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Classification of the growth dynamics of cell populations in vitro
Interdisciplinary Centre for Bioinformatics
University of Leipzig
Michael Block, Eckehard Schöll
Institute for Theoretical Physics
Technical University of Berlin
Jan G. Hengstler
Institute for Toxicology
Medical Faculty of the University of Leipzig
Background: The phenotype of cell populations can be very different and range from sparsely distributed to dense, and from monolayer to multi-layers. The phenotype of multi-layers is explored in a further project (Modelling the effect of deregulated proliferation…, p. 40).
Cell lines that form dense monolayers or quasi-monolayers growing in-vitro have been found to reveal a linear expansion phase in-vitro (Bru et. al., Biophys. J. 2003). The shape of the boundary shows flucturations that can be characterized by macroscopic quantities known from the physics of growing solid interphases. These quantise, so called ‘’critical exponents’’ fingerprints of the microscopic growth and migration processes. Bru et. al. (Phys. Rev. Lett. 1998; Biophys. J., 2003) propose that the growth of tumors in vitro and even in-vivo follow a universal growth dynamics that belong to the ‘’Molecular Beam Epitaxy’’ (MBE) universality class. Based on their observations they suggested a cancer therapy that they in principle have shown to work.
Models: We developed a class of cellular automaton models on a Dirichlet tessellation that are much less run-time extensive than off-lattice models. The rules of the cellular automaton have been chosen according to simulated observations in a single-cell-based off-lattice model in which a cell is parameterized according to measurable cell-biological and cell-biophysical quantities (Drasdo, 2005) to exclude un-biological artefacts. Thereby the cellular automata models permits realistic large scale simulations and systematic sensitivity analyses that are necessary to capture the system behaviour if both, the model assumptions and the model parameters are systematically varied.
Results: We considered a class of models and model parameters so far. Many of these are able to properly explain the growth kinetics observe by Bru et. al.. However, the critical behaviour suggests that the universality class is not MBE, as claimed by Bru et. al. and questioned in a successively appeared comment by Buceta and Galeano (Biophys. J. 2005), but rather KPZ. The latter is also compatible with intrinsic (pushing) growth while the process proposed by Bru et. al. corresponds to a random attachment of cell at the surface and a large migration activity of cells along the surface.
We further used our models to investigate the effect of inhomogeneties between the individual cells or the embedding matrix to explore the potential influence of mutuations that affect the cell-biophysical and cell-biological parameters on the growth kinetics and the multicellular phenotype.
Benefit and outlook: The computer simulations with this efficient method to model the growth dynamics of cell population fulfil two conditions which makes it particularly attractive: 1) it is individual-based hence permits to take into account stochastic fluctuations as well as differences of the cell properties that result from regulation or differentiation. This implies that it permits to study the surface (tumor-environment interface)-effects and the bulk (growth kinetics). Both is difficult in mathematical models that consider instead cell densities. 2) It is nevertheless very fast and permits systematic analyses of wide ranges of the growth dynamics by ‘’screening’’ a wide range of assumptions on cell migration, cell-cell and cell-substrate adhesion, cell division, cell apoptosis etc. at moderate computing time. This is not the case in lattice-free models which are more detailed. We aim at a systematic classification of in-vitro growing cell population and extending the model to capture in-vivo – growth phenomena (in cooperation with J.G. Hengstler).For this the model is extended to capture 3D-phenomena observed in tumor cell lines in which the anoikis-control is lost.