Dynamics of Stress Fibers Turnover in Contractile Cells

Abstract

Numerous experiments have shown that contractile cells like fibroblasts adapt their internal structure to their microenvironment by generating and orienting a network of stress fibers (SFs). This phenomenon has been modeled in previous studies with stability analysis through calculation of the fiber's potential or strain energy, where SFs are assigned a constant elasticity. Recent experiments have shown that the elasticity in SFs is rate dependent, resulting in a different stress fiber organization under constant or cyclic stretching. Here, a thermodynamical model that describes the anisotropic polymerization of the contractile units into SFs via the calculation of the mechanochemical potential of the two constituents is proposed. The stretch-dependent part of the SF potential is made of two terms that describe the passive and active behavior of the SF. In this paper, it is shown that the contributions of these two terms vary widely under constant or cyclic stretching as the SFs exhibit a rate-dependent elasticity and lead to two very different anisotropic SF organizations. It is further demonstrated that the substrate stiffness as well as its Poisson's ratio and anisotropy play a crucial role in the formation and organization of the SFs, consistent with what has been observed in various experiments.

Keywords: Biophysics; Contractile cells; Cyclic strength; Cyclic stretch; Fibers; Mechanobiology; Stress; Stress fiber; Thermodynamics; Tissue engineering.

Fig. 1

(a) System modeled: cells with maximum confluence on a substrate subjected to various stimuli; (b) stimuli induce a production of SF in the cell; and (c) SF exhibit contractile capability (σ*), linear elasticity (E_l), and stress relaxation (E_ν) at long time scales

Fig. 2

(a) General view of the system; (b) corresponding to the slice at angle α defined in (a) (σ^s is the stress generated by the deformation of the substrate and σ^SF is the active and passive stress of SFs)

Fig. 3

(a) Effect of substrate stiffness on the mechanochemical potential ${\mu }_{\alpha }^{\text{SF,mech}}$ (shaded area); (b) contractile stress generated by the cell as a function of the substrate’s stiffness; and (c) experimental results from Ghibaudo et al. (2008)

Fig. 4

Polar plot of the angular volume fraction ${\varphi }_{\alpha }^{\text{SF}}$ showing the effect of the anisotropic substrate on the orientation of SFs; ratio r of the stiffnesses in the directions α = 0 and 90° represents the substrate anisotropy

Fig. 5

General trend for ${\mu }_{\alpha }^{\text{SF,mech}}$ as a function of strain for constant stretch (shaded area)

Fig. 6

(a) Effect of constant stretch on the total volume fraction of SF ϕ^SF; (b) reproduction of the experimental results (Simpson et al. 1999) with the arrows representing the stretch direction

Fig. 7

General trend of the mechanochemical potential ${\mu }_{\alpha }^{\text{SF,mech}}$ in the case of cyclic stretching

Fig. 8

(a) Effect of cyclic stretching for ν ranging from 0; (b) reproduction of experimental result from Kaunas et al. (2005) to 0.5; (c) reproduction of experimental result from Takemasa et al. (1997)