Finite Element Quantification of the Compressive Forces Induced by Keratinocyte on a Liquid Crystal Substrate

Abstract

The traction force of keratinocytes plays a crucial role in sealing a wound. A new method of transducing keratinocyte traction forces in the form of compression on the surface of a cholesteryl ester liquid crystal substrate has been developed. To quantify the compressive force induced by the keratinocyte via the focal adhesion on the liquid crystal substrate, the finite element method was employed. The phase displayed by the surface of the liquid crystals was studied using cross-polarized microscopy. Physical properties of the liquid crystal, dimensions of the focal adhesions and lateral displacement were determined using Atomic Force Microscopy (AFM) based nano-indentation, immunofluorescence staining and cell relaxation techniques, respectively. Traction forces formed between a pair of focal adhesions of a cell and a liquid crystal substrate were examined in a 3D model via the inclusion of the physical parameters of the liquid crystal in a linear static stress analysis based on the Finite Element Method (FEM). The Young’s modulus of the linear viscoelastic liquid crystal surface was determined at 108 ± 20 kPa and the Poisson’s ratio of the liquid crystals was assumed to be 0.49, close to that of the rubber. Vinculin immuno-staining indicated that focal adhesion related to the accumulations of vinculin in cells cultured on the liquid crystals were 1.03 ± 0.4 μm in length. The relaxation of cell in releasing the axial deformation on the surface of the liquid crystals provided a means of determining the lateral displacement of the liquid crystal induced by the compressive force applied via the focal adhesions. This result also confirmed the use of a compression model for the focal adhesion-liquid crystals interface. The model produced compressive forces in the range of 3–38 nN per focal adhesion. This is comparable to the forces reported in previous studies.