Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

Abstract

In mesenchymal cell motility, several migration patterns have been observed, including directional, exploratory and stationary. Two key members of the Rho-family of GTPases, Rac and Rho, along with an adaptor protein called paxillin, have been particularly implicated in the formation of such migration patterns and in regulating adhesion dynamics. Together, they form a key regulatory network that involves the mutual inhibition exerted by Rac and Rho on each other and the promotion of Rac activation by phosphorylated paxillin. Although this interaction is sufficient to generating wave-pinning that underscores cellular polarization comprised of cellular front (high active Rac) and back (high active Rho), it remains unclear how they interact collectively to induce other modes of migration detected in Chinese hamster Ovary (CHO-K1) cells. We previously developed a 6D reaction-diffusion model describing the interactions of these three proteins (in their active/phosphorylated and inactive/unphosphorylated forms) along with other auxiliary proteins, to decipher their role in generating wave-pinning. In this study, we explored, through computational modeling and image analysis, how differences in timescales within this molecular network can potentially produce the migration patterns in CHO-K1 cells and how switching between them could occur. To do so, the 6D model was reduced to an excitable 4D spatiotemporal model possessing three different timescales. The model produced not only wave-pinning in the presence of diffusion, but also mixed-mode oscillations (MMOs) and relaxation oscillations (ROs). Implementing the model using the Cellular Potts Model (CPM) produced outcomes in which protrusions in cell membrane changed Rac-Rho localization, resulting in membrane oscillations and fast directionality variations similar to those seen in CHO-K1 cells. The latter was assessed by comparing the migration patterns of CHO-K1 cells with CPM cells using four metrics: instantaneous cell speed, exponent of mean square-displacement (called α-value), directionality ratio and protrusion rate. Variations in migration patterns induced by mutating paxillin's serine 273 residue was also captured by the model and detected by a machine classifier, revealing that this mutation alters the dynamics of the system from MMOs to ROs or nonoscillatory behaviour through variation in the concentration of an active form of an adhesion protein called p21-Activated Kinase 1 (PAK). These results thus suggest that MMOs and adhesion dynamics are the key ingredients underlying CHO-K1 cell motility.

Excitable dynamics in a molecularly-explicit model of cell motility: Mixed-mode oscillations and beyond

“…This allowed the simulated CPM cell to exhibit three migration patterns that are quite distinct: directed, meandering and non-motile motions. The latter two appeared quite consistent with those migration patterns detected in CHO-K1 cells [31].…”

“…No straight migratory patterns emerge in these CPM cells, because of this episodic activity in protrusions and retractions. This causes the simulated cells in this migration pattern to exhibit meandering trajectories typical of many migrating mesenchymal cells (such as CHO-K1 cells) [31]. This seems to suggest that MMOs are important for generating such migration pattern.…”

“…In the presence of two competitive ECMs, the oscillations became more "random" (due to the presence of a period doubling bifurcation), but the amplitude of such oscillations did not change significantly change. As a result, the migration patterns produced by this model typically did not succeed in combining both exploratory and stationary behaviours in one simulation typically seen in mesenchymal cell motility [31].…”

“…Studying the impact of bistability on cellular polarization has been previously investigated in detail in past modeling studies [37,38]. Because CHO-K1 cells are known to exhibit much more complex migration patterns (manifested as quick increases and decreases in protrusions, indicating variations in the Rac activity) [31], we have decided to increase the complexity of the 1D ODE model, given by Eq. ( 8), to allow the modified model to display a whole set of new and interesting dynamics, including oscillations.…”