process called “retrograde flow” (3, 19). In thelamellipodium, from which filopodia often emanate, the retro-grade flow originates from actin treadmilling due to actin de-polymerization at the rear and polymerization at the front of thelamellipodium. This retrograde flow is further amplified by themotor activity of myosins (20–23). In neurons, the filopodial shaftis deeply anchored in the growth cone and filopodial dynamicsdepends on the balance between actin polymerization at thefilopodial tip and its retrograde flow (19). In other cell types actindepolymerization at the tip has been associated with retractingfilopodia (24).

Different contributions to filopodial force production duringretraction can be considered. A connection between the filopodialtip and retracting actin filaments through transmembrane recep-tors such as integrins could transduce cortical forces applied onthe actin shaft. In macrophages, force measurements on retract-ing filopodia suggested a major role for cortical myosins pullingon filopodial actin bundles (16). These measurements showedthat retraction could be slowed down for forces below 20 pN.Applied forces higher than 20 pN inverted filopodial retraction ofmacrophages (25).Filopodial force production can also be due to membrane

mechanics (26). Forces exerted by actin-free tubes extruded fromthe cell plasma membrane typically range between 5 pN and30 pN (27). Membrane tension could drive filopodial retractionby exerting inward forces against the actin filaments. Moreover,filopodial actin filaments have been found disconnected from themembrane at the tip (28, 29), underlining the importance ofmembrane properties in filopodial mechanics. The contributionsof membrane- and actin-based forces, as well as the mechanicallinks controlling force production during filopodial retraction,are still unclear.Here, we studied the retraction dynamics and the forces exer-

ted by a single filopodium that is contacting an optically trappedbead at its tip. We found that filopodia retracted in associationwith a reduced actin polymerization at their tip at rates belowthose needed to compensate for the retrograde flow. The speed offilopodial retraction was only marginally affected by counter-acting forces up to 50 pN, suggesting that the driving forces for

Significance

Cells can sense their environment by using hair-like structurescalled filopodia that often exert pulling forces upon adhesivetip contact. We show, using optical tweezers and confocalmicroscopy, that the retraction force is generated by the dy-namics of the cortical actin cytoskeleton, constantly pulling onthe filopodial base. The weakest point of force transduction isat the tip between the actin shaft and the membrane. Thisallows tip-bound filopodia to apply controlled forces and touse a “load-and-fail” sensing process.

Author contributions: T.B., S.R., J.-F.J., G.T.V.N., and P.B. designed research; T.B. and S.R.performed research; T.B. and C.L.V. contributed new reagents/analytic tools; T.B., S.R.,and C.L.V. analyzed data; and T.B., S.R., C.L.V., J.-F.J., G.T.V.N., and P.B. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1G.T.V.N. and P.B. contributed equally to this work.2To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1316572110/-/DCSupplemental.

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retraction were not limiting within this range. We argue that actintreadmilling in the cell cortex, that functions far from its stallregime, transduces inward forces to the filopodial actin shaft atthe base via high friction. In addition we found that filopodia canexert passive inward forces of 15 pN by using cell membrane-based forces. External counterforces that are only 5 pN higherthan the membrane force can lead to rupture of connectionsbetween the actin shaft and the membrane at the filopodial tip.These weak contacts at the tip define the maximal pulling force offilopodia and allow cytoskeletal inward forces to operate only forshort time intervals (<25 s). We found that the mechanical dis-connection between membrane and actin filaments is only tran-sient as actin dynamics at the tip are altered after disconnection.A continuous load-and-fail behavior allows thus tip-bound filo-podia to probe the mechanics of their environment.

