LETTERS PUBLISHED ONLINE: 13 NOVEMBER 2011 | DOI: 10.1038/NNANO.2011.186
Mapping nanomechanical properties of live cells using multi-harmonic atomic force microscopy A. Raman1,3†*, S. Trigueros2†, A. Cartagena1,3, A. P. Z. Stevenson2, M. Susilo1, E. Nauman1,4 and S. Antoranz Contera2 The nanomechanical properties of living cells, such as their surface elastic response and adhesion, have important roles in cellular processes such as morphogenesis1, mechano-transduction2, focal adhesion3, motility4,5, metastasis6 and drug delivery7–10. Techniques based on quasi-static atomic force microscopy techniques11–17 can map these properties, but they lack the spatial and temporal resolution that is needed to observe many of the relevant details. Here, we present a dynamic atomic force microscopy18–28 method to map quantitatively the nanomechanical properties of live cells with a throughput (measured in pixels/minute) that is ∼10–1,000 times higher than that achieved with quasi-static atomic force microscopy techniques. The local properties of a cell are derived from the 0th, 1st and 2nd harmonic components of the Fourier spectrum of the AFM cantilevers interacting with the cell surface. Local stiffness, stiffness gradient and the viscoelastic dissipation of live Escherichia coli bacteria, rat fibroblasts and human red blood cells were all mapped in buffer solutions. Our method is compatible with commercial atomic force microscopes and could be used to analyse mechanical changes in tumours, cells and biofilm formation with sub-10 nm detail. We began with a study of the harmonic content of atomic force microscope (AFM) microcantilever vibration as it interacts with soft living cells in physiological buffers. Cantilever vibration at a drive frequency vdr alone implies a tip–sample interaction force that is linear with respect to the tip’s motion; sub- and superharmonic tones of vdr , however, suggest nonlinear interaction forces (Fig. 1a). Figure 1b,c presents typical dynamic approach curves acquired using a moderately soft microcantilever (calibrated stiffness k ¼ 0.5 N m21, acoustic excitation) and a soft microcantilever (calibrated stiffness k ¼ 0.065 N m21, Lorentz force excitation) as they approach the surface of a live Escherichia coli bacterium (Fig. 1b) and a live rat fibroblast cell (Fig. 1c) in phosphate buffered saline (PBS) 1× (see Methods). It can be clearly seen that as the cantilever tip is pressed down against the cells, the first harmonic amplitude A1 decreases and the zeroth harmonic magnitude A0 , or mean cantilever deflection, increases rapidly, monotonically and becomes comparable to and often greater than A1. In E. coli, the second harmonic amplitude A2 ≪ A0, A1 and A2 first increases and then decreases as z is decreased, in line with previous observations13,14. However, for rat fibroblasts and red blood cells A2 is undetectable. Higher harmonics beyond the second were undetectable for all live cells tested. This is a general trend we observed while using soft (,0.1 N m21) and moderately soft (,0.6 N m21) microcantilevers on living cells using both acoustic and Lorentz excitation. The zeroth harmonic is the d.c. component of the cantilever vibration signal and is generated due to cycle-averaged tip–sample
interaction forces; this is, in general, different from the quasi-static deflection for an unexcited cantilever (for discussion, see Supplementary Section C). As well as the exceptional zeroth harmonic signal, a special feature of cantilever dynamics interacting with live cells is seen in Fig. 1b,c, where the z piezo extension or sample indentation required to reduce A1 sufficiently to form an image is in fact much larger than A0 , A1. This observation has major implications for the interpretation of amplitude-modulation (AM) AFM data on live cells; at the imaging setpoint, the tip is not intermittently ‘tapping’ the cell as it does on harder