Abstract
Amoeboid cell migration is characterized by frequent changes of the direction of motion and resembles a persistent random walk on long time scales. Although it is well known that cell migration is typically driven by the actin cytoskeleton, the cause of this migratory behavior remains poorly understood. We analyze the spontaneous dynamics of actin assembly due to nucleation promoting factors, where actin filaments lead to an inactivation of these factors. We show that this system exhibits excitable dynamics and can spontaneously generate waves, which we analyze in detail. By using a phase-field approach, we show that these waves can generate cellular random walks. We explore how the characteristics of these persistent random walks depend on the parameters governing the actin-nucleator dynamics. In particular, we find that the effective diffusion constant and the persistence time depend strongly on the speed of filament assembly and the rate of nucleator inactivation. Our findings point to a deterministic origin of the random walk behavior and suggest that cells could adapt their migration pattern by modifying the pool of available actin.
Highlights
The ability of cells to migrate is one of their most fascinating characteristics
The random walk performed during amoeboid migration is an important aspect of immune cells’ task to scan the organism for pathogens
We have shown that a deterministic, self-organized system describing the actin assembly dynamics in living cells is capable of generating cellular random walks akin to amoeboid migration [10, 21]
Summary
The ability of cells to migrate is one of their most fascinating characteristics. During mesenchymal migration, cells persistently polarize and adhere to the substrate, which leads to persistent directional motion [1, 2]. We use a phase-field approach [23, 24] to study the impact of actin polymerization waves on cell migration. The FHN system can present excitable dynamics, that is, even though the fixpoint is stable against small perturbations, sufficiently large perturbations induce an ‘excursion’ in phase space, before returning to the fixpoint, see Fig 2C This behavior can be observed, when the intersection of the two nullclines is left to the minimum or right to the. Close to the critical values of ωd, the actin-nucleator system forms a spiral wave, see S3 Video These spirals are symmetric and do not deform the phase field. Excitable actin dynamics and amoeboid cell migration the wave speed does not increase with increasing va, Fig 5B. This is in line with the wave velocity, which increases with ωd, see Fig 5C
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