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On the mechanical response of the actomyosin cortex during cell indentations

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Abstract

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

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Acknowledgements

The authors gratefully acknowledge the support from the Portuguese Foundation of Science under Grant SFRH/BD/107860/2015.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Porto, Portugal

    João P. S. Ferreira, Marco Marques, Marco P. L. Parente & Renato M. Natal Jorge

  2. Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Porto, Portugal

    João P. S. Ferreira, Marco Marques & Renato M. Natal Jorge

  3. Department of Biomedical Engineering, Lerner Research Institute, The Cleveland Clinic, Cleveland, OH, USA

    João P. S. Ferreira, Mei Kuang & Margot S. Damaser

  4. Advanced Platform Technology Center, Louis Stokes Cleveland VA Medical Center, Cleveland, OH, USA

    Margot S. Damaser

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  1. João P. S. Ferreira
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Contributions

JF conducted the AFM experiments, performed data analysis, ran the simulations and wrote the results and discussion. MK designed and produced cellular samples. MM built the 3D geometric models. MP and RN contributed to the discussion of the manuscript. MD supervised and approved the cellular experiments, contributed to the AFM financing and to the writing of the manuscript.

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Correspondence to João P. S. Ferreira.

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Appendix

Appendix

We performed FE simulations of tip–cell contact in a simplified geometry with a flat surface to assess the usability of geometric extraction during AFM scans (Fig. 15). The cell is considered as a 3D cuboidal body with height of \({3.3}\,{\upmu \hbox {m}}\), length of \({20}\,{\upmu \hbox {m}}\) and width of \({20}\,{\upmu \hbox {m}}\). All the remaining considerations regarding the initial and boundary conditions and material parameters were kept the same.

Fig. 15
figure 15

Simulated force curves obtained from the AFM indentations with a spherical tip in a cell surface (from AFM scan) and in a flat surface

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Ferreira, J.P.S., Kuang, M., Marques, M. et al. On the mechanical response of the actomyosin cortex during cell indentations. Biomech Model Mechanobiol 19, 2061–2079 (2020). https://doi.org/10.1007/s10237-020-01324-5

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