Three-Dimensional Fourier Monolayer Stress Microscopy

Abstract

Many important biological processes, such as endothelial mechanotransduction of hemodynamic forces and neutrophil extravasation, involve the transmission of stresses across a cell monolayer. During these processes, the monolayer undergoes both lateral distortion due to the in-plane traction forces generated by the cells, and bending due to the out-of-plane component of the traction forces. However, the contribution of this bending to the monolayer stresses has been neglected in the literature. Here, we present a novel technique to determine monolayer stresses that considers both lateral distortion and bending. To illustrate the method, and to quantify the relative importance of the lateral and bending stresses, we measure the monolayer stresses in micropatterned endothelial cell islands of varying sizes and shapes. The cell islands are cultured on flexible polyacrylamide gels embedded with fluorescent beads, which deform due to traction forces exerted by the cells. We measure the three-dimensional gel deformation using previously established 3D Traction Force Microscopy methods, and recover the monolayer stresses from the measured deformation using Kirchoff-Love thin plate theory. The equations are solved numerically in an efficient manner using a Fourier pseudo-spectral method. The boundary conditions corresponding to the geometry of the cell islands are enforced within the Fourier framework using a relaxation iterative method. Our results indicate that, regardless of island shape, the three-dimensional bending stresses are dominant at the center of the island while the lateral stresses are more important near the island edge. Also, comparing the results from islands of different sizes shows that the relative importance of the bending stresses decreases with island size. These results suggest that it is necessary to resolve bending stresses to accurately determine the monolayer stresses, and reveal that the transmission of forces across cell junctions is three-dimensional and more complex than previously believed.