MODELING BIOLOGICAL GEL CONTRACTION BY CELLS - MECHANOCELLULAR FORMULATION AND CELL TRACTION FORCE QUANTIFICATION

Traction forces developed by most cell types play a significant role i n the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering c ell properties and extracellular mechanical matrix responses. Recent e xperimental devices elaborated for measuring cell traction on extracel lular matrix use cell deposits on a piece of gel placed between one fi xed and one moving holder. We formulate here a mathematical model desc ribing the dynamic behaviour of the cell-gel medium in such devices. T his model is based on a mechanical force balance quantification of the gel viscoelastic response to the traction forces exerted by the diffu sing cells. Thus, we theoretically analyzed and simulated the displace ment of the free moving boundary of the system under various condition s for cells and gel concentrations. This model is thee used as the the oretical basis of an experimental device where endothelial cells are s eeded on a rectangular biogel of fibrin cast between two floating hold ers, one fixed and the other linked to a force sensor. From a comparis on of displacement of the gel moving boundary simulated by the model a nd the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are propo sed and the corresponding force quantifications are compared to the tr action force measurements reported for various kind of cells with the use of similar or different experimental devices.