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

doi:10.1002/cm.21561

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 journal › Article › peer-review

4 Scopus citations

Abstract

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 (κ_sub), as a function of the Young's modulus of the substrate (E_Y), 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 language	English (US)
Pages (from-to)	571-585
Number of pages	15
Journal	Cytoskeleton
Volume	76
Issue number	11-12
DOIs	https://doi.org/10.1002/cm.21561
State	Published - 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: http://www.msi.umn.edu . We thank Dr. Patrick W. Alford for the traction force microscopic images of smooth muscle cells published previously in Hald et al. (

Keywords

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

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10.1002/cm.21561

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title = "Modeling distributed forces within cell adhesions of varying size on continuous substrates",

abstract = "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.",

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

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: http://www.msi.umn.edu . We thank Dr. Patrick W. Alford for the traction force microscopic images of smooth muscle cells published previously in Hald et al. ( ",

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doi = "10.1002/cm.21561",

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AU - Hou, Jay C.

AU - Shamsan, Ghaidan A.

AU - Anderson, Sarah M.

AU - McMahon, Mariah M.

AU - Tyler, Liam P.

AU - Castle, Brian T.

AU - Heussner, Rachel K.

AU - Provenzano, Paolo P.

AU - Keefe, Daniel F.

AU - Barocas, Victor H.

AU - Odde, David J.

N1 - 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: http://www.msi.umn.edu . We thank Dr. Patrick W. Alford for the traction force microscopic images of smooth muscle cells published previously in Hald et al. (

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Y1 - 2019/11/1

N2 - 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.

AB - 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.

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KW - cell traction

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KW - traction force microscopy

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

Abstract

Bibliographical note

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