Helical buckling of actin inside filopodiagenerates tractionNatascha Leijnsea,b, Lene B. Oddershedea,b, and Poul M. Bendixa,1

aNiels Bohr Institute and bLundbeck Foundation Center for Biomembranes in Nanomedicine, University of Copenhagen, 2100 Copenhagen, Denmark

Edited by William M. Bement, University of Wisconsin, Madison, WI, and accepted by the Editorial Board December 1, 2014 (received for review June 24, 2014)

Cells can interact with their surroundings via filopodia, which aremembrane protrusions that extend beyond the cell body. Filopo-dia are essential during dynamic cellular processes like motility,invasion, and cell–cell communication. Filopodia contain cross-linked actin filaments, attached to the surrounding cell membranevia protein linkers such as integrins. These actin filaments arethought to play a pivotal role in force transduction, bending,and rotation. We investigated whether, and how, actin withinfilopodia is responsible for filopodia dynamics by conducting si-multaneous force spectroscopy and confocal imaging of F-actin inmembrane protrusions. The actin shaft was observed to periodi-cally undergo helical coiling and rotational motion, which occurredsimultaneously with retrograde movement of actin inside the filo-podium. The cells were found to retract beads attached to thefilopodial tip, and retraction was found to correlate with rotationand coiling of the actin shaft. These results suggest a previouslyunidentified mechanism by which a cell can use rotation of thefilopodial actin shaft to induce coiling and hence axial shorteningof the filopodial actin bundle.

membrane–cytoskeleton interactions | membrane nanotubes |filopodial retrograde flow | helical buckling | filopodia rotation

Tubular membrane remodeling driven by the actin cytoskele-ton plays a major role in both pathogenesis and in a healthy

immune response. For instance, invadopodia, podosomes, andfilopodia are crucial for invasion and migration of cells (1).Filopodia are thin (100 to 300 nm), tube-like, actin-rich struc-tures that function as “antennae” or “tentacles” that cells use toprobe and interact with their microenvironment (2–4). Suchstructures have been studied in vitro using model systems wherethe point-like 3D contacts with the extracellular matrix (ECM)have been mimicked by using optically trapped dielectric par-ticles, functionalized with relevant ligands. These model systemsallow for mechanical and visual control over filopodial dynamicsand have significantly advanced the understanding of cellularmechanosensing (5).Extraction of membrane tubes, using optical trapping, has

been used to investigate mechanical properties of the mem-brane–cytoskeleton system (6–10), or membrane cholesterolcontent (11), and has revealed important insight into themechanism that peripheral proteins use to shape membranes(12). Motivated by the pivotal role of F-actin in the mechanicalbehavior of filopodia and other cellular protrusions, special focushas been on revealing the presence of F-actin within extractedmembrane tubes (1, 13–16). However, apart from a single study(9), fluorescent visualization of the F-actin was achieved bystaining and fixation of the cells, and literature contains con-flicting results regarding the presence or absence of actin inmembrane tubes pulled from living cells (8, 11, 17).Filopodia in living cells have the ability to rotate and bend by

a so-far unknown mechanism (13, 18–20). For instance, filopodiahave been reported to exhibit sharp kinks in neuronal cells (21–23) and macrophages (6). These filopodial kinks have been ob-served both for surface-attached filopodia (23) as well as forfilopodia that were free to rotate in three dimensions (6, 19).

Other filaments such as DNA and bacterial flagella are com-mon examples of structures that shorten and bend in response totorsional twist. Filopodia have previously been shown to have theability to rotate by a mechanism that exists at their base (18, 19)and could have the ability to twist in presence of a frictionalforce. Rotation of the actin shaft results in friction with thesurrounding filopodial membrane, and hence torsional energycan be transferred to the actin shaft. The myosin-Vb motor hasbeen found to localize at the base of filopodia in neurite cells andto be critical for rotational movement of the filopodia; however,inhibition of myosin-Vc did not affect the rotation (19).Here, we reveal how actin filaments can simultaneously rotate

and helically bend within cellular membrane tubes obtained byelongation of preexisting filopodia by an optically trapped bead.Simultaneous force measurements and confocal visualizationreveal how the actin transduces a force as it rotates and retracts.After ∼100 s, the force exerted by the filopodium starts to exhibitpulling events reflecting transient contact between the actin andthe tip region of the filopodium, which is attached to the opti-cally trapped bead. We show that helical bending and rotation ofthe actin shaft (defined as the visible part of the actin) occurssimultaneously with movement of actin coils inside filopodia,which can occur concomitantly with a traction force exerted atthe tip. The velocity of the coils depends on their location alongthe tube, thus indicating that retrograde flow is not the onlymechanism driving the motion. Our data, and accompanyingcalculations, show that the rotation of the actin shaft, and theresulting torsional twist energy accumulated in the actin shaft,can contribute to shortening and bending of the actin shaft inconjunction with a retrograde flow.

Significance

Filopodia are essential membrane protrusions that facilitatecellular sensing and interaction with the environment. Themechanical properties of filopodia are crucial for their ability topush and pull on external objects and are attributed to actindynamics. We confirm the presence of F-actin inside extendedfilopodia and reveal a newmechanism by which actin can exerttraction forces on external objects. This mechanism is mediatedby rotation and helical buckling, which cause shortening andretraction of the actin shaft. By imaging of F-actin and simul-taneous force spectroscopy, we reveal and detail how forcepropagates through this spiral actin structure and show howtorsional twist of the actin shaft is translated into a tractionforce at the filopodial tip.

Author contributions: L.B.O. and P.M.B. designed research; N.L. and P.M.B. performedresearch; N.L. and P.M.B. analyzed data; and N.L., L.B.O., and P.M.B. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. W.M.B. is a guest editor invited by the EditorialBoard.1To whom correspondence should be addressed. Email: bendix@nbi.dk.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1411761112/-/DCSupplemental.

136–141 | PNAS | January 6, 2015 | vol. 112 | no. 1 www.pnas.org/cgi/doi/10.1073/pnas.1411761112

ResultsForce and Actin Dynamics Are Correlated in Filopodia. To investigatethe dynamic behavior of the F-actin present in filopodia, weextended filopodia from living HEK293 cells that were trans-fected to express GFP-Utrophin, a reporter of F-actin (24) asschematically shown in the Inset of Fig. 1A. The cells wereseeded 2–6 h before measurements and the phenotype of thecells was usually rounded as shown in a 3D reconstruction of theactin distribution from a confocal z stack of two cells in Fig. 1A.Freshly seeded round cells allowed us to pull filopodia ata greater height away from the coverslip due to their roundedshape. We elongated existing filopodia primarily to avoid inter-actions with other nearby filopodia that tend to grab onto thebead. With the high density of active filopodia (Fig. 1A),the chance of having neighboring filopodia interact with thetrapped bead (d = 4.95 μm) was very high. Therefore, byextending the filopodial membrane to ∼10 μm, we could per-form force spectroscopy over timescales of 5–20 min. The highdensity of filopodia together with the large size of the beadmakes it unlikely that tubes were pulled from a flat membrane.In the following, “actin-labeled cells” refers to living cells thatwere expressing GFP-Utrophin (24). The actin shaft is assumedto consist of ∼10 actin filaments labeled by GFP-Utrophin, whichhas high affinity for F-actin. The number of filaments is notconstant along the filopodium as the fluorescence intensity wasmeasured to have a negative gradient along the filopodium to-ward the tip (SI Appendix, Fig. S1A). Cells labeled with anothermarker for F-actin, Lifeact-GFP (25), exhibited similar actindynamics. We observed that actin gradually polymerized into theextended filopodium, as shown in SI Appendix, Figs. S2 and S3,with the highest concentration of actin being near the cell body.This gradient in intensity was observed for all tethers (n = 90).As a control, we show how a cytoplasmic dye diffuses into thetether during a few seconds that it took to complete the pulling,as shown in SI Appendix, Fig. S4.The optical trap was integrated with a confocal microscope,

thus enabling us to measure force curves and to simultaneouslyimage the F-actin dynamics inside filopodia (see details on thesetup in ref. 26). A filopodium was extended for 5–20 min whilewe simultaneously recorded the holding force and imaged theF-actin content. As shown in SI Appendix, Fig. S5A, and inagreement with literature (8, 11, 27), the force curves show thefollowing characteristics of membrane tube extraction from cells,namely (i) an initial linear increase in the force, with slopes asgiven in SI Appendix, Fig. S5B, due to elastic deformation of the

cytoskeleton; (ii) a sudden decrease in the force caused by thedelamination of the membrane from the cellular cytoskeleton;and (iii) a subsequent plateau force, which remained constant forshort extractions due to an excess of membrane area reservoir inthe cell (28, 29). However, after an extended period, the forcecurves displayed the dynamics shown in SI Appendix, Figs. S5Cand S6, with transient force jumps of ∼10 pN, which would besufficient to deform ECM fibers (30). The force and actin dy-namics were significantly suppressed after treating the cells withF-actin disrupting agents as shown in SI Appendix, Fig. S7.After a filopodium had been extracted and kept at a constant