ResultsFilopodial Retraction Abruptly Stalls at a Defined Transition Force.Retraction of filopodia can be induced by attaching beads totheir tips and counteracting mechanical forces can stall or eveninvert filopodial retraction (16, 25, 30). To better understand themechanism and the dynamics of filopodial retraction againstforce we analyzed the dependency of retraction speed on coun-teracting forces, using the experimental setup shown in Fig. 1A.HeLa cells were fluorescently labeled with the lipophilic dye

FM4-64 and observed by confocal microscopy. A filopodium thatwas not attached to the substrate was selected and its tip wasapproached to an optically trapped, carboxylated bead (COOHbead). After bead binding, most filopodia retracted (75%, n =101, Fig. S1A), resulting in displacement of the bead relative tothe trap center with velocity vp. (Fig. 1B). For nonmigrating cells,if the positions of the trap and of the substrate are kept constant(“position-clamp” mode), vp represents the filopodial retractionspeed against the force F exerted by the optical trap. The forceincreases with the distance Δx between the bead and the trapcenter according to F = kxΔx , where kx is the trap stiffness (Fig.1B). Only short pulling events of at most 400 nm could be ob-served because retraction stalled abruptly at a transition force Ft.This transition was followed by a force plateau (Fig. 1B), as re-ported previously (30). To study complete retraction of filopodia,we used a feedback system that adjusted the position of thenonmigrating cell by moving the microscope’s stage at a sub-second timescale, thus allowing the displacement of the beadwithin the trap to remain constant (“force-clamp” mode). In thismode, filopodia could be observed retracting against a controlledforce in a linear fashion (Fig. 1B, Insets at t > 8 min). The stageposition (Fig. 1B, Lower) is directly related to the filopodiallength and the retraction speed vf can be measured during thewhole retraction process.Retraction speeds measured in position-clamp mode vp (Fig.

1C) and force-clamp mode vf (Fig. 1D) of individual filopodiawere plotted as a function of F. Filopodia abruptly stalled at anaverage force <Ft> 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). Con-sistently, most filopodia (74%) were observed to retract againstcounteracting forces below 21 pN in the force-clamp mode. Forhigher forces, retraction can be observed for some time (26%of cases, Fig. 1D), but they ultimately led to elongation of thefilopodial structure (Fig. S1C and see Fig. 3).The speed of single filopodia while retracting against forces

between 0 pN and 50 pN did not show any explicit dependencyon force, either in position- or in force-clamp mode until abruptstall or forced elongation occurred. When averaged, the speedsrecorded in different force intervals showed only a slight increasefrom <vp> = −7 ± 1 nm/s to −10 ± 1 nm/s at forces of 5 pN and15 pN, respectively, and no dependency of <vf> = −14 ± 1 nm/sfor forces between 0 and 20 pN (Fig. 1 C and D). For forces

higher than 20 pN, <vf> decreased to −8 ± 2 nm/s, which wassimilar to <vp> = −10 ± 2 nm/s observed in this regime. Thisweak dependency can be explained by the viscoelastic propertiesof 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 aur-atus (CAR) cells and human embryonic kidney cells (HEK-293T)

Fig. 1. Filopodial dynamics against mechanical force. (A) Experimentalsetup for the application of force to the tip of a filopodium via a beadtrapped in an optical trap. Membrane and actin dynamics are monitored byconfocal fluorescence microscopy. (B) Force (Upper) and substrate position(Lower) for a retracting filopodium. Position clamp: The filopodium pulls atvelocity vp and stalls at a transition force Ft. Force clamp: The filopodiumpulls the bead toward the cell at velocity vf. (Insets) Confocal images atmarked times (blue circles). (Scale bar: 4 μm.) (C) Filopodial retraction speedvp in position-clamp mode (red circles, 122 determinations, n = 29). Boxesinclude central 50% of data points in the corresponding force interval, andred lines denote median. Seventy percent of determinations were below themean transition force <Ft>; in remaining cases stall occurred at higher Ft. (D)Filopodial retraction speed vf in the force-clamp mode (green circles, 216determinations, n = 129). Retraction can be observed above <Ft> for sometime (26% of cases). (E) Transition forces Ft from indicated cell types. (F)Retraction speed of filopodia in force-clamp vf and position-clamp vp fordifferent cell types, independently of applied forces. Retraction speeds asa function of applied force are shown in Fig. S2. All speeds are definedpositive when pointing away from the cell body.

