A thermodynamical model for stress-fiber organization in contractile cells

Abstract

Cell mechanical adaptivity to external stimuli is vital to many of its biological functions. A critical question is therefore to understand the formation and organization of the stress fibers from which emerge the cell's mechanical properties. By accounting for the mechanical aspects and the viscoelastic behavior of stress fibers, we here propose a thermodynamic model to predict the formation and orientation of stress fibers in contractile cells subjected to constant or cyclic stretch and different substrate stiffness. Our results demonstrate that the stress fibers viscoelastic behavior plays a crucial role in their formation and organization and shows good consistency with various experiments.

Figure 1

(Color online) Mechano-chemical potential ${\mu }_{\alpha }^{\mathit{sf},\mathit{mech}}$ in direction α as a function of strain for different stretch frequencies (a). SFs assemble in direction α when ${\mu }_{\alpha }^{\mathit{sf},\mathit{mech}}$ decreases, and disassemble when ${\mu }_{\alpha }^{\mathit{sf},\mathit{mech}}$ increases. Mechanical equilibrium at angle α (b).

Figure 2

(Color online) Effect of an isotropic substrate stiffness increase on cell contractility as predicted by (a) the model and (b) experimental methods. (c) Schematic representation of experimental set up in Ref. , with $N_p\simeq 100$. The effect of constant stretch on the volume fraction of SF ${\phi }_0^{\mathit{sf}}$ in direction α = 0 is shown in (d), and (e) shows the orientation and disassembly of myofibrils (when overstretched) with the arrows representing the direction of stretch. (f) is the angular distribution.

Figure 3

(Color online) Effect of cyclic stretching for ν = 0 (b) (experimental result (a) from Ref. 18) and ν = 0.5 (c) (experimental result (d) from Ref. 13).