extension for minutes, retrograde flow of actin occurred togetherwith 3D helical buckling and rotation of the actin shaft as shownschematically in the Inset of Fig. 1A and in Fig. 1B. Rotation wasdetected for 55 actin-containing filopodia out of 90, but theremaining 35 filopodia either appeared straight or had a fluo-rescent signal that was too low to determine possible rotation.Several localized coils could be observed on the same filopo-dium, which traveled toward the cell body as shown in Fig. 2 Aand E. The actin shaft was initially observed to bend locally,followed by translation and rotation around its axis as shown inFig. 2A (Movies S1 and S2). To quantify the shortening of theactin shaft, we calculated the velocity of the coils relative to thetrapped bead by subtracting the displacement of the bead duringforce transduction from the sample reference frame. The ve-locity of the coils in Fig. 2A varies significantly over time asshown in the kymograph in Fig. 2B, and the direction of travel isoccasionally observed to reverse and transiently move toward thetrapped bead (blue boxed region in Fig. 2B). A change in thevelocity of the coil was detected concomitantly with a displace-ment of the trapped bead as shown in Fig. 2C (n = 18) and hencecould be directly related to a change in the force. This kind ofcorrelation indicates that a tensile force can be transduced alongthe actin shaft in presence of a buckle. We show several of thesevelocity changes in the kymographs in SI Appendix, Fig. S8. Anegative velocity (shaded area in Fig. 2C) leads to a smallerdistance between the tip and the location of the coil. During thisnegative velocity regime the force on the trapped bead increasedand reached a peak value, thus suggesting a force-generatingmechanism originating from shortening of the actin shaft. Sub-sequently, we measured a sudden drop in the holding force(green curve in Fig. 2C), indicating a sudden release of tensionwithin the actin shaft. Concomitantly with the drop in force, thevelocity of the coils rapidly changed sign and the coils movedagain toward the cell body (blue curve in Fig. 2C).

Coil Velocity Depends on Filopodial Location. The kymographs fortwo helical coils at two different locations in the same filopo-dium are shown in Fig. 2 D and E. The velocities of the in-dividual coils (Fig. 2F) differ markedly, although they areconnected by an F-actin structure, thus indicating a mechanismthat shortens the actin within the tube. The velocity distributionof 40 different coils confirms that a coil’s velocity depends onits location along the filopodium as shown in Fig. 2G. Actin issubjected to myosin-pulling activity at the cellular base, whichcauses retrograde flow (23). Our data indicate that this is notthe only mechanism responsible for the motion of the coils:actin polymerization at the filopodial tip and depolymerizationat the cell body would cause a linear translation of the helicalcoils traveling toward the cell body contrary to our observationof varying coil velocities.

Torsional Twist in the Actin Shaft Is Responsible for Helical Buckling.The energy of the filopodial curved actin shaft confined withina membrane tube is described in SI Appendix, SI Text. Helicalbuckling in filopodia was predicted theoretically in refs. 31 and32, but the presence of a trapping force, which is applied in ourexperiments, prevents buckling caused by axial compression

Fig. 1. Actin dynamics inside filopodia studied by simultaneous force spec-troscopy and confocal microscopy. (A) HEK293 cells display a high density ofshort filopodia on their surface as visualized by fluorescently labeled F-actin(GFP-Utrophin). Inset shows schematics of the F-actin inside a filopodium held inplace by an optically trapped bead (diameter = 4.95 μm) showing helicalbending of the actin shaft. The yellow double arrow indicates the observeddynamic movement of the actin near the tip of the filopodium. (B) Deconvo-luted 3D reconstruction of the fluorescently labeled F-actin (GFP-Utrophin) in-side an extended filopodium. The images are taken at times t = 50.4, 84.0, 100.8,and 151.2 s after extension with an optically trapped bead. (Scale bar: 3 μm.)

Leijnse et al. PNAS | January 6, 2015 | vol. 112 | no. 1 | 137

BIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

of the membrane tension as explained in SI Appendix, SI Textand Fig. S9.By integrating the curvature (first term in SI Appendix, Eq. S4)

along the actin contour projected onto the image plane, weobtained the maximum bending energies of n = 17 actin shafts assummarized in a histogram in Fig. 3D. While calculating thebending energies in Fig. 3D, it was assumed that each filopodiumcontains 10 not cross-linked actin filaments, as in ref. 18, givinga total persistence length of lp = Nlactin = 150 μm. The bendingenergies span approximately an order of magnitude, which, mostlikely, reflects the fact that filopodia contain different numbers ofactin filaments with varying degree of cross-linking by, e.g., fascin(9). By quantifying the actin intensity in the filopodia just beforebuckling, we show that the thickness of the actin bundle influencesthe curvature of the actin shaft. From the actin intensity, it is clearthat the actin bundles are on average thicker near the cell body (seeSI Appendix, Fig. S2A, and average intensities for 17 actin shafts inSI Appendix, Fig. S1A), and consequently these buckles havea larger extent and lower curvature than buckles further away fromthe cell body, as shown for 34 buckles in SI Appendix, Fig. S1B. Therate of work needed to bend the actin shaft shown in Fig. 3C, isplotted in the Inset of Fig. 3D, which shows the bending energyversus time. The maximum slope of P = 11 KBT/s gives a numberfor the largest power dissipation for the bending shown in Fig. 3C.During buckling of the actin shaft, the filopodial membrane

tube will bend as well. Bending the membrane tube will coun-teract bending of the actin shaft. The energy needed to benda cylindrical tube of radius rtube into an arc of radius R (Fig. 3 Band C) is given by (33):

Ftube =κmem

2R2 πrtubeL; [1]

where the bending rigidity of the membrane has been measuredto be κmem = 6.6 × 10−20 J for blebs pulled from fibroblasts (17).1/R is the curvature of the tube in the θ direction as depicted inFig. 3C. For a curved tube segment (similar to the one in Fig. 3A)with rtube = 145 nm, R = 1 μm, and a typical length of Ltube = 1μm, we get Ftube = 3.8 KBT. Although this number may varysomewhat depending on the above parameters, this calculationshows that the energy required to bend the membrane is muchless than the energy needed to bend an actin bundle. Therefore,the energy needed to bend the filopodial membrane tube doesnot necessarily prevent buckling of the actin shaft but ratherslightly increases the energy threshold for buckling.In case of compressive buckling, we should detect a repulsive

force, pointing away from the cell body, on the trapped particle.However, we always measured an attractive force during buck-ling or no force at all. The bending of the actin shaft occurredsimultaneously with a tensile force on the filopodium and couldeven be correlated with an increase of the holding force (Fig. 2 Band C). A physical mechanism that could contribute to bucklingand pulling, at the same time, is torsional energy accumulatedwithin the actin shaft. This suggests that torsional twist is re-sponsible for bending and shortening the actin shaft much likethe helical bending resulting from twisting a rubber band at oneend while keeping the other end fixed.Torsional twist accumulated within the actin shaft can occur,

provided that sufficient friction between the actin and the sur-rounding membrane tube is generated. The physical problem hassome analogy to the twirling–whirling transition of an elastic rodthat is rotated at one end in a viscous fluid (34). The friction inthe current case arises from filopodia-associated membraneproteins like integrins (10, 35) that are being moved laterallywithin the membrane as depicted in Fig. 3F.Here, we model each transmembrane integrin as a rod-like

cylinder with radius Rprot spanning the membrane as depicted inFig. 3F. During rotation of the actin shaft, each cylinder is movedthrough the viscous membrane, having viscosity ηmem at a fixedspeed of ωo leading to a viscous drag force, Fdrag, that can beassumed to locally act tangential to the membrane surface. Theresulting torque due to the drag from a single anchoring rod is τ1 =rtube × Fdrag, and from N anchors, we get τN =Nanchors τ1. In thisapproximation, we only consider the drag orthogonal to thetube axis.The drag from a single cylinder moving at a constant speed

through the membrane is as follows (36, 37):

Fdrag =4πηmemL

ln�

L2Rprot

�+ α⊥

; [2]

where ηmem is the membrane viscosity, L is the length of thetransmembrane cylinder, Rprot is the radius of the protein, andα⊥ = 0:90 is a correction factor for integrins in a membrane (SIAppendix, SI Text). The total external torque around the axis ofthe shaft therefore becomes τext = rtubeNanchorsFdrag. Using pub-lished values for rtube = 145  nm [for HEK293 cells (11)], ωo = 1.2radians/s (18), and ηmem = 250 cp (38), we get the result plottedin Fig. 3G (red line).A buckling instability for an elastic filament will occur when

the torque exceeds the ratio between the bending modulus andthe length of the filament, B/L (34). The bending modulus ofa bundle of nfilaments = 10 can be expressed as B= nfilamentsκactin forun–cross-linked actin filaments (horizontal blue line in Fig. 3G)and B= n2filamentsκactin for tightly cross-linked actin filaments(horizontal green line in Fig. 3G), where κactin is the bending