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could also be observed following bead attachment to their tip. Forthe tested cell lines, retraction was abruptly stalled at transitionforces Ft in the range of 20–40 pN (Fig. 1E). Additionally, theretraction speed did not significantly vary for different counter-acting forces, either in force-clamp or in position-clamp mode(Fig. S2). Fig. 1F summarizes filopodial retraction speeds of alltested cell lines regardless of the counteracting force. The averageretraction speed was lower when measured in the position-clampmode compared with the force-clamp mode for all tested celllines. Stretching of the viscoelastic filopodia against externalelastic load can account for this difference (Discussion).Together, this suggests that whereas the absolute values of Ft,

vp, and vf may be cell-line specific, the mechanics underlyingfilopodial retraction are conserved.

Bead Adhesion Reduces Actin Polymerization at the Filopodial Tip,Leading to Retraction Driven by the Cortical Retrograde Flow. Toanalyze the underlying actin dynamics, we performed photo-bleaching experiments on cells expressing actin-GFP. First, experi-ments were done in the absence of bead manipulation and bybleaching areas in the fluorescent filopodium and in the adjacentcortex (Fig. 2 A and B). The displacement of bleached areas(movement of positions b and a, Fig. 2A) as a function of time wasanalyzed using kymographs (Fig. 2B, Lower).All analyzed filopodia showed retrograde flow in the actin shaft

vrf and in the adjacent cortex vrc with identical mean velocities of−26 ± 1 nm/s and −27 ± 2 nm/s, respectively. In individual filo-podia, the retrograde flow speed in the shaft correlated with thatin the cortex (Fig. 2C). This points toward high friction betweenfilopodial and cortical actin networks.The speed of filopodial growth and retraction vfilo is determined

by the balance between the retrograde flow in the filopodium andthe actin polymerization rate of newly incorporated actin at thefilopodial tip vpoly (19). The rate of actin polymerization corre-sponding to the assembly of monomers at the filopodial tip wasdetermined from the kymographs as

vpoly =Δðc− bÞ=Δt= vfilo − vrf [1]

for stationary, growing, or retracting filopodia (Fig. 2 A, B, andD). We additionally verified that actin was newly incorporated atthe tip, using two independent fluorescence markers (Fig. S3 Aand B).Based on relation [1], in filopodia with a stationary length, the

tip-polymerization rate vpoly has to exactly balance the speed offilopodial retrograde flow vrf (19), which is similar to the retro-grade flow in the cortex vrc (Fig. 2D). When analyzing elongatingand retracting filopodia, we found that the mean velocities ofretrograde flow (vrf and vrc) remained constant (Fig. 2D). Con-sistently, the mean polymerization rate of actin at the tip vpoly washigher for growing filopodia and lower for retracting ones com-pared with filopodia with stationary length. Of note, we did notobserve depolymerization at the tip (Fig. 2D, vpoly ≥ 0). This sug-gests that the cortical retrograde flow constantly pulls on the filo-podial actin shaft and that filopodia grow or retract, depending onthe actin polymerization rate at their tip.Quantification of the dynamics of individual filopodia con-

firmed that the cortical retrograde flow did not correlate withfilopodial dynamics, whereas the actin polymerization rate at thetip did (Fig. S3 C–E). Thus, the balance between the tip poly-merization rate and the cortical retrograde flow accounts forfilopodial dynamics (Fig. S3 F and G), because of high frictionbetween 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 em-anating from actin-GFP transfected cells, using optical tweezers.We observed filopodial retraction in the force-clamp mode, whilesimultaneously bleaching an area in the filopodial shaft. Kymograph

analysis (Fig. S4A) showed that the actin polymerization rate at thetip was lower than the retrograde flow, with values similar to thosefor bead-free retracting filopodia (Fig. 2E). We obtained consistentresults by analyzing occasionally occurring fluorescence specklesmoving 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 shaftthrough high frictional coupling. Filopodia elongate or retract bycontrolling the actin polymerization rate at the tip that is reducedupon tip adhesion to a bead.

