Abstract
During migration cells exhibit a rich variety of seemingly random migration patterns, which makes unraveling the underlying mechanisms that control cell migration a daunting challenge. For efficient migration cells require a mechanism for polarization, so that traction forces are produced in the direction of motion, while adhesion is released to allow forward migration. To simplify the study of this process cells have been studied when placed along one-dimensional tracks, where single cells exhibit both smooth and stick-slip migration modes. The stick-slip motility mode is characterized by protrusive motion at the cell front, coupled with slow cell elongation, which is followed by rapid retractions of the cell back. In this study, we explore a minimal physical model that couples the force applied on the adhesion bonds to the length variations of the cell and the traction forces applied by the polarized actin retrograde flow. We show that the rich spectrum of cell migration patterns emerges from this model as different \emph{deterministic} dynamical phases. This result suggests a source for the large cell-to-cell variability (CCV) in cell migration patterns observed in single cells over time and within cell populations. The large heterogeneity can arise from small fluctuations in the cellular components that are greatly amplified due to moving the cells' internal state across the dynamical phase transition lines. Temporal noise is shown to drive random changes in the cellular polarization direction, which is enhanced during the stick-slip migration mode. These results offer a new framework to explain experimental observations of migrating cells, resulting from noisy switching between underlying deterministic migration modes.
Highlights
Eukaryote cell migration, whereby cells crawl actively over an external substrate, is a subject of great interest for biological processes such as development and cancer progression
This result suggests a source for the large cell-tocell variability (CCV) in cell migration patterns observed in single cells over time and within cell populations: fluctuations in the cellular components, such as adhesion strength or polymerization activity, can shift the cells from one migration mode to another, due to crossing the dynamical phase transition lines
Within the stick-slip regime, we find that the duration of the limit-cycle increases with increasing r, i.e., the dynamics slow down with increasing substrate adhesiveness [Fig. 3(d)]
Summary
Whereby cells crawl actively over an external substrate, is a subject of great interest for biological processes such as development and cancer progression. The model contains two key, and strongly coupled, components: a slip-bond adhesion module at the cell back and a cellular polarization module We find that these components are sufficient to drive the entire spectrum of observed motility patterns, and explain the transitions between them. Our work demonstrates how a minimal model gives rise to a rich variety of deterministic migration patterns, as opposed to complex motion that is purely driven by different levels of cellular noise. The first part describes a cell that is constantly polarized, with a constant protrusive activity at the leading edge, and slip bond adhesions at the rear [24] This part allows us to expose the oscillatory stick slip behavior through the dynamics of the cell length and adhesion concentration at the rear. This part outlines the conditions for symmetry breaking and the role of noise in choosing a migration direction
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