Cortical cell stiffness is independent of substrate mechanics


Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This ‘soft substrate effect’ leads to an underestimation of a cell’s elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a ‘composite cell–substrate model’. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes.

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Fig. 1: Quantification of substrate displacements in AFM indentation measurements of cells.
Fig. 2: Substrate displacement and stress distribution under cells caused by AFM indentation measurements.
Fig. 3: Numerical validation.
Fig. 4: Experimental validation using PAA beads.
Fig. 5: Application to primary microglial cells.
Fig. 6: Comparison of normalized published and current data analysed by the Hertz model and hypothesis.

Data availability

The data underlying this study are available from the authors upon reasonable request. The AFM force–distance curves raw data can be found at

Code availability

Codes used for processing of AFM and confocal laser scanning microscopy raw data can be found at Comsol models can be found at


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We thank P. Janmey, B. Fabry and U. Schwarz for critical discussions and comments on the manuscript, T. Schäffer for personal support and A. Winkel (JPK) for technical support, as well as J. Tavares and M. Kotter for microglial cells and B. Colledge for NIH 3T3 fibroblasts. We acknowledge funding from the German Science Foundation (DFG grant numbers RH 147/1-1 to J.R., EXC 1003 CiM to T.B.), the Herchel Smith Foundation (postdoctoral fellowship to A.D.), the Royal Society (University Research Fellowship to K.J.C.), the UK EPSRC (programme grant number EP/P030017/1 to M.C.G.), the Human Frontier Science Program (HFSP grant number RGP0018/2017 to T.B.), the European Research Council (consolidator grant numbers 772798 to K.J.C., 771201 to T.B., 647186 to G.C. and 772426 to K.F.), and the UK BBSRC (equipment grant number BB/R000042/1 to G.C. and research project grant number BB/N006402/1 to K.F.).

Author information




J.R. and K.F. conceived the study. J.R. conducted all AFM experiments, analysed all AFM data and developed the model. A.D. conducted all optical imaging and traction force microscopy experiments and analysed data. B.W. and T.B. custom-designed PAA beads. N.M.K. and M.C.G. conducted and analysed ERISM measurements. K.J.C. helped with imaging and data analysis. G.C. helped with AFM experiments. All authors discussed the study. J.R. and K.F. wrote the paper with contributions from all co-authors.

Corresponding authors

Correspondence to Johannes Rheinlaender or Kristian Franze.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–10, discussion and refs. 51–56.

Reporting Summary

Supplementary Video 1

Indentation of a microglial cell cultured on a stiff substrate by AFM.

Supplementary Video 2

Indentation of a microglial cell cultured on a soft substrate by AFM.

Supplementary Video 3

Indentation of a fibroblast cultured on a stiff substrate by AFM.

Supplementary Video 4

Indentation of a fibroblast cultured on a soft substrate by AFM.

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Rheinlaender, J., Dimitracopoulos, A., Wallmeyer, B. et al. Cortical cell stiffness is independent of substrate mechanics. Nat. Mater. 19, 1019–1025 (2020).

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