Fig. 2. Quantification of the velocity of actin coils traveling toward the cellbody. (A) Progressive bending and traveling of two coils. The four imagesshow the same actin filament at four consecutive time points (t1 = 75.9 s, t2 =91.5 s, t3 = 93.6 s, and t4 = 116.5 s). Notably, the leftmost coil initially pointsupward and gradually rotates ∼180°. (Scale bar: 1 μm.) See also Movie S2. (B)Kymograph of the coils in A showing the positions of the coils versus time.Importantly, the position of the coil is consistently quantified in the refer-ence frame of the trapped bead. The blue dashed rectangle shows the oc-currence of a reversal in the velocity of the coil relative to the trapped bead.(Scale bars: 1 μm and 10 s.) (C) Quantification of the coil velocity (blue) and thecorresponding pulling force on the trapped bead (green). The gray shadedarea denotes the approximate time interval during which the velocity becomesnegative in B. (D and E) Examples of two coils located at different distancesrelative to the cell body and traveling at different velocities. The positions ofthe coils are shown in D; these were found as the maximum of the intensitygradient of the raw data shown in E. (Scale bars: 5 μm and 10 s.) (F) The ve-locities of the two coils in D; the blue curve is from the left coil, and the red isfrom the right coil. (G) Distribution of velocities from n = 40 coils as a functionof distance from the cell body. Error bars denote ±1SD.

138 | www.pnas.org/cgi/doi/10.1073/pnas.1411761112 Leijnse et al.

modulus for a single actin filament (18). Assuming no filamentcross-linking, then buckling will occur when 283 actin–membranelinks exist and for a tightly cross-linked actin bundle bucklingrequires ∼2,800 actin–membrane links. Although the exact densityof actin–membrane linkages is unknown in filopodia, it has beenshown that the membrane of red blood cells has a density of 1,000/μm2 linkages with the underlying skeleton (39), and with a totalarea of a filopodium of ∼10 μm2 such a density would easily allow>1,000 filopodial actin–membrane anchors to exist.

Transduction of Force Is Propagated Through Actin. Bending of theactin filaments also occurred concomitantly with an increase inthe measured holding force (Inset images in Fig. 4C). If the forceexerted on the bead was propagated through the actin shaft fromthe cell body, it would mean that bending could be sustained inpresence of longitudinal stress along the actin shaft, thus stronglysupporting the idea that the bending and retraction stem fromtorsional twist in the actin. As shown in Fig. 4, the presence ofa peak in the force exerted by the cell on the trapped beadcorrelates with the observation of Lifeact-GFP at the tip of thefilopodium. When the actin appeared at the tip (Fig. 4 A and B,and squares in Fig. 4C), an increase in the force on the bead,directed toward the cell, was observed (as shown by the circles inFig. 4C). Detachment of actin from the tip of the filopodiumresulted in actin gliding toward the cell body, thus dissipating the

tension built up in the actin filament. As this happened, thetrapped bead moved back to its previous equilibrium position, asshown in Fig. 4C by the blue and red asterisks (see SI Appendix,Fig. S10, for two other examples). The strong correlation be-tween the force and actin signal clearly suggests that the forceexerted by the cell to retract the filopodial tip is transduced alongthe actin shaft. We note that, in many experiments, actin was notdetectable at the tip and yet we measured transient forces thatcould be caused by poorly fluorescent-expressing cells and alimited detection efficiency of our system.

DiscussionOur results strongly suggest that retrograde flow and a rotationalmechanism are synergistically responsible for the observedbending and traction performed by filopodia. Retrograde flowoccurs in filopodia (13, 40) and can be assisted by a pulling forcearising from the frictional coupling mechanism within the cellbody as described previously (9). Our experimental observationsshow that coils on the actin shaft move at different velocitiesdepending on their proximity to the cell body. The data shown inFig. 2 reveal a pulling mechanism within the actin shaft that isinconsistent with retrograde flow as being the only mechanism offorce generation. If only retrograde flow was responsible for themovement, the actin shaft would be translated backward ina linear fashion and coils on the same actin shaft should have the

Fig. 3. Helical bending dynamics of actin filaments inside filopodia. (A and B) Bending of the F-actin (A) also induces a local bending of the membrane(labeled with DiD) as shown in B. (Scale bar: 3 μm.) (C) Plot of a tube, containing F-actin, which is bent into an arc of radius R. The overlay images below showprogressive buckling of an actin bundle near the cell body. The colors represent three different relative time points at tred = 0 s, tgreen = 13 s, and tblue = 30 s.(Scale bar: 2 μm.) (D) Histogram of the maximum bending energy calculated from n = 17 filopodia displaying different degrees of bending. The energy iscalculated assuming a bundle of 10 parallel actin filaments. The Inset shows the progressive increase in curvature energy versus time for the single buckleshown in C. The highest power consumed to bend the actin bundle reaches 11 KBT/s. (E) Example of a coiled actin structure inside a filopodium captured atdifferent time points separated by 2 s. (Scale bar: 3 μm.) See also Movie S3. (F) Axial rotation of the actin within the membrane tube leads to friction betweenthe membrane and the actin. Two initial scenarios depicting an actin filament within a membrane tube. In a filopodium, the actin will align along the innermembrane either as a straight rod (upper sketch) or a deformed shape, possibly a helix (lower sketch), within the tube. We model the actin–membranelinkages as connections between the actin and transmembrane integrins as shown by the XY projection of the membrane tube with an actin filament tracinga helix (with same radius as the tube) within the tube. The integrins (red cylinders) are dragged through the membrane by the rotating actin filament. (G) Thetotal external torque on the actin shaft depends linearly on the number of anchors, Nanchors, connecting the actin with the membrane. Two critical bucklingtorques, τcrit, are plotted by the horizontal lines; these correspond to an actin shaft consisting of 10 actin filaments that are cross-linked (green line) or notcross-linked (blue line).

Leijnse et al. PNAS | January 6, 2015 | vol. 112 | no. 1 | 139

BIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

same velocities irrespective on the location within the filopo-dium. Because myosin-II motors are typically not detected withinnarrow structures like filopodia (13), an internal acto-myosincontractile mechanism is unlikely to be a mechanism at playhere. Moreover, the contractile motor myosin-II has previouslybeen inhibited using blebbistatin without any significant effect onfilopodial mechanics (6). However, the observation of bending,shortening, and rotation of the actin shaft indicates that rotationof the actin shaft accumulates torsional energy in the actin thatcan be released by helical bending. The combination of twist andaxial load is more efficient in buckling the actin shaft than twistalone. However, in this work, we hold the membrane by an op-tical trap and therefore demonstrate that helical buckling canoccur efficiently in absence of the axial load delivered by themembrane tension in free filopodia. To accumulate torsionalenergy within the actin shaft, an active rotation mechanism isrequired at one end and friction, or a fixed contact point witha substrate, is needed along the actin filaments. Actin-linkedintegrins and other filopodia-associated proteins containing an

IBAR domain will create a density-dependent friction duringrotation of the actin within the filopodium. Interestingly, it wasshown recently that β3-integrins upconcentrated in filopodia offibroblasts after ∼100 s (41), which corresponds well to the du-ration before we observe the onset of buckling. We confirmed thatthe filopodial actin contributes to the friction between the actinand the membrane by performing fast elongation of the filopodium(1 μm/s). In the presence of actin, the force increased by up to ∼40pN (SI Appendix, Fig. S7A), which corresponds to a maximumviscosity of ∼20 pNs/μm. After disrupting actin (blue curve in SIAppendix, Fig. S7B), we measured a viscosity of ∼2 pNs/μm, whichis closer to the values for tethers from pure membrane vesicles (26).The rigidity of the actin shaft is highly dependent on the

concentration and dynamic binding rates of fascin cross-linkers.Fascin is found in filopodia (40, 42) and cross-links actin fila-ments into stiff bundles. Interestingly, fascin has an off-rate of1.2 s−1 and can therefore allow slow deformation rates of bun-dled actin as shown in ref. 40. Another actin-binding protein,cofilin, can shorten actin filaments in filopodial bundles andhas been associated with disassembly of retracting filopodia(43). Notably, cryoelectron tomography images of filopodia inDictyostelium revealed that actin bundles do not consist of longparallel bundles but instead contain discontinuously bundledactin filaments (44). These biochemical cellular factors have theability to change the mechanical requirements and significantlylower the buckling thresholds plotted in Fig. 3G.The transient increase in force from retracting filopodia often