surfaces, but rather the tip interacts with the cell over its entire oscillation cycle while maintaining a large net average indentation (d0). Therefore, at a specific imaging amplitude setpoint A 1 ≪ d0. The maps of A0 , A1 , A2 and corresponding phases f1 , f2 can be acquired easily on live cells in buffer solutions, as shown for E. coli (Fig. 2), rat fibroblasts (Fig. 3) and human red blood cells (Fig. 4). It is clear that the strongest, most easily accessible signals that reflect local material properties are those of A0 and f1 , while the A2 , f2 signals are smaller in magnitude on stiffer bacterial cells and below the noise level on softer fibroblast and red blood cells. It can be seen that the A0 images provide maps of local properties at the resolution of tapping-mode AFM (sub-10 nm) and thus A0 , f1 , A2 and f2 are the four channels that must convey information about the local material properties of the cells. The strong contrast in A0 is surprising, because theory29 would suggest that A0 be independent of the local material property. Closer scrutiny reveals that the theory30 assumes a short contact time, an assumption that is inapplicable to live cells. To understand the physics of image formation we have developed a theory that links the multi-harmonic observables A0 , A1 , f1 , A2 , f2 acquired using Lorentz force or magnetic excitation to the local mechanical properties of the cell, as described in detail in Supplementary Section D. Briefly, we find that for soft materials such as live cells (1–1,000 kPa), first harmonic data can be used to extract the linear gradients of the tip–sample interaction forces, that is, stiffness ksample (N m21) and damping csample (N s m21), while the first and second harmonic data can be combined to extract the second-order force gradient ksample,d (N m22) at each point on the cell. These are effective quantities evaluated at the average tip indentation d0 (nm) into the cell. By combining these with the A0 maps it becomes possible to map d0 and the complex loss elastic modulus of the viscoelastic sample (Estorage sample and Esample (Pa)) after assuming a contact mechanics model such as the Hertzian contact model. All the extracted maps of local material properties shown in this Letter use the theory that includes the nearsurface hydrodynamic corrections described in Supplementary Section D (equations S15a–d and S18).
1
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA, 2 Department of Physics and Institute of Nanoscience for Medicine, Oxford Martin School, University of Oxford, Oxfordshire, UK, 3 Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, USA, 4 Weldon School of Biomedical Engineering, West Lafayette, Indiana, USA; † These authors contributed equally to this work. * e-mail:
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Figure 1 | Harmonic content of the AFM microcantilever as it interacts with soft living cells. a, Schematic of an oscillating AFM cantilever interacting with a live cell in liquid, showing that tip–sample force nonlinearity leads to anharmonics at nvn of the drive frequency (n ¼ 0, 2, 3, . . .). b, Plots of cantilever harmonic amplitudes (A0 , A1 , A2) acquired using an acoustically excited Olympus TR800 cantilever on a live E. coli cell. The zeroth harmonic is dominant and the second harmonic amplitude is much smaller, first increasing, then decreasing on approaching the sample. c, Plots of cantilever harmonic amplitudes (A0 , A1) acquired using a Lorentz force excited Olympus TR400 cantilever on a live rat tail fibroblast. Here, the zeroth harmonic is dominant, and the second harmonic amplitude could not be detected at these drive amplitudes. The zeroth harmonic indicates a steady cantilever deflection component induced by the interaction forces. Insets: topography images of the cells from which the curves were acquired, using imaging parameters described in the Methods.
