Intracellular stresses in patterned cell assemblies

Abstract

Confining cells on adhesive patterns allows performing robust, weakly dispersed, statistical analysis. A priori, adhesive patterns could be efficient tools to analyze intracellular cell stress fields, in particular when patterns are used to force the geometry of the cytoskeleton. This tool could then be very helpful in deciphering the relationship between the internal architecture of the cells and the mechanical, intracellular stresses. However, the quantification of the intracellular stresses is still something delicate to perform. Here we first propose a new, very simple and original method to quantify the intracellular stresses, which directly relates the strain the cells impose on the extracellular matrix to the intracellular stress field. This method is used to analyze how confinement influences the intracellular stress field. As a result, we show that the more confined the cells are, the more stressed they will be. The influence of the geometry of the adhesive patterns on the stress patterns is also discussed.

Inference of Internal Stress in a Cell Monolayer

“…The comparison relies on three numerical simulations: in addition to the Viscous and Elastic 1 data sets studied above, another simulation of an elastic tissue, named Elastic 2, has been performed, using the elastic coefficients E = 10 kPa µm and ν 2D = 0.5, as advocated in [36]. Each variant of MSM assumes a tissue rheology, and thus relies on a set of material parameters.…”

“…Each variant of MSM assumes a tissue rheology, and thus relies on a set of material parameters. To perform MSM and MSMu, we use the same tissue elastic coefficients as in the Elastic 1 [26] and Elastic 2 [36] simulations respectively. To perform MSMη, we use the same tissue viscosity coefficients as in the Viscous simulation.…”

“…Coefficients of determination R 2 σ obtained with BISM, MSM, MSMu and MSMη (see text for definitions). Traction force data sets were obtained with material parameter values η = 10 3 kPa µm s, η = η (Viscous); E = 10 2 kPa µm, ν 2D = 0.5 [26] (Elastic 1 ), E = 10 kPa µm, ν 2D = 0.5 [36] (Elastic 2 ). A white noise of relative amplitude 5% is added in all cases.…”

“…Numerical data (first column) for: (a) pressure; (b) shear stress; (c) stress orientation (angle θ between the principal stress eigenvector and the x axis, θ ∈ [−π/2, π/2]) are compared with inferred data obtained with BISM, MSM, MSMu and MSMη (see text for definitions, spatial resolution: 4 µm). Traction force data sets were obtained with material parameter values η = 10 3 kPa µm s, η = η (Viscous); E = 10 2 kPa µm, ν 2D = 0.5 [26] (Elastic 1 ), E = 10 kPa µm, ν 2D = 0.5 [36] (Elastic 2 ). A white noise of relative amplitude 5 % is added in all cases.…”

Traction force microscopy on soft elastic substrates: A guide to recent computational advances

“…This concept has been implemented both for forces between few cells [40,41] and for forces within laterally extended cell monolayers [42,43]. In the latter case (monolayer stress microscopy), one assumes that the cell monolayer behaves like a thin elastic film coupled to the underlying matrix by stresses (alternatively one can assume coupling by strain [44,45]). Combined with a negative pressure that represents the effect of actomyosin contractility, the physics of thin elastic films is now increasingly used to describe forces of cell monolayers in general [46][47][48][49].…”