One-dimensional cell motility patterns

Abstract

During migration, cells exhibit a rich variety of seemingly random migration patterns, which makes unraveling the underlying mechanisms that control cell migration a difficult 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 a slow elongation of the cell, which is followed by a rapid retraction of the cell rear. 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 to 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 deterministic dynamical phases. 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. Temporal noise is shown to drive random changes in the cellular polarization direction, which is enhanced during the stick-slip migration mode. The model contains an emergent critical length for cell polarization, whereby cells that retract below this length loose polarity, and are prone to making direction changes in migration. These results offer a new framework to explain experimental observations of migrating cells, resulting from noisy switching between underlying deterministic migration modes.

Chemokine-biased robust self-organizing polarization of migrating cells in vivo

“…This positive feedback can be described by the same set of equations previously proposed in refs. 20 , 21 , and naturally explains many of the observations reported above.…”

“…We showed that such a run-and-tumble behavior can arise naturally in our theoretical model ( SI Appendix , Fig. S7 B ) ( 21 ), in a regime when both polarized and unpolarized states can develop.…”

“…S7 B . The model also explains the formation of a polarized cell when two competing fronts exit initially ( 21 ) ( Fig. 3 B and SI Appendix , Fig.…”

“…PGCs were imaged between 60% and 90% epiboly using epifluorescence or spinning disk microscopy. One-cell-stage embryos were injected with RNA encoding for the specific polarity markers and/or MO oligonucleotides directed against Cxcl12a ( 21 ) (GeneTools) ( SI Appendix , Table S5 ). Images were processed using FIJI.…”

“…An important component in this model for establishing cell polarization is the net actin retrograde flow away from the side of the cell that becomes the cell front. According to this model, the front can be maintained at this location by a positive feedback between the actin flow and the flow of inhibitors of actin polymerization away from it ( 21 ). Experimentally, in the context of cell migration, actin retrograde flow was first shown to be important in processes of focal-adhesion-dependent motility.…”