Bifurcations in Insect Morphogenesis I

  • Stuart A. Kauffman
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 75)


The past decade has witnessed a renewal of deep interest in the problem of pattern formation in developmental biology. In large measure, the resurgence of enthusiasm coincides with Wolpert’s reformulation of this fundamental problem in terms of the concept of positional information [Wolpert, 1969, 1971]. Novel features of Wolpert’s theory have led both to proposals of alternative “coordinate systems” supplying positional information, and to a rich variety of experiments designed to test the alternatives. The present article provides a brief review of the major alternatives which leads to the formulation of a new class of models based on the unrecognized, but common capacity of biochemical reaction-diffusion systems to generate transverse (cross) gradients in growing asymmetrical tissue domains.


Positional Information Imaginal Disc Polar Model Wing Disc Complementary Fragment 
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  1. Apter, M.J., 1966, “Cybernetics and Development,” International Series of Monographs in Pure and Applied Biology/Zoology Division, Vol. 29, Pergamon Press, New York, London.Google Scholar
  2. Auchmuty, J.F.G., 1977, Qualitative effects of diffusion in chemical systems, Lectures on Mathematics in the Life Sciences, 10: 49.MathSciNetGoogle Scholar
  3. Auchmuty, J.F.G., and Nicolis, G., 1975, Bifurcation analysis of nonlinear reaction-diffusion equations. I. Evolution and the steady state solutions, Bull,. Math. Biol., 37: 323.MathSciNetMATHGoogle Scholar
  4. Babloyantz, A., and Hiernaux, J., 1975, Models for cell differentiation and generation of polarity in diffusion-governed morphogenetic fields, Bull. Math. Biol., 37: 637.MATHGoogle Scholar
  5. Bohn, H., 1965, Analyse der Regenerationsfahigkeit der Insektenextre-mität durch Amputations und Transplantationsversuche an Larven der Afrikanischen Schabe Leucophaea maderae Fabr. (Blattaria). I. Regenerationspotenzen, Wilhelm Roux’s Archives, 156: 49.CrossRefGoogle Scholar
  6. Bohn, H., 1970, Interkalare Regeneration und segmentale Gradienten bei den Extremitäten von Leucophaea-Larven (Blattaria). I. Femur und Tibia, Wilhelm Roux’s Archives, 165: 303.CrossRefGoogle Scholar
  7. Bohn, H., 1971, Interkalare Regeneration und segmentale Gradienten bei den Extremitäten von Leucophaea-Larven (Blattaria). III. Die Herkunft des interkalaren Regenerates, Wilhelm Roux’s Archives, 167: 209.CrossRefGoogle Scholar
  8. Bohn, H., 1972, The Origin of the epidermis in the supernumerary regenerates of triple legs in cockroaches (Blattaria), J. Embryol. Exp. Morphol., 28: 185.Google Scholar
  9. Bryant, P.J., 1975, Pattern formation in the imaginai wing disc of Prosophila melanogaster: fate map, regeneration and duplication, J. Exp. Biol., 193: 49.Google Scholar
  10. Bryant, P.J., Bryant, S.V., and French, V., 1977, Biological regeneration and pattern formation, Sei. Amer., 237: 66.ADSGoogle Scholar
  11. Bryant, P.J., and Hsei, B.W., 1977, Pattern formation in asymmetrical imaginai discs of Drosophila melanogaster, Amer. Zool., 17: 595.Google Scholar
  12. Bryant, P.J. and Schubiger, G., 1971, Giant and duplicated imaginai discs in a new lethal mutant of Drosophila melanogaster, Dev. Biol., 24: 233.CrossRefGoogle Scholar
  13. Bryant, S.V., 1978, Pattern regulation and cell commitment in amphibian limbs, in: “The Clonal Basis of Development.” 36th Symp. Soc. Develop. Biol.Google Scholar