In Figs 2–4, we study the heterogeneities of different kinds of live cells including E. coli, rat tail fibroblasts and human red blood cells in buffer solutions (see Materials and Methods) to extract their local mechanical properties using the theory described previously. It is important to note that the extracted property maps are only valid on the cell where the tip oscillation is small compared to the average indentation, allowing the valid use of the Taylor series representation in the Methods, and not on the substrate where the tip intermittently taps on the sample. 810
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Using the zeroth, first and second harmonic data we extracted the mechanical properties of E. coli cells, namely ksample and csample (refs 27,29), and also the second-order force gradient ksample,d , because their deformation is not described by Hertzian contact mechanics but rather by membrane or shell theory. In these experiments we selected bacterial cells with the same size (lengths 2.1+0.4 mm, widths 0.8+0.1 mm) from a culture in exponential growth phase. The mapped local stiffnesses (N m21) on the bacterial cell are generally greater than those extracted from quasi-static force–distance curves (Supplementary Section E). Moreover, although the maps of ksample , csample show subtle variations (10–20% changes) over the top of the bacterial cell, the second-order force gradient ksample,d map is uniformly small (,1 × 10211 N m22) over the cell and in the region immediately above the cell where the remnants of another bacterial cell are probably present. This indicates a high degree of linearity of the tip–sample force with respect to tip motion on the bacterial cell in comparison to the hard substrate. Small values of ksample,d may also be used as a direct indicator of those regions on the map where the tip–sample nonlinearity is small and the extracted sample properties are reliable. The tip-induced deformation of rat fibroblast cells is reasonably described by Hertzian mechanics, at least for small indentations, and we use equation (S18) (Supplementary Section D) to map loss Estorage sample, Esample. The rat fibroblasts in Figs 3 and 5, which have the biological function of wound healing, clearly display contrasts in mechanical properties on the nucleus and the cytoskeleton, with loss the actin fibres clearly visible in the maps. Estorage sample, Esample in these maps (30–80 kPa) are generally greater than previous studies (1–30 kPa) performed at low strain rates (Supplementary Table S1). However, other experimental methods that evaluate the rotational stiffness of the membrane have demonstrated substantially softer material properties (0.3–1 kPa). This suggests that the cells exhibit fundamentally different material properties across hierarchical length scales. Moreover, the differences in elastic modulus between this study and quasi-static force–distance curves suggests that bacteria and fibroblasts exhibit a significant viscoelastic dependence on excitation frequency or loading rate (Supplementary Section E). (Statistics and material property maps for additional cells are provided in Supplementary Sections E and F.) For red blood cells we find that the cells are very soft with large tip indentations, leading to a significant deviation from Hertzian contact mechanics, so we chose to display the local properties in terms of local stiffness and damping (ksample and csample). In Fig. 4, the red blood cell ksample , csample maps clearly demarcate a stiffer core region (ksample ≈ 0.05 N m21) and a significantly compliant peripheral region (ksample , 0.01 N m21), which is in agreement with their function and adaptability to move through the human body. A comparison of the resolution and speed of the proposed method with existing quasi-static techniques is shown in Table 1. The table clearly shows that the proposed method enables the acquisition of mechanical property maps on live cells using commercial AFM systems at 8–64 times higher resolution and up to 1–75 times faster. Combining the metrics of resolution (pixels) and acquisition time (min), the imaging throughput (pixels/min) of the proposed method in mapping local mechanical properties of cells represents 10–1,000 times improvement compared to existing quasi-static techniques. Furthermore, because the AM–AFM method described herein makes it possible to obtain the mean indentation of the AFM tip, which varies over the sample, the effective modulus is obtained at a given indentation depth. Varying this depth allows one to separate the contributions of the cell wall/membrane, cytoskeleton and focal adhesions. To demonstrate the ability of the proposed method to track timevarying changes in the mechanical properties of cells in Fig. 5, we
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Figure 2 | Multi-harmonic images of E. coli bacteria. a, Topography image of a live E. coli cell scanned using a Lorentz force excited Olympus TR800 cantilever (see Methods). b,c,g,h, Maps of the multi-harmonic data (A0 , f1 , A2, f2) acquired simultaneously with the topography, showing heterogeneities in local mechanical properties. d–f, Maps of the mean indentation (nm), local dynamic stiffness (N m21) and damping (N s m21) can be extracted from the measured zeroth and first harmonic data using the theory described in the text. i, Map of the local second-order force gradient (N m22), which measures the extent of nonlinearity in the local tip–sample forces. This map is extracted using the second harmonic data in conjunction with the zeroth and first harmonic data. Scale bar, 500 nm; 256 × 256 pixel image. The extracted property maps are only valid on the cell where the tip oscillation is small compared to the average indentation and not on the substrate where the tip intermittently taps on the sample.
