Exploring the Energetics of Cell Movement via Finite Element Analysis

Abstract Two different cytoskeleton architectures corresponding to the mesenchymal cell and the fibroblast cell, are proposed in this work. They are subsequently modelled by Finite Elements in ANSYS APDL and are tested in two different constraint cases: polarized and unpolarized. Polarization in the context of this work is when the cell disintegrates all its focal adhesions except the ones at the leading edge and the tail edge. The opposite of a polarized cell is defined as an unpolarized cell, which has all the focal adhesions intact. The focal adhesions were simulated by constraining the nodes in x and y axes to prevent movement along the substrate surface. The FE models are tested by displacing three nodes a certain distance to simulate the movement of the leading edge of the cell. The strain energy was measured at each displacement and was analysed with both linear and nonlinear (geometric) analysis. The increase in strain energy from the stationery state was of interest as work energy principle can be used to see how much work a cell does to move a certain distance, discounting non-conservative forces. The increase in strain energy thus allows the comparison of the energy efficiency of the cells when they move a certain distance. The nonlinear analysis was having issues with convergence so through experimentation, the Arc Length Method extension was found to be the optimal adaptation for the solver to improve the convergence of the solution.The strain energy data suggests that polarization allows both types of cells to move in an energy efficient manner compared to the unpolarized cases. Changing the cytoskeleton architecture from the mesenchymal type to fibroblast type also allows the cell to move in a more energy efficient manner. Comparison between the linear and nonlinear analysis shows that the linear analysis underestimates the strain energy stored and the stiffness of the cell. When the front part of the cell was displaced 4 microns, the residual forces on the nodes were measured. The nodal forces show a ‘V’ shape at the leading edge for both cells in both constraint cases, which explains why the new pseudopod forms from the bifurcation of the leading-edge pseudopod using the theory of force dependent maturation of focal complexes. The only exceptions to this trend were the polarized cases for both cells in the linear analysis.