  14. Bryant, S.V., French, V., and Bryant, P., 1980, Distal regeneration and symmetry, submitted for publication.Google Scholar
  15. Bryant, S.V., and Iten, L.B., 1976. Supernumerary limbs in amphibians: Experimental production in Notophthalmus viridescens and a new interpretation of their formation, Dev. Biol., 50: 212.CrossRefGoogle Scholar
  16. Bulliere, D., 1970, Interpretation des régénerats multiples chez les insectes, J. Embryol. Exp. Morphol., 23: 337.Google Scholar
  17. Bulliere, D., 1971, Utilisation de la régénération intercalaire pour l’étude de la détermination cellulaire au cours de la morpho-genèse chez Blabera cranifer (Insecte Dictyoptere), Dev. Biol., 25: 672.CrossRefGoogle Scholar
  18. Bunow, B., Kernevez, J, P., Joly, G., and Thomas, D., 1980, Pattern formation by reaction-diffusion instabilities: Applications to morphogenesis in Drosophila, J. Theor. Biol., 84: 629.MathSciNetCrossRefGoogle Scholar
  19. Butler, E.G., 1955, Regeneration of the urodele forelimb after reversal of its proximodistal axis, J. Morphol., 96: 265.CrossRefGoogle Scholar
  20. Carlson, B.M., Civiletto, S.E., and Goshgarian, H.G., 1974, Nerve interactions and regenerative processes occurring in newt limbs fused end-to-end, Dev. Biol., 37: 248.CrossRefGoogle Scholar
  21. Chung, S.H., and Cooke, J., 1975. Polarity of structure and of ordered nerve connections in the developing amphibian brain, Nature, 258: 126.ADSCrossRefGoogle Scholar
  22. Cohen, N., 1971, Amphibian transplantation reactions: A review., Amer. Zool., 11: 193.Google Scholar
  23. Cooke, J., 1975, The emergence and regulation of spatial organization in early animal development, Annu. Rev. Biophys. Bioeng., 4: 185.CrossRefGoogle Scholar
  24. Cummins, F.W., and Prothero, J.W., 1978, A model of pattern formation in multicellular organisms, Collective Phenomena, 3: 41.Google Scholar
  25. Deak, I.I., 1980, A model linking segmentation, compartmentalization and regeneration in Drosophila development, J. Theor. Biol., 84: 477.CrossRefGoogle Scholar
  26. Dent, J.N., 1954, A study of regenerates emanating from limb trans-plants with reversed proximodistal polarity in the adult newt, Anat. Ree., 118: 841.CrossRefGoogle Scholar
  27. Duranceau, C., 1977, Control of growth and pattern formation in the imaginal wing disc of Drosophila melanogaster, Ph.D. Thesis, Univ. Calif., Irvine.Google Scholar
  28. Erneux, T., and Hiernaux, J., 1980, Transition from polar to duplicate patterns, J. Math. Biol., 9: 193.MathSciNetMATHCrossRefGoogle Scholar
  29. French, V., 1976, Leg regeneration in the cockroach, Blattella germanica. I. Regeneration from a congruent tibial graft-host junction, Wilhelm Roux’s Archives, 179: 57.CrossRefGoogle Scholar
  30. French, V., 1976, Leg regeneration in the cockroach, Blattella germanica. II. Regeneration from a noncongruent tibial graft-host junction, J. Embryol. Exp. Morphol. 35: 267.Google Scholar
  31. French, V., Bryant, P.J., and Bryant, S.V., 1976, Pattern regulation in epimorphic fields, Science, 193: 969.ADSCrossRefGoogle Scholar
  32. Gehring, W., 1966, Bildung eines vollständigen Mittelbeins mit Sternopleura in der Antennenregion bei der Mutante Nasobemia (Ns) von Drosophila melanogaster, Arch. Julius Klaus-Stift. Vereb. Forsch, 41: 44.Google Scholar
  33. Gehring, W., and Nöthiger, R., 1973, The imaginal discs of Drosophila, in: “Developmental Systems: Insects,” S.J. Counce and C. Waddington, ed., Academic Press, New York.Google Scholar
  34. Gierer, A., and Meinhardt, H., 1972, A theory of biological pattern formation, Kybernetik, 12: 30.CrossRefGoogle Scholar
