Abstract
The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.
Highlights
The dynamics of the actin cytoskeleton determines internal cell structure, cell shape, and cell motility
In summary we have explored extensions of the wave-pinning model (WP) (Mori et al 2008, 2011) that coupled the non-conservative variant proposed by Verschueren and
We found that the combined model (CM) borrows features from both, with moving peaks and wave trains, as well as more complex hybrid dynamics
Summary
The dynamics of the actin cytoskeleton determines internal cell structure, cell shape, and cell motility. The interactions of Rac, Rho, Cdc, and other molecular players has been modeled in previous work (Mori et al 2008; Verschueren and Champneys 2017; Holmes et al 2012a; Holmes and Edelstein-Keshet 2016; Zmurchok et al 2018; Walther et al 2012; Edelstein-Keshet et al 2013; Jilkine and Edelstein-Keshet 2011; Otsuji et al 2007) both in 1D and 2D. These studies made different modelling decisions and ranged from simple (Mori et al 2008) to detailed (Marée et al 2008). This motivates studying minimal models that showcase the possible realms of predicted behavior
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