1932

Abstract

Patterns are ubiquitous in living systems and underlie the dynamic organization of cells, tissues, and embryos. Mathematical frameworks have been devised to account for the self-organization of biological patterns, most famously the Turing framework. Patterns can be defined in space, for example, to form stripes; in time, such as during oscillations; or both, to form traveling waves. The formation of these patterns can have different origins: purely chemical, purely mechanical, or a combination of the two. Beyond the variety of molecular implementations of such patterns, we emphasize the unitary principles associated with them, across scales in space and time, within a general mechanochemical framework. We illustrate where such mechanisms of pattern formation arise in biological systems from cellular to tissue scales, with an emphasis on morphogenesis. Our goal is to convey a picture of pattern formation that draws attention to the principles rather than solely to specific molecular mechanisms.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-cellbio-120420-095337
2022-10-06
2024-04-29
Loading full text...

Full text loading...

/deliver/fulltext/cellbio/38/1/annurev-cellbio-120420-095337.html?itemId=/content/journals/10.1146/annurev-cellbio-120420-095337&mimeType=html&fmt=ahah

Literature Cited

  1. Abercrombie M, Heaysman JEM, Pegrum SM. 1970. The locomotion of fibroblasts in culture I. Movements of the leading edge. Exp. Cell Res. 59:3393–98
    [Google Scholar]
  2. Alégot H, Pouchin P, Bardot O, Mirouse V. 2018. Jak-Stat pathway induces Drosophila follicle elongation by a gradient of apical contractility. eLife 7:e32943
    [Google Scholar]
  3. Allard J, Mogilner A. 2013. Traveling waves in actin dynamics and cell motility. Curr. Opin. Cell Biol. 25:1107–15
    [Google Scholar]
  4. Alt W, Tranquillo RT. 1995. Basic morphogenetic system modeling shape changes of migrating cells: how to explain fluctuating lamellipodial dynamics. J. Biol. Syst. 3:4905–16
    [Google Scholar]
  5. An Y, Xue G, Shaobo Y, Mingxi D, Zhou X et al. 2017. Apical constriction is driven by a pulsatile apical myosin network in delaminating Drosophila neuroblasts. Development 144:122153–64
    [Google Scholar]
  6. Antunes M, Pereira T, Cordeiro JV, Almeida L, Jacinto A 2013. Coordinated waves of actomyosin flow and apical cell constriction immediately after wounding. J. Cell Biol. 202:2365–79
    [Google Scholar]
  7. Aoki K, Kondo Y, Naoki H, Hiratsuka T, Itoh RE, Matsuda M. 2017. Propagating wave of ERK activation orients collective cell migration. Dev. Cell 43:3305–17.e5
    [Google Scholar]
  8. Bailles A, Collinet C, Philippe J-M, Lenne P-F, Munro E, Lecuit T. 2019. Genetic induction and mechanochemical propagation of a morphogenetic wave. Nature 572:7770467–73
    [Google Scholar]
  9. Balaji R, Bielmeier C, Harz H, Bates J, Stadler C et al. 2017. Calcium spikes, waves and oscillations in a large, patterned epithelial tissue. Sci. Rep. 7:42786
    [Google Scholar]
  10. Banerjee DS, Munjal A, Lecuit T, Rao M. 2017. Actomyosin pulsation and flows in an active elastomer with turnover and network remodeling. Nat Commun 8:1121
    [Google Scholar]
  11. Bargiello TA, Jackson FR, Young MW. 1984. Restoration of circadian behavioural rhythms by gene transfer in Drosophila. Nature 312:5996752–54
    [Google Scholar]
  12. Bargiello TA, Young MW. 1984. Molecular genetics of a biological clock in Drosophila. PNAS 81:72142–46
    [Google Scholar]
  13. Barrio RA, Varea C, Aragón JL. 1999. A two-dimensional numerical study of spatial pattern formation in interacting Turing systems. Bull. Math. Biol. 61:3483–505
    [Google Scholar]
  14. Bement WM, Leda M, Moe AM, Kita AM, Larson ME et al. 2015. Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium. Nat. Cell Biol. 17:111471–83
    [Google Scholar]
  15. Bender A, Pringle JR. 1989. Multicopy suppression of the cdc24 budding defect in yeast by CDC42 and three newly identified genes including the ras-related gene RSR1. PNAS 86:249976–80
    [Google Scholar]
  16. Beta C, Kruse K. 2017. Intracellular oscillations and waves. Annu. Rev. Condens. Matter Phys. 8:239–64
    [Google Scholar]
  17. Bischof J, Brand CA, Somogyi K, Májer I, Thome S et al. 2017. A cdk1 gradient guides surface contraction waves in oocytes. Nat Commun 8:849
    [Google Scholar]
  18. Blanchard GB, Murugesu S, Adams RJ, Martinez-Arias A, Gorfinkiel N. 2010. Cytoskeletal dynamics and supracellular organisation of cell shape fluctuations during dorsal closure. Development 137:162743–52
    [Google Scholar]
  19. Bois JS, Jülicher F, Grill SW. 2011. Pattern formation in active fluids. Phys. Rev. Lett. 106:2028103
    [Google Scholar]