Actin Linkage to the Tip Membrane Limits Force Exertion. To de-termine components involved in the mechanical stall and forcedfilopodial elongation that occurs at relatively small transitionforces (<Ft> ∼ 20 pN, Fig. 1E), we applied forces higher than<Ft> while analyzing actin and membrane dynamics, using con-focal fluorescence microscopy.

Fig. 2. Actin dynamics of filopodia. (A) Schematic of a filopodium pro-truding from the cortex. Tracking of photobleached areas allows measuringthe retrograde flow speeds in the filopodium (vrf) and in the cortex (vrc). Thefilopodial growth or retraction velocity vfilo is given by the movement of thetip (position c). Speeds are defined positive when pointing away from the cellbody. (B) (Upper) Representative confocal microscopy time-lapse z-projec-tions of HeLa cells transfected with actin-GFP. (Scale bar: 2 μm.) Marked areaswere bleached (dashed white boxes). (Lower) Kymographs taken along thefilopodium 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 filo-podium (vrf) and in the adjacent cortex (vrc) measured at the same time. Reddashed line denotes bisector. Points show a Pearson correlation of r = 0.48(68 determinations, n = 26). (D) Distribution of actin polymerization speedsat the tip (vpoly) and reversed retrograde flow speed in the shaft, −vrf, andin the cortex, −vrc, grouped for stationary, growing, and retracting filopodia(68 determinations, n = 26). vpoly was determined using Eq. 1. (E) Distributionof actin polymerization speeds at the tip (vpoly) and retrograde flow in theshaft vrf for bead-bound filopodia in force-clamp mode (n = 9).

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Fig. 3A shows a force and substrate-position trace for a bead-bound filopodium pulling against a constant force Fa = 7 pN inthe force-clamp mode (“before”). The filopodium was retractingwith a constant velocity vf (Fig. 3A, Lower). After 160 s, thefeedback force was abruptly increased to Fτ = 45 pN, a valuelarger than the average transition force <Ft>. The filopodiuminstantaneously stretched over a length Δx due to its viscoelasticproperties, sustained the force during a time τ, and suddenlyelongated (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 Fb. A com-plete detachment of the filopodium from the bead was onlyrarely observed (8%, n = 163). This sudden elongation wasreminiscent of the extension dynamics of pure membrane tubes(27), indicating disconnection between the cell’s actin cytoskel-eton and the membrane (Fig. S1C). To localize where this dis-connection occurred, filopodia were imaged immediately beforeand after filopodial elongation, using different fluorescentmarkers (Fig. 3B). Staining with the lipophilic dye FM4-64confirmed that the filopodial membrane remained attached to thebead and elongated after rupture. In contrast, F-actin labeling

with LifeAct-RFP and Fascin-GFP showed a discontinuous dis-tribution after the force release. A quantitative analysis of thefluorescence intensity ratios at the filopodial tip and at its basebefore (A/B) or following rupture (C/D) revealed a depletion ofF-actin at the ruptured tip region (Fig. 3B). These observationsare consistent with rupture of the linkage between the membraneand actin filaments at the filopodial tip, suggesting this linkageas 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 multiplefilopodia and for different applied forces Fτ. Fig. 3C shows theprobability distribution Pu(τ) that rupture occurred when a forceFτ was exerted for a time τ. When applying forces Fτ of 20 pN,35 pN, and 45 pN, most filopodia (∼60%) immediately elongatedwithin less than 2 s. In the remaining cases, filopodia continuedpulling and showed rupture only after several seconds, as shownin the example in Fig. 3A. For these latter filopodia, the prob-ability of having observed rupture increased with time (Fig. 3C).In addition, the probability for inducing rupture after a definedtime increases with increasing forces Fτ. A Bell–Evans model forthe rupture of multiple links explains the observed dependencyof 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 pointtoward the strength of the connection between actin filaments andthe membrane at the tip as the limiting factor for force production.

