Fluidization of tissues by cell division and apoptosis

Abstract

During the formation of tissues, cells organize collectively by cell division and apoptosis. The multicellular dynamics of such systems is influenced by mechanical conditions and can give rise to cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. In the absence of division and apoptosis, we consider the tissue to behave as an elastic solid. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the system is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the expression for the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems using dissipative particle dynamics.

Fig. 1.

Tissue growth simulation. The figure shows the first cell division and the early stages of tissue growth. Each cell is represented by two spheres.

Fig. 2.

Viscosity in a shear simulation. The viscosity is determined for different tissue parameters: standard/reference tissue (red), reduced growth force (B^∗ = 0.5, blue), reduced adhesion (, pink), and reduced noise intensity (, light blue). The viscosity is rescaled to the value obtained for the reference tissue with reference cell division or apoptosis rate. We use simulation units p₀, t₀ and l₀; see SI Text. In these units, the viscosity of the standard tissue is η_ref = 0.15p₀t₀. The asterisks indicate dimensionless parameters that take the value 1 for the standard tissue (Table S1).

Fig. 3.

Diffusion coefficient of cells D in a tissue simulation. Here, the dependence of D on the division rate k_d in the homeostatic state is shown for a reference system (red), simulations with reduced growth force (B^∗ = 0.5, blue), and decreased adhesion strength (, purple). The green line shows a linear fit to the data. The diffusion coefficient is rescaled to the value obtained for the reference tissue with reference cell division or apoptosis rate. In simulation units (see Table S1), .