Prediction of the proliferation capacity of adipose-derived stromal cells in vitro

Abstract

In this study, the proliferation of adipose-derived stromal cells was modelled and compared to experimental measurements. The fundamental characteristics of contact-inhibited proliferation were investigated by implementing a reductionist cellular automata model that assumed space-constraints as the only limiting factor of proliferation. The cellular automata were measured in terms of confluency and their mitotic fraction, which meant that the influence of various factors could be investigated independently of the cell count and simulated matrix size. The seeded confluency and the migration of cells were found to have important effects on the mitotic fraction, and it was discovered that this effect could be summarised by calculating a measure of spatial dispersion. While the cellular automata model is based on previously published models, the relationship that was discovered between the mitotic fraction, confluency and spatial dispersion is new. A Markov population model that describes the number of cells as a function of cell cycles and the mitotic fraction was derived from first-principles. A population model with a time or cycle varying mitotic fraction has not previously been formally described in the literature. Two models for the variable mitotic fraction were derived from two well-known population equations: the Verhulst and generalised logistic equations. The Verhulst model provided reasonable approximations for the cellular automata simulations, but could not accurately describe very low or high seeding densities. The generalised logistic model included parameters that had no previously defined biological meaning. A relationship between spatial dispersion and the undefined parameters was discovered, and by including a measure of spatial dispersion, the generalised logistic model more accurately described the cellular automata simulations than the Verhulst model. The relationship between the undefined parameters in the generalised logistic model and confluency and spatial dispersion has not been previously described in the literature. The population model was converted to a function of time to allow comparison to experimental measurements. The Verhulst and generalised logistic mitotic fraction models performed similarly when describing and predicting the experimental data, and no statistically significant difference was found between the root-mean-square error of each model. This could either indicate that spatial dispersion is not a causal predictor of adipose-derived stromal/stem cell (ASC) proliferation in vitro, or that the comparatively low spatial dispersion that was measured had a minimal effect on proliferation. Cells from the same patient that were seeded at different densities were found to have different population limits. Confluency was quantified for the lower population limit, and it was found that a plateau was reached at less than 60% confluency. This indicates that space constraints may not the only limiting factor of proliferation, and that other factors, such as cell-to-cell interactions, may influence the proliferation of ASCs. The population models were tested for their predictive capacity, but it was found that accurate estimates of the population limit required the inclusion of measurements of slowing growth. When considering that slowing growth usually occurs when a population approaches confluency, this limits the predictive utility of the models in a clinical setting.