Ruptured Filopodia Pull with Passive Membrane Forces and with anActive Load-and-Fail Mechanism. The relative weakness of mem-brane–actin links at the filopodial tip highlights the importanceof the plasma membrane for filopodial force exertion duringretraction. In intact filopodia, where the actin cytoskeleton isconnected to the bead-bound tip, discrimination between mem-brane- and actin-based force production is difficult because theyare closely related (31). We thus analyzed ruptured filopodia todetermine their relative force contributions.After rupture and fast elongation (Fig. 3A, “after”), the re-

maining structures showed different force dynamics; two distinctexamples are shown in Fig. 4A. In all cases, we observed a forcerelaxation toward an average plateau force Fb = 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).Empty cell-membrane tubes behave as viscous fluids at low

frequencies, exhibiting low elasticity as long as the cell mem-brane reservoir is not depleted (27, 32, 33). To determine thecontribution of inward forces that are only due to the plasmamembrane, we probed the elasticity of filopodial structures afterforced elongation and selected those with low elastic moduli.The viscoelastic properties of ruptured filopodia were measuredby imposing a series of step movements to the substrate during2–3 s and by averaging between 5 and 50 corresponding responsetraces (Fig. S5 A–C). Fig. 4C shows the averaged response traces(blue) from four filopodia. Fitting the response functions givesthe elasticity of the probed structure (dashed red traces in Fig.4C and Fig. S5C). When they were measured during a forceplateau (Fig. 4A, “const-f”), we observed elasticity values widelyspread between zero and more than 200 pN/μm (Fig. 4D). Thesevalues varied among filopodia and variation could also be ob-served for a single filopodium over time (Fig. S5D). We postulatethat filopodia with a low stiffness (<7 pN/μm) corresponded toruptured filopodia with actin filaments completely disconnectedfrom the membrane at the tip. The corresponding plateau forcesFb(k ∼ 0) for those filopodia are shown in Fig. 4B. The meanforce <Fb(k ∼ 0)> = 15.3 ± 0.7 pN matches the mean force of

Fig. 3. Forced elongation of filopodia. (A) Force (Upper) and substrateposition (Lower) for a retracting filopodium probed in force clamp. Before:Retraction against a force Fa with speed vf. Stepwise increase to a probeforce Fτ led to stretching Δx of the filopodium. After a time τ, fast elonga-tion occurred (“release”) and the feedback was turned off (“after”). (B)Confocal images (average of three images taken during 15 s) of filopodialabeled with the indicated fluorescent markers immediately before and afterrelease. (Scale bars: 2 μm.) (Lower) Ratios of average fluorescence intensityvalues for individual filopodia at areas A–D equivalent to those depicted inthe 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 oc-curred before a time τ for different probe forces Fτ. Determinations: Fτ = 45pN (n = 60), 35 pN (n = 28), and 20 pN (n = 14). Dashed lines show fits of thedata to Eq. S7 (SI Text).

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control tethers pulled directly from the plasma membrane,<Fmem> = 13.6 ± 1.4 pN. This demonstrates that the filopodialplasma membrane itself exerts forces of 15 pN after detachmentfrom 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, highmedian values around 100 pN/μm were observed (Fig. 4D,“rise”). The pulling speed during these rise phases, vp = 10 ±2 nm/s (n = 28), was similar to the pulling speed observed fornonruptured retracting filopodia (Fig. 1C), suggesting that activepulling via the retrograde flow resumed, and thus reconnectionbetween membrane and filopodial actin filaments allowed cyto-skeletal force transduction.To elucidate how actin reconnection at the filopodial tip oc-

curred after rupture, LifeAct-RFP fluorescence was quantified atdifferent positions within the filopodium after extended timeperiods (>3 min) (Fig. 4 E and F). More than 3 min after rup-ture, 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. Incontrast, the relative fluorescence intensity next to the bead in-creased in some cases (6 of 16, “E/G”). This indicates thatfollowing rupture, increased actin polymerization rates at the tipmay allow the reestablishment of the actin–membrane connectionfor some filopodia.Taken together, we show that an actin-based inward force can

act concomitantly with a passive and constant inward force dueto the plasma membrane. The transient aspect of the active risephases suggests that connection of the actin filaments is rees-tablished for short periods, until rupture occurs again, leadingto a load-and-fail behavior.

