Two‐Dimensional Diffusion Limited System For Cell Growth

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Abstract
A new cell system, designed to supplement multicellular spheroids as tumour analogues, was analysed theoretically and experimentally. This ''sandwich'' system is a single layer of cells, subject to self-created gradients of nutrients and metabolic products. Due to these gradients the sandwich system develops a border of viable cells and an inner region of necrotic cells corresponding to the viable rim and the necrotic center of a spheroid. However, sandwiches differ from spheroids in several ways. All the cells in the sandwich can be microscopically viewed during the entire experiment. In sandwiches there is no three-dimensional cell to cell contact. Also, the gradients are less steep in our sandwich system, so the width of the viable region in a sandwich is about 10 times as large as the width of the viable rim in a spheroid. Indeed, in sandwiches the experimenter has some control over the steepness of the gradients and thus can vary the width of this viable border. We used DNA labelling studies and flow cytometry along with visual observation to analyse the system. Our experiments show that the observed cell necrosis, similar to that found in spheroids, is due to diffusion limitations. The results are consistent with the idea that oxygen deprivation stops cell cycling and, when extreme and prolonged, leads to necrosis. The possibility that substances other than oxygen are involved is not excluded by the data. The data also suggests that in the final, near-equilibrium state the average overall oxygen consumption rate for the viable sandwich population may be about one-quarter of that for an exponentially growing population of the same cell line.