Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Towards a physical understanding of developmental patterning

Nature Reviews Genetics volume 22, pages 518–531 (2021)Cite this article

Subjects

Abstract

The temporal coordination of events at cellular and tissue scales is essential for the proper development of organisms, and involves cell-intrinsic processes that can be coupled by local cellular signalling and instructed by global signalling, thereby creating spatial patterns of cellular states that change over time. The timing and structure of these patterns determine how an organism develops. Traditional developmental genetic methods have revealed the complex molecular circuits regulating these processes but are limited in their ability to predict and understand the emergent spatio-temporal dynamics. Increasingly, approaches from physics are now being used to help capture the dynamics of the system by providing simplified, generic descriptions. Combined with advances in imaging and computational power, such approaches aim to provide insight into timing and patterning in developing systems.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The interplay between timing and patterning.
Fig. 2: Patterning by wavefronts.
Fig. 3: Patterning by genetic oscillators.
Fig. 4: Temporal versus spatial phase shifts in genetic oscillators.
Fig. 5: Systems that model sequential concentration pulses of components in gene regulatory networks.
Fig. 6: Patterning with genetic timers.
Fig. 7: The vertebrate segmentation clock has a combination of genetic oscillators and travelling wavefronts.

Similar content being viewed by others

References

  1. Zaret, K. S. Pioneer transcription factors initiating gene network changes. Annu. Rev. Genet. 54, 367–385 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Peter, I. S. & Davidson, E. H. Assessing regulatory information in developmental gene regulatory networks. Proc. Natl Acad. Sci. USA 114, 5862–5869 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Bolouri, H. & Davidson, E. H. Modeling DNA sequence-based cis-regulatory gene networks. Dev. Biol. 246, 2–13 (2002).

    Article  CAS  PubMed  Google Scholar 

  4. Davidson, E. H. & Levine, M. S. Properties of developmental gene regulatory networks. Proc. Natl Acad. Sci. USA 105, 20063–20066 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. DiFrisco, J. & Jaeger, J. Genetic causation in complex regulatory systems: an integrative dynamic perspective. BioEssays 42, 1900226 (2020).

    Article  Google Scholar 

  6. Rodriguez, E. A. et al. The growing and glowing toolbox of fluorescent and photoactive proteins. Trends Biochem. Sci. 42, 111–129 (2017).

    Article  CAS  PubMed  Google Scholar 

  7. Lee, H. N., Mehta, S. & Zhang, J. Recent advances in the use of genetically encodable optical tools to elicit and monitor signaling events. Curr. Opin. Cell Biol. 63, 114–124 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Shakirova, K. M., Ovchinnikova, V. Y. & Dashinimaev, E. B. Cell reprogramming with CRISPR/Cas9 based transcriptional regulation systems. Front. Bioeng. Biotechnol. 8, 882 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  9. Santos-Moreno, J., Tasiudi, E., Stelling, J. & Schaerli, Y. Multistable and dynamic CRISPRi-based synthetic circuits. Nat. Commun. 11, 2746 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Royer, L. A., Lemon, W. C., Chhetri, R. K. & Keller, P. J. A practical guide to adaptive light-sheet microscopy. Nat. Protoc. 13, 2462–2500 (2018).

    Article  CAS  PubMed  Google Scholar 

  11. Reynaud, E. G., Peychl, J., Huisken, J. & Tomancak, P. Guide to light-sheet microscopy for adventurous biologists. Nat. Methods 12, 30–34 (2015).

    Article  CAS  PubMed  Google Scholar 

  12. Liu, T.-L. et al. Observing the cell in its native state: Imaging subcellular dynamics in multicellular organisms. Science 360, eaaq1392 (2018).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  13. Sbalzarini, I. F. Modeling and simulation of biological systems from image data. BioEssays 35, 482–490 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Marcon, L., Diego, X., Sharpe, J. & Müller, P. High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals. eLife 5, e14022 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  15. Guckenheimer, J., Holmes, P., Guckenheimer, J. & Sirovich, L. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, 2013).

  16. Hohenberg, P. C. & Krekhov, A. P. An introduction to the Ginzburg–Landau theory of phase transitions and nonequilibrium patterns. Phys. Rep. 572, 1–42 (2015).

    Article  Google Scholar 

  17. Schweisguth, F. & Corson, F. Self-organization in pattern formation. Dev. Cell 49, 659–677 (2019).

    Article  CAS  PubMed  Google Scholar 

  18. Hamant, O. & Saunders, T. E. Shaping organs: shared structural principles across kingdoms. Annu. Rev. Cell Dev. Biol. 36, 385–410 (2020).