show the spatiotemporal resolution possible with our technique. We have been able to observe the details of changes in the cytoskeleton structure of a live rat fibroblast cell at tapping-mode AFM resolution when imaged at 1× PBS near-physiological condition at a temperature of 37 8C. The goal of this study was to observe the time frame within which cells show structural changes. Figure 5 shows two whole rat fibroblast live cells at high resolution at three different progressions of time spaced 15 min apart. In the first row, the f1 and Estorage maps clearly show that the two cells are well attached to the surface with a network of actin filaments. In the second row (images taken 15 min later), the progressive disruption of the filament network can be seen accompanied by a slight increase in Estorage. In the third row, a significant increase in Estorage can be observed for both cells, and the filament network of both cells appears more disrupted. Moreover, in the last stage we can see a clear
difference in trace and retrace images, implying a greater degree of detachment from the gelatin-coated surface. In conclusion, we have presented a new method using multiharmonic channels in liquid-environment AM-AFM to obtain quantitative maps and spatial patterns of the local mechanical properties of live cells at 10–1,000 times better imaging throughput (pixels/min) than the standard force–volume method. The combined use of the zeroth, first and second harmonics of cantilever vibration on live cells in buffer solutions can be used to extract and map the effective values of local nanomechanical properties over the cell. We have demonstrated the method with three completely different cell lines: prokaryotic cells, which lack a nucleus or a distinctive cytoskeleton (bacteria); non-tissue forming eukaryotic cells (red blood cells); and wound-healing mammalian eukaryotic cells (3T3 cells). It is anticipated that this multi-harmonic capability
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Figure 3 | Multi-harmonic images of rat fibroblasts. a, Topography image of a live rat tail fibroblast cell scanned in buffer solution using a Lorentz force excited Olympus TR400 cantilever (see Methods). b,c, Maps of (A0 , f1) acquired simultaneously with the topography showing high-resolution contrasts in local mechanical properties over the cell. d–f, Maps of the mean indentation, local storage elastic modulus and local loss modulus can be extracted from the multi-harmonic variables using the theory described in the text. Scale bar, 10 mm; 256 × 256 pixel image. The extracted property maps are only valid on the cell where the tip oscillation is small compared to the average indentation and not on the substrate where the tip intermittently taps on the sample.
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Figure 4 | Multi-harmonic images of a human red blood cell. a, Topography image of a live human red blood cell scanned in buffer solution using a Lorentz force excited Olympus TR400 cantilever (see Methods). The absence of the characteristic biconcave topography is closely correlated to the pH and concentration of the buffer used in the experiment (Supplementary Section G). b,c, Maps of (A0 , f1), showing strong contrasts in local properties between the core and the periphery of the cell. d–f, Maps of mean indentation, local dynamic spring constant and damping can be extracted from the multi-harmonic variables using the theory described in the text. Scale bar, 10 mm; 256 × 256 pixel image. The extracted property maps are only valid on the cell where the tip oscillation is small compared to the average indentation and not on the substrate where the tip intermittently taps on the sample. 812
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Figure 5 | Tracking time-varying changes in the mechanical properties of rat fibroblasts. A sequence of topography and (A0 , f1) images scanned in buffer solution using a Lorentz force excited Olympus TR400 cantilever (see Methods) reveals the spatiotemporal details of the changes in cytoskeleton structure of two live rat fibroblast cells at high resolution (256 × 256 pixels; image size 60 × 60 mm). Corresponding material property maps are also shown. The images clearly show the progression of local mechanical property maps of two rat fibroblast cells over a period of 1 h with 1× PBS buffer. The extracted property maps are only valid on the cell where the tip oscillation is small compared to the average indentation and not on the substrate where the tip intermittently taps on the sample.
Table 1 | Comparison of spatial and temporal resolution of the proposed AM-AFM technique with existing methods. Ref.
