Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space
Fig 3
Block diagram of latent variable superposition model and schematic of the relationship between polarity direction, leading edge and direction of maximum stiffness.
A: The ECM changes its latent state with the autoregressive feedback through matrix G as well as with the feedforward path which collects the latent variable states of all the individual cells zc,k(k = 1, …, ncell) through matrices Dk. Each cell changes its latent variable state with autoregressive feedback through A and are exposed to the ECM forces represented by latent vector ze in two separate paths. The path through the cell polarity block and matrix B can be viewed as an “active input”. This feedback path includes a cell’s internal decision as to which direction it extends lamellipodia. In contrast, the other feedback path through a gain matrix C does not have a high-level cell decision, but is reactive, playing a “passive role”. B: The cell polarity direction rotates dynamically in such a way that the polarity vector may align with the direction of the maximum stiffness
. The leading edge of the cell is indicated by a right circular cone with apex angle
having its centerline aligned with the polarity direction. The membrane nodes of the k-th cell within the cone have nonzero lamellipodial forces (
). Membrane nodes outside this cone have zero lamellipodial forces (
).