    Article  CAS  PubMed  Google Scholar 

  19. Ayad, N. M. E., Kaushik, S. & Weaver, V. M. Tissue mechanics, an important regulator of development and disease. Philos. Trans. R. Soc. B Biol. Sci. 374, 20180215 (2019).

    Article  CAS  Google Scholar 

  20. Naganathan, S. R. & Oates, A. C. Mechanochemical coupling and developmental pattern formation. Curr. Opin. Syst. Biol. 5, 104–111 (2017).

    Article  Google Scholar 

  21. Hannezo, E. & Heisenberg, C.-P. Mechanochemical feedback loops in development and disease. Cell 178, 12–25 (2019).

    Article  CAS  PubMed  Google Scholar 

  22. Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993). This extensive monograph describes the physics of pattern formation.

    Article  CAS  Google Scholar 

  23. Deneke, V. E., Melbinger, A., Vergassola, M. & Di Talia, S. Waves of Cdk1 activity in S phase synchronize the cell cycle in drosophila embryos. Dev. Cell 38, 399–412 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Vergassola, M., Deneke, V. E. & Di Talia, S. Mitotic waves in the early embryogenesis of Drosophila: bistability traded for speed. Proc. Natl Acad. Sci. USA 115, E2165–E2174 (2018). In this work, the authors explain the transition between mitotic phase waves and trigger waves in the syncytial D. melanogaster embryo.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Richardson, K. A., Schiff, S. J. & Gluckman, B. J. Control of traveling waves in the mammalian cortex. Phys. Rev. Lett. 94, 028103 (2005).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  26. Bub, G., Shrier, A. & Glass, L. Global organization of dynamics in oscillatory heterogeneous excitable media. Phys. Rev. Lett. 94, 028105 (2005).

    Article  PubMed  CAS  Google Scholar 

  27. Chang, J. B. & Ferrell, J. E. Jr. Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle. Nature 500, 603–607 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Cheng, X. & Ferrell, J. E. Apoptosis propagates through the cytoplasm as trigger waves. Science 361, 607–612 (2018). This article describes the discovery and analysis of apoptotic trigger waves.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Süel, G. M., Garcia-Ojalvo, J., Liberman, L. M. & Elowitz, M. B. An excitable gene regulatory circuit induces transient cellular differentiation. Nature 440, 545–550 (2006).

    Article  PubMed  CAS  Google Scholar 

  30. Tyson, J. J. & Keener, J. P. Singular perturbation theory of traveling waves in excitable media (a review). Phys. Nonlinear Phenom. 32, 327–361 (1988).

    Article  Google Scholar 

  31. Zykov, V. S. & Bodenschatz, E. Stabilized wave segments in an excitable medium with a phase wave at the wave back. N. J. Phys. 16, 043030 (2014).

    Article  Google Scholar 

  32. Swaney, K. F., Huang, C.-H. & Devreotes, P. N. Eukaryotic chemotaxis: a network of signaling pathways controls motility, directional sensing, and polarity. Annu. Rev. Biophys. 39, 265–289 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Palsson, E. et al. Selection for spiral waves in the social amoebae Dictyostelium. Proc. Natl Acad. Sci. 94, 13719–13723 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Sgro, A. E. et al. From intracellular signaling to population oscillations: bridging size-and time-scales in collective behavior. Mol. Syst. Biol. 11, 779 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Tayar, A. M., Karzbrun, E., Noireaux, V. & Bar-Ziv, R. H. Propagating gene expression fronts in a one-dimensional coupled system of artificial cells. Nat. Phys. 11, 1037–1041 (2015). In this work, the authors observed transitions between trigger waves and phase waves that are in agreement with theoretical predictions.

    Article  CAS  Google Scholar 

  36. Goldstein, R. E. Traveling-wave chemotaxis. Phys. Rev. Lett. 77, 775–778 (1996).

    Article  CAS  PubMed  Google Scholar 

  37. Skoge, M. et al. Cellular memory in eukaryotic chemotaxis. Proc. Natl Acad. Sci. 111, 14448–14453 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Nakajima, A., Ishihara, S., Imoto, D. & Sawai, S. Rectified directional sensing in long-range cell migration. Nat. Commun. 5, 5367 (2014).

