Measuring the nanomechanical properties of cancer ...

IOP PUBLISHING

NANOTECHNOLOGY

Nanotechnology 19 (2008) 384015 (7pp)

doi:10.1088/0957-4484/19/38/384015

Measuring the nanomechanical properties of cancer cells by digital pulsed force mode imaging Othmar Marti1 , Michael Holzwarth1 and Michael Beil2 1 2

Institute of Experimental Physics, Ulm University, D-89069 Ulm, Germany Department of Internal Medicine, Ulm University, D-89069 Ulm, Germany

E-mail: [email protected], [email protected] and [email protected]

Received 6 March 2008, in final form 1 June 2008 Published 12 August 2008 Online at stacks.iop.org/Nano/19/384015 Abstract In this paper, we demonstrate that the digital pulsed force mode data can distinguish two cancer cell lines (HeLa, Panc) by their mechanical properties. The live cells were imaged in buffer solution. The digital pulsed force mode measured 175 force–distance curves per second which, due to the speed of the measurement, were distorted by the viscous drag in the buffer. We show that this drag force causes a sinusoidal addition to the force–distance curves. By subtracting the viscous drag effect one obtains standard force–distance curves. The force–distance curves are then evaluated to extract key data on the curves, such as adhesion energies, local stiffness or the width of the hysteresis loop. These data are then correlated to classify the force–distance curves. We show examples based on the width of the hysteresis loop and the adhesion energies. Outliers in this classification scheme are points where, potentially, interesting new physics or different physics might happen. Based on classification schemes adapted to experimental settings, we propose that the digital pulsed force mode is a tool to evaluate the time evolution of the mechanical response of cells. (Some figures in this article are in colour only in the electronic version)

filament genes, e.g. keratin genes, interfere with the mechanical properties of cells. They change the cell adhesion complexes and, consequently, reduce the mechanical stability of the affected epithelia [24, 30, 37]. Other types of intermediate filaments such as vimentin in blood vessels [12] take part in the regulation of cell functions. Apart from the mechanical properties of single filaments [34], the network architecture of the keratin filaments is an important component of the response of epithelial cells to viscoelastic loads. The increased bundling of primary filaments increases the elasticity of K8/18 networks in vitro and improves resistance to shear stresses [8]. Keratin filaments govern the cell’s response to large deformations while actin filaments are important for small deformations [4, 35]. To understand the response to mechanical stimuli of cells the topology of extracted cytoskeletons is measured and compared to mathematical tessellation models [3]. The parameters of the tessellation model allow comparing

1. Introduction Tumor growth and cell motility determine the prognosis of cancer. Whereas many drugs are now used to control cell proliferation, migration of cancer cells leading to infiltration of neighboring organs and metastasis represents an unresolved problem. Cancer cells moving through dense tissue structures can secrete proteolytic enzymes to create a pathway or modify their structural and mechanical properties to move through preformed channels or gaps [38]. Apart from defining cell shape, the cytoskeleton is pivotal for the regulation of the mechanical properties of cells and, thus, contributes to the control of cancer cell motility [23]. The filamentous cytoskeleton is composed of three biopolymer systems: the actin filament system, the system of microtubuli and the system of intermediate filaments [34]. Actin networks regulate the mechanical properties of peripheral cell compartments [21]. Mutations of intermediate 0957-4484/08/384015+07$30.00

1

© 2008 IOP Publishing Ltd Printed in the UK

Nanotechnology 19 (2008) 384015

O Marti et al

the networks resulting from the application of models of cytoskeleton growth to real networks. For meaningful results of these simulations it is, however, necessary to know the elastic properties of single filaments, which could be difficult to measure [6, 39]. Alternatively, one can perform micro- and nanomechanical experiments on fixed and living cells [10, 13, 9, 35]. By using drugs interfering with the polymerization processes [29] of specific filament systems one can estimate the mechanical properties of these filaments from measurements of living cells. The measurement of local mechanical properties of cells by atomic force microscopy (AFM) [5, 20, 1, 18, 19, 11, 15] requires the use of small and controlled interaction forces. Force– distance curves [2, 22, 33, 36] and intermittent contact mode [26, 25, 16] are used to determine the mechanical properties. Surface force gradients are measured with force– distance curves while the cantilever is oscillating at its resonance [25]. The calibration of forces in intermittent contact mode is more demanding than for pulsed force mode. In the latter case, static data can be used.

