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 (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.
Highlights
Adherent cells exert mechanical forces on the extracellular matrix (ECM) to regulate adhesions, propel their migration [1] and to sense the ECM stiffness by a process generally referred as mechanosensing [2,3]
The past few years have witnessed the development of several 2D traction force microscopy (TFM) methods, which allow investigators to measure only the in-plane components of the traction stresses generated by cells adhering to plane substrata [10,11,12,13,14,15]
This study presents a novel traction force microscopy (TFM) algorithm that provides the 3D traction stresses from measurements of the 3D deformation of a thin layer below the surface of the substratum
Summary
Adherent cells exert mechanical forces on the extracellular matrix (ECM) to regulate adhesions, propel their migration [1] and to sense the ECM stiffness by a process generally referred as mechanosensing [2,3]. 3D TFM methods have been introduced allowing for the determination of the out-of-plane (normal) component of the traction stresses [5,16] These 3D TFM methods are based on numerical calculations performed on large volumetric grids, which can limit their ability to deal with large experimental sets containing many samples. Some of these techniques [16] rely on the acquisition of thick zstacks containing a large number of confocal images, which subjects the cells to high levels of laser radiation, and constrains the temporal resolution of the measurements
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