  20. Bonny M, Fischer-Friedrich E, Loose M, Schwille P, Kruse K. 2013. Membrane binding of MinE allows for a comprehensive description of Min-protein pattern formation. PLOS Comp. Biol. 9:12e1003347
    [Google Scholar]
  21. Boocock D, Hino N, Ruzickova N, Hirashima T, Hannezo E. 2020. Theory of mechano-chemical patterning and optimal migration in cell monolayers. Nat. Phys. 17:267–74
    [Google Scholar]
  22. Borgqvist J, Malik A, Lundholm C, Logg A, Gerlee P, Cvijovic M. 2021. Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability. NPJ Syst. Biol. Appl. 7:13
    [Google Scholar]
  23. Bretschneider T, Anderson K, Ecke M, Müller-Taubenberger A, Schroth-Diez B et al. 2009. The three-dimensional dynamics of actin waves, a model of cytoskeletal self-organization. Biophys. J. 96:72888–900
    [Google Scholar]
  24. Brinkmann F, Mercker M, Richter T, Marciniak-Czochra A. 2018. Post-Turing tissue pattern formation: advent of mechanochemistry. PLOS Comput. Biol. 14:7e1006259
    [Google Scholar]
  25. Buck J, Buck E. 1968. Mechanism of rhythmic synchronous flashing of fireflies. Science 159:38211319–27
    [Google Scholar]
  26. Buijs RM, Kalsbeek A. 2001. Hypothalamic integration of central and peripheral clocks. Nat. Rev. Neurosci. 2:7521–26
    [Google Scholar]
  27. Cai L, Dalal CK, Elowitz MB. 2008. Frequency-modulated nuclear localization bursts coordinate gene regulation. Nature 455:7212485–90
    [Google Scholar]
  28. Caldarelli P, Chamolly A, Alegria-Prévot O, Gros J, Corson F. 2021. Self-organized tissue mechanics underlie embryonic regulation. bioRxiv 463661. https://doi.org/10.1101/2021.10.08.463661
    [Crossref]
  29. Ceriani MF, Darlington TK, Staknis D, Más P, Petti AA et al. 1999. Light-dependent sequestration of TIMELESS by CRYPTOCHROME. Science 285:5427553–56
    [Google Scholar]
  30. Chang JB, Ferrell JE Jr. 2013. Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle. Nature 500:7464603–7
    [Google Scholar]
  31. Chant J, Herskowitz I. 1991. Genetic control of bud site selection in yeast by a set of gene products that constitute a morphogenetic pathway. Cell 65:1203–12
    [Google Scholar]
  32. Cohen M, Georgiou M, Stevenson NL, Miodownik M, Baum B. 2010. Dynamic filopodia transmit intermittent Delta-Notch signaling to drive pattern refinement during lateral inhibition. Dev. Cell 19:178–89
    [Google Scholar]
  33. Collinet C, Lecuit T. 2021. Programmed and self-organized flow of information during morphogenesis. Nat. Rev. Mol. Cell Biol. 22:4245–65
    [Google Scholar]
  34. Collinet C, Rauzi M, Lenne P-F, Lecuit T. 2015. Local and tissue-scale forces drive oriented junction growth during tissue extension. Nat. Cell Biol. 17:101247–58
    [Google Scholar]
  35. Corson F, Couturier L, Rouault H, Mazouni K, Schweisguth F. 2017. Self-organized Notch dynamics generate stereotyped sensory organ patterns in Drosophila. Science 356:6337eaai7407
    [Google Scholar]
  36. Dasbiswas K, Hu S, Schnorrer F, Safran SA, Bershadsky AD. 2018. Ordering of myosin II filaments driven by mechanical forces: experiments and theory. Philos. Trans. R. Soc. B 373:174720170114
    [Google Scholar]
  37. de Boer PAJ, Crossley RE, Rothfield LI. 1989. A division inhibitor and a topological specificity factor coded for by the minicell locus determine proper placement of the division septum in E. coli. Cell 56:4641–49
    [Google Scholar]
  38. De Simone A, Evanitsky MN, Hayden L, Cox BD, Wang J et al. 2021. Control of osteoblast regeneration by a train of Erk activity waves. Nature 590:7844129–33
    [Google Scholar]
  39. Delacour D, Salomon J, Robine S, Louvard D. 2016. Plasticity of the brush border—the yin and yang of intestinal homeostasis. Nat. Rev. Gastroenterol. Hepatol. 13:3161–74
    [Google Scholar]
  40. Deneke VE, Melbinger A, Vergassola M, Di Talia S. 2016. Waves of Cdk1 activity in S phase synchronize the cell cycle in Drosophila embryos. Dev. Cell 38:4399–412
    [Google Scholar]
  41. Depasquale JA. 2018. Actin microridges. Anat. Rec. 301:122037–50
    [Google Scholar]
  42. Dierkes K, Sumi A, Solon J, Salbreux G. 2014. Spontaneous oscillations of elastic contractile materials with turnover. Phys. Rev. Lett. 113:14148102
    [Google Scholar]
  43. Driscoll MK, McCann C, Kopace R, Homan T, Fourkas JT et al. 2012. Cell shape dynamics: from waves to migration. PLOS Comput. Biol. 8:3e1002392
    [Google Scholar]
  44. Economou AD, Ohazama A, Porntaveetus T, Sharpe PT, Kondo S et al. 2012. Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate. Nat. Genet. 44:3348–51
    [Google Scholar]
  45. El-Sherif E, Averof M, Brown SJ. 2012. A segmentation clock operating in blastoderm and germband stages of Tribolium development. Development 139:234341–46
    [Google Scholar]