displays a step-like behavior (SI Appendix, Fig. S12) resemblingthe pulling behavior of a molecular motor. Stepwise pullingforces have previously been reported for filopodia in macro-phages after inhibition of myosin-II (6). According to ref. 19, therotation of filopodia in neurites is driven by the spiral inter-actions between myosin-Va or -Vb and the actin filaments.Myosin-Va,b could therefore be involved in building up torsionalenergy in the actin shaft, eventually leading to coiling andshortening of the actin shaft. The power measured in the Inset ofFig. 3D of 11 KBT/s can be provided by the hydrolysis of ∼0.5ATP/s. This energy consumption corresponds to ∼50% of thework performed by one single myosin-V motor per step (45) but ismost likely an underestimation due to dissipative loss in the frictionbetween the actin and the membrane. Although the bending of themembrane tube requires additional energy, these calculations showthat the collective action of a few myosin motors would be suffi-cient to generate the power needed to bend the actin shaft.The surrounding membrane, which has a radius below the

optical resolution, acts to stabilize the filament against buckling,as previously shown for microtubules within membrane vesicles,in a tension-dependent manner (46). The filopodia membranesin our experiments were indeed under tension as we showed bythe rapid elongation and retraction of a calcein-filled filopodiumin SI Appendix, Fig. S13. Rapid elongation of membrane tethersresulted in a transient increase in the membrane tension, whichacted to reduce the radius of the filopodium as shown by thedecrease in the calcein signal. Even when the trapped bead wasmoved toward the cell body with 1 μm/s, the membrane did notbuckle. Instead, the membrane tube becomes slightly thicker dueto a decrease in tension (SI Appendix, Fig. S13).In ref. 4, it was shown that a force originating from retrograde

flow in filopodia was transduced to a compliant substrate whendynamic linkers attached the actin to an external substrate. This so-called motor-clutch mechanism is consistent with our findings thatthe actin–bead contact, shown in Fig. 4, correlates with a tractionforce on the bead. The traction force on the bead has been pro-posed to originate from retrograde flow in filopodia (9, 40), but wesuggest an additional force contribution originating from twist in-duced buckling that leads to shortening of the actin shaft. In-terestingly, in ref. 23, a similar buckling and shortening of actin infilopodia was found in neuronal cells in conjunction with actin flow

Fig. 4. Force generation correlates with presence of actin at the tip of thefilopodium. (A) Schematics of the attachment of the filopodium to thetrapped bead. A small patch of membrane adheres to the bead substrate,thus allowing actin to bind to a fixed membrane at the tip. Binding of actinto the side walls of the tubular and fluid membrane results in a frictionaldissipative force during rotation and directed flow of actin. (B) Images of theF-actin (magenta, labeled with Lifeact-GFP) at the tip of the filopodiumoverlaid with the reflection signal from the trapped bead (white). Correla-tion of successive detachment and reattachment of the actin to the beadwith the forces exerted reveal a load-and-fail behavior of the actin filamentsat the tip. Yellow arrows show the direction of movement of the opticallytrapped bead. See also Movie S4. (C) Quantification of the results shown inB. The blue curve shows the intensity of actin at the tip of the filopodium(see Movie S5 and SI Appendix, Fig. S11, for details). The green curve showsthe change in the pulling force on the bead in the optical trap. The red andblue asterisks mark two time points; red, just before detachment of actinfrom the tip; blue, just after detachment of actin from the tip. The corre-sponding images (Inset) reveal that bending of the actin (shown by the solidline, which is the tracked skeleton of the actin shaft) is present both beforeand after release of tension.

140 | www.pnas.org/cgi/doi/10.1073/pnas.1411761112 Leijnse et al.

toward the cell body. However, no force was detected in ref. 23, andhence the mechanism behind the buckling could not be resolved.

ConclusionThrough simultaneous visualization of actin filaments in filopodiaand measurements of the associated retraction force, we reveala new mechanism for force generation by the actin shaft insidefilopodia. This mechanism is based on the rotation and conse-quent helical coiling of the actin, which leads to shortening ofthe actin shaft by release of torsional energy. We consistentlyobserved rotation, bending, and shortening of the actin withinthe filopodia. This behavior could not be explained by theo-retical calculations of compressive buckling of the polymerizingactin against the filopodial tip. Helical coiling was even presentwhen a tensional pulling force was transduced along the actinshaft, which suggests that torsional twist is involved in the actin-mediated force generation.

MethodsCell Culture. HEK293 cells (ATTC; CRL-1573), denoted as “HEK cells,” werecultured in DMEM [Gibco; supplemented with 9% (vol/vol) FBS, 1%

PenStrep] in T25 or T75 tissue culture flasks (BD Falcon) at 37 °C in a 5% CO2

incubator. They were passaged by washing with 4 mL of Dulbecco’s PBS (1×,[−] CaCl2, [−] MgCl2; Gibco), detaching with 0.5–0.7 mL of TrypLE Express(Gibco) and diluting with growth medium before they were seeded in newflasks. All cells used were in passages 2–22. Sample preparation and methodsfor labeling cellular actin and cytoplasm are described in detail in SIAppendix, SI Text. F-actin was disrupted using either 5 μM cytochalasin Dor 1 μM latrunculin B (SI Appendix, SI Text).

Simultaneous Optical Tweezers and Confocal Laser-Scanning Measurements.The setup is described in more detail in ref. 26. More details concerningthe experimental setup and Matlab analysis (47) are provided in SI Appendix,SI Text.

Image Analysis. Details concerning data and image analysis are provided in SIAppendix, SI Text.

ACKNOWLEDGMENTS. We are grateful to Alexander R. Dunn for pro-viding us with the GFP-Utrophin plasmid and Szabolcs Semsey for assistingwith plasmid amplification. We acknowledge financial support from theVillum Kann Rasmusen Foundation, the University of Copenhagen ExcellenceProgram, and the Lundbeck Foundation.

1. Murphy DA, Courtneidge SA (2011) The “ins” and “outs” of podosomes and in-vadopodia: Characteristics, formation and function. Nat Rev Mol Cell Biol 12(7):413–426.

2. Mattila PK, Lappalainen P (2008) Filopodia: Molecular architecture and cellularfunctions. Nat Rev Mol Cell Biol 9(6):446–454.

3. Möller J, Lühmann T, Chabria M, Hall H, Vogel V (2013) Macrophages lift off surface-bound bacteria using a filopodium-lamellipodium hook-and-shovel mechanism. SciRep 3:2884.

4. Chan CE, Odde DJ (2008) Traction dynamics of filopodia on compliant substrates.Science 322(5908):1687–1691.

5. Wang Y, et al. (2005) Visualizing the mechanical activation of Src. Nature 434(7036):1040–1045.

6. Kress H, et al. (2007) Filopodia act as phagocytic tentacles and pull with discrete stepsand a load-dependent velocity. Proc Natl Acad Sci USA 104(28):11633–11638.

7. Pontes B, et al. (2013) Membrane elastic properties and cell function. PLoS One 8(7):e67708.

8. Pontes B, et al. (2011) Cell cytoskeleton and tether extraction. Biophys J 101(1):43–52.9. Bornschlögl T, et al. (2013) Filopodial retraction force is generated by cortical actin

dynamics and controlled by reversible tethering at the tip. Proc Natl Acad Sci USA110(47):18928–18933.

10. Romero S, et al. (2012) Filopodium retraction is controlled by adhesion to its tip. J CellSci 125(Pt 21):4999–5004, and erratum (2012) 125(Pt 22):5587.

11. Khatibzadeh N, Gupta S, Farrell B, Brownell WE, Anvari B (2012) Effects of cholesterolon nano-mechanical properties of the living cell plasma membrane. Soft Matter 8(32):8350–8360.

12. Roux A, et al. (2010) Membrane curvature controls dynamin polymerization. Proc NatlAcad Sci USA 107(9):4141–4146.

13. Bornschlögl T (2013) How filopodia pull: What we know about the mechanics anddynamics of filopodia. Cytoskeleton (Hoboken) 70(10):590–603.

14. Nürnberg A, Kitzing T, Grosse R (2011) Nucleating actin for invasion. Nat Rev Cancer11(3):177–187.

15. Arjonen A, Kaukonen R, Ivaska J (2011) Filopodia and adhesion in cancer cell motility.Cell Adhes Migr 5(5):421–430.

16. Stylli SS, Kaye AH, Lock P (2008) Invadopodia: At the cutting edge of tumour invasion.J Clin Neurosci 15(7):725–737.

17. Raucher D, et al. (2000) Phosphatidylinositol 4,5-bisphosphate functions as a secondmessenger that regulates cytoskeleton-plasma membrane adhesion. Cell 100(2):221–228.

18. Zidovska A, Sackmann E (2011) On the mechanical stabilization of filopodia. Biophys J100(6):1428–1437.

19. Tamada A, Kawase S, Murakami F, Kamiguchi H (2010) Autonomous right-screw ro-tation of growth cone filopodia drives neurite turning. J Cell Biol 188(3):429–441.

20. Forscher P, Smith SJ (1988) Actions of cytochalasins on the organization of actin fil-aments and microtubules in a neuronal growth cone. J Cell Biol 107(4):1505–1516.

21. Mallavarapu A, Mitchison T (1999) Regulated actin cytoskeleton assembly at filopo-dium tips controls their extension and retraction. J Cell Biol 146(5):1097–1106.

22. Dai J, Sheetz MP (1995) Mechanical properties of neuronal growth cone membranesstudied by tether formation with laser optical tweezers. Biophys J 68(3):988–996.

23. Schaefer AW, Kabir N, Forscher P (2002) Filopodia and actin arcs guide the assemblyand transport of two populations of microtubules with unique dynamic parameters inneuronal growth cones. J Cell Biol 158(1):139–152.

24. Burkel BM, von Dassow G, Bement WM (2007) Versatile fluorescent probes for actinfilaments based on the actin-binding domain of utrophin. Cell Motil Cytoskeleton64(11):822–832.

25. Riedl J, et al. (2008) Lifeact: A versatile marker to visualize F-actin. Nat Methods 5(7):605–607.

26. Ramesh P, et al. (2013) FBAR syndapin 1 recognizes and stabilizes highly curved tu-bular membranes in a concentration dependent manner. Sci Rep 3:1565.

27. Li Z, et al. (2002) Membrane tether formation from outer hair cells with opticaltweezers. Biophys J 82(3):1386–1395.

28. Cuvelier D, Chiaruttini N, Bassereau P, Nassoy P (2005) Pulling long tubes from firmlyadhered vesicles. Eur Phys Lett 71(6):1015–1021.

29. Raucher D, Sheetz MP (1999) Characteristics of a membrane reservoir bufferingmembrane tension. Biophys J 77(4):1992–2002.

30. Velegol D, Lanni F (2001) Cell traction forces on soft biomaterials. I. Microrheology oftype I collagen gels. Biophys J 81(3):1786–1792.

31. Daniels DR, Turner MS (2013) Islands of conformational stability for filopodia. PLoSOne 8(3):e59010.

32. Pronk S, Geissler PL, Fletcher DA (2008) Limits of filopodium stability. Phys Rev Lett100(25):258102.

33. Derényi I, Jülicher F, Prost J (2002) Formation and interaction of membrane tubes.Phys Rev Lett 88(23):238101.

34. Wada H (2011) Geometry of twist transport in a rotating elastic rod. Phys Rev E StatNonlin Soft Matter Phys 84(4 Pt 1):042901.

35. Beaty BT, et al. (2013) beta1 integrin regulates Arg to promote invadopodial matu-ration and matrix degradation. Mol Biol Cell 24(11):1661–1675, S1–S11.

36. Tirado M, Torre J (1979) Translational friction coefficients of rigid, symmetric topmacromolecules. Application to circular cylinders. J Chem Phys 71:2581–2587.

37. Saffman PG, Delbrück M (1975) Brownian motion in biological membranes. Proc NatlAcad Sci USA 72(8):3111–3113.

38. Chang M, et al. (2014) Aptamer-based single-molecule imaging of insulin receptors inliving cells. J Biomed Opt 19(5):051204.

39. Mohandas N, Evans E (1994) Mechanical properties of the red cell membrane in re-lation to molecular structure and genetic defects. Annu Rev Biophys Biomol Struct 23:787–818.

40. Aratyn YS, Schaus TE, Taylor EW, Borisy GG (2007) Intrinsic dynamic behavior of fascinin filopodia. Mol Biol Cell 18(10):3928–3940.

41. Hu W, Wehrle-Haller B, Vogel V (2014) Maturation of filopodia shaft adhesions isupregulated by local cycles of lamellipodia advancements and retractions. PLoS One9(9):e107097.

42. Vignjevic D, et al. (2006) Role of fascin in filopodial protrusion. J Cell Biol 174(6):863–875.

43. Breitsprecher D, et al. (2011) Cofilin cooperates with fascin to disassemble filopodialactin filaments. J Cell Sci 124(Pt 19):3305–3318.

44. Medalia O, et al. (2007) Organization of actin networks in intact filopodia. Curr Biol17(1):79–84.

45. Rief M, et al. (2000) Myosin-V stepping kinetics: A molecular model for processivity.Proc Natl Acad Sci USA 97(17):9482–9486.

46. Fygenson DK, Marko JF, Libchaber A (1997) Mechanics of microtubule-based mem-brane extension. Phys Rev Lett 79(22):4497–4500.

47. Hansen PM, Tolic-Norrelykke IM, Flyvbjerg H, Berg-Sorensen K (2006) tweezercalib2.1: Faster version of MatLab package for precise calibration of optical tweezers.Comput Phys Commun 175(8):572–573.

Leijnse et al. PNAS | January 6, 2015 | vol. 112 | no. 1 | 141

BIOPH

YSICSAND

COMPU

TATIONALBIOLO

GY

Supporting InformationLeijnse et al. 10.1073/pnas.1411761112

Movie S1. Three-dimensional visualization of the filopodial F-actin while it retracts and performs rotation and helical coiling.

Movie S1

Movie S2. Local bending and coiling occurs simultaneously with retrograde flow. The curved region travels backward, but occasionally the velocity stalls andeven reverses (in the reference frame of the optically trapped bead) due to contraction of the actin shaft.

Movie S2

Movie S3. Bending and rotation of the actin shaft can occur at multiple locations along the filopodium.

Movie S3

Leijnse et al. www.pnas.org/cgi/content/short/1411761112 1 of 3

Movie S4. Direct correlation between F-actin at the tip and force transduction from the filopodium to the optically trapped bead. As the F-actin signalincreases near the tip, a displacement of the trapped bead is observed.

Movie S4

Leijnse et al. www.pnas.org/cgi/content/short/1411761112 2 of 3

Other Supporting Information Files

SI Appendix (PDF)

Movie S5. A dynamic region of interest (ROI) is placed near the tip of the actin shaft. The position of the ROI is kept constant in the reference frame of thebead, and hence the same region of the filopodium is being quantified.

Movie S5

Leijnse et al. www.pnas.org/cgi/content/short/1411761112 3 of 3

Supporting Information:

Helical buckling of actin inside filopodia generates

traction N. Leijnse†,$, L. B. Oddershede†,$, & P.M. Bendix*,†

$Lundbeck Foundation Center Biomembranes in Nanomedicine, University of Copenhagen, 2100

Copenhagen, Denmark

†Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark

*Corresponding author: bendix@nbi.dk

Address: Niels Bohr Institute, University of Copenhagen,

Blegdamsvej 17, 2100 Copenhagen, Denmark

Mechanics of filopodia pulling

The mechanical behavior of filopodia is dictated by the material properties of the cell membrane

including membrane tension, the membrane-cytoskeleton adhesion as well the mechanics of the

filopodial actin. The holding force of a membrane tube which has been pulled from a cell is given

by

𝑓 = 2𝜋�2𝜅mem(𝜎𝑜 + 𝑊𝑜) , [S1]

where 𝜅mem is the bending rigidity of the membrane and 𝜎𝑡 = 𝜎𝑜 + 𝑊𝑜 is the total membrane

tension composed of the bound membrane tension 𝜎𝑜 and the additional tension 𝑊𝑜 that arises

from the membrane-cytoskeleton adhesion. The radius of the tube rtube is determined from the

bending rigidity and membrane tension

𝑟tube = �(𝜅mem/2𝜎𝑡) . [S2]

The radius is affected by the extrusion velocity vpull through the membrane tension in Eq. S2.

Changes in pulling velocity leads to a transient change in σt and causes a change in tether radius.

By having a cytosolic dye like calcein within the tube we can detect the changes in the tube radius

by measuring the fluorescent signal during extrusion as shown in Fig. S13. The calcein signal scales

with radius as �𝐼calcein ∝ 𝑟tube. A positive extrusion velocity leads to an increase in membrane

tension and hence a decrease in radius (and decrease in fluorescence signal). Likewise a negative

extrusion velocity (moving of the bead towards the cell) leads to a decrease in membrane tension

and hence an increase in tube radius as shown by the increase in fluorescent signal in Fig. S13.

