Spontaneous pattern formation in Turing systems relies on feedback. But patterns in cells and tissues seldom form spontaneously—instead they are controlled by regulatory biochemical interactions that provide molecular guiding cues. The relationship between these guiding cues and feedback in controlled biological pattern formation remains unclear. Here, we explore this relationship during cell-polarity establishment in the one-cell-stage Caenorhabditis elegans embryo. We quantify the strength of two feedback systems that operate during polarity establishment: feedback between polarity proteins and the actomyosin cortex, and mutual antagonism among polarity proteins. We characterize how these feedback systems are modulated by guiding cues from the centrosome, an organelle regulating cell cycle progression. By coupling a mass-conserved Turing-like reaction–diffusion system for polarity proteins to an active-gel description of the actomyosin cortex, we reveal a transition point beyond which feedback ensures self-organized polarization, even when cues are removed. Notably, the system switches from a guide-dominated to a feedback-dominated regime well beyond this transition point, which ensures robustness. Together, these results reveal a general criterion for controlling biological pattern-forming systems: feedback remains subcritical to avoid unstable behaviour, and molecular guiding cues drive the system beyond a transition point for pattern formation.
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P.G. acknowledges a EMBO Long-Term Fellowship for funding. The research of K.V.K. is supported by the Department of Biotechnology, India through a Ramalingaswami Re-entry Fellowship, and the Max Planck Society and the Department of Science and Technology, India through a Max Planck Partner Group at ICTS-TIFR. N.W.G. was supported by the Francis Crick Institute, which receives its core funding from Cancer Research UK (FC001086), the UK Medical Research Council (FC001086) and the Wellcome Trust (FC001086), and is a member of the GENiE network supported by COST Action BM1408 and EMBO. S.W.G was supported by the DFG (SPP 1782, GSC 97, GR 3271/2, GR 3271/3, GR 3271/4), the European Research Council (grants 281903 and 742712), ITN grants 281903 and 641639 from the EU, the Max-Planck-Society as a Max-Planck-Fellow, and the Human Frontier Science Program (RGP0023/2014). J.S.B. acknowledges the Human Frontier Science Program for funding. We thank D. Dickinson, B. Goldstein, F. Motegi and G. Seydoux for sharing C. elegans strains. We thank P. Gönczy, L. Hubatsch, T. Hyman, K. Kruse and M. Labouesse for discussion and insightful comments on the manuscript.
Supplementary Discussion, Supplementary Equations, Supplementary Figures 1–15, Supplementary Tables 1–4, Supplementary References 1–27
Concentration field of PAR-2::GFP (blue, N = 8) and PAR-6::mCherry (red, N = 8), during mlc-4 RNAi, over time. Error bands represent the standard error of the mean. The solid line shows the best fit, using equations as described in Supplementary Table 1, with parameters shown in Supplementary Tables 2 and 3.
Ensemble-averaged concentration field of NMY-2::GFP (grey, N = 8) and the ensemble-averaged NMY-2 flow field (green, N = 10), during par-2 and par-6 double RNAi, over time. Error bands represent the standard error of the mean. The solid line shows the best fit, using equations as described in Supplementary Table 1, with parameters shown in Supplementary Tables 2 and 3.
Ensemble-averaged concentration field of PAR-2-MT-::GFP (blue, N = 9) and PAR-6::mCherry (red, N = 9) NMY-2::mKate2 (grey, N = 6) and the ensemble-averaged NMY-2 flow field (green, N = 9) for the PAR-2 MT- condition, over time. Error bands represent the standard error of the mean. The solid line shows the model prediction, using equations as described in Supplementary Table 1, with parameters shown in Supplementary Tables 2 and 3.
Ensemble-averaged concentration field of PAR-2::GFP (blue, N = 6) and PAR-6::mCherry (red, N = 6) NMY-2::GFP (grey, N = 8) and the ensemble-averaged NMY-2 flow field (green, N = 12) for the unperturbed condition, over time. Error bands represent the standard error of the mean. The solid line shows the model prediction, using equations as described in Supplementary Table 1, with parameters shown in Supplementary Tables 2 and 3.
Ensemble-averaged concentration field of PAR-2::GFP (blue, N = 6) and PAR-6::mCherry (red, N = 6) NMY-2::GFP (grey, N = 8) and the ensemble-averaged NMY-2 flow field (green, N = 12) for the unperturbed condition, over time. Error bands represent the standard error of the mean. The solid line shows a fit to the model, using equations as described in Supplementary Table 1, as shown in Supplementary Fig. 9