Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 6, pp 2063–2075 | Cite as

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

  • Tamer Abdalrahman
  • Laura Dubuis
  • Jason Green
  • Neil Davies
  • Thomas FranzEmail author
Original Paper


Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus \(\textit{E}_\mathrm{s}\) on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of \(\lambda =1.1\), were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and \(\textit{E}_\mathrm{s}\,=\,\)140 KPa and (2) \(\textit{E}_\mathrm{s}\,=\,10\), 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35\(\text {e}^{-2}\), 0.235\(\text {e}^{-2}\) and 0.6\(\text {e}^{-2}\)) than for FA attachment (0.0952\(\text {e}^{-2}\), 0.0472\(\text {e}^{-2}\) and 0.05\(\text {e}^{-2}\)). For increasing \(\textit{E}_\mathrm{s}\), the largest maximum principal strain was 4.4\(\text {e}^{-4}\), 5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\) and 5.3\(\text {e}^{-4}\) in the membrane, 9.5\(\text {e}^{-4}\), 1.1\(\text {e}^{-4}\), 1.2\(\text {e}^{-3}\) and 1.2\(\text {e}^{-3}\) in the cytosol, and 4.5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\), 5.7\(\text {e}^{-4}\) and 5.7\(\text {e}^{-4}\) in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.


Cell mechanics Focal adhesion Substrate stiffness Finite element modelling 



The research reported in this publication was supported by the National Research Foundation of South Africa (UID 92531 and 93542), and the South African Medical Research Council under a Self-Initiated Research Grant (SIR 328148). Views and opinions expressed are not those of the NRF or MRC but of the authors.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Division of Biomedical Engineering, Department of Human Biology, Faculty of Health SciencesUniversity of Cape TownObservatorySouth Africa
  2. 2.Cardiovascular Research Unit, Chris Barnard Division of Cardiothoracic SurgeryUniversity of Cape TownObservatorySouth Africa
  3. 3.Bioengineering Science Research Group, Engineering Sciences, Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

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