  46. El-Sherif E, Zhu X, Fu J, Brown SJ. 2014. Caudal regulates the spatiotemporal dynamics of pair-rule waves in Tribolium. PLOS Genet 10:10e1004677
    [Google Scholar]
  47. Emery P, So WV, Kaneko M, Hall JC, Rosbash M. 1998. CRY, a Drosophila clock and light-regulated cryptochrome, is a major contributor to circadian rhythm resetting and photosensitivity. Cell 95:5669–79
    [Google Scholar]
  48. Eom DS, Bain EJ, Patterson LB, Grout ME, Parichy DM. 2015. Long-distance communication by specialized cellular projections during pigment pattern development and evolution. eLife 4:e12401
    [Google Scholar]
  49. Ermentrout B. 1991. Stripes or spots? Nonlinear effects in bifurcation of reaction–diffusion equations on the square. Proc. R. Soc. A 434:1891413–17
    [Google Scholar]
  50. Etoc F, Metzger J, Ruzo A, Kirst C, Yoney A et al. 2016. A balance between secreted inhibitors and edge-sensing controls gastruloid self-organization. Dev. Cell 39:3302–15
    [Google Scholar]
  51. Evans T, Rosenthal ET, Youngblom J, Distel D, Hunt T. 1983. Cyclin: a protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division. Cell 33:2389–96
    [Google Scholar]
  52. Fernandez-Gonzalez R, de Matos Simoes S, Röper J-C, Eaton S, Zallen JA. 2009. Myosin II dynamics are regulated by tension in intercalating cells. Dev. Cell 17:5736–43
    [Google Scholar]
  53. Ferrell JE Jr., Tsai TY-C, Yang Q. 2011. Modeling the cell cycle: Why do certain circuits oscillate?. Cell 144:6874–85
    [Google Scholar]
  54. FitzHugh R. 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1:6445–66
    [Google Scholar]
  55. Frohnhöfer HG, Krauss J, Maischein H-M, Nüsslein-Volhard C. 2013. Iridophores and their interactions with other chromatophores are required for stripe formation in zebrafish. Development 140:142997–3007
    [Google Scholar]
  56. Gallagher KD, Mani M, Carthew RW. 2022. Emergence of a geometric pattern of cell fates from tissue-scale mechanics in the Drosophila eye. eLife 11:e72806
    [Google Scholar]
  57. Gavish A, Shwartz A, Weizman A, Schejter E, Shilo B-Z, Barkai N. 2016. Periodic patterning of the Drosophila eye is stabilized by the diffusible activator Scabrous. Nat. Commun. 7:10461
    [Google Scholar]
  58. Gelens L, Anderson GA, Ferrell JE. 2014. Spatial trigger waves: positive feedback gets you a long way. Mol. Biol. Cell 25:223486–93
    [Google Scholar]
  59. Gerisch G, Fromm H, Huesgen A, Wick U. 1975. Control of cell-contact sites by cyclic AMP pulses in differentiating Dictyostelium cells. Nature 255:5509547–49
    [Google Scholar]
  60. Giannone G, Dubin-Thaler BJ, Döbereiner H-G, Kieffer N, Bresnick AR, Sheetz MP. 2004. Periodic lamellipodial contractions correlate with rearward actin waves. Cell 116:3431–43
    [Google Scholar]
  61. Giannone G, Dubin-Thaler BJ, Rossier O, Cai Y, Chaga O et al. 2007. Lamellipodial actin mechanically links myosin activity with adhesion-site formation. Cell 128:3561–75
    [Google Scholar]
  62. Gierer A, Meinhardt H. 1972. A theory of biological pattern formation. Kybernetik 12:130–39
    [Google Scholar]
  63. Gjorevski N, Nikolaev M, Brown TE, Mitrofanova O, Brandenberg N et al. 2022. Tissue geometry drives deterministic organoid patterning. Science 375:6576eaaw9021
    [Google Scholar]
  64. Goehring NW, Trong PK, Bois JS, Chowdhury D, Nicola EM et al. 2011. Polarization of PAR proteins by advective triggering of a pattern-forming system. Science 334:60591137–41
    [Google Scholar]
  65. Goryachev AB, Pokhilko AV. 2008. Dynamics of Cdc42 network embodies a Turing-type mechanism of yeast cell polarity. FEBS Lett 582:101437–43
    [Google Scholar]
  66. Gray P, Scott SK. 1984. Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A + 2B → 3B; B → C. Chem. Eng. Sci. 39:61087–97
    [Google Scholar]
  67. Greenberg MJ, Arpağ G, Tüzel E, Ostap EM. 2016. A perspective on the role of myosins as mechanosensors. Biophys. J. 110:122568–76
    [Google Scholar]
  68. Gross P, Kumar KV, Goehring NW, Bois JS, Hoege C et al. 2019. Guiding self-organized pattern formation in cell polarity establishment. Nat. Phys. 15:3293–300
    [Google Scholar]
  69. Gross P, Kumar KV, Grill SW. 2017. How active mechanics and regulatory biochemistry combine to form patterns in development. Annu. Rev. Biophys. 46:337–56
    [Google Scholar]
  70. Halatek J, Brauns F, Frey E. 2018. Self-organization principles of intracellular pattern formation. Philos. Trans. R Soc. B 373:174720170107
    [Google Scholar]
  71. Hamaguchi MS, Hiramoto Y. 1978. Protoplasmic movement during polar-body formation in starfish oocytes. Exp. Cell Res. 112:155–62
    [Google Scholar]
  72. Hannezo E, Dong B, Recho P, Joanny J-F, Hayashi S. 2015. Cortical instability drives periodic supracellular actin pattern formation in epithelial tubes. PNAS 112:288620–25
    [Google Scholar]
