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Deterministic patterns in cell motility


Cell migration paths are generally described as random walks, associated with both intrinsic and extrinsic noise. However, complex cell locomotion is not merely related to such fluctuations, but is often determined by the underlying machinery. Cell motility is driven mechanically by actin and myosin, two molecular components that generate contractile forces. Other cell functions make use of the same components and, therefore, will compete with the migratory apparatus. Here, we propose a physical model of such a competitive system, namely dendritic cells whose antigen capture function and migratory ability are coupled by myosin II. The model predicts that this coupling gives rise to a dynamic instability, whereby cells switch from persistent migration to unidirectional self-oscillation, through a Hopf bifurcation. Cells can then switch to periodic polarity reversals through a homoclinic bifurcation. These predicted dynamic regimes are characterized by robust features that we identify through in vitro trajectories of dendritic cells over long timescales and distances. We expect that competition for limited resources in other migrating cell types can lead to similar deterministic migration modes.

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Figure 1: System illustration (cell reference frame).
Figure 2: Switch from continuous migration to motility pulses.
Figure 3: Approach to a stable limit cycle.
Figure 4: Switch from unidirectional to bidirectional oscillations through a homoclinic bifurcation.
Figure 5: Approach to a bidirectional limit cycle.


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The authors thank M. Chabaud and M. Heuzé who performed the experimental study23 and have kindly contributed the data; R. Attia, M. Bretou, P. Vargas and P. Maiuri for discussions; and A. Monge and E. Bellin for language editing. N.S.G. would like to thank the ISF grant 580/12 for support. This work is made possible through the historic generosity of the Perlman family.

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Authors and Affiliations



I.L. created the analytic model with input by all authors, designed and implemented the analysis of both the model and the experiments, and prepared the manuscript; M.P. and A.-M.L.-D. conceived and supervised the experiments and contributed the data; N.S.G. jointly conceived the theoretical study with R.V., supervised the work and edited the manuscript. All authors reviewed the manuscript.

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Correspondence to Ido Lavi.

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The authors declare no competing financial interests.

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Lavi, I., Piel, M., Lennon-Duménil, AM. et al. Deterministic patterns in cell motility. Nature Phys 12, 1146–1152 (2016).

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