  35. Gmitro, J.I., and Sciven, L.E., 1966, in: “Intracellular Transport,” K.B. Warren, ed., Academic Press, New York.Google Scholar
  36. Harrison, R.G., 1918, Experiments on the development of the forelimb of Amblystoma, a self-differentiating equipotential system, J. Exp. Zool., 25: 413.Google Scholar
  37. Harrison, R.G., 1921, On relations of symmetry in transplanted limbs, J. Exp. Zool. 32: 1.CrossRefGoogle Scholar
  38. Harrison, R.G., 1969, “Organization and Development of the Embryo,” S. Wilens, ed., Yale University Press, New Haven.Google Scholar
  39. Haynie, J.L., and Bryant, P.J., 1976, Intercalary regeneration in imaginal discs of Drosophila melanogaster, Nature, 259: 659.ADSCrossRefGoogle Scholar
  40. Haynie, J.L., and Schubiger, G., 1979, Absence of distal to proximal intercalary regeneration in imaginal wing discs of Drosophila melanogaster, Dev. Biol., 68: 151.CrossRefGoogle Scholar
  41. Herschkowitz-Kaufman, M., 1975, Bifurcation analysis of nonlinear reaction-diffusion equations. II. Steady state solutions and comparison with numerical simulations, Bull. Math. Biol., 37: 589.MathSciNetMATHCrossRefGoogle Scholar
  42. Hiernaux, J., and Erneux, T., 1979, Chemical patterns in circular morphogenetic fields, Bull. Math. Biol. 41: 461.MathSciNetGoogle Scholar
  43. Holder, N., Tank, P., and Bryant, S.V., 1980, Regeneration of symmetrical forelimbs in the axolotl, Ambystoma mexicanam, Dev. Biol., 74: 302.CrossRefGoogle Scholar
  44. Hunt, R.K., 1975, Developmental programming for retinotectal patterns, in: “Cell Patterning,” Ciba Foundation Symposium 29, Associated Scientific Publishers, Amsterdam.Google Scholar
  45. Jacobson, M., 1968, Development of neuronal specificity in retinal ganglion cells of Xenopus, Dev. Biol., 17: 202.CrossRefGoogle Scholar
  46. Jürgens, G., and Gateff, E., 1979, Pattern specification in imaginal discs of Drosophila melanogaster: Developmental analysis of a temperature-sensitive mutant producing duplicated legs, Wilhelm Roux’s Archives, 186: 1.CrossRefGoogle Scholar
  47. Kauffman, S.A., 1978, A Cartesian coordinate model of positional information in imaginal discs of Drosophila, 20th Annual Drosophila Conference.Google Scholar
  48. Kauffman, S.A., and Ling, E., 1981, Regeneration by complementary wing disc fragments of Drosophila melanogaster, Dev. Biol., 82: 238.CrossRefGoogle Scholar
  49. Kauffman, S.A., Shymko, R., and Trabert, K., 1978, Control of sequential compartment formation in Drosophila, Science, 199: 259.ADSCrossRefGoogle Scholar
  50. Kernevez, J. P., 1980, “Enzyme Mathematics,” North Holland, Amsterdam, in press.Google Scholar
  51. Krivi, G.G., and Schneiderman, H.A., 1980, Pattern regulation in Drosophila wing disc reaggregates, submitted for publication.Google Scholar
  52. Lacalli, T.C., and Harrison, L.G., 1978, The regulatory capacity of Turing’s model for morphogenesis, with application to slime moulds., J. Theor. Biol., 70: 273.MathSciNetCrossRefGoogle Scholar
  53. Meinhardt, H.A., 1977, A model of pattern formation in insect embryogenesis, J. Cell. Sci., 23: 117.Google Scholar
  54. Milosevic, B.D., 1924, Beiträge zur Frage über die Determination der Regenerate, Wilhelm Roux’s Archives, 103: 80.Google Scholar
  55. Morgan, T.H., 1901, “Regeneration,” MacMillan, New York.Google Scholar
  56. Needham, A.E., 1965, “Regeneration in Animals and Related Problems,” V. Kortsis and H. Trampusch, ed., North Holland, Amsterdam.Google Scholar
  57. Nicolis, G., and Prigogine, I., 1977, “Self-organization in Non-equilibrium Systems,” