cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy...

JOURNAL OF MOLECULAR RECOGNITIONJ. Mol. Recognit. 2007; 20: 459–466Published online 21 September 2007 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/jmr.829
*Correspon

Medicina, U

E-mail: dnayPaper pres

conference,zProfessor

Copyright

Cell dynamic adhesion and elastic propertiesprobed with cylindrical atomic forcemicroscopy cantilever tipsy

Felix Rico1, Pere Roca-Cusachs1, Raimon Sunyer1, Ramon Farre1,2 and Daniel Navajas1,2,3*,z

1Unitat de Biofısica i Bioenginyeria, Facultat de Medicina, Universitat de Barcelona-IDIBAPS, Barcelona, Spain2CIBER Enfermedades Respiratorias, Spain3Institut de Bioenginyeria de Catalunya (IBEC), Barcelona, Spain

Cell adhesion is required for essential biological functions such as migration, tissue formation and woundhealing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on theextracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion atboth single molecule and whole cell levels. However, the measurement of inherent cell adhesion propertiesrequires a constant cell–probe contact area during indentation, a requirement which is not fulfilled incommon pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB)technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tipswith a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindricaltips showed a fairly linear force–indentation behaviour on both gels and cells for indentations >200 nm.Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elasticproperties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, thedeformation applied to the cells before rupture was fairly constant within the probed dynamic range. Takentogether, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elasticresponse to keep a constant cell deformation regardless of the applied pulling rate. Copyright # 2007 JohnWiley & Sons, Ltd.

Keywords: AFM; cell adhesion; cell mechanics; cell stiffness

Received 21 April 2007; accepted 25 May 2007

INTRODUCTION

Living cells are constantly subjected to or developingmechanical forces, which are supported by integrins andother adhesion receptors. Adherent cells attach specificallyto the extracellular matrix (ECM) and to neighbouring cellsto form tissues, while some suspended cells arrest in thevessels by adhering selectively to the endothelium. Bothtypes of cell adhesion are mediated by transmembranereceptor molecules which recognize selective ligands andmay cooperate to enhance the interaction (Bell, 1978). Infact, adhesion between cells and the extracellular matrix isusually mediated by micrometer-sized structures formedby clustering of adhesion receptors and other proteinslinked to the cytoskeleton, such as focal adhesions,(Springer, 1990; Horwitz, 1997). As a consequence, celladhesion often involves the cooperation of multipleindividual binding sites forming clusters, leading to a

dence to: D. Navajas, Unitat de Biofısica i Bioenginyeria, Facultat de

niversitat de Barcelona, Casanova 143, Barcelona 08036, Spain.

[email protected]

ented as part of a special issue of papers from the ‘AFM BioMed

Barcelona 2007’.

of Physiology.

# 2007 John Wiley & Sons, Ltd.

dynamic behaviour different from that observed on singlemolecule interactions. Thus, the dynamic response ofmultiple bonds under parallel loading is of crucial interestto understand cell adhesion. Several authors havetheoretically described the forces needed to break multiplebonds under loading (Seifert, 2000; Evans, 2001; Teeset al., 2001; Williams, 2003; Boulbitch, 2003; Pierrat et al.,2004), but few are the experimental works and fewer thoseinvolving living cells (Prechtel et al., 2002; Sulchek et al.,2005; Ratto et al., 2006). These works coincide insuggesting that the adhesion strength of multiple bondsstrongly depends on the loading rate (LR) and is not thesimple addition of the behaviour of individual bonds.However, the dynamical rupture behaviuor of multiplebonds on living cells is still poorly understood.