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55 N/A N/A 205 7–410
31 32 33 10 34
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In live cells, we can reach sub-10 nm resolution in times of 4–15 min per 256 × 256 pixel scan depending on the type of live cell being scanned. In comparison with classical force spectroscopy (force–volume method), our proposed multi-harmonic amplitude modulation AFM enables local mechanical property mapping of live cells in buffer solutions at 8–64 times higher resolution at up to 1–75 times faster speeds. Combining the metrics of resolution (pixels) and acquisition time (min), the imaging throughput (pixels/min) of our proposed method in mapping local mechanical properties of cells represents 10–1,000 times improvement in imaging throughput compared to the standard force–volume method.
in AFM can be used to study cell motility, morphogenesis, tumour metastasis, neurotrauma due to physical trauma, and the mechanical properties of live bacteria or live cells under the action of new drugs.
Methods Cell culture. E. coli strain DH5a was used as a model Gram-negative organism. Cell suspensions were prepared by inoculating cells from agar plates into 30 ml lysogeny broth (LB) medium and growing them overnight at 37 8C with shaking (120 r.p.m.). Cells were freshly inoculated into new 30 ml LB medium until they reached an optical density of 0.7 at a wavelength of 595 nm. Cell growth was stopped by
harvesting using centrifugation at 3,000 rpm for 2 min and washing four times in PBS 1× , before final re-suspension in PBS 1× pH 7.4. For cell surface immobilization, the cells were re-suspended to an optimal density of 0.3 at 595 nm. The bacterial cell sample was prepared by incubating on a polylysine-coated slide for 30 min with PBS 1× solution at room temperature. Rat fibroblasts (3T3) were cultured in Dulbecco’s modified Eagle’s medium (DMEM) (Invitrogen) containing D-glucose (1,000 mg l21), 10% fetal bovine serum (FBS) (Invitrogen), 1% penicillin-streptomycin (Invitrogen) and 0.1% amphotericin B (Sigma-Aldrich) and expanded in T-75 flasks for use in the AFM experiments. The cells were trypsinized with a 0.5% trypsin/ethylenediaminetetraacetic acid (EDTA) solution and the cell suspension placed on polystyrene plasma-treated 60 mm × 15 mm Petri dishes (BD Falcon) pre-coated with 0.1% gelatin in water. The 3T3 cells were seeded on the dish 1–2 days before the experiment and maintained in an incubator at 37 8C in a 5% CO2 atmosphere. Before dynamic AFM imaging, the cells were rinsed twice with 5 ml PBS (Invitrogen) and then 2 ml of PBS was added to simulate near-physiological conditions during imaging. Fresh human red blood cells were obtained from a healthy volunteer from the group and rinsed once with PBS 1× at pH 7.4 to eliminate soluble glycoproteins present in the plasma. The red blood cells were prepared by incubation over a polylysine-coated slide for 30 min with PBS 1× solution. The cell surface was then gently rinsed with PBS 1× to remove loosely attached cells. AFM experiments were conducted with PBS 1× pH 7.4 at 37 8C. AFM imaging and data analysis. All AFM imaging and elastic measurements of living cells were performed with two systems, an MFP-3D BioAFM located at the University of Oxford and an MFP-3D BioAFM (Asylum Research) mounted on an IX-71 Olympus inverted optical microscope (Olympus) at the Birck Nanotechnology Center at Purdue University. Many different types of soft cantilevers have been used in our experiments, including the Olympus TR/RC400 and Olympus TR/RC 800 in both the acoustic and I-drive Lorentz force excitation modes. In each case, the cantilever stiffness k was calibrated by the thermal noise method. To calibrate the photodiode output sensitivity (nm V21), static force–displacement curves were first acquired on freshly cleaved mica in the PBS buffer solution, and the head was immediately transferred to the actual sample on a lysine- or gelatin-coated substrate, under exactly the same buffer solution. For the case of I-drive cantilevers, the specific experimental imaging parameters (k; resonance frequency far from sample, vfar; Q-factor far from sample, Qfar;