The scan time per line was 4 s for the HeLa cell and 5 s for the Panc cell. Each image with all the force–distance curves amounted to 48–60 GB of raw data. These raw data were transferred to a computer dedicated for analysis. Force– distance curves were extracted using custom-written software and transferred to R [14, 27]. 2.3. Elimination of the viscous drag effect The output of the digital pulsed force mode box is a time series of deflection values z defl (kτ + τ0 ), where τ is the sampling interval and τ0 is the starting time. k is the running index of the measurement. For simulation purposes, this time series is replaced by a continuous function z measured (t). It was found experimentally that the effect of the viscous drag could be eliminated by subtracting a suitably chosen sinusoidal function from the z measured :

z 1 (t) = z measured (t) − A sin(ωPFM t − δPFM ). A, ωPFM and δPFM are the amplitude, the angular velocity and the phase, respectively. A simple model based on two different viscoelastic responses of a harmonic oscillator shows that this procedure is most likely valid. In a first approximation, the movement of the cantilever is that of a driven damped harmonic oscillator. Away from the sample the cantilever with its spring constant kc moves in a liquid with a given viscoelastic damping δc . The distributed mass of the cantilever is modeled by a concentrated mass m c . In contact with the sample, the effective mass of the oscillator is increased by an effective moved mass of the sample m s . The velocity proportional damping δs of the sample is in parallel with the cantilever damping. Finally, complex indentation behavior of the tip into the sample is modeled by an effective spring constant ks , which is again in parallel to the cantilever’s spring. Together the movement of the cantilever is given by the equations ⎧ k z + 2δc z˙ + m c z¨ , ⎪ ⎪ c ⎪ ⎨ for z > 0; kc cos(ωt) = (1) ⎪ (kc + ks )z + 2(δc + δs )˙z + (m c + m s )¨z , ⎪ ⎪ ⎩ for z 0.

2. Materials and methods 2.1. Cells Cells have been cultivated in DMEM/F12-medium (from Gibco, Karlsruhe, Germany) with 10% FCS (fetal calf serum), 4.5 g l−1 glucose and 2 mM L-glutamine. The cells were cultivated under physiological conditions (310 K, 5% CO2 ) in the medium for two days. Before the actual measurement the medium was rinsed-off with PBS (phosphate buffered saline, Dulbecco’s PBS, with Ca2+ and Mg2+ , PAA Laboratories GmbH, A-4061 Pasching) which also served as liquid environment during the measurement. 2.2. Atomic force microscope All images and force–distance curves were acquired by a WITec alpha300 microscope with a digital pulsed force mode attachment [32, 41]. The scanning area of the system is 100 μm × 100 μm laterally and 20 μm in height. The cells were imaged by PPP-LFMR-50 type cantilevers from Nanosensors [40]. They have a length of 255 ± 10 μm, a width of 48 ± 7.5 μm and a thickness of 1.0–0.9 + 1 μm. The tip height was 12.5 ± 2.5 μm. The curvature of the tip out of the box was typically 20 nm. The nominal force constant was 0.2 N m−1 with a variation from 0.01 to 1.87 N m−1 . The nominal resonance frequency was at 23 kHz and ranging from 1 to 57 kHz. The measured force constant [7] for the HeLa measurement was 0.072 N m−1 . The cantilever used to measure the Panc cells had a measured force constant of 0.057 N m−1 . The pulsed force mode imaging uses a sinusoidal movement of the cantilever away from any resonance [17, 28, 31]. The amplitude of the pulsed force mode movement ranged between 375 nm and 2.29 μm at a repetition rate of 175 Hz. The digital pulsed force mode measures force– distance curves at 16-bit resolution and a sampling rate of 5 mega-samples per second. The images were acquired with 600 points by 600 lines. The scanning range was 50 μm × 50 μm.