Most of the cell adhesion complexes are mechanicallylinked to the cytoskeleton and have to support tensional andpulling forces transmitted along its filament network (Tanet al., 2003; Ganz et al., 2006). Consequently, the elasticproperties of cells have a direct link with adhesion. Indeed,recent works have shown that cell adhesion strength stronglycorrelates with the elasticity of cells (Wojcikiewicz et al.,2003; Trache et al., 2005; Leporatti et al., 2006). Thisdependence is caused by two main reasons. First, the elasticproperties of the cells directly determine the LR applied to

460 F. RICO ET AL.

the adhesion bonds while pulling, thereby affecting therupture force. Second, cell elastic properties determine thecontact area when the cell makes contact with anothersurface, a parameter which directly affects the number offormed bonds and thus the rupture force (Wojcikiewiczet al., 2003; Zhang et al., 2006). Therefore, it is essential tobe able to simultaneously determine the dynamic pullingelasticity and the adhesive properties on living cells.

Atomic force microscopy (AFM) has been widely usedto measure adhesion properties on living cells both at singleand multiple molecule levels (Lehenkari and Horton, 1999;Zhang et al., 2002; Wojcikiewicz et al., 2003; Zhang et al.,2004b). Typical adhesion measurements consist in theacquisition of force–distance curves obtained by bringinginto contact a functionalized surface with the surface of aliving cell, and subsequently separating them at a constantspeed (Benoit and Gaub, 2002; Hyonchol et al., 2002; Kimet al., 2003; Kokkoli et al., 2004). Retraction curves arethen analysed by measuring the force peak and, in the caseof multiple bonds, the work of adhesion necessary forcomplete detachment. Adhesion strength is usuallycharacterized by the detachment force and the work ofadhesion at a single LR. However, these parametersstrongly depend on the area of contact between the twosurfaces. Therefore, they do not only reflect intrinsic cellproperties, as they also depend on the geometry of theprobing system. To obtain intrinsic adhesive properties ofcells, it is necessary to control the area of contact(Hyonchol et al., 2002; Kim et al., 2003). However, intypical AFM tip geometries the contact area increases withindentation, providing a nonlinear force response. Aflat-ended cylindrical AFM probe, with a constant contactarea during indentation and pulling, would thus be mostsuitable to measure both adhesion and pulling elasticity. Amethod to obtain AFM tips with a flat-ended geometry isfocused ion beam (FIB) technology (Hodges et al., 2001;Obataya et al., 2005a; Obataya et al., 2005b). However, themilling processes applied to date lead to flat-ended tipswith prismatic shapes presenting sharp edges. Suchirregular geometry may result in high local strains appliedto soft samples while indenting, causing disruption. Indeed,such tips with irregular contact areas have been used tobreak the cell surface and reach the nucleus (Obataya et al.,2005a; Obataya et al., 2005b). A flat-ended cylindrical tipshould therefore provide a better geometry to probe cellelasticity and adhesion.

In this work we fabricated and validated cylindricalAFM cantilever tips to probe the dynamic elastic andadhesive properties of living cells under controlled contactconditions. Pyramidal tips of commercial AFM cantileverswere modified using FIB technology to obtain flat-endedcylindrical tips. Tips were characterized by scanningelectron microscopy (SEM). As a validation procedure, theindentation range with constant area was determined byobtaining force-displacement (F–z) curves on soft agarosegels and alveolar epithelial cells. After validation, thedynamic cell adhesive and elastic properties weremeasured from F–z curves during pulling using cylindricaltips coated with cell ligands. The fabricated tips wereappropriate to measure the dynamical rupture of multiplebonds under loading and the pulling elasticity on livingcells.

Copyright # 2007 John Wiley & Sons, Ltd.

MATERIALS AND METHODS

Cantilever tip modification

Silicon cantilevers (nominal spring constant k¼ 0.03N/m;MikroMasch, Tallinn, Estonia) with pyramidal tips (15–20mm height) were placed on the FIB (FEI Company,Hillsboro, Oregon, USA) sample holder. Tips were milledusing a ring-like pattern (2mm inner diameter, 5mm outerdiameter) centred on the tip apex but tilted by an angle of 88with respect to the axis of the pyramid. This process wascarried out by repetitive passes (with dwell times of 100 ns)reducing progressively the outer diameter (Tseng, 2004).The tip end was then removed by milling a straight-linepattern perpendicular to the cylinder axis. SEM images wereobtained after fabrication to determine the actual radii andheights of the cylinders.

Tip functionalization

Modified silicon cantilevers were cleaned using piranhasolution (70% H2SO4, 30% H2O2, 30min), acetone (5min)and UVirradiation (15min). Cantilevers were then soaked ina solution of 5% 3-aminopropyltriethoxysilane (Fluka,Buchs, Switzerland) in acetone, rinsed with distilled waterand shaken for 30min in a solution of 0.5% glutaraldehyde(Sigma Chemical, St Louis, MO,USA). Cantilevers werethen washed with distilled water and air dried. Afterwards,cantilevers were immersed in 0.1mg/ml solution ofGRGDSP peptide (Calbiochem, Giessen, Bundesland,Germany) for at least 2 h. Unbound proteins were removedby rinsing with phosphate buffered saline (PBS). Cantileverswere immersed in a solution of 0.1% bovine serum albumin(BSA) in PBS for 30min, and rinsed again with PBS.Functionalized cantilevers were stored in PBS at 48C untiluse.

Gel samples

Purified agarose (Type I-A: Low EEO, A-0169, SigmaChemical) 0.3% w/v in Milli-RX water (Millipore Corpor-ation, Bedford, MA, U.S.A) was boiled for �20min whilestirring continuously. The agarose solution was poured into a35mm diameter Petri dish to obtain a gel thickness ofapproximately 500mm. A small region of the Petri dishwas left bare to allow calibration of the AFM photodiode.After gelation of the solution occurred (�5min), thesample was covered with 2ml of Milli-RX water and storedat 48C.

Cell culture

Cell measurements were carried out in living humanalveolar epithelial cells, line A549 (CCL-185, ATCC,Manassas, VA, USA). Culture medium consisted of HEPES(Sigma Chemical) buffered RPMI 1640 with 10% inacti-vated fetal calf serum (Biological Industries, Kibbutz BeitHaemek, Israel), 1mM L-glutamine, 100U/ml penicillin,

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DOI: 10.1002/jmr

CELL ADHESION PROBED BY CYLINDRICAL AFM TIPS 461

100mg/ml streptomycin (GIBCO, Gaithersburg, MD, USA)and 2mg/ml amphotericin B (Bristol-Myers Squibb, NewBrunswick, NJ, USA). Cells were incubated at 378Cin 5% CO2. Two days before the experiments, cells weretrypsinized and plated on 12mm diameter glass coverslips.The culture medium used during the experiments wasserum free.

AFM measurements

Validation experiments on agarose gels and cells werecarried out using a custom-built AFM-based system(Alcaraz et al., 2003) mounted on the stage of an invertedoptical microscope (Axiovert S100, Zeiss, Germany). Thecantilever was positioned using a single axis piezoactuator(P.841.20, Physik Instrumente, Karlsruhe, Germany) servo-controlled with a proportional-integral analog circuit. Thedeflection (d) of the cantilever was measured using theoptical beam deflection method. The laser beam (62FCM,SchafterþKirchhoff GmbH, Hamburg, Germany) wasfocused at the backside of the cantilever, where it reflectedoff and reached a four-segment photodiode (S4349,Hamamatsu, Japan). Validation of the reliability of theconstant area of contact was first performed by indentingagarose gels and analysing the force response. Force curveswere recorded (3mmpeak to peak, 0.3Hz) at three randomlyselected regions of five agarose gels reaching an indentationof approximately 1mm. Validation was also carried out inliving cells following a similar protocol. Measurements wereperformed by acquiring force curves on A549 cells (4mm,0.3Hz) reaching an indentation of approximately 1mm.

Cell measurements were carried out using a custom-builtAFM-based system mounted on the stage of an invertedoptical microscope (TE2000, Nikon, Tokyo, Japan). Briefly,the cantilever was positioned by means of long-rangepiezoelectric translators with strain-gauge position sensors,ranging 32mm (z) and approximately 80� 80mm2 (xy)(Piezosystem Jena, Jena, Germany). Displacement wasservocontrolled by an analog proportional-integral circuit.The deflection of the cantilever was measured using theoptical lever method. A near infrared laser beam (Schaf-terþKirchhoff GmbH) was reflected off the backside of thecantilever and detected using a 4-quadrant photodiode(Hamamatsu photonics, Hamamatsu, Japan). Adhesionmeasurements were carried out by acquiring high amplitudeF–z curves on A549 cells at different retraction speeds(15mm peak-to-peak at 0.1–1Hz) on eight cells fromdifferent culture coverslips. The cantilever was kept incontact at an indentation of approximately 0.5mm for 20 sbefore retraction. To test the specificity of adhesion, asimilar protocol (at a single frequency of 0.3 Hz) was appliedon cells preincubated for 20min in a solution of 0.5mg/ml ofGRGDSP peptide.

Figure 1. SEM image of a cylindrical tip after the FIB millingprocess. Inset: details of the cylindrical flat-end.

Data processing

Validation measurements were interpreted in terms of elasticcontact theory. Force was obtained from cantilever deflec-tion by means of the Hooke’s law (F¼ kd). Indentation wascomputed as d¼ z� zc� dþ d0, with z being the piezo-


electric displacement, zc the point of contact and d0 thedeflection offset. Samples were assumed to be incompres-sible (Poisson ratio n¼ 0.5). The Young’s modulus (E), zc,and d0 were estimated simultaneously using a nonlinear leastsquares algorithm (Matlab 7.0, The MathWorks Inc., MA,USA) which fitted the whole loading part of F–z curves withthe contact model of a flat-ended cylinder indenting anelastic half space (Johnson, 1985)

F ¼ kd0 þ 2E

1 � n2ad (1)

To analyse the dependence of E on indentation, we usedthe fitted values of zc and d0 to compute the indentation. Ewas then isolated from Equation 1 and recalculated for eachindentation point.

The high amplitude retracting curves were used to obtainthe work of adhesionW and the detachment force F�.W wascomputed by integrating the force over the displacement ofthe cantilever tip during retraction from the contact point tothe last adhesion event, and then normalizing by the knownarea of contact. F� was computed from the force peak of theunloading curve and normalized by the perimeter of thecylinder flat end. The deformation applied before rupture D�

was estimated by measuring the distance from the pointwhere force crossed the horizontal axis to the maximumpeak. The slope of the retraction speed before rupture wasused to compute the pulling Young’s modulus usingEquation 1. LR was the result of multiplying the slope bythe retraction speed. The drag force exerted on the cantileverdue to the surrounding medium was corrected by computingthe viscous drag coefficient at different distances from thesurface (Alcaraz et al., 2002). Unless otherwise specified,data are reported as mean� SD.

RESULTS

The resulting microfabricated tips were flat-ended cylinders(�1.3mm diameter, �10mm high) tilted 88 (Figure 1). Thepurpose of the tilt was to compensate for the inclinationangle at which the cantilever chip is mounted on the AFM

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DOI: 10.1002/jmr

Figure 2. Dependence of the Young’s modulus (E) on indentation (d) in an agarose gels (a) and in an epithelial cells (b). Aplateau value is reached at indentations of approximately 200nm in both cases. Insets: representative example of loadingand unloading deflection-indentation curves (dotted and dashed lines, respectively) with the cylindrical contactmodel fit tothe loading part (solid lines). The last 2.5mm are shown. The residual errors are plotted above. Data are presented asmean�SE.

462 F. RICO ET AL.

cantilever holder. No sharp edges were observed afterfabrication. Cylindrical tip radii a, measured fromSEM images acquired after FIB modification, were a¼668� 46 nm. Cantilever spring constants as computed fromthe thermal fluctuations method (Hutter and Bechhoefer,1993; Butt and Jaschke, 1995) differed considerably fromtheir nominal values (k¼ 0.096� 0.021N/m). The differ-ence may be explained by the high variability of cantileverthickness as a result of its fabrication process, and by theadded Cr-Au coating (Sader et al., 1995).

A representative force curve on an agarose gel with thecorresponding fit of Equation 1 is shown in Figure 2(a). Thecurves reflected a fairly linear behaviour. The residual errorplot showed only minor deviations from the model near thepoint of contact, with a fit quality of r2¼ 0.9989� 0.0003. Thefitted E for the gels was 1.79� 1.09 kPa. The coefficient ofvariation (CoV) of E computed from consecutive force curvesat the same point of a gel was 1.5� 1.1%, reflecting therepeatability of the measurements. The CoVof E for differentpoints inside the same gel was 27� 20%. To test the linearregime of the force–indentation curves obtained withcylindrical tips, we computed E at each indentation point.After a pronounced fall for indentations below approximately200nm, a plateau was observed until the maximumindentations were reached (�1mm) indicating a linearbehaviour (Figure 2(a)).

A representative force–indentation curve obtained withcylindrical tips on an A549 cell is shown in Figure 2(b).Curves presented a fairly linear behaviour similar to thatobtained on gels. The fit of the cylindrical model to theloading curve was good (r2¼ 0.9883� 0.0091). Minorsystematic deviations were observed near the point ofcontact. Retraction curves usually presented rupture eventsdue to the RGD functionalization of the tips (Figure 2(b)). E


in A549 cells was 0.72� 0.56 kPa. The low coefficient ofvariance (CoV) of E computed from consecutive forcecurves at a same point of a cell (4.7� 4.7%) reflected therepeatability of the method and the stability of the sample.The indentation dependence of E was parallel to thatobtained on agarose gels, reaching the plateau value atsimilar depths (Figure 2(b)).

A representative unloading force curve obtained on cellsis shown in Figure 3. The force response while pulling thecell before rupture was fairly linear. The dependence of themean detachment force on the LR is shown in Figure 4(a)with both parameters normalized by the perimeter P of thecylinder’s flat-end. A power law was fitted to the data,represented in Figure 4(a) as a solid line. The fit was verygood and led to an exponent of 0.37 (r2¼ 0.98). The work ofadhesion is represented in Figure 4(b) as a function ofthe LR, with both parameters normalized by the area A of thecylinder’s flat-end. Pre-treatment of A549 cells with solubleRGD containing peptide for 20min induced a significantdecrease (�60%) in adhesion strength (F� and W), showingthe specificity of the interaction. The Young’s moduluscomputed from retracting curves showed an importantincrease with retraction velocity (Figure 5). In contrast, thedeformation applied to the cells before initial ruptureremained constant, regardless of the LR (Figure 6).

DISCUSSION

An FIB procedure was implemented to obtain flat-endedcylindrical AFM cantilever tips. The tips were validated onlinear, elastic samples (agarose gels) and, afterwards, onliving cells, verifying that the area of contact was constant

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Figure 4. Dynamic cell adhesion parameters. (a) Detachmentforce (F �) versus LR in alveolar epithelial cells. Both parameterswere normalized by the rim perimeter P of the cylindrical tips .The solid line represents the best fit of a power law, giving anexponent of 0.37. (b) Work of adhesion W versus LR. Bothparameters were normalized by the area A of the cylindricalflat-end. The high dispersion in the results may be due to theformation of cell membrane tethers during unloading.