An effective viscosity, ηeff, arising from the membrane-cytoskeleton system results in an increase

in the velocity dependent force on the trapped bead during extraction, as shown in Fig. S7A. This

can be understood by isolating σt from Eq. S2 and inserting into Eq. S1 which gives the friction

dependent force expressed as (1)

𝑓 = 2𝜋�2𝜅mem𝜎𝑡 = 2𝜋𝜅mem𝑟tube

. [S3]

Hence, a dynamic increase in tension, during rapid extension, leads to a decrease in the diameter

of the membrane tube and results in a dynamic increase in the force f, as shown in Fig. S7A.

The total membrane tension, however, contains a considerable contribution from the membrane-

cytoskeleton adhesion. By disrupting the actin, using cytochalasin D or latrunculin B, we measure a

significant drop in both the stationary as well as dynamic force as shown in Fig. S7B. This decrease

results from the fact that Wo becomes close to zero in Eq. S1.

Buckling of the actin The energy of a filopodium held by the optical trap depends on the

magnitude of the holding force f, delivered by the optical trap and the physical properties of the

membrane and the actin shaft. Assuming a membrane tube with radius 𝑟tube, membrane tension

γ, and bending rigidity 𝜅mem, enclosing an actin shaft of contour length l, we obtain the energy by

integrating the square of the curvature, c=�𝜕2𝒓

𝜕𝑠2�, along the contour parameterized by s (2, 3),

𝐸 = 𝐾𝐵𝑇𝑇𝑝2 ∫ �𝜕

2𝒓𝜕𝑠2�2𝑑𝑑𝑇

0 + �𝜋𝜅mem𝑟tube

+ 2𝜋𝜋𝑟tube − 𝑓� 𝐿tube [S4]

where lp is the persistence length of the actin shaft, KBT is the thermal energy and 𝐿tube is the

length of the membrane tube. The first term in Eq. S4 is the energy of bending of the actin shaft

whereas the remaining energy terms relate to the bending and stretching of the membrane (4).

The actin shafts of filopodia typically formed localized helical buckles or exhibited a wavy

character, as shown in Fig. 3A,E. We investigated if this could be caused by compressive helical

buckling as theoretically predicted to occur in free filopodia due to the axial compressive load

caused by the membrane tension (2, 3). The stability of a helical conformation can be tested by

minimizing the energy given in Eq. S4. The outline of a helix with winding number n (helical

windings per unit length) and radius R inside a tube of length L, can be mathematically described

by

𝒓(𝑑) = �𝑥(𝑑)𝑦(𝑑)𝑧(𝑑)

= �𝑅cos (2𝜋𝜋𝑑)𝑅sin (2𝜋𝜋𝑑)𝑑√1 − 𝜋2𝜋2𝑅2

, [S5]

for a tube of length Ltube = 𝑙√1 − 𝜋2𝜋2𝑅2. Eq. S5 has the shape of a helix as plotted inside the tube

in Fig. 3F. Integration of Eq. S4 for a helix then gives the total energy of the membrane-actin

system per unit contour length (3)

𝐸/𝑙 = 𝐾𝐵𝑇𝑇𝑝2𝑅2

�1 − 𝐿2

𝑇2�2

+ �𝜋𝜅𝑅

+ 2𝜋𝜋𝑅 − 𝑓� 𝐿/𝑙 [S6]

and is plotted in Fig. S9. There exists an energy minimum for a relative shortening of L/l ≈ 0.95 for

a tube with R ≈ 95 nm. However, after adding the external force needed to hold a pure

membrane tube of 𝑓 = 2𝜋�2𝜅𝑚𝑚𝑚𝜎 ≈ 8 pN no energy minimum is obtained (see Fig. S9B).

Although we often measured a transient decrease in the force as shown in Fig. S6, the measured

holding forces were typically much higher than 8 pN. Therefore we exclude the possibility that the

helical buckles, are caused solely by axial compressive load by the membrane. This could still be

relevant for free cellular filopodia but in our experiments the optical trap diminishes the axial load

on the actin and hence compressive buckling cannot occur.

Drag of a cylinder in a membrane The correction factor 𝛼+ in Eq. 2 in the manuscript depends on

the length to thickness ratio, p = L/2𝑅prot, of the cylindrical rod. The subscript means that we

consider the drag orthogonal to the cylindrical rod. The drag from a single cylinder moving at a

constant speed through the membrane is (5, 6):

𝐹drag = 4𝜋𝜂mem𝐿

ln� 𝐿2𝑅prot

�+𝛼+ , [S7]

where 𝜂mem is the membrane viscosity, L is the length of the transmembrane cylinder, 𝑅prot is the

radius of the protein, and 𝛼+ is a correction factor which depends on the ratio p = L/2𝑅prot and

the subscript denotes that we are considering the transverse drag on the cylinder. Tabulated

values exist for 𝛼+ (5) and these can be interpolated by the function 𝛼+(𝑝) = 0.84 + 0.19/𝑝 +

0.23/𝑝2 (7). Using 𝑅prot = 0.64 nm (8) and L = 5 nm (approximate thickness of membrane) we

get 𝛼+ = 0.90.

The total torque around the axis of the shaft therefore becomes

𝜏N = 𝑟tube𝑁anchors𝐹drag = 𝑟tube𝑁anchors4𝜋𝜂mem𝐿

ln� 𝐿2𝑅prot

�+𝛼+. [S8]

Image analysis

The location of a coil was found by summing the pixel intensities from the actin orthogonal to the

filopodium after subtracting off the background intensity. Each image was therefore represented

by a vector at a given time point and bending of the actin appeared as an intensity peak.

Kymographs were obtained by constructing a matrix from these vectors in which every row

represents a given time point. Importantly, to obtain the correct location of the coil relative to the

tip of the filopodium, we performed parallel tracking of the centroid intensity from the bead which

allowed us to correct for any movement of the trapped bead and possible axial shortening could

thus be detected within the actin shaft. Velocities of the coils were quantified as the slope in of

the trajectories that appeared in the kymographs (see Fig. 2D). Rather than quantifying the

average velocity, we resolved the local velocities as a function of distance relative to the cell body

by calculating the local gradient along the curve resulting in data as presented in Fig. 2G.

Curvatures of the actin along the filopodium were quantified by fitting a Gaussian function to the

intensity distribution for every pixel line orthogonal to the filopodium. The interpolated center

position of the Gaussian fit yields a sub-pixel resolution estimate for the location of the

filopodium. The resulting center positions for all orthogonal pixel lines constitute the skeleton of

the filopodium as shown by the solid lines in the insets of Fig. 4C. The curvature along the

filopodial skeleton is calculated using the expression

𝑐(𝑥) = �𝑦′′(𝑥)�(1+(𝑦′(𝑥))2)3/2 , [S9]

where y is the position along the orthogonal direction and x is along the filopodium. y’(x) and

y’’(x) denote the spatial derivatives with respect to x.

Investigation of the correlation between the force and the presence of the actin at specific

positions within the filopodium was carried out by finding areas of intensity falling above a

threshold defined by threshold = <I>bg + σbg, where <I>bg is the average intensity in a background

region of interest and σbg is the standard deviation of the intensities from the same region of

interest. Only connected clusters of pixels were quantified to filter out single pixel noise. By

selecting regions of interests along the filopodium, we tested for correlation between the

measured force (resulting in a displacement of the trapped bead) and the actin signal which were

acquired simultaneously. An example of the analysis is shown in Fig. S11 and in Supplementary

Movie 5.

Three dimensional rendering Three dimensional (3D) images of filopodia during retraction of the

actin were obtained from confocal images taken at different heights. Images were deblurred in

ImageJ (9) using the Richards-Wolf model Point Spread Function for deconvolution. A 3D volume

viewer in ImageJ was used to reconstruct the deblurred images into 3D images as shown in Fig.

1A,B and Movie 1.

Coil velocities Kymographs were analysed using Image Processing Toolbox in Matlab (10). Intensity

edges were detected using the canny method within the built-in Matlab edge.m function which

detects local maxima of the intensity gradients in an image. The resulting binary image (BW) was

area-filtered using the Matlab function bwareaopen.m to remove edges resulting from image

noise. Finally, the edges of interest were identified and selected using the Matlab function

bwselect.m. The coordinates (x,y) were located using the find.m function, ([x,y] = find(BW == 1)),

and subsequently the velocities were obtained by calculating the corresponding spatial gradients

of the connected pixels within the image. To ensure that coil displacements were within the

reference frame of the trapped bead, the position of the coil was corrected with any displacement

of the trapped bead. The bead was tracked using centroid tracking (of the intensity distribution) of

the signal from the light reflected by the bead.