  73. Hannezo E, Heisenberg C-P. 2019. Mechanochemical feedback loops in development and disease. Cell 178:112–25
    [Google Scholar]
  74. Hara K, Tydeman P, Kirschner M. 1980. A cytoplasmic clock with the same period as the division cycle in Xenopus eggs. PNAS 77:1462–66
    [Google Scholar]
  75. Harris AK, Stopak D, Warner P. 1984. Generation of spatially periodic patterns by a mechanical instability: a mechanical alternative to the Turing model. J. Embryol. Exp. Morphol. 80:11–20
    [Google Scholar]
  76. Harris AK, Stopak D, Wild P. 1981. Fibroblast traction as a mechanism for collagen morphogenesis. Nature 290:5803249–51
    [Google Scholar]
  77. Hashimoto H, Robin FB, Sherrard KM, Munro EM. 2015. Sequential contraction and exchange of apical junctions drives zippering and neural tube closure in a simple chordate. Dev. Cell 32:2241–55
    [Google Scholar]
  78. Hayakawa K, Tatsumi H, Sokabe M. 2011. Actin filaments function as a tension sensor by tension-dependent binding of cofilin to the filament. J. Cell Biol. 195:5721–27
    [Google Scholar]
  79. He L, Wang X, Tang HL, Montell DJ. 2010. Tissue elongation requires oscillating contractions of a basal actomyosin network. Nat. Cell Biol. 12:121133–42
    [Google Scholar]
  80. Heberlein U, Wolff T, Rubin GM. 1993. The TGFβ homolog dpp and the segment polarity gene hedgehog are required for propagation of a morphogenetic wave in the Drosophila retina. Cell 75:5913–26
    [Google Scholar]
  81. Heimburg T, Jackson AD. 2007. On the action potential as a propagating density pulse and the role of anesthetics. Biophys. Rev. Lett. 2:157–78
    [Google Scholar]
  82. Heyde A, Guo L, Jost C, Theraulaz G, Mahadevan L. 2021. Self-organized biotectonics of termite nests. PNAS 118:5e2006985118
    [Google Scholar]
  83. Hino N, Rossetti L, Marín-Llauradó A, Aoki K, Trepat X et al. 2020. ERK-mediated mechanochemical waves direct collective cell polarization. Dev. Cell 53:6646–60.e8
    [Google Scholar]
  84. Hiscock TW, Megason SG. 2015. Mathematically guided approaches to distinguish models of periodic patterning. Development 142:3409–19
    [Google Scholar]
  85. Ho WKW, Freem L, Zhao D, Painter KJ, Woolley TE et al. 2019. Feather arrays are patterned by interacting signalling and cell density waves. PLOS Biol 17:2e3000132
    [Google Scholar]
  86. Hodgkin AL, Huxley AF. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:4500–44
    [Google Scholar]
  87. Houk AR, Jilkine A, Mejean CO, Boltyanskiy R, Dufresne ER et al. 2012. Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration. Cell 148:1175–88
    [Google Scholar]
  88. Howard J, Grill SW, Bois JS. 2011. Turing's next steps: the mechanochemical basis of morphogenesis. Nat. Rev. Mol. Cell Biol. 12:6392–98
    [Google Scholar]
  89. Howell AS, Jin M, Wu C-F, Zyla TR, Elston TC, Lew DJ. 2012. Negative feedback enhances robustness in the yeast polarity establishment circuit. Cell 149:2322–33
    [Google Scholar]
  90. Hu Z, Lutkenhaus J. 1999. Topological regulation of cell division in Escherichia coli involves rapid pole to pole oscillation of the division inhibitor MinC under the control of MinD and MinE. Mol. Microbiol. 34:182–90
    [Google Scholar]
  91. Huang C-H, Tang M, Shi C, Iglesias PA, Devreotes PN. 2013. An excitable signal integrator couples to an idling cytoskeletal oscillator to drive cell migration. Nat. Cell Biol. 15:111307–16
    [Google Scholar]
  92. Iglesias PA, Devreotes PN. 2008. Navigating through models of chemotaxis. Curr. Opin. Cell Biol. 20:135–40
    [Google Scholar]
  93. Inagaki N, Katsuno H. 2017. Actin waves: origin of cell polarization and migration?. Trends Cell Biol 27:7515–26
    [Google Scholar]
  94. Irazoqui JE, Gladfelter AS, Lew DJ. 2003. Scaffold-mediated symmetry breaking by Cdc42p. Nat. Cell Biol. 5:121062–70
    [Google Scholar]
  95. Jaffe LF. 2008. Calcium waves. Philos. Trans. R Soc. B 363:14951311–17
    [Google Scholar]
  96. Kapustina M, Weinreb GE, Costigliola N, Rajfur Z, Jacobson K, Elston TC. 2008. Mechanical and biochemical modeling of cortical oscillations in spreading cells. Biophys. J. 94:124605–20
    [Google Scholar]
  97. Khuong A, Gautrais J, Perna A, Sbaï C, Combe M et al. 2016. Stigmergic construction and topochemical information shape ant nest architecture. PNAS 113:51303–8
    [Google Scholar]
  98. Kim HY, Davidson LA. 2011. Punctuated actin contractions during convergent extension and their permissive regulation by the non-canonical Wnt-signaling pathway. J. Cell Sci. 124:4635–46
    [Google Scholar]
  99. Koch AJ, Meinhardt H. 1994. Biological pattern formation: from basic mechanisms to complex structures. Rev. Mod. Phys. 66:41481–507
    [Google Scholar]
