Abstract
Cellular traction force microscopy (TFM) requires knowledge of the mechanical properties of the substratum where the cells adhere to calculate cell-generated forces from measurements of substratum deformation. Polymer-based hydrogels are broadly used for TFM due to their linearly elastic behavior in the range of measured deformations. However, the calculated stresses, particularly their spatial patterns, can be highly sensitive to the substratum’s Poisson’s ratio. We present two-layer elastographic TFM (2LETFM), a method that allows for simultaneously measuring the Poisson’s ratio of the substratum while also determining the cell-generated forces. The new method exploits the analytical solution of the elastostatic equation and deformation measurements from two layers of the substratum. We perform an in silico analysis of 2LETFM concluding that this technique is robust with respect to TFM experimental parameters, and remains accurate even for noisy measurement data. We also provide experimental proof of principle of 2LETFM by simultaneously measuring the stresses exerted by migrating Physarum amoeboae on the surface of polyacrylamide substrata, and the Poisson’s ratio of the substrata. The 2LETFM method could be generalized to concurrently determine the mechanical properties and cell-generated forces in more physiologically relevant extracellular environments, opening new possibilities to study cell-matrix interactions.
Highlights
The mechanical properties of the extracellular environment affect cellular behavior and processes such as cell migration, proliferation, growth, differentiation, and spreading[1,2,3]
We have developed a new traction force microscopy method that enables the simultaneous calculation of the Poisson’s ratio of the gel and the traction forces that a cell exerts on it
Elastic polymer-based hydrogels such as polyacrylamide are broadly used as substrata to calculate the traction stresses exerted by cells
Summary
The mechanical properties of the extracellular environment affect cellular behavior and processes such as cell migration, proliferation, growth, differentiation, and spreading[1,2,3]. Several traction force microscopy methods have been developed to measure the forces exerted by stationary and/ or migrating cells on flat elastic polymer-based hydrogels[9,10,11,12,13,14,15] These gels exhibit a linearly elastic behavior in the range of the small deformations produced by the cells[16,17,18]. The uncertainty in the Poisson’s ratio poses an important limitation to TFM methods since for a given deformation field, the magnitude and the spatial distribution of the traction forces depends on the Poisson’s ratio[25] To address this issue, we have developed a new traction force microscopy method that enables the simultaneous calculation of the Poisson’s ratio of the gel and the traction forces that a cell exerts on it. It is important to note, that this method cannot determine the Young’s modulus of the substratum because this parameter modulates the deformations in the same manner everywhere in the substratum and, it does not affect the deformation patterns
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