Actin and force correlation The actin intensity near the tip was obtained by selecting a Region Of

Interest (ROItip) containing the filopodial tip. The intensity within the ROItip was quantified by

summing all intensities above the background threshold which was obtained from another ROIbg

(mean + standard deviation of the pixel values) containing a background area outside the cell. The

actual quantification relied on first making the area within ROItip binary with all pixels below the

background threshold being ‘0’ and all pixels above the threshold being ‘1’. Single pixel noise was

filtered out using bwareaopen.m. The binary image was multiplied, pixel-by-pixel, with the raw

image and finally all the elements in the resulting matrix were summed to give the total actin

signal. The corresponding displacement (and consequently the force) of the trapped bead was

calculated using centroid tracking of the trapped bead (in the reflection channel) or by using the

signal from the quadrant photodiode.

Actin curvatures Curvatures along the actin shaft were analyzed using Matlab by tracking the

skeleton of the actin shaft. The size of the buckles presented in Fig. S1 was found by integrating

the area under the curve by tracing the skeleton of the actin shaft. Before integration the images

were rotated such that the filopodium was aligned with the x-axis of the image.

Experimental setup

The setup consisted of an optical trap with a quadrant photodiode detection system integrated in

a confocal laser scanning microscope. The setup allows optical trapping and measurements of

forces exerted on the bead simultaneous with confocal imaging of fluorescent signals. The optical

trap consisted of a Nd:YVO4 (5 W Spectra Physics BL106C, TEM00, λ=1064 nm) laser implemented

in an inverted Leica confocal microscope (TCS SP5). The laser was focused through a high

numerical aperture water immersion objective (Leica 63 x, 1.2 NA, apochromatic water (No.

11506279)) to a diffraction limited spot inside the sample chamber. A three dimensional

piezoelectric stage (PI 731.20, Physik Instrumente, Germany) allowed positioning of the sample

relative to the laser focus with nanometer precision. The scattered laser light passing the sample

was collected by a condenser (Leica, P1 1.40 oil S1) and focused onto a quadrant photodiode

(S5981, Hamamatsu). Optical trapping data was acquired by a data acquisition card (NI PCI-6040E)

at a sampling frequency of 1 kHz and processed by custom written LabVIEW programs (LabVIEW

2010, National Instruments). For simultaneous force measurements and confocal imaging, a bead

inside the chamber, visualized in bright field mode, was optically trapped and a high frequency

time series (22 kHz) of its positions was acquired in order to calculate the trap stiffness via power

spectral analysis using a Matlab program (11). The fluorescent GFP-Utrophin (excited at λex=488

nm) and the reflection signal (λrefl=458 nm laser) from the cell and the trapped bead (after

optimizing the image acquisition settings) were recorded using Leica's LAS AF software. The

trapped bead was brought into contact with a HEK cell for less than one second and pulled back to

form a contact with a filopodium either by translating the stage manually or via a LabVIEW

program with a controlled velocity. A telescope lens in the beam path of the optical trap allowed

adjustment of the trap focus with respect to the microscope focus in order to align the tether with

the imaging plane. A pinhole of 1 airy unit was used in the confocal imaging to reject out of focus

light.

Cell and sample preparation

F-actin labeling Cells cultured in T25 flasks (90% confluent) were transfected to express GFP-

Utrophin, a live cell reporter for F-actin (12), using Effectene transfection reagent (Quiagen)

according to the manufacturer's protocol and 0.6-1 μg/μl plasmid. While the effectene-plasmid

mix was prepared, the cells washed with DPBS and detached from the bottle using with 0.5 ml

TrypLE Express. They were re-suspended in 5 mL warm growth medium and centrifuged at 1000

rpm for 5 mins. The supernatant was removed and the cells were re-suspended in 4ml fresh

growth medium. 1ml of cell suspension together with 2 ml of fresh growth medium were added to

one well of a 6-well plate (Nunclon ∆ Surface, Nunc). The effectene-plasmid mix was added and

the cells were left in the incubator for 4 hrs before the medium was carefully exchanged with fresh

warm growth medium. The cells were used for measurements 1-2 days after transfection.

We tested the effect of transfection and fluorescent excitation of GFP-Utrophin by measuring the

holding force of a filopodium in cells that were transfected with GFP-Utrophin and not

transfected, respectively, over time a course of 500 s. We measured similar force dynamics for

transfected and not transfected cells as shown in Fig. S6A as well as for cells transfected with

Lifeact-GFP (Ibidi) (13) which was used to transfect the cell in used in Fig. 4B,C. Similarly, the

fluorescent excitation did not alter the force dynamics of the transfected cells as shown in Fig. S6.

Sample preparation For photodiode force detection measurements we used thin closed chambers

made from two clean coverslips (24x50 mm #1.5 and 18x18 mm #1, both, Menzel-Gläser). For

experiments where the bead movement was calculated from image analysis (centroid tracking),

the cells were seeded in MatTek glass bottom dishes. HEK cells transfected to express GFP-

Utrophin were detached from a 6-well, suspended in warm growth medium, and were poured into

a petri dish containing 2 clean coverslips (24x50 mm #1.5) or into 4 MatTek dishes. The samples

were left in the incubator (typically for 2-6 h) in order to allow the cells to adhere to the coverslips

(while still having rounded shape). The density of cells was chosen such that most cells were

isolated. A coverslip with attached cells was taken out of the petri dish and a perfusion chamber

was created by adding two stripes of vacuum grease on this coverslip and placing a clean coverslip

(18x18 mm, #1, Menzel-Gläser) on top. The chamber was filled with Dulbecco’s PBS (DPBS) (1X, [+]

CaCl2, [+] MgCl2, Gibco), which was used as imaging medium, containing d = 4.95 μm streptavidin

coated polystyrene beads (Bangs Laboratories) and sealed off with vacuum grease. The

experiments were conducted at room temperature and the chambers were used for ~2.5 h after

being prepared.

Cytoplasmic labeling The cells were cultured and closed chambers were prepared as described

above. Before sealing the chamber it was flushed once with DPBS and then incubated for 1 min

with 250 μL (DPBS):1 μL (Calcein AM (Invitrogen)) and preparation continued as described above.

Cytochalasin D and and Latruculin B treatment The cells were cultured, transfected to express

GPF-Utrophin, and the chambers were prepared as described above. Before sealing the chamber,

5 μM cytochalasin D (Sigma, stock solution in DMSO) or 1 μM latruculin B (Sigma, stock solution in

DMSO) in DPBS was added to the chamber together with d = 4.95 μm streptavidin coated

polystyrene beads and sealed off with vacuum grease. The chamber was left to incubate at room

temperature for 30 min (cytochalasin D) or 1 h (latrunculin B) before conducting experiments.

Figure S1 | Size of the actin buckles correlates with the thickness of the actin shaft and hence

the proximity to the cell body. (A) Normalized average intensity of 17 actin shafts that were in

focus just prior to buckling. The quantification reveals that the intensity decreases as a function

of the distance to the cell body. Since the actin fluorescence scales with the number of F-actin

filaments this shows that the actin shafts are, on average, thicker near the cell body. Image

shows an example of a typical shaft before buckling, scale bar is 2 μm. (B) Quantification of the

projected area under single buckles shows that buckles have a larger extent when the buckle is

located within 3 μm from the cell body (blue circles) than when the buckle is located further

away than 3 μm from the cell body (red squares). Inset shows the mean area of buckles in the

two distance regimes. The total number of buckles analyzed was N = 34. (C) Typical images of

buckles at different distances from the cell body. The top left image is from the same

experiment as in Fig. 1B in the manuscript. Scale bars 3 μm.

Figure S2 | Kinetics of F-actin in a filopodial membrane tube at various time points (t = 0

corresponds to tether formation). (A) Images of actin polymerizing into the membrane tube

followed by bending of the actin shaft after ca. 200 s. (B) Quantification of the extension of the

F-actin shaft into the tube versus time. (C) Total intensity of the actin inside the filopodium

versus time.

Figure S3 | Actin polymerization velocity into a membrane tube. (A) Images showing how the

actin intensity increases from the cell body (right) towards the trapped bead (left). Scale bar, 3

μm. (B) Intensity profiles along the actin shaft at a few different time points. Initially, the

intensity along the shaft exhibits a high gradient near the cell body. The location of this high

gradient region subsequently moves away from the cell body with time. The red squares denote

the maximum in gradient of the respective curves. (C) The displacement and velocity of the red

squares in (B) as a function of time. The curves in (C) are smoothed with a running average of 5

time points.

Figure S4 | Kinetics of calcein diffusion within the pulled tube. Unlike GFP-Utrophin, calcein AM

fills the tube immediately during pulling and subsequently only bleaching is detected. Images

show a typical example of the intensity of calcein during pulling. After pulling the tube with 1

μm/s for 10 s, the pulling speed is set to 0.05 μm/s after which the intensity is recorded within

the blue, green and red squares for 100 s. The graph shows the quantification of the intensity

over time for the three respective regions on the tube and the similar bleaching rates confirm

that diffusive mixing is fast.

Figure S5 | Force behavior during elongation and long term holding of a filopodium. (A) Force

curves for three different filopodia elongations using vpull = 1 μm/s for 13 s. Initially, (i) the force

rises linearly, reflecting the Hookean behavior of the cytoskeleton that is deformed before a

tether is pulled away from the cell. (ii) Subsequently, a sudden decrease in force occurs upon

cytoskeleton detachment from the plasma membrane (iii) and is followed by a nearly flat

plateau as a filopodium is extracted. As the extraction velocity is set to zero (at t =13 s) the

viscoelastic filopodium/actin system relaxes exponentially to a lower plateau. (B) Statistics of

the initial slopes (i) as shown in (a) which equal the spring constant κ of the elastic response of

the cytoskeleton to filopodial extension. (C) Force dynamics of entire experiment in (A) lasting

200 s. The initial pulling velocity was vpull = 1 μm/s and was set to zero after 13 seconds.

Figure S6 | Effect of the confocal scanning laser, for imaging the actin, on the force dynamics of

membrane tethers held by an optical trap for ca. 300 s. (A) The force recorded in absence of the

scanning laser in wild type (blue curve) and in GPP-Utrophin expressing HEK cells (red curve). (B)

Two different examples of the force recorded before and after the scanning laser was turned on

after 200 s in GFP-Utrophin expressing HEK cells.

Figure S7 | Actin-membrane friction during step pulling. (A) Slow pulling at vpull = 0.05 μm/s

followed by two consecutive fast pulls with vpull = 1 μm/s leads to an increase in the force to a

higher plateau value due to viscous friction of the combined actin and membrane system. The

force asymptotically approaches F(t) = F∞ - ( F∞ -F1 )*exp(-(t-t1)/ τ)) where F1 is the initial force

and τ = 1.7 ±0.4s (N = 8, first pull) and τ = 2.3 ±0.7s (N=8, second pull). Upon termination of the

pulling (vpull = 0) the force relaxes again towards a lower plateau value in a dissipative manner.

(B) The frictional effect of the actin cytoskeleton is observed by disrupting the actin using

cytochalasin D. The rapid elongation at the end of the time series (vpull = 1 μm/s) after the

filopodium has been held constant for around 285 s produces a significantly lower increase in

the force when the actin is disrupted (blue curve) compared to when the F-actin is still present

(red curve) thus showing the large contribution from the actin-membrane friction. Inset images

show that the actin signal is still present but no dynamics is observed. (C) Disruption of actin

using latrunculin B. Three tethers are pulled and subsequently the GFP-Utrophin signal is

recorded every 2 s. No actin or force dynamics was observed in such tethers. The remaining

stationary and uniformly fluorescent signal stems from GFP-Utrophin in the cytosol. Some

filopodia were still visible as in the middle right image and these were also stationary for the

594 s of acquisition. The three tethers have a length of ~15, ~10 and ~20 μm.

Figure S8 | Examples of coil velocities that occurred simultaneously with an increase in force on

the optically trapped bead. The yellow arrows point at events where the coil velocity either

reversed sign (travelled away from the cell body as in Fig. 2B in the manuscript) or nearly

became zero. Scale bars in all images correspond to 1 μm (horizontal) and 10 s (vertical).

Figure S9 Calculations of the energy of a system consisting of an actin bundle (10 not cross-

linked filaments) of contour length l = 10 μm inside a membrane tube of Radius 𝒓𝐭𝐭𝐭𝐭, and tube

length Ltube, see Eq. S4 and Eq. S6. (A) The plot shows the energy without an optical trapping

force applied to the tip. The system has an energy minimum when 𝒓𝐭𝐭𝐭𝐭 ≈ 90 nm (red circle) and

at a relative shortening of Ltube/l ≈ 0.95. (B) When an optical trap is used to hold the membrane

tube (holding force 8 pN), the energy minimum disappears, and hence no compressive helical

buckling takes place, in contrast to experimental observations. The colorbar is in units of KBT

/nm.

Figure S10 | Correlation between the presence of actin at the tip and a displacement of the

trapped bead towards the cell body (pulling). (A) Kymograph showing the position of helical

bends on the actin shaft versus time. An abrupt change in velocity is detected at ~41 s. Scale bar,

2 μm. (B) Simultaneous recording and quantification of the pulling force and actin signal

recorded near the tip as a function of time. After ~41 s the actin content (blue curve) decreases

abruptly simultaneously with the force (green curve). (C) Snap shots of the data from (A,B)

reveal that the actin shaft is bending locally and traveling backwards. Even during significant

pulling (t = 40 s) the actin shaft is observed to bend locally thus excluding the possibility of

compressive buckling. The images are formed by an overlay of the actin (cyan) and reflection

signal from the bead (white). Scale bar, 2 μm. (D) Kymograph of another experiment showing

several buckles moving along the filopodium. After ~100s the actin polymerized into the

membrane tube which is detected as an edge in the kymograph with positive slope.

Subsequently, several buckles appeared which are detected as high intensity gradients in the

kymograph. Scale bar, 2 μm and 10 s. (E) Simultaneous detection of the intensity of actin (2 μm

tip region) and the corresponding force on the trapped bead. The bead displacements in this

figure were detected using image analyzes and not the photodiode detection system.

Figure S11 | Quantification of actin at the filopodial tip. (A) A Region Of Interest (ROI) is chosen

near the tip including a minor area on the trapped bead. The position of the ROI is corrected in

every image such that the location is constant relative to the centroid of the trapped bead (red

dot) which becomes displaced during pulling or pushing (see Movie 5). This ensures that the

same region of the tether is quantified in all images. (B) Quantification is performed by

thresholding the image with the background intensity plus the standard deviation of the noise

as the threshold. Pixels having intensity levels higher or lower than the threshold are given a

binary value ‘1’ or ‘0’, respectively. Element by element multiplication of the binary matrix with

the raw image followed by summation of all pixels gives the total intensity.

Figure S12 | Evidence of stepwise pulling indicating motor activity in the force transduction

mechanism. (A) Time trace showing an example of stepwise behavior. The position of the

trapped bead moves in discrete steps towards the cell (cell pulls on the bead). Red line is a

running average. Horizontal lines indicate possible steps. (B) Histograms of the positions

recorded in (A) to visualize possible steps.

Figure S13 | Filopodia membrane tube is under lateral tension. (A) Rapid elongation and

retraction (10 μm) of a calcein AM labeled membrane tube reveals a velocity dependent calcein

intensity. (B) Quantification of the fluorescent intensity versus time. The five different curves

represent measurements performed on different filopodial tethers.

1. Brochard-Wyart F, Borghi N, Cuvelier D, & Nassoy P (2006) Hydrodynamic narrowing of tubes

extruded from cells. Proceedings of the National Academy of Sciences of the United States of

America 103(20):7660-7663.

2. Daniels DR & Turner MS (2013) Islands of conformational stability for filopodia. PloS one

8(3):e59010.

3. Pronk S, Geissler PL, & Fletcher DA (2008) Limits of filopodium stability. Physical review letters

100(25).

4. Derenyi I, Julicher F, & Prost J (2002) Formation and interaction of membrane tubes. Physical

review letters 88(23).

5. Tirado M & Torre J (1979) Translational friction coefficients of rigid, symmetric top

macromolecules. Application to circular cylinders. J Chem Phys 71:2581.

6. Saffman PG & Delbruck M (1975) Brownian motion in biological membranes. Proceedings of the

National Academy of Sciences of the United States of America 72(8):3111-3113.

7. Tirado M, Martínez C, & Torre J (1984) Comparison of theories for the translational and rotational

diffusion coefficients of rod like macromolecules. Application to short DNA fragments. J. Chem

Phys 81:2047.

8. Erb E, Tangemann K, Bohrmann B, Muller B, & Engel J (1997) Integrin alphaIIbeta3 Reconstituted

into Lipid Bilayers Is Nonclustered in Its Activated State but Clusters after Fibrinogen Binding.

Biochem 36:7395-7402.

9. Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA,

http://imagej.nih.gov/ij/, 1997-2014.

10. Matlab and Image Processing Toolbox Release 2012b, The MathWorks, Inc., Natick,

Massachusetts, United States.

11. Hansen PM, Tolic-Norrelykke IM, Flyvbjerg H, & Berg-Sorensen K (2006) tweezercalib 2.1: Faster

version of MatLab package for precise calibration of optical tweezers. Comput Phys Commun

175(8):572-573.

12. Burkel BM, von Dassow G, & Bement WM (2007) Versatile fluorescent probes for actin filaments

based on the actin-binding domain of Utrophin. Cell motility and the cytoskeleton 64(11):822-

832.

13. Riedl J, et al. (2008) Lifeact: a versatile marker to visualize F-actin. Nature methods 5(7):605-607.