- Open Access
Measuring Vibrational Modes in Living Human Cells
PRX Life 2, 013003 – Published 18 January, 2024
DOI: https://doi.org/10.1103/PRXLife.2.013003
Abstract
The question of whether human living cells in physiological conditions exhibit mechanical resonances has remained unresolved for more than 70 years. We here construct a theoretical model to predict how these hypothetical vibration modes of a living cell can modify the stochastic response of a supporting micromechanical resonator. The key signatures that demonstrate the existence of these vibration modes are then searched for experimentally. To this aim, single human breast epithelial cells were attached to the surface of compliant small microcantilevers. Close examination of the frequency spectra of the thermal fluctuations of the microcantilever over a high-frequency range of 1 kHz–1 MHz revealed anomalies that are consistent with our theoretical predictions. We identify the stochastic coupling of the first and third vibration modes of the cell with the torsional and flexural vibration modes of the cantilever, respectively. These mechanical resonances are very broad and are located at 10–30 kHz and 150–180 kHz, respectively. The analysis of the experiments allows us to obtain information on the temporal evolution of several physical properties of the cell, in addition to the resonance frequencies, during the adhesion process—such as the mass, viscoelasticity, and contact area. These results open multiple avenues in our understanding of single cell mechanobiology, vibrational spectrometry of living cells and mechanical destruction of cancerous cells by targeting specific cell frequencies.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (44)
- E. Ackerman, Mechanical resonances of amphiuma erythrocytes, J. Acoust. Soc. Am. 26, 257 (1954).
- H. Kinsloe, E. Ackerman, and J. J. Reid, Exposure of microorganisms to measured sound fields, J. Bacteriol. 68, 373 (1954).
- E. Ackerman, Resonances of biological cells at audible frequencies, Bull. Math. Biophys. 13, 93 (1951).
- P. V. Zinin, J. S. Allen, and V. M. Levin, Mechanical resonances of bacteria cells, Phys. Rev. E 72, 061907 (2005).
- P. V. Zinin and J. S. Allen, Deformation of biological cells in the acoustic field of an oscillating bubble, Phys. Rev. E 79, 021910 (2009).
- E. Gil-Santos, J. J. Ruz, O. Malvar, I. Favero, A. Lemaître, P. M. Kosaka, S. García-López, M. Calleja, and J. Tamayo, Optomechanical detection of vibration modes of a single bacterium, Nat. Nanotechnol. 15, 469 (2020).
- S.-J. Tang, M. Zhang, J. Sun, J.-W. Meng, X. Xiong, Q. Gong, D. Jin, Q.-F. Yang, and Y.-F. Xiao, Single-particle photoacoustic vibrational spectroscopy using optical microresonators, Nat. Photon. 17, 951 (2023).
- E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, The cytoplasm of living cells behaves as a poroelastic material, Nat. Mater. 12, 253 (2013).
- J. Hu, S. Jafari, Y. Han, A. J. Grodzinsky, S. Cai, and M. Guo, Size- and speed-dependent mechanical behavior in living mammalian cytoplasm, Proc. Natl. Acad. Sci. USA 114, 9529 (2017).
- M. L. Yubero, P. M. Kosaka, Á. San Paulo, M. Malumbres, M. Calleja, and J. Tamayo, Effects of energy metabolism on the mechanical properties of breast cancer cells, Commun. Biol. 3, 590 (2020).
- Y. M. Efremov, A. X. Cartagena-Rivera, A. I. M. Athamneh, D. M. Suter, and A. Raman, Mapping heterogeneity of cellular mechanics by multi-harmonic atomic force microscopy, Nat. Protoc. 13, 2200 (2018).
- A. Rigato, A. Miyagi, S. Scheuring, and F. Rico, High-frequency microrheology reveals cytoskeleton dynamics in living cells, Nat. Phys. 13, 771 (2017).
- A. Geltmeier, B. Rinner, D. Bade, K. Meditz, R. Witt, U. Bicker, C. Bludszuweit-Philipp, and P. Maier, Characterization of dynamic behaviour of MCF7 and MCF10A cells in ultrasonic field using modal and harmonic analyses, PLoS ONE 10, e0134999 (2015).
- P. G. Childs, C. A. Boyle, G. D. Pemberton, H. Nikukar, A. S. G. Curtis, F. L. Henriquez, M. J. Dalby, and S. Reid, Use of nanoscale mechanical stimulation for control and manipulation of cell behaviour, Acta Biomater. 34, 159 (2016).
- G. Bas, S. Loisate, S. F. Hudon, K. Woods, E. J. Hayden, X. Pu, R. Beard, J. T. Oxford, and G. Uzer, Low intensity vibrations augment mesenchymal stem cell proliferation and differentiation capacity during in vitro expansion, Sci. Rep. 10, 9369 (2020).
- A. Tijore, M. Yao, Y.-H. Wang, A. Hariharan, Y. Nematbakhsh, B. L. Doss, C. T. Lim, and M. Sheetz, Selective killing of transformed cells by mechanical stretch, Biomaterials 275, 120866 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PRXLife.2.013003 for additional information.
- A. F. Bower, Applied Mechanics of Solids (CRC Press, Boca Raton, FL, 2009).
- P. Kollmannsberger and B. Fabry, Linear and nonlinear rheology of living cells, Annu. Rev. Mater. Res. 41, 75 (2011).
