Stochastic nonlinear dynamics of confined cell migration in two-state systems

Abstract

Migrating cells in physiological processes, including development, homeostasis and cancer, encounter structured environments and are forced to overcome physical obstacles. Yet, the dynamics of confined cell migration remains poorly understood, and thus there is a need to study the complex motility of cells in controlled confining microenvironments. Here, we develop two-state micropatterns, consisting of two adhesive sites connected by a thin constriction, in which migrating cells perform repeated stochastic transitions. This minimal system enables us to obtain a large ensemble of single-cell trajectories. From these trajectories, we infer an equation of cell motion, which decomposes the dynamics into deterministic and stochastic contributions in position–velocity phase space. Our results reveal that cells in two-state micropatterns exhibit intricate nonlinear migratory dynamics, with qualitatively similar features for a cancerous (MDA-MB-231) and a non-cancerous (MCF10A) cell line. In both cases, the cells drive themselves deterministically into the thin constriction; a process that is sped up by noise. Interestingly, however, these two cell lines have distinct deterministic dynamics: MDA-MB-231 cells exhibit a limit cycle, while MCF10A cells show excitable bistable dynamics. Our approach yields a conceptual framework that may be extended to understand cell migration in more complex confining environments.

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Fig. 1: Experimental set-up of two-state micropatterns with MDA-MB-231 cells.
Fig. 2: Statistics of the hopping process (MDA-MB-231).
Fig. 3: Deterministic and stochastic contributions to the equation of motion for MDA-MB-231 cells with and without constriction, and MCF10A cells with constriction (L = 35 µm).
Fig. 4: Nonlinear deterministic dynamics of the cell migration (L= 35 µm).

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.

Change history

  • 18 March 2019

    In the version of this Article originally published online, in the ‘Journal peer review information’ statement, the reviewer Henrik Flyvbjerg was mistakenly not included; the statement has now been updated accordingly.

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Acknowledgements

We thank E. Frey, F. Brauns, G. Gradziuk, D. Lubensky, P. Ronceray, K. Bassler and N. Wingreen for useful comments, C. Leu for the preparation of wafers and A. Reiser for providing the transfection protocol. This work was supported by grants from the German Science Foundation (DFG) through the Collaborative Research Center (SFB) 1032 (projects B01 and B12). D.B.B. is supported by a DFG fellowship within the Graduate School of Quantitative Biosciences Munich and by the Joachim Herz Stiftung.

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Contributions

A.F., C.S., P.J.F.R. and J.O.R designed experiments; A.F. and C.S. performed experiments; D.B.B., A.F. and C.S. analysed data. D.B.B. and C.P.B. developed the theoretical model. D.B.B., A.F., C.S., J.O.R. and C.P.B. wrote the manuscript.

Corresponding authors

Correspondence to Joachim O. Rädler or Chase P. Broedersz.

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The authors declare no competing interests.

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Journal peer review information: Nature Physics thanks Henrik Flyvbjerg, Jonas Pedersen, Ulrich Schwarz and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figures 1–20 and Supplementary References 1–7.

Reporting Summary

Supplementary Video 1

Single MDA-MB-231 cells transitioning repeatedly between the square adhesion sites of the two-state micropattern. Transitions are usually preceded by the formation of a protrusion along the bridge. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. The bridge length is L = 16 µm. Scale bar, 25 µm.

Supplementary Video 2

Single MDA-MB-231 cells transitioning repeatedly between the square adhesion sites of the two-state micropattern. Transitions are usually preceded by the formation of a protrusion along the bridge. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. The bridge length is L = 35 µm. Scale bar, 25 µm.

Supplementary Video 3

Single MDA-MB-231 cells transitioning repeatedly between the square adhesion sites of the two-state micropattern. Transitions are usually preceded by the formation of a protrusion along the bridge. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. The bridge length is L = 56 µm. Scale bar, 25 µm.

Supplementary Video 4

Exemplary field of view of MDA-MB-231 cells migrating on two-state micropatterns of the same bridge length (L = 35 µm). All cells perform transitions between the square adhesion sites. Not all micropatterns are occupied, which is due to the low cell seeding density used to ensure single-cell occupancy. Cell nuclei are labelled for semi-automated detection of cell positions. Scale bar, 25 µm.

Supplementary Video 5

Single MDA-MB-231 cells transfected with LifeAct-GFP to visualize actin on two-state micropatterns of bridge length L = 35 µm. The outline of the underlying micropattern is drawn as a reference up to scale. Actin hotspots are visible at the tip of the transition-mediating lamellipodium, as well as during the dynamic exploration of the square adhesion sites. Actin fibres reorganize dynamically.

Supplementary Video 6

Single MDA-MB-231 cells transfected with LifeAct-GFP to visualize actin on two-state micropatterns of bridge length L = 35 µm. The outline of the underlying micropattern is drawn as a reference up to scale. Actin hotspots are visible at the tip of the transition-mediating lamellipodium, as well as during the dynamic exploration of the square adhesion sites. Actin fibres reorganize dynamically.

Supplementary Video 7

Single MDA-MB-231 cell on a stripe micropattern without constriction of total length 103 µm. The cell moves back and forth, repolarizing on contact with the pattern’s borders. When the cell is positioned in the middle of the pattern, quick changes in the direction of lamellipodia formation can be seen. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions.

Supplementary Video 8

Sparsely seeded MDA-MB-231 cells freely migrating on a homogeneous fibronectin-coated 2D surface. Cells move randomly on the surface. Cell nuclei are fluorescently labelled for automated cell tracking. Scale bar, 100 µm.

Supplementary Video 9

Single MCF10A cell transitioning repeatedly between the square adhesion sites of the two-state micropattern. Transitions are usually preceded by the formation of a protrusion along the bridge. Several times, protrusions along the bridge are formed that do not lead to a transition. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. Bridge length L = 35 µm.

Supplementary Video 10

Single MDA-MB-436 cell transitioning between the square adhesion sites of the two-state micropattern. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. Bridge length L = 35 µm.

Supplementary Video 11

Single MDCK cell transitioning between the square adhesion sites of the two-state micropattern. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. Bridge length L = 35 µm.

Supplementary Video 12

Single HuH7 cell transitioning between the square adhesion sites of the two-state micropattern. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. Bridge length L = 35 µm.

Supplementary Video 13

Single A549 cell transitioning between the square adhesion sites of the two-state micropattern. The cell nucleus is fluorescently labelled to allow automated tracking of cell positions. Bridge length L = 35 µm.

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Brückner, D.B., Fink, A., Schreiber, C. et al. Stochastic nonlinear dynamics of confined cell migration in two-state systems. Nat. Phys. 15, 595–601 (2019). https://doi.org/10.1038/s41567-019-0445-4

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