The equation is solved by numerical integration with a fourth-order Runge–Kutta procedure. Figure 1(a) shows the force–distance curve together with the viscoelastic drag in the liquid phase above the sample. The influence of the viscoelastic drag is modeled by a sine wave with a known frequency ω (the same as the excitation), an unknown amplitude A, phase φ and, possibly, an offset A0 :

f (t) = A sin(ωt − φ) + A0 .

(2)

The three unknown parameters A, φ and A0 of the sine wave are obtained by fitting f (t) to the right-hand part of the force–distance curve in figure 1(a). This function is then subtracted from the measured force–distance curve. The result is displayed in figure 1(b). In this rather crude model calculation, the viscoelastic drag in the free liquid is compensated rather well. However, the part of the force– distance curve in contact with the sample is broadened. 2


O Marti et al

Figure 1. (a) Simulated force–distance curve and (b) the resulting curve after our correction procedure.

Figure 2. (a) Measured force–distance curve in water on the substrate. 175 curves per second were sampled. (b) The resulting curve after our correction procedure.

Figure 2 shows in (a) a measured force–distance curve on a substrate covered by poly-L-lysine. 175 curves per second were sampled. The right-hand side of the figure demonstrates the correction procedure. The function f (t) = 0.262 sin(1119t − (−1.168)) + 0.013 was obtained by the fitting procedure to the parts of the force–distance curve far away from the sample surface. This function f (t) was then subtracted from (a). The result is displayed in (b). Comparing the simulation in figure 1 with the real measured data in figure 2 it must be noted that the correction for the repulsive part works much better for the measured data. The poly-L-lysine, on the other hand, shows a large adhesion, obvious in the corrected data. The simulation did not include any adhesion. Based on the inspection of many force–distance curves on hard substrates we conclude that the subtraction of a sine with appropriate amplitude and phase efficiently compensates the effects of viscous drag on force–distance curves. The simulation was carried out to have further evidence for the proposed algorithm, not as a proof of the procedure. Further investigations have to be carried out. These investigations will have to deal with the time dependence of the viscous part, too.

2.4. Analysis methods for force–distance curves Force–distance curves contain a wealth of information. The shape of the curves depends on the viscoelastic properties of the cells and on the structure of the cell surface and the subsurface properties. Pull-off forces reveal the adhesion or, under certain circumstances, the molecular interaction with few to single molecules. Using R [7, 27] characteristic measures were extracted from the datasets. Figure 3 shows the definition of the values analyzed in this paper. For every force–distance curve we have recorded the maximum indentation force Fmax , the z position of the maximum force z(Fmax ), then the positions where 3 Fmax /4, Fmax /2 and Fmax /4 were reached on the indentation path. The area under the curve up to z(Fmax ) is the total energy E 1 stored in the cell by the indentation. During the unloading cycle z(0) is the position where the force curve crosses the zero force line. The area under this curve is the energy E 2 released in the retraction cycle. The difference E 1 − E 2 is the viscoelastic loss in the sample. z(Fmin ) is the position of the peak adhesive force Fmin . The area from z(0) to z(Fmin ), corresponding to the energy E 3 , and the area from z(Fmin ) to where the force– 3


O Marti et al

defined above. The cells were prepared on poly-L-lysine coated cover glasses. The poly-L-lysine serves as an adhesive to attach the cells. Therefore the adhesion on the substrate is higher than on the cell. The appearance of figure 4(b), the plot of the adhesion energy on the HeLa cell, indicates that roughly in the middle of the image the properties of the tip have changed. This change is not visible in the topography. The cell has a total height of 3.6 μm. The adhesion energy on the HeLa cell varies from roughly zero to 2.7 × 10−14 J. The adhesion energy on the Panc cell varies much less, from roughly zero to 1.89 × 10−15 J. This variation is about ten times less. The magnitude of the difference could be due to the increase in the adhesion of the tip while measuring the HeLa cell or, partially, due to the different composition of the surface of the Panc cell compared to the HeLa cell. Figure 5 shows the locations where force–distance curves have been analyzed on the HeLa cell (part (a)) and on the Panc cell (part (b)). The locations of the force–distance curves were selected on the rim, since we wanted to avoid the influence of the nuclei on the results. Figure 6 shows some selected force–distance curves (not the best ones!) from the HeLa cell (a) and from the Panc cell (b). Each figure shows three curves. Curve 05 in (a) was measured on the substrate. This curve shows a very stiff response with little hysteresis. The adhesion on the substrate is quite high, since the cover glass slides were covered by polyL-lysine to improve cell adhesion. Curve 20 was measured on the cell periphery in the upper half of the figure where the adhesion energy is even higher (140% of the adhesion energy of curve 05). The indentation curve is broader and ends in a force gradient as steep as the substrate. This indicates that the tip has probed the cell, which is about 1 μm thick at this site, down to the substrate. Finally curve 48 was measured on a thicker part of the cell. Judging from the indentation curve, the

Figure 3. Definition of the values analyzed.

distance curve is back at zero, corresponding to the energy E 4 , represent the total adhesive energy E adh = E 3 +E 4 . Once these values are found correlation plots will show how significantly a pair of measured values will describe the variations from one force–distance curve to the others. The correlation plots allow a classification of the force–distance curves which, in turn, can be mapped back onto the spatial coordinates.

3. Results and discussions Figure 4 shows a comparison of a measurement of a HeLa cell with that of a Panc cell. The left column, figures 4(a) and (c), show the topographic information of the HeLa cell (top) and the Panc cell, respectively. The right column, figures 4(b) and (d), shows the corresponding adhesion energies E adh , as

Figure 4. (a) Topography of the HeLa cell calculated from the force–distance curves. (b) Adhesion energy of the HeLa cell calculated from the force–distance curves. (c) Topography of the Panc cell calculated from the force–distance curves. (d) Adhesion energy of the Panc cell calculated from the force–distance curves.

4


O Marti et al

Figure 5. (a) Topography of the HeLa cell. The numbered marks show the positions of the force–distance curves that have been analyzed in the text and in figures 7(a) and (b). Two exemplary curves are shown in figure 6(a). (b) Topography of the Panc cell. The numbered marks show the positions of the force–distance curves that have been analyzed in the text and in figures 7(c) and (d). Two exemplary curves are shown in figure 6(b).

–0.4

–0.2

0.0

0.2

0.4

Figure 6. (a) Force–distance curves measured on the HeLa cell at positions 05 (dashed, red), 20 (dotted, green) and 48 (full, blue) in figure 5(a). (b) Force–distance curves measured on the Panc cell at positions 05 (dashed, red), 20 (dotted, green) and 48 (full, blue) in figure 5(b).

shows some selected correlation plots. Parts (a) and (b) are the plots for the HeLa cell and (c) and (d) for the Panc cell. The left column (a) and (c) shows the correlation between the width of the force–distance curve at the levels Fmax /4 and 3 Fmax /4 (see figure 3 for the definition). The right column (b) and (d) shows the correlation of the adhesion energies E 4 with E 3 . The correlation plot of the widths shows for both cells a positive correlation. The point cloud is spread out. For further analysis one can identify regions of points and then select those points that fall into that region. Outliers are especially interesting points. There one might find singular events. The positive correlation simply means that locations with high viscosity at a shallow depth are also locations with a high viscosity at higher depths. The widths of the force–distance curves on the HeLa cell vary more than that on the Panc cell. Furthermore the force–distance curves of points 11–41 have a higher spread than the other points. The corresponding correlation plot of the Panc cell is less spread, but has more outliers. The correlation of the energies E 3 and E 4 shows approximately a power law dependence. This purely empirical finding needs to be further evaluated.

cell was stiffer at this location, probably because the density of cell material inside was higher. The adhesion energy is, however, lower (90%) than that of curve 05. The force–distance curves measured on the Panc cell, figure 6(b), have a different characteristic. Curve 05 was measured on the rim of the cell. The total amplitude of the pulsed force mode was only 375 nm. As the curves indicate, the tip never really broke loose of the cell. The curves therefore do not represent force–distance curves but they are rather a rheological experiment at 175 Hz. Nevertheless the force– distance curve was measured at the cell surface. Curves 20, measured further away from the rim, and curve 48, measured on a thicker part, indicate that the compliance of the cell was lower. It is justified to assume that at the very rim, where the cell is thin, the substrate influences the measured stiffness and increases it. The dissipation at the rim (curve 05) and on the cell body (curve 48) is large, whereas curve 20 shows considerably less area (or energy) (about 50% of curves 05 and 48). Using R [27] we analyzed 3392 force–distance curves measured on the HeLa cell and 3156 force–distance curves measured on the Panc cell. The location of the measured force– distance curves is indicated in figure 5 and table 1. Figure 7 5


O Marti et al

Figure 7. (a) Correlation plot of the hysteresis between indentation and retraction on the HeLa cell (levels 1/4 and 3/4 of Fmax ). (b) Correlation plot of the HeLa cell energies E 4 versus E 3 . (c) Correlation plot of the hysteresis between indentation and retraction on the Panc cell (levels 1/4 and 3/4 of Fmax ). (d) Correlation plot of the Panc cell energies E 4 versus E 3 . Please note the different scales for the HeLa and the Panc cells. The colors correspond to the points in figure 5.

Table 1. Summary of the analyzed force–distance curves (FDC). Location

HeLa Number Comment

01–10 11–41 42–46 47–52

640 1920 448 384

Substrate Rim Away from rim Away from rim

3392

Sum

Location 01–06 07–11 12–20 21–35 36–39 40–45 46–50

Panc Number Comment 384 320 576 916 256 384 320 3156

Rim Rim Rim Rim near nucleus Inside Inside Inside Sum

A simple model of a harmonic oscillator with two speeddependent damping factors demonstrated that the separation method for the viscous drag in the buffer does work. The resulting force–distance curves after subtraction of the viscous drag effect can then be analyzed using the standard toolbox of AFM. To date, the correction procedure gives an accurate way to obtain relative mechanical parameters of the substrate. To be able to calculate absolute values, experiments varying the frequency of the force–distance curves from very slow to our values are needed.

4. Conclusions We have shown in this paper that the digital pulsed force mode is able to acquire data suitable to classify locations on a single cell or to classify the results of different cell types. As prototypes we have discussed measurements on a HeLa cell and a Panc cell. We have shown that the measurement of living cells in a buffer solution is possible. The distortions of the force–distance curves induced by the viscous drag of the buffer can be separated from the force–distance curves. 6


O Marti et al

The fact that the digital pulsed force mode is able to acquire force–distance curve data on an entire cell during several tens of minutes with data rates in the mega-sample range opens the possibility to data mine for singular events. We have shown that the classification of force–distance curves with correlation plots can identify classes of response curves or outliers. The latter are potential candidates for singular events. Even though the digital pulsed force mode measures some 175 force–distance curves per second, the acquisition of an image still takes more than 10 min. If one reduces, for instance, the vertical scan size, the digital pulsed force mode AFM could be used to track changes of mechanical properties and spatial distributions of mechanical properties of cells. This offers another way to quantify the effect of drugs on the mechanical properties of cells [29]. It would not only give an overall measure of the effect, but also could, potentially, identify cell compartments affected first or last by the drug.

[10] Haga H, Sasaki S, Kawabata K, Ito E, Ushiki T and Sambongi T 2000 Ultramicroscopy 80 253–8 [11] Hansma P K et al 1994 Appl. Phys. Lett. 64 1738–40 [12] Henrion D et al 1977 J. Clin. Invest. 100 2909–14 [13] Holzwarth M J, Gigler A M and Marti O 2006 Imag. Microsc. 8 37–8 [14] Hornik K 2008 The R FAQ http://CRAN.R-project.org/doc/ FAQ/R-FAQ.html [15] Johnson K L, Kendall K and Roberts A D 1971 Proc. R. Soc. A 324 301–13 [16] Knowles T P J, Smith J F, Craig A, Dobson C M and Welland M E 2006 Phys. Rev. Lett. 96 238301/1–4 [17] Krotil H U, Stifter T, Waschipky H, Weishaupt K, Hild S and Marti O 1999 Surf. Interface Anal. 27 336–40 [18] Marti O, Colchero J and Mlynek J 1990 Nanotechnology 1 141–4 [19] Meyer G and Amer N M 1990 Appl. Phys. Lett. 57 2089–91 [20] Meyer G and Amer N M 1988 Appl. Phys. Lett. 53 1045–7 [21] Mott R E and Helmke B P 2007 Am. J. Physiol. Cell Physiol. 293 C1616–26 [22] Nagao E and Dvorak J A 1998 J. Microsc. 191 8–19 [23] Näthke I 2006 Nat. Rev. Cancer 6 967–74 [24] Owens D W and Lane E B 2004 J. Pathol. 204 377–85 [25] Putman C a J, Van Der Werf K O, De Grooth B G and Van Hulst N F 1994 Appl. Phys. Lett. 64 2454–6 [26] Putman C a J, Van Der Werf K O, De Grooth B G, Van Hulst N F and Greve J 1994 Biophys. J. 67 1749–53 [27] R Development Core Team 2008 R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0 [28] Rosa-Zeiser A, Weilandt E, Hild S and Marti O 1997 Meas. Sci. Technol. 8 1333–8 [29] Rotsch C and Radmacher M 2000 Biophys. J. 78 520–35 [30] Russell D, Andrews P D, James J and Lane E B 2004 J. Cell Sci. 117 5233–43 [31] Spizig P, Sanchen D, Förstner J, Koenen J and Marti O 2005 European Patent Specification EP1342049B1 [32] Spizig P M 2002 Dynamische Rasterkraftmikroskopie University of Ulm, Faculty of Natural Sciences [33] Stolz M, Raiteri R, Daniels A U, Van Landingham M R, Baschong W and Aebi U 2004 Biophys. J. 86 3269–83 [34] Strelkov S V, Herrmann H and Aebi U 2003 Bioessays 25 243–51 [35] Suresh S, Spatz J, Mills J P, Micoulet A, Dao A, Lim C T, Beil M and Seufferlein T 2005 Acta Biomaterial. 1 15–30 [36] Weisenhorn A L, Maivald P, Butt H J and Hansma P K 1992 Phys. Rev. B 45 11226–32 [37] Windoffer R, Borchert-Stuhltrager M and Leube R E 2002 J. Cell Sci. 115 1717–32 [38] Wolf K, Mazo I, Leung H, Engelke K, von Andrian U H, Deryugina E I, Strongin A Y, Bröc E B and Friedl P 2003 J. Cell Biol. 160 267–77 [39] Yamazaki M, Furuike S and Ito T 2002 J. Muscle Res. Cell Motil. 23 525–34 [40] Nanosensors (www.nanosensors.com) [41] WITec GmbH, 89081 Ulm, Germany (www.witec.de)

Acknowledgments The authors thank Ulla Nolte for preparing the cells and maintaining the local store for the cell lines. Intensive discussions with Paul Walther (Central Electron Microscopy Facility, Ulm University), Volker Schmidt and Frank Fleischer, both Institute of Applied Information Processing & Department of Stochastics, helped clarify important aspects. Florian Schmid wrote a small utility to transform binary data into text mode data suitable for further analysis by R. The data conversion was done in collaboration with WITec GmbH. This work was funded in part by the German Science Foundation (Collaborative Research Grants SFB-518 and SFB 569).

References [1] Alexander S, Hellemans L, Marti O, Schneir J, Elings V, Hansma P K, Longmire M and Gurley J 1989 J. Appl. Phys. 65 164–7 [2] Banerjea A, Smith J R and Ferrante J 1990 J. Phys.: Condens. Matter 2 8841–6 [3] Beil M, Eckel S, Fleischer F, Schmidt H, Schmidt V and Walther P 2006 J. Theor. Biol. 241 62–72 [4] Beil M et al 2003 Nat. Cell Biol. 5 803–11 [5] Binnig G, Quate C F and Gerber C 1986 Phys. Rev. Lett. 56 930–3 [6] Charras G T and Horton M A 2002 Biophys. J. 83 858–79 [7] Cleveland J P, Manne S, Bocek D and Hansma P K 1993 Rev. Sci. Instrum. 64 403–5 [8] Coulombe P A and Omary M B 2002 Curr. Opin. Cell Biol. 14 110–22 [9] Gigler A, Holzwarth M and Marti O 2007 J. Phys.: Conf. Ser. 61 780–4

7