  100. Koenigsberger M, Seppey D, Bény J-L, Meister J-J. 2010. Mechanisms of propagation of intercellular calcium waves in arterial smooth muscle cells. Biophys. J. 99:2333–43
    [Google Scholar]
  101. Kondo S, Miura T. 2010. Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329:59991616–20
    [Google Scholar]
  102. Konopka RJ, Benzer S. 1971. Clock mutants of Drosophila melanogaster. PNAS 68:92112–16
    [Google Scholar]
  103. Koride S, He L, Xiong L-P, Lan G, Montell DJ, Sun SX. 2014. Mechanochemical regulation of oscillatory follicle cell dynamics in the developing Drosophila egg chamber. Mol. Biol. Cell 25:223709–16
    [Google Scholar]
  104. Kovács M, Thirumurugan K, Knight PJ, Sellers JR. 2007. Load-dependent mechanism of nonmuscle myosin 2. PNAS 104:249994–99
    [Google Scholar]
  105. Kruse K, Joanny JF, Jülicher F, Prost J, Sekimoto K. 2005. Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16:15–16
    [Google Scholar]
  106. Kryuchkov M, Bilousov O, Lehmann J, Fiebig M, Katanaev VL. 2020. Reverse and forward engineering of Drosophila corneal nanocoatings. Nature 585:7825383–89
    [Google Scholar]
  107. Kumar KV, Bois JS, Jülicher F, Grill SW. 2014. Pulsatory patterns in active fluids. Phys. Rev. Lett. 112:20208101
    [Google Scholar]
  108. Lecuit T, Lenne P-F. 2007. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nat. Rev. Mol. Cell Biol. 8:633–44
    [Google Scholar]
  109. Lecuit T, Lenne P-F, Munro E. 2011. Force generation, transmission, and integration during cell and tissue morphogenesis. Annu. Rev. Cell Dev. Biol. 27:157–84
    [Google Scholar]
  110. Li W, Llopis J, Whitney M, Zlokarnik G, Tsien RY. 1998. Cell-permeant caged InsP3 ester shows that Ca2+ spike frequency can optimize gene expression. Nature 392:6679936–41
    [Google Scholar]
  111. Liu C, Fu X, Liu L, Ren X, Chau CKL et al. 2011. Sequential establishment of stripe patterns in an expanding cell population. Science 334:6053238–41
    [Google Scholar]
  112. Loose M, Fischer-Friedrich E, Ries J, Kruse K, Schwille P. 2008. Spatial regulators for bacterial cell division self-organize into surface waves in vitro. Science 320:5877789–92
    [Google Scholar]
  113. Lotka AJ. 1920. Undamped oscillations derived from the law of mass action. J. Am. Chem. Soc. 42:81595–99
    [Google Scholar]
  114. Lubensky DK, Pennington MW, Shraiman BI, Baker NE. 2011. A dynamical model of ommatidial crystal formation. PNAS 108:2711145–50
    [Google Scholar]
  115. Machacek M, Hodgson L, Welch C, Elliott H, Pertz O et al. 2009. Coordination of Rho GTPase activities during cell protrusion. Nature 461:726099–103
    [Google Scholar]
  116. Machado PF, Blanchard GB, Duque J, Gorfinkiel N. 2014. Cytoskeletal turnover and Myosin contractility drive cell autonomous oscillations in a model of Drosophila Dorsal Closure. Eur. Phys. J. Spec. Top. 223:71391–402
    [Google Scholar]
  117. Mahalwar P, Walderich B, Singh AP, Nüsslein-Volhard C. 2014. Local reorganization of xanthophores fine-tunes and colors the striped pattern of zebrafish. Science 345:62021362–64
    [Google Scholar]
  118. Maini PK. 2004. Using mathematical models to help understand biological pattern formation. C. R. Biol. 327:3225–34
    [Google Scholar]
  119. Maini PK, Woolley TE, Baker RE, Gaffney EA, Lee SS. 2012. Turing's model for biological pattern formation and the robustness problem. Interface Focus 2:4487–96
    [Google Scholar]
  120. Maître J-L, Niwayama R, Turlier H, Nédélec F, Hiiragi T. 2015. Pulsatile cell-autonomous contractility drives compaction in the mouse embryo. Nat. Cell Biol. 17:7849–55
    [Google Scholar]
  121. Mammoto T, Ingber DE. 2010. Mechanical control of tissue and organ development. Development 137:91407–20
    [Google Scholar]
  122. Martin AC, Kaschube M, Wieschaus EF. 2009. Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457:7228495–99
    [Google Scholar]
  123. Menshykau D, Michos O, Lang C, Conrad L, McMahon AP, Iber D. 2019. Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback. Nat. Commun. 10:239
    [Google Scholar]
  124. Mercker M, Brinkmann F, Marciniak-Czochra A, Richter T. 2016. Beyond Turing: mechanochemical pattern formation in biological tissues. Biol. Direct 11:22
    [Google Scholar]
  125. Miao H, Blankenship JT. 2020. The pulse of morphogenesis: actomyosin dynamics and regulation in epithelia. Development 147:17dev186502
    [Google Scholar]
  126. Michaux JB, Robin FB, McFadden WM, Munro EM. 2018. Excitable RhoA dynamics drive pulsed contractions in the early C. elegans embryo. J. Cell Biol. 217:124230–52
    [Google Scholar]
  127. Michel M, Dahmann C. 2020. Tissue mechanical properties modulate cell extrusion in the Drosophila abdominal epidermis. Development 147:5dev179606
    [Google Scholar]
  128. Morse ES. 1916. Fireflies flashing in unison. Science 43:1101169–70
