Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.Author summary: The effect of mechanical resistance on the growth of tumor cells remains today largely unquantified. We studied data from two different experimental setups that monitor the growth of tumor cells under mechanical compression. The existing data in the first experiment examined growing CT26 cells in an elastic permeable capsule. In the second experiment, growth of tumor cells under osmotic stress of the same cell line as well as other cell lines were studied. We have developed an agent-based model with measurable biophysical and cell-biological parameters that can simulate both experiments. Cell cycle progression in our model is a Hill-type function of cell volumetric strain, derived from a bio-mechanical relation between applied pressure and cell compressibility. After calibration of the model parameters within the data of the first experiment, we are able predict the growth rates in the second experiment. We show that that the growth response of cell populations upon externally applied mechanical stress in the two different experiments and over different cell lines can be predicted using the same growth progression function once the growth kinetics of the cell lines in abscence of mechanical stress is known.