- Y. M. Efremov, W.-H. Wang, S. D. Hardy, R. L. Geahlen, and A. Raman, Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves, Sci. Rep. 7, 1541 (2017).
- G. Fläschner, C. I. Roman, N. Strohmeyer, D. Martinez-Martin, and D. J. Müller, Rheology of rounded mammalian cells over continuous high-frequencies, Nat. Commun. 12, 2922 (2021).
- D. Martínez-Martín, G. Fläschner, B. Gaub, S. Martin, R. Newton, C. Beerli, J. Mercer, C. Gerber, and D. J. Müller, Inertial picobalance reveals fast mass fluctuations in mammalian cells, Nature (London) 550, 500 (2017).
- I. Incaviglia, S. Herzog, G. Fläschner, N. Strohmeyer, E. Tosoratti, and D. J. Müller, Tailoring the sensitivity of microcantilevers to monitor the mass of single adherent living cells, Nano Lett. 23, 588 (2023).
- J. Tamayo, J. J. Ruz, V. Pini, P. Kosaka, and M. Calleja, Quantification of the surface stress in microcantilever biosensors: Revisiting Stoney's equation, Nanotechnology 23, 475702 (2012).
- E. Gil-Santos, D. Ramos, A. Jana, M. Calleja, A. Raman, and J. Tamayo, Mass sensing based on deterministic and stochastic responses of elastically coupled nanocantilevers, Nano Lett. 9, 4122 (2009).
- S.-O. Kim, J. Kim, T. Okajima, and N.-J. Cho, Mechanical properties of paraformaldehyde-treated individual cells investigated by atomic force microscopy and scanning ion conductance microscopy, Nano Convergence 4, 5 (2017).
- J. W. Choi and D. K. Stoecker, Effects of fixation on cell volume of marine planktonic protozoa, Appl. Environ. Microbiol. 55, 1761 (1989).
- R. Cheng, F. Zhang, M. Li, X. Wo, Y.-W. Su, and W. Wang, Influence of fixation and permeabilization on the mass density of single cells: A surface plasmon resonance imaging study, Front. Chem. 7, 588 (2019).
- P. R. Saulson, Thermal noise in mechanical experiments, Phys. Rev. D 42, 2437 (1990).
- M. R. Paul, M. T. Clark, and M. C. Cross, The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: Fluctuations from dissipation, Nanotechnology 17, 4502 (2006).
- C. A. Van Eysden and J. E. Sader, Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order, J. Appl. Phys. 101, 044908 (2007).
- S. Basak, A. Raman, and S. V. Garimella, Hydrodynamic loading of microcantilevers vibrating in viscous fluids, J. Appl. Phys. 99, 114906 (2006).
- J. E. Sader, J. A. Sanelli, B. D. Adamson, J. P. Monty, X. Wei, S. A. Crawford, J. R. Friend, I. Marusic, P. Mulvaney, and E. J. Bieske, Spring constant calibration of atomic force microscope cantilevers of arbitrary shape, Rev. Sci. Instrum. 83, 103705 (2012).
- J. Tamayo, P. M. Kosaka, J. J. Ruz, Á. S. Paulo, and M. Calleja, Biosensors based on nanomechanical systems, Chem. Soc. Rev. 42, 1287 (2013).
- A. Sanz-Jiménez et al., High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators, Commun. Biol. 5, 1227 (2022).
- R. R. Grüter et al., Disentangling mechanical and mass effects on nanomechanical resonators, Appl. Phys. Lett. 96, 023113 (2010).
- M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy, Cell 158, 822 (2014).
- G. Longo, L. Alonso-Sarduy, L. M. Rio, A. Bizzini, A. Trampuz, J. Notz, G. Dietler, and S. Kasas, Rapid detection of bacterial resistance to antibiotics using AFM cantilevers as nanomechanical sensors, Nat. Nanotechnol. 8, 522 (2013).
- D. Cuvelier, M. Théry, Y.-S. Chu, S. Dufour, J.-P. Thiéry, M. Bornens, P. Nassoy, and L. Mahadevan, The universal dynamics of cell spreading, Curr. Biol. 17, 694 (2007).
- A. P. Cuny, K. Tanuj Sapra, D. Martinez-Martin, G. Fläschner, J. D. Adams, S. Martin, C. Gerber, F. Rudolf, and D. J. Müller, High-resolution mass measurements of single budding yeast reveal linear growth segments, Nat. Commun. 13, 3483 (2022).
- E. A. Corbin, O. O. Adeniba, O. V. Cangellaris, W. P. King, and R. Bashir, Evidence of differential mass change rates between human breast cancer cell lines in culture, Biomed. Microdevices 19, 10 (2017).
- A. Pietuch and A. Janshoff, Mechanics of spreading cells probed by atomic force microscopy, Open Biol. 3, 130084 (2013).
- H. Kähler, H. Arthaber, R. Winkler, R. G. West, I. Ignat, H. Plank, and S. Schmid, Transduction of single nanomechanical pillar resonators by scattering of surface acoustic waves, Nano Lett. 23, 4344 (2023).
- S. Tiwari and R. N. Candler, Using flexural MEMS to study and exploit nonlinearities: A review, J. Micromech. Microeng. 29, 083002 (2019).