    [Google Scholar]
  129. Müller P, Rogers KW, Jordan BM, Lee JS, Robson D et al. 2012. Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system. Science 336:6082721–24
    [Google Scholar]
  130. Munjal A, Philippe J-M, Munro E, Lecuit T. 2015. A self-organized biomechanical network drives shape changes during tissue morphogenesis. Nature 524:7565351–55
    [Google Scholar]
  131. Munro E, Nance J, Priess JR. 2004. Cortical flows powered by asymmetrical contraction transport PAR proteins to establish and maintain anterior-posterior polarity in the early C. elegans embryo. Dev. Cell 7:3413–24
    [Google Scholar]
  132. Murray JD, Oster GF. 1984. Generation of biological pattern and form. Math. Med. Biol. 1:151–75
    [Google Scholar]
  133. Murray JD, Oster GF, Harris AK. 1983. A mechanical model for mesenchymal morphogenesis. J. Math. Biol. 17:1125–29
    [Google Scholar]
  134. Nakamasu A, Takahashi G, Kanbe A, Kondo S. 2009. Interactions between zebrafish pigment cells responsible for the generation of Turing patterns. PNAS 106:218429–34
    [Google Scholar]
  135. Newman SA, Frisch HL. 1979. Dynamics of skeletal pattern formation in developing chick limb. Science 205:4407662–68
    [Google Scholar]
  136. Nishikawa M, Naganathan SR, Jülicher F, Grill SW. 2017. Controlling contractile instabilities in the actomyosin cortex. eLife 6:e19595
    [Google Scholar]
  137. Nishimura M, Inoue Y, Hayashi S. 2007. A wave of EGFR signaling determines cell alignment and intercalation in the Drosophila tracheal placode. Development 134:234273–82
    [Google Scholar]
  138. Novák B, Tyson JJ. 2008. Design principles of biochemical oscillators. Nat. Rev. Mol. Cell Biol. 9:12981–91
    [Google Scholar]
  139. Ogura Y, Wen F-L, Sami MM, Shibata T, Hayashi S. 2018. A switch-like activation relay of EGFR-ERK signaling regulates a wave of cellular contractility for epithelial invagination. Dev. Cell 46:2162–72.e5
    [Google Scholar]
  140. Oster GF, Murray JD. 1989. Pattern formation models and developmental constraints. J. Exp. Zool. 251:2186–202
    [Google Scholar]
  141. Owen JP, Yates CA, Kelsh RN. 2021. Differential growth is a critical determinant of zebrafish pigment pattern formation. bioRxiv 448058. https://doi.org/10.1101/2021.06.11.448058
    [Crossref]
  142. Özkaya N, Leger D, Goldsheyder D, Nordin M. 2017. Mechanical properties of biological tissues. Fundamentals of Biomechanics: Equilibrium, Motion, and Deformation361–87 Cham, Switz: Springer Int. , 4th ed..
    [Google Scholar]
  143. Palmeirim I, Henrique D, Ish-Horowicz D, Pourquié O. 1997. Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis. Cell 91:5639–48
    [Google Scholar]
  144. Palmquist KH, Tiemann SF, Ezzeddine FL, Yang S, Pfeifer CRet al 2022. Reciprocal cell-ECM dynamics generate supracellular fluidity underlying spontaneous follicle patterning. Cell 185:11196073.e11
    [Google Scholar]
  145. Pálsson E, Cox EC. 1996. Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories. PNAS 93:31151–55
    [Google Scholar]
  146. Park H-O, Bi E. 2007. Central roles of small GTPases in the development of cell polarity in yeast and beyond. Microbiol. Mol. Biol. Rev. 71:148–96
    [Google Scholar]
  147. Peleg B, Disanza A, Scita G, Gov N. 2011. Propagating cell-membrane waves driven by curved activators of actin polymerization. PLOS ONE 6:4e18635
    [Google Scholar]
  148. Perna A, Theraulaz G. 2017. When social behaviour is moulded in clay: on growth and form of social insect nests. J. Exp. Biol. 220:183–91
    [Google Scholar]
  149. Pourquié O. 2003. The segmentation clock: converting embryonic time into spatial pattern. Science 301:5631328–30
    [Google Scholar]
  150. Purvis JE, Lahav G. 2013. Encoding and decoding cellular information through signaling dynamics. Cell 152:5945–56
    [Google Scholar]
  151. Pye K, Chance B. 1966. Sustained sinusoidal oscillations of reduced pyridine nucleotide in a cell-free extract of Saccharomyces carlsbergensis. PNAS 55:4888–94
    [Google Scholar]
  152. Rashevsky N. 1940. An approach to the mathematical biophysics of biological self-regulation and of cell polarity. Bull. Math. Biophys. 2:115–25
    [Google Scholar]
  153. Raskin DM, de Boer PAJ. 1999. Rapid pole-to-pole oscillation of a protein required for directing division to the middle of Escherichia coli. PNAS 96:94971–76
    [Google Scholar]
  154. Raspopovic J, Marcon L, Russo L, Sharpe J. 2014. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science 345:6196566–70
    [Google Scholar]
  155. Rauzi M, Lenne P-F, Lecuit T. 2010. Planar polarized actomyosin contractile flows control epithelial junction remodelling. Nature 468:73271110–14
    [Google Scholar]
