Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy

TL;DR

This paper presents a fast, accurate 3D traction force microscopy method that measures cellular forces in three dimensions, revealing how cells sense substrate thickness and stiffness through out-of-plane stresses.

Contribution

A novel 3D TFM technique using Fourier analysis for real-time measurement of cellular traction stresses, including out-of-plane components, and analysis of their role in mechanosensing.

Findings

3D traction stresses can extend four times deeper into the substrate.

Out-of-plane traction stresses can indicate substrate stiffness up to 10 times greater.

2D TFM methods may be sufficiently accurate under certain conditions.

Abstract

We introduce a novel three-dimensional (3D) traction force microscopy (TFM) method motivated by the recent discovery that cells adhering on plane surfaces exert both in-plane and out-of-plane traction stresses. We measure the 3D deformation of the substratum on a thin layer near its surface, and input this information into an exact analytical solution of the elastic equilibrium equation. These operations are performed in the Fourier domain with high computational efficiency, allowing to obtain the 3D traction stresses from raw microscopy images virtually in real time. We also characterize the error of previous two-dimensional (2D) TFM methods that neglect the out-of-plane component of the traction stresses. This analysis reveals that, under certain combinations of experimental parameters (\ie cell size, substratums' thickness and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by neglecting the out-of-plane component of the traction stresses. Finally, we consider the cell's mechanosensing of substratum thickness by 3D traction stresses, finding that, when cells adhere on thin substrata, their out-of-plane traction stresses can reach four times deeper into the substratum than their in-plane traction stresses. It is also found that the substratum stiffness sensed by applying out-of-plane traction stresses may be up to 10 times larger than the stiffness sensed by applying in-plane traction stresses.