Analysis of the contraction of fibroblast-collagen gels and the traction force of individual cells by a novel elementary structural model

Based on the experimental data of the contraction ratio of fibroblast-collagen gels with different initial collagen concentrations and cell numbers, we analyzed the traction force exerted by individual cells through a novel elementary structural model. We postulate that the mechanical mechanism of the gel contraction is mainly because that populated cells apply traction force to some of the surrounding collagen fibrils with such proper length potential to be pulled straight so as to be able to sustain the traction force; this traction induce the cells moving closely to each other and consequently compact the fibrillar network; the bending force of the fibrils in turn resists the movement. By employing fiber packing theory for random fibrillar networks and network alteration theory, the bending force of collagen fibrils was deduced. The traction force exerted by individual fibroblasts in the gels was balanced by the bending force and the resistance from interstitial fluid since inertial force can be neglected. The maximum traction force per cell under free floating condition is in the range of 0.27-9.02 nN depending on the initial collagen concentration and populated cell number. The most important outcome of this study is that the traction force of individual cells dynamically varies under different gel conditions, whereas the adhesion force between cell and individual fibrils is relatively converging and stable.