  156. Razzell W, Wood W, Martin P. 2014. Recapitulation of morphogenetic cell shape changes enables wound re-epithelialisation. Development 141:91814–20
    [Google Scholar]
  157. Ready DF, Chang HC. 2021. Calcium waves facilitate and coordinate the contraction of endfeet actin stress fibers in Drosophila interommatidial cells. Development 148:22dev199700
    [Google Scholar]
  158. Ready DF, Hanson TE, Benzer S. 1976. Development of the Drosophila retina, a neurocrystalline lattice. Dev. Biol. 53:2217–40
    [Google Scholar]
  159. Reddy P, Zehring WA, Wheeler DA, Pirrotta V, Hadfield C et al. 1984. Molecular analysis of the period locus in Drosophila melanogaster and identification of a transcript involved in biological rhythms. Cell 38:3701–10
    [Google Scholar]
  160. Ren Y, Effler JC, Norstrom M, Luo T, Firtel RA et al. 2009. Mechanosensing through cooperative interactions between myosin II and the actin crosslinker cortexillin I. Curr. Biol. 19:171421–28
    [Google Scholar]
  161. Rodríguez-Franco P, Brugués A, Marín-Llauradó A, Conte V, Solanas G et al. 2017. Long-lived force patterns and deformation waves at repulsive epithelial boundaries. Nat. Mater. 16:101029–37
    [Google Scholar]
  162. Rogers KW, Lord ND, Gagnon JA, Pauli A, Zimmerman S et al. 2017. Nodal patterning without Lefty inhibitory feedback is functional but fragile. eLife 6:e28785
    [Google Scholar]
  163. Roth S, Lynch JA. 2009. Symmetry breaking during Drosophila oogenesis. Cold Spring Harb. Perspect. Biol. 1:2a001891
    [Google Scholar]
  164. Ryan GL, Petroccia HM, Watanabe N, Vavylonis D. 2012a. Excitable actin dynamics in lamellipodial protrusion and retraction. Biophys J 102:71493–502
    [Google Scholar]
  165. Ryan GL, Watanabe N, Vavylonis D. 2012b. A review of models of fluctuating protrusion and retraction patterns at the leading edge of motile cells. Cytoskeleton 69:4195–206
    [Google Scholar]
  166. Sarfati R, Hayes JC, Peleg O. 2021. Self-organization in natural swarms of Photinus carolinus synchronous fireflies. Sci. Adv. 7:28eabg9259
    [Google Scholar]
  167. Schauer A, Pinheiro D, Hauschild R, Heisenberg C-P. 2020. Zebrafish embryonic explants undergo genetically encoded self-assembly. eLife 9:e55190
    [Google Scholar]
  168. Scholes NS, Schnoerr D, Isalan M, Stumpf MPH. 2019. A comprehensive network atlas reveals that Turing patterns are common but not robust. Cell Syst 9:3243–57.e4
    [Google Scholar]
  169. Schweisguth F, Corson F. 2019. Self-organization in pattern formation. Dev. Cell 49:5659–77
    [Google Scholar]
  170. Scoones JC, Hiscock TW. 2020. A dot-stripe Turing model of joint patterning in the tetrapod limb. Development 147:8dev183699
    [Google Scholar]
  171. Segel LA, Jackson JL. 1972. Dissipative structure: an explanation and an ecological example. J. Theor. Biol. 37:3545–59
    [Google Scholar]
  172. Sekine R, Shibata T, Ebisuya M. 2018. Synthetic mammalian pattern formation driven by differential diffusivity of Nodal and Lefty. Nat. Commun. 9:5456
    [Google Scholar]
  173. Serra-Picamal X, Conte V, Vincent R, Anon E, Tambe DT et al. 2012. Mechanical waves during tissue expansion. Nat. Phys. 8:8628–34
    [Google Scholar]
  174. Shlomovitz R, Gov NS. 2007. Membrane waves driven by actin and myosin. Phys. Rev. Lett. 98:16168103
    [Google Scholar]
  175. Shyer AE, Rodrigues AR, Schroeder GG, Kassianidou E, Kumar S, Harland RM. 2017. Emergent cellular self-organization and mechanosensation initiate follicle pattern in the avian skin. Science 357:6353811–15
    [Google Scholar]
  176. Simões S, Oh Y, Wang MFZ, Fernandez-Gonzalez R, Tepass U. 2017. Myosin II promotes the anisotropic loss of the apical domain during Drosophila neuroblast ingression. J. Cell Biol. 216:51387–404
    [Google Scholar]
  177. Simunovic M, Metzger JJ, Etoc F, Yoney A, Ruzo A et al. 2019. A 3D model of a human epiblast reveals BMP4-driven symmetry breaking. Nat. Cell Biol. 21:7900–10
    [Google Scholar]
  178. Slaughter BD, Smith SE, Li R. 2009. Symmetry breaking in the life cycle of the budding yeast. Cold Spring Harb. Perspect. Biol. 1:3a003384
    [Google Scholar]
  179. Solon J, Kaya-Çopur A, Colombelli J, Brunner D. 2009. Pulsed forces timed by a ratchet-like mechanism drive directed tissue movement during dorsal closure. Cell 137:71331–42
    [Google Scholar]
  180. Staddon MF, Munro EM, Banerjee S. 2022. Pulsatile contractions and pattern formation in excitable actomyosin cortex. PLOS Comput. Biol 183e1009981
  181. Steinberg MS. 1962. On the mechanism of tissue reconstruction by dissociated cells, III. Free energy relations and the reorganization of fused, heteronomic tissue fragments. PNAS 48:101769–76
    [Google Scholar]
  182. Theraulaz G, Bonabeau E, Nicolis SC, Solé RV, Fourcassié V et al. 2002. Spatial patterns in ant colonies. PNAS 99:159645–49
