Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space
Fig 4
Comparison of ECM compaction between nonlinear computational model and linear latent variable models.
A: Two cells placed 30 μm apart are embedded in a 3-D cylindrical ECM that measures 40 μm in diameter and 100 μm in length. B: The ECM is subdivided along the longitudinal axis into 10 μm length cylinders. The volume (V) of each subdivided cylinder may be estimated at multiple time points during the compaction simulation. C: ECM comparison at the subdivided segments at time t = 10 min, 30 min, and 50 min. Compaction predicted by the latent variable model simulations (blue) agrees well with the full nonlinear simulations (green). The compaction volume is normalized with the initial volume of each segment. The compaction is most significant in-between the cells (the region between the dashed lines in the plots). This is further verified by the corresponding cross-sectional images of the 2-cell cylindrical ECM simulations. Polarity directions of both cells (red arrows initially pointing in arbitrary directions) shift to point inward, indicating that larger stresses are detected in the area between the cells. D: Comparison of single cell (cyan) and two cell (blue) compaction predicted by the latent variable superposition model. As can be seen, the single cell model predicts more localized shrinkage of the ECM volume from its original unstressed state whereas the two cell model shows more global shrinkage extended to within the region between cells.