Modeling distributed forces within cell adhesions of varying size on continuous substrates

Jay C. Hou, Ghaidan A. Shamsan, Sarah M. Anderson, Mariah M. McMahon, Liam P. Tyler, Brian T. Castle, Rachel K. Heussner, Paolo P. Provenzano, Daniel F. Keefe, Victor H. Barocas, David J. Odde

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Cell migration and traction are essential to many biological phenomena, and one of their key features is sensitivity to substrate stiffness, which biophysical models, such as the motor-clutch model and the cell migration simulator can predict and explain. However, these models have not accounted for the finite size of adhesions, the spatial distribution of forces within adhesions. Here, we derive an expression that relates varying adhesion radius (R) and spatial distribution of force within an adhesion (described by s) to the effective substrate stiffness (κsub), as a function of the Young's modulus of the substrate (EY), which yields the relation, κsub = R/s EY, for two-dimensional cell cultures. Experimentally, we found that a cone-shaped force distribution (s = 1.05) can describe the observed displacements of hydrogels deformed by adherent U251 glioma cells. Also, we found that the experimentally observed adhesion radius increases linearly with the cell protrusion force, consistent with the predictions of the motor-clutch model with spatially distributed clutches. We also found that, theoretically, the influence of one protrusion on another through a continuous elastic environment is negligible. Overall, we conclude cells can potentially control their own interpretation of the mechanics of the environment by controlling adhesion size and spatial distribution of forces within an adhesion.

Original languageEnglish (US)
Pages (from-to)571-585
Number of pages15
Issue number11-12
StatePublished - Nov 1 2019

Bibliographical note

Funding Information:
). This work was supported by NIH grant U54 CA210190 to D.J.O., by Research Scholar Grant (RSG‐14‐171‐01‐CSM) from the American Cancer Society to P.P.P., by the NIH (U54CA210190 University of Minnesota Physical Sciences in Oncology Center Project 2 to P.P.P. and R01CA181385 to P.P.P.), and by the NSF Graduate Research Fellowship 00039202 to R.K.H. The authors acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper. URL: . We thank Dr. Patrick W. Alford for the traction force microscopic images of smooth muscle cells published previously in Hald et al. (


  • cell migration
  • cell migration simulator
  • cell traction
  • motor clutch model
  • traction force microscopy


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