Discussion–ConclusionWe propose a mechanical model that explains how a single filo-podium exerts a pulling force via its tip (Fig. 5). We have shownthat two inward forces are exerted by filopodia: a passive force viathe membrane and an active cytoskeletal force produced by theretrograde flow in the cortex that is transduced via high frictionalcoupling to the filopodial actin shaft at its base. Such frictionalcoupling might also drive retrograde flow in filopodia of othercell types (19, 34), where it could account for high pulling forcesup to 1 nN (4, 5). It also allows the filopodial actin filaments toexert pulling and pushing forces against the membrane at the tip,depending on the polymerization rate vpoly. The filopodial actinshaft can be seen as a viscoelastic Kelvin–Voigt material (25) witha stiffness kfilo. If the filopodium pulls against an elastic substrate,such as the bead held in the optical trap in the position-clampmode, stretching of the actin shaft will lead to a reduced apparentpulling speed vBead =

vpoly + vrcð1+ keff =kfiloÞ (SI Text, Eqs. S1 and S2). In this

case, keff is given by the trap stiffness ktrap that was between 60 pN/μm and 100 pN/μm in our experiments (SI Text). In the force-clamp mode the effective trap stiffness keff is zero and the pullingspeed reflects the balance between the negative speed of retro-grade flow and the polymerization speed at the tip. Consistentlywe observe smaller pulling speeds vp in position-clamp modecompared with the force-clamp mode vf for all tested cell lines(Fig. 1F). We also determined the stiffness kfilo of intact filopodiafrom HeLa cells by applying strain fluctuations (Fig. S5E). Themeasured value kfilo = 73 ± 22 pN/μm (n = 13, Fig. S5F) accountswell for the dependency of the retraction speed on trap stiffness(SI Text).We have shown that most filopodia cannot withstand forces

higher than 20 pN because of weak connections between theactin shaft and the membrane at the tip (corresponding to bint,Fig. 5). After disruption of these links the membrane alone canexert forces of 15 pN. This value could be an underestimation formembrane forces in intact filopodia, if the actin shaft alters theradius of the filopodium compared with the equilibrium radius ofan empty membrane tube (31, 35). Relative tube radii can bededuced by analyzing the fluorescence signal of the membrane

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 riseswere observed in the remaining cases. (B) Distribution of plateau forces afterforced elongation for individual filopodia. Fb, all determinations; Fb(k ∼ 0),filopodia with stiffness smaller than 7 pN/μm (n = 39); Fmem, membranetubes directly pulled from the lamellipodium (n = 15). Rare control tethersshowing load-and-fail behavior (37) were excluded. (C) Stiffness measure-ments: Step displacements (gray) lasting 2–3 s were imposed to filopodia indifferent states (see Fig. S5 A–C for protocol). Blue traces: Averagedresponses 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 (>200pN/μm) have been grouped. (E) LifeAct-RFP images of a filopodium imme-diately before and after rupture and more than 3 min later. (F) Relativeintensity values measured at positions N, C, E, and F showing that the filo-podial actin shaft stops retracting after rupture (n = 17).

Fig. 5. Mechanical model for filopodia. Force production via the tip arisesfrom the parallel action of membrane forces (Fmem) and from actin dynamics.Cortical retrograde flow (vrc) couples with high friction to the filopodialactin shaft, modeled as a Kevin–Voigt body with an elastic modulus kfilo anda viscosity cfilo. Polymerization at the tip (vpoly) slower than the corticalretrograde flow leads to retraction. Cytoskeletal force transduction can faildue to weak actin–membrane linkage at the tip (bint). An elastic force withstiffness keff controlled by the optical trap is exerted on the bead.