Figure 3. Representative example of a retraction F–z curveobtained on an A549 cell using a cylindrical tip at a retractionspeed of 10mm/s. An initial steep force ramp is observed on theright side of the figure, followed by secondary peaks as thesample is progressively pulled. The work of adhesion W wascomputed as the area below the zero force level (shaded area).The detachment force was computed as the minimum forcevalue F �. The slope of the curve before the minimum force valuedetermined the effective stiffness, and was multiplied by canti-lever velocity to compute the LR. The deformation before rupture(D�) was measured as the distance between zero force and peakforce levels in retraction curves.


for indentations deeper than 200 nm. Tips coated withligands were used to probe the dynamic elastic properties ofliving human epithelial cells during adhesion and pulling.Unloading curves were used to measure the detachmentforce, work of adhesion, Young’s modulus and deformationbefore rupture. Both adhesion strength and elasticity showeda strong dynamic rate dependent behaviour. Noticeably, thedeformation suffered by cells before rupture was fairlyconstant at the LRs applied.

The modification of the cantilever tips was carried outby implementing a new procedure based on FIB etching.Obataya and co-workers also modified AFM cantilever tips topenetrate inside the cytoplasm of human epidermal melan-ocytes, obtaining thin needles with diameters of approxi-mately 200–300 nm and sharp irregular edges (Obataya et al.,2005b). In contrast, our milling process led to flat-endedcylindrical tips without irregularities, ensuring the smoothcontact and low strains required to obtain reliable estimates ofelastic properties. Due to the higher diameter of our tips and tothe absence of sharp edges, we never registered a force curvedenoting rupture of the cell membrane. The milling processwas designed to minimize the presence of smoothed edgesand tilted cylinder walls known to occur under high intensitiesand long exposure times (Tseng, 2004). Figure 1 shows thatthe rounding of the edges was minimal. The tilted wallsresulted in a tip diameter slightly smaller at the tip end thanthe original 2mm. This expected limitation was the reason toacquire SEM images of each tip after modification to verifythe actual diameter.

The validity of the constant contact area of the fabricatedtips was determined by indentation force curves on linear,elastic samples and on cells. The overall fit of Equation 1was excellent, although minor deviations were observednear the point of contact (Figure 2). This divergence has


been observed before on similar measurements and has beenattributed to steric forces caused by the brush-like interfacedue to free-end fibres (on agarose gels) and to the glycocalix(on living cells) (Lee and Marchant, 2000; Rico et al., 2005;Obataya et al., 2005b). Another contribution to thenonlinearity near the point of contact might be the slightrounding of the flat-end rim (radius of curvature ofapproximately 50 nm, inset in Figure 1). The indentationdependence of E on both gels and cells showed the range ofvalidity of the constant contact area (Figure 2). On both gelsand cells, a clear plateau was reached at indentations>200 nm, as expected for a linear, elastic material. Thisshows that a constant area of contact was ensured atindentations >200 nm, lending support to the appliedcontact model, and showing that the fabricated cylindricaltips are appropriate to measure indentation elastic proper-ties. The plateaus also confirmed the linearity of gels andreflected the linear behaviour of cells at the applied

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DOI: 10.1002/jmr

Figure 6. Deformation before initial rupture D � applied to livingcells as a function of the LR (normalized by the cantileverperimeter, P ). The dashed line shows the mean value.

Figure 5. Young’s modulus E of cell obtained from unloadingcurves as a function of the retraction velocity. Data are presentedas mean�SE.

464 F. RICO ET AL.

deformations. Given the linear behaviour observed atindentations far from the contact point in elastic gels, ahypothetic nonlinear F�d relationship far from the point ofcontact would indicate nonlinear elastic properties of theprobed material. Thus, cylindrical tips are ideally suited tostudy nonlinear responses of living cells under high strains(Stamenovic andWang, 2000; Trepat et al., 2004; Fernandezet al., 2006). Moreover, they are more convenient thanconventional pyramidal tips to measure viscoelastic proper-ties, as low amplitude oscillations can be applied in a linearmanner, independently of the absolute indentation (Mahaffyet al., 2000; Mathur et al., 2001; Rico et al., 2005).

The cylindrical flat end ensures a constant and controlledcontact area during indentation, contact and pulling. This isa clear advantage when measuring adhesion properties.Similar AFM measurements conducted at relatively longcontact times (20 s) using conventional tip geometries wouldpresent important difficulties, avoided with cylindrical tips.First, relaxation of stress after application of a force to a cell


would produce a decrease in the apparent elasticity, causingan increase in indentation during the contact time. Thiswould result in a time varying and difficult-to-quantifycontact area. Second, the observed dynamic behaviour ofboth force and work would be hidden in traditional AFMmeasurements carried out by controlling the maximumcontact force. Due to their viscoelastic behaviour, cellsappear stiffer when probed at high rates. This feature,reported to be universal in living cells (Maksym et al., 2000;Fabry et al., 2001; Alcaraz et al., 2003; Desprat et al., 2005;Smith et al., 2005; Trepat et al., 2005; Roca-Cusachs et al.,2006), is observed in Figure 6. As cell stiffness augmentswith the probing rate, a fixed contact force will lead to asmaller indentation and a consequent smaller contact area,resulting in a proportional decrease in the measuredadhesion parameters. Thus, an underestimation of theadhesion strength will occur at higher LRs. Therefore andas previously acknowledged (Wojcikiewicz et al., 2003), anychange in cell elasticity will induce a variation in adhesionparameters, even if the intrinsic cell adhesion propertiesremain unchanged. Our fabricated cylindrical tips resolvethis limitation, ensuring a constant and known area ofcontact even if changes in sample stiffness take place.

Another important advantage of the fabricated cylinders isthat the known, controlled area allowed us to report ouradhesion data using general and comparable parametersindependent of the probe geometry and inherent to thesample. The maximum rupture force strongly depends onthe number of bonds formed at the rim of contact, that ison the perimeter of the contact. In addition, the LR applied tothe contact zone is shared by all bonds, so that each bondsupports an effective LR. Thus, both force and LR werenormalized by the flat-end perimeter. Regarding adhesionstrength, it would be meaningful to quantify it through thecomputation of the work of adhesion, as this is a commonlyused estimate of the surface energy or energy density ofbodies in contact (Johnson, 1985; Boal, 2002). However,most of the AFM studies carried out on living cells reportedthe adhesion strength in terms of the absolute detachmentwork, leading to incomparable results (Benoit and Gaub,2002; Zhang et al., 2004a; Leporatti et al., 2006; Zhanget al., 2006). We thus normalized the computed work ofadhesion by the area of the cylindrical flat-end. Therefore,our adhesion parameters (F�/P and W/A) provide inherentquantification of the adhesion strength. These parameters areindependent of the probe geometry and are comparable withindependent adhesion measurements from micropipetteaspiration measurements, adhesion work measurementsusing spherical AFM tips and even static force measure-ments using elastic microneedles (Prechtel et al., 2002; Tanet al., 2003; Kim et al., 2003).

Despite recent studies reporting dynamic adhesionproperties of living cells, to the best of our knowledge thiswork is the first study providing a detailed description ofdynamical rupture using AFM (Prechtel et al., 2002; Zhanget al., 2004a). As shown in Figure 4, rupture forces exhibitedstrong LR dependence. Indeed, a power law with exponent0.37 fitted to our data very well. This dynamic response maybe interpreted as an experimental proof of a recentlydeveloped model which predicted a power law response ofthe rupture force of a number of parallel reversible bondsunder dynamic loading (Seifert, 2000). Recent experimental

