Collective cell migration and residual stress accumulation: Rheological consideration

Mechanical Oscillations in 2D Collective Cell Migration: The Elastic Turbulence

“…The inflow for v r < 0 (where v r is the radial velocity component) corresponds to the compression and the outflow for v r > 0 corresponds to extension. Multicellular systems are much complex than polymer solutions, but their viscoelastic nature significantly influences cell rearrangement and should not be neglected [8,9]. Flow instabilities generated during collective cell migration show similar rheological properties as ones recognized for other viscoelastic systems.…”

“…The viscoelastic force arises as a consequence of the residual stress accumulation. While stress relaxation time corresponds to a time scale of minutes, the residual stress accumulation corresponds to a time scale of hours [8,9,27]. The parameters R e and W i can be estimated based on experimental data from the literature such as (1) the cell velocity v x ∼ 0.5 µm min [2]; (2) the characteristic length L =v x τ (where τ is the period of oscillation equal to τ ≈ 4 − 6 h, [2]); (3) the density of cells could be close to the density of water, i.e., ρ ∼ 1 g cm 3 ; (4) the viscosity of epithelium η = 4.4 × 10 5 Pas [27]; (5) the stress relaxation time τ R = 3 − 14 min [24]; and (6) the characteristic time of residual stress accumulation corresponds to the period of mechanical oscillations τ [2,3].…”

“…Consequently, the modeling consideration accounts for the following steps: (1) the expression of cell velocity − → v c as the rate of change the cell displacement field, i.e., d − → u c dτ (where − → u c is the cell displacement field) [8,9]; (2) the formulation of local cell shear and volumetric strainsε cS andε cv , respectively, as a function of the cell displacement field [8,9]; (3) the introduction of a constitutive viscoelastic model for cellsσ c =σ c (ε c ) (wherẽ σ c is the cell stress andε c is the cell strain) [28,29]; (4) the formulation of the rate of change the matrix displacement field [29,30], (5) the formulation of local matrix shear and volumetric strainsε mS ,ε mv , respectively, as a function of the matrix displacement field [29,30]; (6) the discussion of the rheological behaviors of various matrix applied as a substrate for 2D collective cell migrationσ m =σ m ε m (whereσ m is the matrix stress andε m is the matrix strain) [2,3,30] as the viscoelastic force, the traction force, and the surface tension force based on modified model proposed by Murray et al [15]; and (10) the formulation of the interrelation between the cell velocity − → v c and the forces that influences generation of propagative waves and standing wave based on the corresponding momentum balance. Discussion of cell longtime rearrangement in the context of the elastic turbulence proposed by Groisman and Steinberg [23] is the main goal of this paper.…”

“…Viscoelasticity of multicellular systems caused by collective cell migration has been considered on two time scales [8,9]. The stress relaxation happens at a short-time scale t, whereas the long time scale τ is important for tracking the strain change and the residual stress accumulation as shown in Figures 2A,B for (A), a monolayer free expansion inspired by Serra-Picamal et al [2], and (B), swirling motion of a confluent monolayer inspired by Notbohm et al [3].…”

“…Collective cell migration within a monolayer induces spontaneous generation of mechanical waves [1][2][3][4][5]. A more comprehensive account of oscillatory patterns generation is essential for a wide range of biological processes such as morphogenesis, wound healing, regeneration, and cancer invasion [6][7][8][9]. Specifically, in this review, we concentrate on mechanical oscillations, a term we use to identify all periodical fluctuations of mechanical parameters, such as cell velocity, the resulting strain, substrate tractions, and stresses.…”