Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro

Abstract

We present a three-dimensional individual cell-based, biophysical model to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations in vitro. The model includes explicit representations of typical epithelial cell growth regulation and control mechanisms, namely 1), a cell-cell contact-mediated form of growth inhibition; 2), a cell-substrate contact-dependent cell-cycle arrest; and 3), a cell-substrate contact-dependent programmed cell death (anoikis). The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. First, we study by variation of these cell-specific parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Second, we apply selective knockouts of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together. Thereby our simulation studies cover the growth behavior of epithelial cell populations ranging from undifferentiated stem cell populations via transformed variants up to tumor cell lines in vitro. We find that the cell-specific parameters, and in particular the strength of the cell-substrate anchorage, have a significant impact on the population morphology. Furthermore, they control the efficacy of the growth regulation and control mechanisms, and consequently tune the transition from controlled to uncontrolled growth that is induced by the failures of these mechanisms. Interestingly, however, we find the qualitative and quantitative growth kinetics to be remarkably robust against variations of cell-specific parameters. We compare our simulation results with experimental findings on a number of epithelial and tumor cell populations and suggest in vitro experiments to test our model predictions.

FIGURE 1

Cell-cell and cell-substrate contact formation. V_A and V_T are the actual and the target cell volumes, respectively. During contact formation R increases to R′ to restore the target volume V_T. The terms x_c and x_s are the terms used in Eq. 2.

FIGURE 2

Top view on cell populations. The first row shows a normal growing population at population size of N₁ = 2000, N₂ = 5000, and N₃ = 10,000. In the second row a growth arrest was applied to all cells at N₂. The growth arrest results in a stress relaxation as explained in the text. In the third row 50% of all cells of the population were removed immediately after the population size reached N₂. This injury is followed by a fast regrowth. In all cases the shaded value of the cells is a marker of the cell target volume V_T. Dark-shaded cells indicate imminent cell division.

FIGURE 3

Properties of the reference cell population (normal growth). (Population size: dotted line, N₁ = 2000; dashed line, N₂ = 5000; and solid line, N₃ = 10.000. (A) Average relative actual cell volume V_A/V₀. (B) Average number density of the cells ρ. The width of the proliferation zone (shaded range, ∼70 μm) is independent of N.

FIGURE 4

Growth kinetics: cell population size N and radius of the population R_P versus time t for the reference population. (Solid lines, normal growth; dashed lines, relaxation after growth arrest; and dotted lines, regrowth after removing 50% of the cells.)

FIGURE 5

Radius R_P and averaged cell age versus time t of populations with different cell-substrate anchorage ɛ_s. (Solid lines, ɛ_s = 600 μN/m; dashed lines, ɛ_s = 400 μN/m; and dotted lines, ɛ_s = 200 μN/m.) Additional vertical sections of the populations at N = 10,000 are shown. Shaded values as in Fig. 2.

FIGURE 6

Top views on cell populations (N = 10,000) with different intrinsic cell growth time τ. Populations with different cell-substrate anchorage are compared. Shaded values as in Fig. 2.

FIGURE 7

Vertical sections through cell populations with N = 5000 cells for a cell substrate anchorage of (A) 600 μN/m and (B) 200 μN/m. The growth regulation states [XXX] are indicated. Shaded level as in Fig. 2.

FIGURE 8

Population radius R_P and averaged cell age versus time t of populations with different threshold compression V_P/V₀. (Full lines, V_P/V₀ = 0.99; dashed lines, V_P/V₀ = 0.95; and dotted lines, V_P/V₀ = 0.90.) Additional vertical sections through the populations at N = 10.000 are shown. Shaded values as in Fig. 2.

FIGURE 9

Stretched elastic substrate. Top view of a reference cell population of size N = 10,000. Whereas the left-hand boundary of the underlying substrate is fixed, the right-hand boundary is moved with a constant velocity of 5 μm/h. (Inset) Number of cells N versus time t. For comparison, the result for static substrate is included (dashed line).