Simulation of cell-substrate traction force dynamics in response to soluble factors

Abstract

Finite element (FE) simulations of contractile responses of vascular muscular thin films (vMTFs) and endothelial cells resting on an array of microposts under stimulation of soluble factors were conducted in comparison with experimental measurements reported in the literature. Two types of constitutive models were employed in the simulations, i.e. smooth muscle cell type and non-smooth muscle cell type. The time histories of the effects of soluble factors were obtained via calibration against experimental measurements of contractile responses of tissues or cells. The numerical results for vMTFs with micropatterned tissues suggest that the radius of curvature of vMTFs under stimulation of soluble factors is sensitive to width of the micropatterned tissue, i.e. the radius of curvature increases as the tissue width decreases. However, as the tissue response is essentially isometric, the time history of the maximum principal stress of the micropatterned tissues is not sensitive to tissue width. Good agreement has been achieved for predictions of the vasoconstrictor endothelin-1-induced contraction stress between the FE numerical simulation and the experiment-based approach of Alford (Integr Biol 3:1063–1070, 2011) for the vMTFs with 40, 60, 80 and 100 $\upmu \hbox {m}$ width patterns. This may suggest the contraction stress is weakly sensitive to the tissue width for these patterns. However, for 20 $\upmu \hbox {m}$ width tissue patterning, the numerical simulation result for contraction stress is less than the average value of experimental measurements, which may suggest the thinner and more elongated spindle-like cells within the 20 $\upmu \hbox {m}$ width tissue patterning have higher contractile output. The constitutive model for non-smooth muscle cells was used to simulate the contractile response of the endothelial cells. The substrate was treated as an effective continuum. For agonists such as lysophosphatidic acid and vascular endothelial growth factor, the deformation of the cell diminishes from edge to centre and the central part of the cell is essentially under isometric state. Numerical studies demonstrated the scenarios that cell polarity can be triggered via manipulation of the effective stiffness and Possion’s ratio of the substrate.