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dye (36). Intact filopodia show a quasi-cylindrical shape (Fig. 3B,Left, “A/B”) in agreement with EM images (30). Actin-depletedtubes pulled from filopodia kept the cylindrical shape afterrupture (Fig. 3B, Left, “C/D”), with similar radii to those of theactin-filled filopodia (Fig. 3B, Left, “D/B”), suggesting alsomembrane forces of 15 pN in intact filopodia. This implies thatpulling forces higher than 15 pN are solely due to the retrogradeflow of actin filaments.Our measurements show that upon binding to a bead, filo-

podia retract in association with a reduction of the actin poly-merization speed at the tip. Surprisingly, although mechanicallystalled filopodia still show retrograde flow (Fig. S4C), we did notobserve further retraction of the actin shaft after forced rupture(Fig. 4F, F/G ≈ N/D). Following mechanical rupture, the rate ofactin polymerization at the tip could increase to compensate oreven overcome the retrograde flow. Such behavior would pointtoward a control mechanism at the tip that senses rupture andadjusts the actin polymerization rate, ensuring contact betweenthe actin shaft and the membrane.Our paper provides evidence that actin–membrane links at the

tip control the extent of cytoskeletal forces transduced to thesubstrate by filopodia. The nature and strength of these links maydepend on the specific type of external tip adhesion to the sub-strate. Previously measured average stall forces for filopodia ofHeLa cells varied with the type and density of adhesive links todifferently coated beads, but stayed below 15 pN (30). In addi-tion, when probing filopodial dynamics and mechanics using fi-bronectin-coated beads that specifically bind integrins (Fig. S6A–C), we observed no drastic changes compared with COOHbeads. In sharp contrast, filopodia from professional phagocytessuch as macrophages can resist mechanical rupture against highforces 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 po-lymerization at the tip (25) or due to weak frictional coupling atthe 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 externalmechano-chemical signals by controlling the actin polymerizationrate. A future challenge will be to identify implicated molecularplayers and to reveal how they help in translating chemical andmechanical signals to coordinate filopodial actin dynamics.

Materials and MethodsCell Culture. Human cervical adenocarcinoma cells (HeLa), human embryonickidney cells (HEK-293T), and goldfish fin fibroblast cells (CAR) were culturedas described in SI Text. Cells were plated on glass coverslips and, if men-tioned, transfected using the Fugene HD (Roche) or jetPEI (Polyplus)reagents (SI Text). Before experiments, cells were rinsed three times in EMbuffer (120 mM NaCl, 7 mM KCl, 1.8 mM CaCl2, 0.8 mM MgCl2, 5 mM glu-cose, and 25 mM Hepes, pH 7.3) and mounted on a microscope chamber.

Experimental Setup. Fluorescence recovery after photobleaching (FRAP) experi-ments without bead manipulation were performed on an Eclipse Ti confocalmicroscope (Nikon) equipped with a 100× objective (NA 1.4) in a 37 °Ccontrolled environment (SI Text). Experiments with bead manipulation wereperformed on a Nikon TE2000 confocal microscope with a temperature-controlled objective (100×, NA 1.3) and a custom-build optical trap. Theforce detection and the calibration of the optical trap via the bead’s powerspectrum are detailed in SI Text.

ACKNOWLEDGMENTS. The authors thank P. Lepine, M. Nemethova, andN. Carpi for 293T, FishCar, and S-LA cells and D. Vignjevic and B. Sinha forfascin and LifeAct plasmids. This work was supported by the Institut Nationalde la Santé et de la Recherche Médicale, by the Agence National de laRecherche Grant 08-MIEN-011-02, by the Institut Curie, and by the CentreNational de la Recherche Scientifique. P.B.’s group belongs to the Frenchresearch consortium “CellTiss.” T.B. thanks the “Human Frontier Science Pro-gram” for funding.

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