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Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations

Jörg Galle, Dirk Drasdo
Interdisciplinary Centre for Bioinformatics
University of Leipzig

Markus Löffler
Institute for Medical Informatics, Statistics and Epidemiology
University of Leipzig

Background: Epithelial tissues are organized in sheets that form protective barriers at inner and outer surfaces of organisms. For diagnosis and therapy of many diseases that involve epithelia it is essential to understand the principles underlying epithelial organization. This process is a result of cell division, cell differentiation, programmed cell death, and cell migration involving a complex interplay between different interaction, regulation and control mechanisms on the cellular and sub-cellular scale.

Figure 1: Colony growth. A) Model regulation mechanisms: I) cell-cell contact mediated inhibition of growth II) anchorage dependent growth, III) anchorage dependent programmed cell death. V indicates the cell volume and Ac the cell-substrate contact area. Vp is the threshold volume that triggers contact inhibition of growth. B) Top view on growing Widr populations after 14 days stained by Brdu. C) Simulation results related to B). Scale Bars: 200Ám.
Models: We develop a novel class of 3d individual cell based, computer models to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations. The models include explicit representations of typical epithelial cell growth regulation and control mechanisms (see Fig 1). We apply our model to describe colony growth of a number of different colorectal carcinoma cell lines such as Widr (Fig. 1, cooperation with G. Aust). The models base on Langevin dynamics in an overdamped regime and account for short-range interaction exclusively. We represent an isolated cell by a sphere of radius R. Each cell is characterised by an intrinsic target volume VT, which is the volume the cell adopts if it is isolated. If a cell gets into contact with the substrate or with other cells, its shape changes by flattening at the contact areas. To allow for a balance of the cell volume reduction due to flattening at the contact zone we introduce the cell radius R as a dynamic variable, which increases during contact formation to adjust the actual volume VA to the target volume VT of the cell. The displacement and volume change of the cells are modelled in separate equations. For example, for the translational cell movement of cell i with velocity vi=dri/dt holds:


Here, Fif is the sum over all friction forces for the translational movement, FiD the sum over the deterministic forces (cell deformation, compression, adhesion), and FiS the stochastic force (cell migration) on the centre of cell i. Ci,j is a (3x3) friction coefficient matrix for the friction between cells i and j, Ci,s denote the corresponding quantities for the friction between cell i and the substrate s. The friction with the surrounding medium is approximated by the constant cM.
The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. We study by variation of these parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Furthermore, we apply selective knock-outs of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together.

Results: 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 (Fig. 2). Furthermore, they control the efficacy of the growth regulation and control mechanisms and consequently tune the transition from controlled to uncontrolled growth induced by failures of these mechanisms. In contrast we find that the qualitative and quantitative growth kinetics is remarkably robust against variations of cell-specific parameters. Our studies demonstrate that IBMs, are capable of explaining the complex pattern formation and growth processes of cell populations. In particular, they were shown to be capable of describing the large variety of growth scenarios of colorectal carcinoma cell lines. Ongoing work focuses on additional modes of active cell motion.
Figure 2: Loss of growth control. Vertical sections through cell populations with 5000 cells for a cell substrate anchorage of (A) 200 ÁN/m and (B) 600ÁN/m. Blue cells are cells with substrate contact, green cells are cells without that contact. In all cases the colour saturation of the cells is a marker of the cell target volume VT. Fully saturated cells indicate imminent cell division.

Galle, J., M. Loeffler and D. Drasdo. 2003
On the temporal-spatial organisation of epithelial cell populations in vitro.
In: Mathematical Modelling and Computing in Biology and Medicine. MIRIAM, ed. V. Capasso, 413-420.
Galle J, Loeffler M, Drasdo D. 2005
Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro.
Biophys J. 2005. 88(1): 62-75.