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amplitude of oscillation far from sample, A1far; amplitude of oscillation near sample just before tip–sample interactions begin, A1near; phase lag near sample just before tip–sample interactions begin, f1near; set point amplitude, A1) used for Figs 2, 3, 4 and 5 were as follows (f1far ¼ 90 degrees in all cases): Figure 2 k ¼ 0.4 N m21; vfar ¼ 21.7 kHz; Qfar ¼ 2.5; A1far ¼ 6.13 nm; A1near ¼ 2.4 nm; f1near ¼ 1108; A1 ¼ 1.89 nm; scan rate ¼ 0.8138 Hz/line Figure 3 k ¼ 0.02 N m21; vfar ¼ 8.0 kHz; Qfar ¼ 1.9; A1far ¼ 8.72 nm; A1near ¼ 1.8 nm; f1near ¼ 1168; A1 ¼ 1.35 nm; scan rate ¼ 0.25 Hz/line Figure 4 k ¼ 0.09 N m21; vfar ¼ 8.9 kHz; Qfar ¼ 2.1; A1far ¼ 11.1 nm; A1near ¼ 2.2 nm; f1near ¼ 1158; A1 ¼ 1.87 nm; scan rate ¼ 0.25 Hz/line Figure 5 k ¼ 0.065 N m21; vfar ¼ 7.4 kHz; Qfar ¼ 1.7; A1far ¼ 22.5 nm; A1near ¼ 4.51 nm; f1near ¼ 1158; A1 ¼ 3.16 nm; scan rate ¼ 0.25 Hz/line In each case, the setpoint amplitudes and feedback control gains were chosen to minimize the error maps. The rat fibroblasts and red blood cells were imaged for a size of 70 mm × 70 mm in 8–15 min, whereas the 5 mm × 5 mm images of the E. coli cells typically took 3–5 min to acquire. For all images presented in this Letter, the trace and retrace images of the topography coincided excellently, except for the red blood cells, where both the topography and zeroth harmonic images showed some scanning direction-dependent features due to their extremely low elastic modulus. To acquire the A0 data, the unfiltered photodiode output was passed through a low-pass filter (cutoff frequency in the range 300–500 Hz), and the second lock-in to track the second harmonic data was adjusted to an exact multiple of 2 of the drive frequency with a cutoff frequency of 1 kHz. In converting the measured harmonic maps into local material properties using the theory described in Supplementary Section D, the following important steps were considered. First, because the reflected spot location on the photodiode can drift between images, it is important to offset the acquired A0. In practice, we find that offsetting this by a value that allows the measured A0 to be 0 nm on the hard substrate provides consistent quantitative numbers on the cell. Second, recording the value of f1far on top of the cell is important in reconstructing the local material properties because the near-surface hydrodynamics changes this value from (f1far ¼ 90 degrees).
Received 1 August 2011; accepted 28 September 2011; published online 13 November 2011
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Acknowledgements A.R. acknowledges financial support from the National Science Foundation (grant no. CMMI 0927648; programme manager, E. Misawa) and the Keeley visiting fellowship (awarded by Wadham Collage, University of Oxford) to support his stay at the University of Oxford. S.C. and A.R. also acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC, grant no. EPSRC-EP/H043659/1). S.C. also acknowledges support from the Research Councils UK and Oxford Martin School.
Author contributions A.R. and S.T. are lead authors and contributed equally to this work. A.R. discovered the important experimental channels for material contrast. S.T., A.C., A.S, A.R., E.N. and M.S. developed experimental protocols for sample preparation. A.R., S.T. and S.C. conceived and designed the experiments. A.R. developed the theory and A.C. performed the numerical simulations and developed the code to implement the theory on the acquired AFM images. A.R., A.C., A.S. and S.T. performed the experiments. A.R. and S.T. co-wrote the paper. All authors discussed the results and commented on the manuscript.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://www.nature.com/reprints. Correspondence and requests for materials should be addressed to A.R.
NATURE NANOTECHNOLOGY | VOL 6 | DECEMBER 2011 | www.nature.com/naturenanotechnology
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