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Boundary Stiffness Regulates Fibroblast Behavior in Collagen Gels

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Abstract

Recent studies have illustrated the profound dependence of cellular behavior on the stiffness of 2D culture substrates. The goal of this study was to develop a method to alter the stiffness cells experience in a standard 3D collagen gel model without affecting the physiochemical properties of the extracellular matrix. A device was developed utilizing compliant anchors (0.048–0.64 N m−1) to tune the boundary stiffness of suspended collagen gels in between the commonly utilized free and fixed conditions (zero and infinite stiffness boundary stiffness). We demonstrate the principle of operation with finite element analyses and a wide range of experimental studies. In all cases, boundary stiffness has a strong influence on cell behavior, most notably eliciting higher basal tension and activated force (in response to KCl) and more pronounced remodeling of the collagen matrix at higher boundary stiffness levels. Measured equibiaxial forces for gels seeded with 3 million human foreskin fibroblasts range from 0.05 to 1 mN increasing monotonically with boundary stiffness. Estimated force per cell ranges from 17 to 100 nN utilizing representative volume element analysis. This device provides a valuable tool to independently study the effect of the mechanical environment of the cell in a 3D collagen matrix.

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Acknowledgments

The authors would like to thank Jacquelyn Youssef for her technical assistance in the laboratory. This work was supported in part by the American Heart Association Grant SDG 0535265N (KLB) and the National Institutes of Health 1R15HL087257 (KLB). The authors have no financial relationships that represent conflicts of interest.

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Authors and Affiliations

  1. Department of Biomedical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609, USA

    Jeffrey John, Angela Throm Quinlan & Kristen Billiar

  2. Graduate School of Biomedical Sciences, University of Massachusetts Medical School, Worcester, MA, 01655, USA

    Angela Throm Quinlan

  3. Department of Civil Engineering, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Chiara Silvestri

  4. Department of Surgery, University of Massachusetts Medical School, Worcester, MA, 01655, USA

    Kristen Billiar

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  1. Jeffrey John
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Correspondence to Kristen Billiar.

Appendix

Appendix

Estimation of the Force Per Cell Using the RVE Method

To estimate the average force per cell, we assume that the cells are oriented randomly in the plane of the tissue, and that each cell pulls predominantly in one direction (i.e., bipolar cells). Using the RVE method, the total force measured along one axis, F T, can be computed from the average force per cell, F C, by integration:

$$ F_{\text{T}} = \int_{{ - {\frac{\pi }{2}}}}^{{{\frac{\pi }{2}}}} {{n_{\text{E}}}R(\theta )F_{\text{C}} \cos (\theta )d\theta } $$
(A.1)

where n E is the number of cells in parallel (RVEs a cross-section), and R(θ) is the angular distribution of cells. If the distribution of cells orientations is assumed uniform (constant with θ), and we note that the integral of R(θ) = 1 by definition, then:

$$ F_{\text{T}} = n_{\text{E}} \left[ {\sin {\frac{\pi }{2}} - \sin {\frac{ - \pi }{2}}} \right]F_{\text{C}} = 2{n_{\text{E}}}F_{\text{C}}. $$
(A.2)

Thus, F C = F T/2n E in our system.

To determine the size of an RVE, the final volume of the gel is calculated by multiplying the projected area (from digital images, e.g., Fig. 8a) by the thickness (from histological sections, e.g., Fig. 8d) and is divided by the total number of cells in the gel. The number of cells (RVEs) contributing to the total force is estimated by dividing the cross-sectional area in the central region of interest perpendicular to the axis on which force is measured by the cross-sectional area of the RVE which is assumed to be a cube. As the shape of the contracted gel is roughly cruciform, the width of the region of interest is approximately half of the maximum dimension of the gel.

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John, J., Throm Quinlan, A., Silvestri, C. et al. Boundary Stiffness Regulates Fibroblast Behavior in Collagen Gels. Ann Biomed Eng 38, 658–673 (2010). https://doi.org/10.1007/s10439-009-9856-1

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