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and numerical results for similar multiple parallel detach-ment also support the model (Seifert, 2002; Prechtel et al.,2002). The observed experimental dynamic behaviour maythus be taken as a signature of the rupture of multiple parallelbonds, as further supported by the systematic profile of theunloading curves (Figure 3). This rupture process can beunderstood as follows. When pulling an elastic half spacewith a rigid flat-ended punch, the force is developedaround the periphery of the contact. Thus, the bonds locatedat the circular rim are those which support loading during thelinear increase in the pulling force (Yang and Li, 2001). Wecan therefore interpret the kinetics of rupture profiles in threemain steps: (1) cooperative detachment of the outermost ringof bonds (peak of force and subsequent drop), especially athigh LRs where cooperativity is known to be enhanced(Zhang and Moy, 2003), (2) successive sequential unbindingof the remaining inner complexes (further jumps precededby linear force ramps) and (3) occasional formation of longmembrane tethers (jumps preceded of force plateaus rangingfew microns) (Sun et al., 2005). It is noteworthy that theslope of the secondary force ramps, caused by the remaininginner bonds, diminished with retraction distance. Thisreflects the sequential reduction of the area of contact. Takentogether, these results suggest that the maximum forcesupported by a collectivity of adhesion receptors (such as afocal adhesion) depends mainly on the perimeter length ofthe cluster and not on its area. It is remarkable that the workof adhesion presented also a strong dynamical response, butwith a higher measurement uncertainty (Figure 4(b)). Thishigher dispersion compared with F� values may be a reflexof the formation of tethers, which occurred only in some ofthe curves (Sun et al., 2005; Cuvelier et al., 2005). Thedynamic strength behaviour of adhesion clusters on livingcells should be similar to that observed here, due to theanalogous geometry.

A remarkable result was that the deformation appliedbefore initial rupture had a fairly constant value within theLRs tested (Figure 6). If cells were purely elastic bodies, asdetachment force increases with LR, an increase in celldeformation would be expected before rupture. The constantD� suggests that cells may dynamically counterbalance theincrease in adhesion strength with LR, resulting in constantdeformation. We suggest that this balance comes from thedynamic behaviour of cellular stiffness, which is known toincrease with probing rate (Fabry et al., 2001; Alcaraz et al.,


2003; Trepat et al., 2005; Bursac et al., 2005; Roca-Cusachset al., 2006). Indeed, our results showed a notable increase inthe Young’s modulus with retraction speed (Figure 5). Theseresults suggest that cell detachment occurs at constantdeformation. We, therefore, propose D� as a relevant para-meter in the determination of adhesion strength which couldbe equivalent to the binding potential width in singlemolecule rupture events (Evans and Ritchie, 1997). Thus,cells have to be deformed by a certain amount D� to inducerupture of their receptor–ligand complexes. As mentionedabove, human cells are constantly subjected to or exertingcyclic mechanical forces which may vary in their applicationrate. The proposed counterbalance mechanism assuresconstant stretch, preventing possible rupture of adhesioncontacts, cell disruption and tissue damage. Cells experiencethe same deformation whatever the applied rate of force.

In conclusion, flat-ended cylindrical tips enable us tomeasure the mechanical properties of soft biologicalsamples, such as polymer gels and living cells, maintaininga constant area of contact at indentations>200 nm. Owing tothis feature, the used tips enabled us to report inherentadhesion parameters, independently of probe geometry. Thepresent work draws attention to the importance of thenormalization of adhesion parameters, and of their dynami-cal acquisition, to make them comparable with independentmeasurements. The fabricated cylindrical tips represent anideally suited tool to measure the dynamical strength ofparallel bonds under loading, a key event in cellularadhesion. Remarkably, our results showed a strong depen-dence of the adhesion parameters and the pulling Young’smodulus on the applied LR, whereas the deformation beforerupture remained unaffected. This finding is physiologicallyimportant, as it suggests that both adhesion strength andstiffness are dynamically balanced to regulate the overalldeformation supported by living cells possibly reflecting thesame fundamental mechanism.

Acknowledgments

Supported in part by Ministerio de Educacion y Ciencia (NAN2004-09348-C04-04, SAF2005-00110) and Ministerio de Sanidad y Consumo(CibeRes-ISCiii-CB06/06, FIS-PI040929). The authors thankM.A.Rodrıguezfor his technical assistance and E. Martınez for her expertise in using theFIB apparatus.

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