    [Google Scholar]
  183. Thomas D. 1976. Artificial enzyme membranes. Transport, memory and oscillatory phenomena. Analysis and Control of Immobilized Enzyme Systems: Proceedings of an International Symposium115–50 New York: Elsevier
    [Google Scholar]
  184. Tkachenko E, Sabouri-Ghomi M, Pertz O, Kim C, Gutierrez E et al. 2011. Protein Kinase A governs a RhoA-RhoGDI protrusion-retraction pacemaker in migrating cells. Nat. Cell Biol. 13:6660–67
    [Google Scholar]
  185. Tlili S, Gauquelin E, Li B, Cardoso O, Ladoux B et al. 2018. Collective cell migration without proliferation: density determines cell velocity and wave velocity. R. Soc. Open Sci. 5:5172421
    [Google Scholar]
  186. Tsai TY-C, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JE Jr. 2008. Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321:5885126–29
    [Google Scholar]
  187. Turing AM. 1952. The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237:64137–72
    [Google Scholar]
  188. van Loon AP, Erofeev IS, Goryachev AB, Sagasti A. 2021. Stochastic contraction of myosin minifilaments drives evolution of microridge protrusion patterns in epithelial cells. Mol. Biol. Cell 32:161501–13
    [Google Scholar]
  189. Veerman F, Mercker M, Marciniak-Czochra A. 2021. Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback. Philos. Trans. R. Soc. A. 379:20200278
    [Google Scholar]
  190. Vergassola M, Deneke VE, Talia SD. 2018. Mitotic waves in the early embryogenesis of Drosophila: bistability traded for speed. PNAS 115:10E2165–74
    [Google Scholar]
  191. Vicker MG. 2002. F-actin assembly in Dictyostelium cell locomotion and shape oscillations propagates as a self-organized reaction–diffusion wave. FEBS Lett 510:1–25–9
    [Google Scholar]
  192. Volterra V. 1926. Fluctuations in the abundance of a species considered mathematically. Nature 2972:558–60
    [Google Scholar]
  193. Wagner EL, Shin J-B. 2019. Mechanisms of hair cell damage and repair. Trends Neurosci 42:6414–24
    [Google Scholar]
  194. Walton KD, Mishkind D, Riddle MR, Tabin CJ, Gumucio DL. 2018. Blueprint for an intestinal villus: species-specific assembly required. Wiley Interdiscip. Rev. Dev. Biol. 7:4e317
    [Google Scholar]
  195. Warmflash A, Sorre B, Etoc F, Siggia ED, Brivanlou AH. 2014. A method to recapitulate early embryonic spatial patterning in human embryonic stem cells. Nat. Methods 11:8847–54
    [Google Scholar]
  196. Watanabe M, Kondo S. 2015a. Comment on “Local reorganization of xanthophores fine-tunes and colors the striped pattern of zebrafish. .” Science 348:6232297
    [Google Scholar]
  197. Watanabe M, Kondo S. 2015b. Is pigment patterning in fish skin determined by the Turing mechanism?. Trends Genet 31:288–96
    [Google Scholar]
  198. Wedlich-Soldner R, Altschuler S, Wu L, Li R. 2003. Spontaneous cell polarization through actomyosin-based delivery of the Cdc42 GTPase. Science 299:56101231–35
    [Google Scholar]
  199. Wedlich-Söldner R, Betz T. 2018. Self-organization: the fundament of cell biology. Philos. Trans. R. Soc. B 373:174720170103
    [Google Scholar]
  200. Weiner OD, Marganski WA, Wu LF, Altschuler SJ, Kirschner MW. 2007. An actin-based wave generator organizes cell motility. PLOS Biol 5:9e221
    [Google Scholar]
  201. Wettmann L, Kruse K. 2018. The Min-protein oscillations in Escherichia coli: an example of self-organized cellular protein waves. Philos. Trans. R. Soc. B 373:174720170111
    [Google Scholar]
  202. Wigbers MC, Tan TH, Brauns F, Liu J, Swartz SZ et al. 2021. A hierarchy of protein patterns robustly decodes cell shape information. Nat. Phys. 17:5578–84
    [Google Scholar]
  203. Wu Z, Su M, Tong C, Wu M, Liu J. 2018. Membrane shape-mediated wave propagation of cortical protein dynamics. Nat. Commun. 9:1136
    [Google Scholar]
  204. Yang Y, Wu M. 2018. Rhythmicity and waves in the cortex of single cells. Philos. Trans. R Soc. B 373:174720170116
    [Google Scholar]
  205. Yu JC, Fernandez-Gonzalez R. 2016. Local mechanical forces promote polarized junctional assembly and axis elongation in Drosophila. eLife 5:e10757
    [Google Scholar]
  206. Zehring WA, Wheeler DA, Reddy P, Konopka RJ, Kyriacou CP et al. 1984. P-element transformation with period locus DNA restores rhythmicity to mutant, arrhythmic Drosophila melanogaster. Cell 39:2, Part 1369–76
    [Google Scholar]
  207. Zhang S, Teng X, Toyama Y, Saunders TE. 2020. Periodic oscillations of myosin-II mechanically proofread cell-cell connections to ensure robust formation of the cardiac vessel. Curr. Biol. 30:173364–77.e4
    [Google Scholar]
/content/journals/10.1146/annurev-cellbio-120420-095337
Loading
/content/journals/10.1146/annurev-cellbio-120420-095337
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error