Fig. 5: An active phenomenological model characterizes the bimodal stress response of the cell pair under different strain rates.

a A schematic illustration of the active phenomenological model which includes a spring labeled \({E}_{1}\) symbolizing the elastic modulus of the cell pair. The model also incorporates an active branch, consisting of an active element \({\sigma }_{A}\) to signify the contractile stress generation in the actomyosin network, along with a dashpot labeled \({\eta }_{A}\), to represent the dissipation of the force generated by the myosin motor proteins through a viscous-like mechanism. b The average relaxed and tensioned stress-time curves of the cell pairs stretched to 50% strain at 25% s⁻¹ are fitted using Eq. (6) according to the active model. c The values of \({\eta }_{A}\) are calculated for tensioned curves at high rates (i.e., 10%s⁻¹, 25%s⁻¹, and 50%s⁻¹). These values are then averaged and kept as a constant for the relaxed curves. d The values of \({\sigma }_{A}\) obtained from fitting the individual curves for different rates with Eq. (6). e, f Comparing the values of \(B\) (e) and \(C\) (f) derived from fitting the empirical and the active (\(B={E}_{{eq}}\) and \(C=\left(\frac{1}{{\varepsilon }_{0}}\right)\cdot \frac{{\sigma }_{A}-{E}_{{eq}}\cdot {\varepsilon }_{0}}{\tau },\) where \({E}_{{eq}}=\frac{{E}_{1}\cdot {E}_{b}}{{E}_{1}+{E}_{b}}\) and \(\tau =\frac{{\eta }_{A}}{{E}_{{eq}}}\)) models on the average of the relaxed and tensioned curves for the data collected for 50% strain applied at various rates.