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Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines
Fig 2
Model calibration overview.
Simulations were performed with a center-based model (CBM). In step 1, the contact forces in CBM were calibrated from DCM simulations with parameters (Ecor, hcor, K), yielding a variable effective contact stiffness 
of the CBM for each individual cell depending on the compression level. In step 2 the parameters 
of the CBM for cell line CT26 were determined. Comparing simulations of the CBM with stress-free growth of multicellular CT26 spheroids in experiment I determines most parameters of 
(Fig 1B, full black line). step 3: those cell-line parameters that are affected by the capsule, are specified by comparison with the data from experiment I in presence of the thin capsule. The set of experiment-specific parameters 
(Young modulus and thickness of the capsule) are given by the experimental setting. For the so specified complete set of parameters the simulation reproduces the experimental data I for the thin capsule (Fig 1B, dashed black line), and, after replacement of the capsule thickness, predicts the experimental data for the thick capsule (see Fig 5B). For CT26 cells growing in experiment setting II the cell parameters remain unchanged 
. The deviation of the growth dynamics of stress-free growth from an exponential in experiment II (Fig 1B, full red line) is taken into account by an experiment-specific parameter, namely the proliferative rim. Without any further fit parameter, the model then predicts the correct growth dynamics subject to dextran-mediated stress (Fig 1B, dashed red line). In order to predict the stress-affected growth kinetics of the cell lines j = {CT26, AB6, HT29, BC52, FHI}, their cell cycle duration is modified to capture the stress-free growth analogously to that of CT26 cells in experimental setting II (Fig 1D–1G, full red lines). After determining the parameters, the growth kinetics of these cell lines subject to stress could be predicted (Fig 1D–1G, dashed red lines).
doi: https://doi.org/10.1371/journal.pcbi.1006273.g002