Three-Dimensional Cellular Traction Force Microscopy and Simulation on a Flat Substrate
Hsuan Yang1*, Wen-hung Chou1,2, Yu-chi Ai1, Giovanni J. Paylaga1,3, Jia-yang Juang4, Keng-hui Lin1
1Institute of Physics, Academia Sinica, Taipei, Taiwan
2Department of Physics, National Taiwan University, Taipei, Taiwan
3Department of Physics, National Central University, Taoyuan, Taiwan
4Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan
* presenting author:Hsuan Yang,
Cellular traction force is involved for a cell to form adhesion, migrate, and differentiation. The technique to map cellular traction stress is referred as traction force microscopy (TFM), which is carried out by tracking the movement of marker particles embedded in a compliant substrate, which a cell exerts force on. Cell traction stress can be reconstructed mathematically from the displacement of particles based on the properties of substrate. To date, most of TFM often measure the shear stress on a planar substrate. Recent advances in TFM reveal the normal stress whose magnitude is not negligible and correlate with cell migration speed [1]. Nevertheless, there was some discrepancy on the distribution of normal stress measured by different groups. Legant et al. [2] show that upward/downward normal stress is at the distal/proximal side of a focal adhesion. Many groups reported the downward normal stress is near the cell nucleus while upward normal stress is at the periphery of the cell. We employed the finite element method to simulate pairs of force dipoles on a circle at different particle density and reconstructed force considering tracking accuracy and random sampling. To save computation resource, we used non-uniform mesh for the model: fine uniform meshes where forces are exerted and coarse expanding meshes where forces should be null. We also simulated the traction recovery with different bead distributions, the bead distributed in the whole gel and on the gel surface only. We found that both reducing tracking accuracy and sampling frequency, i.e., particle density will increase the distance of the force dipoles and explained the discrepancy. Based on this finding, we experimentally performed high-resolution 3D TFM and observed out-of-plane rotational moment around focal adhesion and its dynamics.

[1] H. Delanoƫ-Ayari; J.P. Rieu, and M. Sano, "4D Traction Force Microscopy Reveals Asymmetric Cortical Forces in Migrating Dictyostelium Cells," Phys. Rev. Lett., 105, 248103 (2010).
[2] W.R. Legant et al., "Multidimensional traction force microscopy reveals out-of-plane
rotational moments about focal adhesions," Proc. Natl. Acad. Sci. USA, 110, 881-886 (2013).

Keywords: 3D traction force microscopy, finite element method, live cell