Reaction–diffusion networks underlie pattern formation in a range of biological contexts, from morphogenesis of organisms to the polarization of individual cells. One requirement for such molecular networks is that output patterns be scaled to system size. At the same time, kinetic properties of constituent molecules constrain the ability of networks to adapt to size changes. Here, we explore these constraints and the consequences thereof within the conserved PAR cell polarity network. Using the stem-cell-like germ lineage of the Caenorhabditis elegans embryo as a model, we find that the behaviour of PAR proteins fails to scale with cell size. Theoretical analysis demonstrates that this lack of scaling results in a size threshold below which polarity is destabilized, yielding an unpolarized system. In empirically constrained models, this threshold occurs near the size at which germ lineage cells normally switch between asymmetric and symmetric modes of division. Consistent with cell size limiting polarity and division asymmetry, genetic or physical reduction in germ lineage cell size is sufficient to trigger loss of polarity in normally polarizing cells at predicted size thresholds. Physical limits of polarity networks may be one mechanism by which cells read out geometrical features to inform cell fate decisions.
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We thank N. Tapon, B. Baum, R. Endres, C. Weber, J. Pfanzelter, J. Bois and members of the Goehring Lab for critical comments, H. Baumann, B. Atkinson from Intelligent Imaging Innovations (3i), and R. Henriques for providing access to and training for a Marianas LightSheet microscope, the Salbreux Lab for helpful discussions, and T. Hyman and S. Grill, in whose laboratories some of the initial observations were made. This work was supported by the Francis Crick Institute (N.W.G.), which receives its core funding from Cancer Research UK (FC001086), the UK Medical Research Council (FC001086) and the Wellcome Trust (FC001086), the EU Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement 675407 (N.W.G.) and a Bogue Fellowship from University College London (L.H.). N.W.G. is a member of the GENiE network supported by COST Action BM1408 and EMBO. We also acknowledge the Santa Barbara Advanced School of Quantitative Biology and the Kavli Institute for Theoretical Physics, supported by NSF grant PHY-1748958, NIH grant R25GM067110 and the Gordon and Betty Moore Foundation grant 2919.01. Some strains were provided by the CGC, which is funded by the NIH Office of Research Infrastructure Programs (P40 OD010440).
The authors declare no competing interests.
Peer review information: Nature Physics thanks James Feng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Supplementary Figs. 1–5 and Tables 1–3.
Time evolution of the symmetric PAR model.
Time-lapse video of an embryo from the zygote stage until division of P4.
Time-lapse videos capturing P3 division in C27D9.1 (top) and ima-3 (bottom) embryos.
Time-lapse videos of dissected P0ex (left) and P1ex (right) cells.
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Nature Physics (2019)