    Article  CAS  PubMed  Google Scholar 

  39. Takahashi, J. S. Transcriptional architecture of the mammalian circadian clock. Nat. Rev. Genet. 18, 164–179 (2017).

    Article  CAS  PubMed  Google Scholar 

  40. Wilds, R. & Glass, L. An atlas of robust, stable, high-dimensional limit cycles. Int. J. Bifurc. Chaos 19, 4055–4096 (2009).

    Article  Google Scholar 

  41. Monk, N. A. M. Oscillatory expression of Hes1, p53, and NF-κB driven by transcriptional time delays. Curr. Biol. 13, 1409–1413 (2003).

    Article  CAS  PubMed  Google Scholar 

  42. Tyson, J. J., Chen, K. C. & Novak, B. Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr. Opin. Cell Biol. 15, 221–231 (2003).

    Article  CAS  PubMed  Google Scholar 

  43. Novák, B. & Tyson, J. J. Design principles of biochemical oscillators. Nat. Rev. Mol. Cell Biol. 9, 981–991 (2008).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  44. Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Avalon Publishing, 2014).

  45. Pikovsky, A., Rosenblum, M. & Kurths, J. Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge University Press, 2001).

  46. Kuramoto, Y. Cooperative dynamics of oscillator community: a study based on lattice of rings. Prog. Theor. Phys. Suppl. 79, 223–240 (1984). This seminal work describes phase synchronization in a tractable way.

    Article  CAS  Google Scholar 

  47. Kuramoto, Y. & Nakao, H. On the concept of dynamical reduction: the case of coupled oscillators. Philos. Trans. R. Soc. Math. Phys. Eng. Sci. 377, 20190041 (2019).

    Google Scholar 

  48. Kotani, K. et al. Nonlinear phase-amplitude reduction of delay-induced oscillations. Phys. Rev. Res. 2, 033106 (2020).

    Article  CAS  Google Scholar 

  49. Tigges, M., Marquez-Lago, T. T., Stelling, J. & Fussenegger, M. A tunable synthetic mammalian oscillator. Nature 457, 309–312 (2009).

    Article  CAS  PubMed  Google Scholar 

  50. Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338 (2000). This article describes proof by synthesis of a delayed-negative-feedback genetic oscillator.

    Article  CAS  PubMed  Google Scholar 

  51. Stricker, J. et al. A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Niederholtmeyer, H. et al. Rapid cell-free forward engineering of novel genetic ring oscillators. eLife 4, e09771 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  53. Tsimring, L. S. Noise in biology. Rep. Prog. Phys. 77, 026601 (2014).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  54. Lax, M. Classical noise. V. Noise in self-sustained oscillators. Phys. Rev. 160, 290–307 (1967).

    Article  CAS  Google Scholar 

  55. Pikovsky, A., Rosenblum, M. & Kurths, J. Phase synchronization in regular and chaotic systems. Int. J. Bifurc. Chaos 10, 2291–2305 (2000).

    Article  Google Scholar 

  56. Winfree, A. T. Biological rhythms and the behavior of populations of coupled oscillators. J. Theor. Biol. 16, 15–42 (1967).

    Article  CAS  PubMed  Google Scholar 

  57. Riedel-Kruse, I. H., Muller, C. & Oates, A. C. Synchrony dynamics during initiation, failure, and rescue of the segmentation clock. Science 317, 1911–1915 (2007).

    Article  CAS  PubMed  Google Scholar 

  58. Danino, T., Mondragón-Palomino, O., Tsimring, L. & Hasty, J. A synchronized quorum of genetic clocks. Nature 463, 326–330 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Tayar, A. M., Karzbrun, E., Noireaux, V. & Bar-Ziv, R. H. Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells. Proc. Natl Acad. Sci. USA 114, 11609–11614 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Lažetic´, V. & Fay, D. S. Molting in C. elegans. Worm 6, e1330246 (2017).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  61. Johnstone, I. L. & Barry, J. D. Temporal reiteration of a precise gene expression pattern during nematode development. EMBO J. 15, 3633–3639 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. Hendriks, G.-J., Gaidatzis, D., Aeschimann, F. & Großhans, H. Extensive oscillatory gene expression during C. elegans larval development. Mol. Cell 53, 380–392 (2014). This article describes the discovery of a genome-wide phase-locked developmental oscillator correlated with moulting.

    Article  CAS  PubMed  Google Scholar 

  63. Meeuse, M. W. et al. Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans. Mol. Syst. Biol. 16, e9498 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Sarrazin, A. F., Peel, A. D. & Averof, M. A segmentation clock with two-segment periodicity in insects. Science 336, 338–341 (2012).

    Article  CAS  PubMed  Google Scholar 

  65. El-Sherif, E., Averof, M. & Brown, S. J. A segmentation clock operating in blastoderm and germband stages of Tribolium development. Development 139, 4341–4346 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Okuda, K. Variety and generality of clustering in globally coupled oscillators. Phys. Nonlinear Phenom. 63, 424–436 (1993).

    Article  Google Scholar 

  67. Grosskortenhaus, R., Pearson, B. J., Marusich, A. & Doe, C. Q. Regulation of temporal identity transitions in drosophila neuroblasts. Dev. Cell 8, 193–202 (2005).

    Article  CAS  PubMed  Google Scholar 

  68. Gliech, C. R. & Holland, A. J. Keeping track of time: the fundamentals of cellular clocks. J. Cell Biol. 219, e202005136 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Raff, M. Intracellular developmental timers. Cold Spring Harb. Symp. Quant. Biol. 72, 431–435 (2007).

    Article  CAS  PubMed  Google Scholar 

  70. MacDonald, N. Biological Delay Systems: Linear Stability Theory (Cambridge Univ. Press, 1989).

  71. Lemaire, V., Lee, C. F., Lei, J., Métivier, R. & Glass, L. Sequential recruitment and combinatorial assembling of multiprotein complexes in transcriptional activation. Phys. Rev. Lett. 96, 198102 (2006).

    Article  PubMed  CAS  Google Scholar 

  72. Métivier, R. et al. Estrogen receptor-α directs ordered, cyclical, and combinatorial recruitment of cofactors on a natural target promoter. Cell 115, 751–763 (2003).

    Article  PubMed  Google Scholar 

  73. May, R. M. & Leonard, W. J. Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29, 243–253 (1975).

    Article  Google Scholar 

  74. Rabinovich, M. I., Varona, P., Selverston, A. I. & Abarbanel, H. D. I. Dynamical principles in neuroscience. Rev. Mod. Phys. 78, 1213–1265 (2006).

    Article  Google Scholar 

  75. Afraimovich, V., Tristan, I., Huerta, R. & Rabinovich, M. I. Winnerless competition principle and prediction of the transient dynamics in a Lotka–Volterra model. Chaos Interdiscip. J. Nonlinear Sci. 18, 043103 (2008).

    Article  Google Scholar 

  76. Kuznetsov, A. & Afraimovich, V. Heteroclinic cycles in the repressilator model. Chaos Solitons Fractals 45, 660–665 (2012).

    Article  Google Scholar 

  77. Panovska-Griffiths, J., Page, K. M. & Briscoe, J. A gene regulatory motif that generates oscillatory or multiway switch outputs. J. R. Soc. Interface 10, 20120826 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  78. Balaskas, N. et al. Gene regulatory logic for reading the sonic hedgehog signaling gradient in the vertebrate neural tube. Cell 148, 273–284 (2012). This article describes quantitative modelling of a gradient-driven genetic timer network.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  79. Dessaud, E. et al. Interpretation of the sonic hedgehog morphogen gradient by a temporal adaptation mechanism. Nature 450, 717–720 (2007).

    Article  CAS  PubMed  Google Scholar 

  80. Tufcea, D. E. & François, P. Critical timing without a timer for embryonic development. Biophys. J. 109, 1724–1734 (2015). This study provides a systematic theoretical analysis of a strongly interconnected and repressive GRN.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Averbukh, I., Lai, S.-L., Doe, C. Q. & Barkai, N. A repressor-decay timer for robust temporal patterning in embryonic Drosophila neuroblast lineages. eLife 7, e38631 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  82. Homem, C. C. F. & Knoblich, J. A. Drosophila neuroblasts: a model for stem cell biology. Development 139, 4297–4310 (2012).

    Article  CAS  PubMed  Google Scholar 

  83. Zhu, X. et al. Speed regulation of genetic cascades allows for evolvability in the body plan specification of insects. Proc. Natl Acad. Sci. USA 114, E8646–E8655 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Kambadur, R. et al. Regulation of POU genes by castor and hunchback establishes layered compartments in the Drosophila CNS. Genes Dev. 12, 246–260 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Isshiki, T., Pearson, B., Holbrook, S. & Doe, C. Q. Drosophila neuroblasts sequentially express transcription factors which specify the temporal identity of their neuronal progeny. Cell 106, 511–521 (2001). This article describes the discovery of a sequential genetic timer in D. melanogaster neuroblasts.

    Article  CAS  PubMed  Google Scholar 

  86. Wolpert, L., Tickle, C. & Arias, A. M. Principles of Development (Oxford University Press, 2015).

  87. Li, X. et al. Temporal patterning of Drosophila medulla neuroblasts controls neural fates. Nature 498, 456–462 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  88. Suzuki, T., Kaido, M., Takayama, R. & Sato, M. A temporal mechanism that produces neuronal diversity in the Drosophila visual center. Dev. Biol. 380, 12–24 (2013).

    Article  CAS  PubMed  Google Scholar 

  89. Le Dréau, G. & Martí, E. Dorsal-ventral patterning of the neural tube: a tale of three signals. Dev. Neurobiol. 72, 1471–1481 (2012).

    Article  PubMed  CAS  Google Scholar 

  90. Cross, M. & Greenside, H. Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge University Press, 2009).

  91. Oates, A. C., Morelli, L. G. & Ares, S. Patterning embryos with oscillations: structure, function and dynamics of the vertebrate segmentation clock. Development 139, 625–639 (2012).

    Article  CAS  PubMed  Google Scholar 

  92. Gomez, C. et al. Control of segment number in vertebrate embryos. Nature 454, 335–339 (2008).

    Article  CAS  PubMed  Google Scholar 

  93. Cooke, J. & Zeeman, E. C. A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. J. Theor. Biol. 58, 455–476 (1976).

    Article  CAS  PubMed  Google Scholar 

  94. Palmeirim, I., Henrique, D., Ish-Horowicz, D. & Pourquié, O. Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis. Cell 91, 639–648 (1997). This article describes the discovery of the molecular segmentation clock in the chick embryo.

    Article  CAS  PubMed  Google Scholar 

  95. Morelli, L. G. et al. Delayed coupling theory of vertebrate segmentation. HFSP J. 3, 55–66 (2009).

    Article  PubMed  Google Scholar 

  96. Ares, S., Morelli, L. G., Jörg, D. J., Oates, A. C. & Jülicher, F. Collective modes of coupled phase oscillators with delayed coupling. Phys. Rev. Lett. 108, 204101 (2012).

    Article  PubMed  CAS  Google Scholar 

  97. Jörg, D. J., Morelli, L. G., Soroldoni, D., Oates, A. C. & Jülicher, F. Continuum theory of gene expression waves during vertebrate segmentation. N. J. Phys. 17, 093042 (2015).

    Article  CAS  Google Scholar 

  98. Webb, A. B. et al. Persistence, period and precision of autonomous cellular oscillators from the zebrafish segmentation clock. eLife 5, e08438 (2016).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  99. Hubaud, A., Regev, I., Mahadevan, L. & Pourquié, O. Excitable dynamics and yap-dependent mechanical cues drive the segmentation clock. Cell 171, 668–682.e11 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Lauschke, V. M., Tsiairis, C. D., François, P. & Aulehla, A. Scaling of embryonic patterning based on phase-gradient encoding. Nature 493, 101–105 (2013).

    Article  PubMed  CAS  Google Scholar 

  101. Venzin, O. F. & Oates, A. C. What are you synching about? Emerging complexity of Notch signaling in the segmentation clock. Dev. Biol. 460, 40–54 (2020).

    Article  CAS  PubMed  Google Scholar 

  102. Delaune, E. A., François, P., Shih, N. P. & Amacher, S. L. Single-cell-resolution imaging of the impact of notch signaling and mitosis on segmentation clock dynamics. Dev. Cell 23, 995–1005 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Shih, N. P., Francois, P., Delaune, E. A. & Amacher, S. L. Dynamics of the slowing segmentation clock reveal alternating two-segment periodicity. Development 142, 1785–1793 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Yoshioka-Kobayashi, K. et al. Coupling delay controls synchronized oscillation in the segmentation clock. Nature https://doi.org/10.1038/s41586-019-1882-z (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  105. Soroldoni, D. et al. A Doppler effect in embryonic pattern formation. Science 345, 222–225 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  106. Morelli, L. G. & Jülicher, F. Precision of genetic oscillators and clocks. Phys. Rev. Lett. 98, 228101 (2007).

    Article  PubMed  CAS  Google Scholar 

  107. Tsiairis, C. D. & Aulehla, A. Self-organization of embryonic genetic oscillators into spatiotemporal wave patterns. Cell 164, 656–667 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  108. Dubrulle, J., McGrew, M. J. & Pourquié, O. FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal hox gene activation. Cell 106, 219–232 (2001).

    Article  CAS  PubMed  Google Scholar 

  109. Sawada, A. et al. Fgf/MAPK signalling is a crucial positional cue in somite boundary formation. Dev. Camb. Engl. 128, 4873–4880 (2001).

    CAS  Google Scholar 

  110. Bajard, L. et al. Wnt-regulated dynamics of positional information in zebrafish somitogenesis. Development 141, 1381–1391 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  111. Moreno, T. A. & Kintner, C. Regulation of segmental patterning by retinoic acid signaling during xenopus somitogenesis. Dev. Cell 6, 205–218 (2004).

    Article  CAS  PubMed  Google Scholar 

  112. Sonnen, K. F. et al. Modulation of phase shift between Wnt and Notch signaling oscillations controls mesoderm segmentation. Cell 172, 1079–1090.e12 (2018). This study provides evidence for a phase shift coincidence arrest mechanism in the mouse segmentation clock.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  113. Beaupeux, M. & François, P. Positional information from oscillatory phase shifts: insights from in silico evolution. Phys. Biol. 13, 036009 (2016).

    Article  CAS  PubMed  Google Scholar 

  114. Verd, B. et al. A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila. PLoS Biol. 16, e2003174 (2018).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  115. Verd, B., Crombach, A. & Jaeger, J. Dynamic maternal gradients control timing and shift-rates for drosophila gap gene expression. PLoS Comput. Biol. 13, e1005285 (2017).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  116. Verd, B., Monk, N. A. & Jaeger, J. Modularity, criticality, and evolvability of a developmental gene regulatory network. eLife 8, e42832 (2019). This article demonstrates the use of concepts from dynamical systems to obtain new insight into a well-studied genetic system.

    Article  PubMed  PubMed Central  Google Scholar 

  117. Krotov, D., Dubuis, J. O., Gregor, T. & Bialek, W. Morphogenesis at criticality. Proc. Natl Acad. Sci. USA 111, 3683–3688 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. DiFrisco, J. & Jaeger, J. Beyond networks: mechanism and process in evo-devo. Biol. Philos. 34, 54 (2019).

    Article  Google Scholar 

  119. Salazar-Ciudad, I. & Jernvall, J. The causality horizon and the developmental bases of morphological evolution. Biol. Theory 8, 286–292 (2013).

    Article  Google Scholar 

  120. Bauer, G. et al. The science of living matter for tomorrow. Cell Syst. 6, 400–402 (2018).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

The authors thank A. Pumir, L. Morelli, A. Bercowsky and L. A. Rohde for critical feedback on the manuscript.

Author information

Authors and Affiliations

  1. Institute of Bioengineering, School of Life Sciences and School of Engineering, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Jose Negrete Jr & Andrew C. Oates

Authors
  1. Jose Negrete Jr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrew C. Oates
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors contributed equally to all aspects of the article.

Corresponding author

Correspondence to Andrew C. Oates.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Genetics thanks H. Grosshans and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Glossary

Syncytial

Describes a cell that is multinucleated.

Kinematic structures

Spatial structures that move without transmission of a signal.

Bistable systems

Dynamical units that have two stable states, and the simplest dynamical systems that exhibit memory. The genetic toggle switch, in which two genes mutually repress the expression of each other, is an example of a synthetic gene regulatory network that is bistable.

Excitable medium

Spatially distributed, coupled excitable units that transmit information from one point to another in the form of travelling pulses.

Critical point

Also known as a bifurcation point. A transition point in parameter values (for example, a degradation rate) where a system moves between qualitatively different states; for example, between oscillatory and non-oscillatory states.

Phase reduction method

A mathematical technique that allows the study of limit cycle oscillations (that is, a system with oscillatory dynamics with a fixed amplitude and period that will return to its initial amplitude and period after perturbation, although its phase will drift) by tracking only the time evolution of the phase.

Heteroclinic cycles

A dynamical system that transitions between states in repetitive non-periodic cycles, with the period increasing in each successive cycle.

Asymmetrical cell division

A cell division in which a property or set of factors is present in only one of the daughter cells.

Type IIIo system

In the physics of pattern formation, patterns with a tendency towards a spatially uniform state that oscillates in time.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Negrete, J., Oates, A.C. Towards a physical understanding of developmental patterning. Nat Rev Genet 22, 518–531 (2021). https://doi.org/10.1038/s41576-021-00355-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41576-021-00355-7

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing