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Measuring the elastic modulus of soft culture surfaces and three-dimensional hydrogels using atomic force microscopy


Growing interest in exploring mechanically mediated biological phenomena has resulted in cell culture substrates and 3D matrices with variable stiffnesses becoming standard tools in biology labs. However, correlating stiffness with biological outcomes and comparing results between research groups is hampered by variability in the methods used to determine Young’s (elastic) modulus, E, and by the inaccessibility of relevant mechanical engineering protocols to most biology labs. Here, we describe a protocol for measuring E of soft 2D surfaces and 3D hydrogels using atomic force microscopy (AFM) force spectroscopy. We provide instructions for preparing hydrogels with and without encapsulated live cells, and provide a method for mounting samples within the AFM. We also provide details on how to calibrate the instrument, and give step-by-step instructions for collecting force-displacement curves in both manual and automatic modes (stiffness mapping). We then provide details on how to apply either the Hertz or the Oliver-Pharr model to calculate E, and give additional instructions to aid the user in plotting data distributions and carrying out statistical analyses. We also provide instructions for inferring differential matrix remodeling activity in hydrogels containing encapsulated single cells or organoids. Our protocol is suitable for probing a range of synthetic and naturally derived polymeric hydrogels such as polyethylene glycol, polyacrylamide, hyaluronic acid, collagen, or Matrigel. Although sample preparation timings will vary, a user with introductory training to AFM will be able to use this protocol to characterize the mechanical properties of two to six soft surfaces or 3D hydrogels in a single day.

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Fig. 1: The influence of matrix stiffness and cell-pericellular matrix interactions on cellular behaviors.
Fig. 2: Concept for measuring relative differences between 3D cell structures embedded within 3D hydrogels.
Fig. 3: AFM setup and procedure for carrying out F-D measurements.
Fig. 4: F-D curve interpretation and modeling.
Fig. 5: Anticipated results.

Data availability

All data presented in Fig. 5 are available within the supporting primary research articles (Foyt et al.17, Ferreira et al.22 and Jowett et al.24) or are available from the corresponding author upon reasonable request.

Code availability

The MATLAB code described in this paper is freely available at


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M.D.A.N. acknowledges funding from the London Interdisciplinary Doctoral Programme, which is funded by the BBSRC. S.A.F. acknowledges a Springboard Fellowship from the Imperial College London Institutional Strategic Support Fund, which was established with funding from the Wellcome Trust. G.M.J. acknowledges a PhD studentship from the Wellcome Trust (203757/Z/16/A). L.B. acknowledges funding from a University College London Impact Award and industrial sponsorships. E.G. acknowledges a Philip Leverhulme Prize from the Leverhulme Trust. This work was partly funded by generous support from the Rosetrees Trust. The authors are especially grateful for technical support from R. Thorogate at London Centre for Nanotechnology and to T. Ahmed and S. T. Lust for helpful conversations regarding the MATLAB code.

Author information




M.D.A.N., S.A.F. and G.M.J. developed experimental protocols, designed and conducted experiments, and analyzed the data. M.D.A.N., S.A.F., G.M.J., L.B. and E.G. conceived the ideas and contributed to experimental interpretation. All authors wrote and revised the manuscript.

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Correspondence to Laurent Bozec or Eileen Gentleman.

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Key references using this protocol

Ferreira, S. A. et al. Nat. Commun. 9, 4049 (2018):

Foyt, D. A. et al. Acta Biomater. 89, 73–83 (2019):

Jowett, G. M. et al. Nat. Mater. 20, 250–259 (2021):

Supplementary information

Supplementary Note 1

Supplementary Note and instructions for executing the MATLAB code.

Reporting Summary

Supplementary Software 1

MATLAB code for identifying the contact point of F-D curves

Supplementary Software 2

MATLAB code for calculating E using the Oliver-Pharr model

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Norman, M.D.A., Ferreira, S.A., Jowett, G.M. et al. Measuring the elastic modulus of soft culture surfaces and three-dimensional hydrogels using atomic force microscopy. Nat Protoc 16, 2418–2449 (2021).

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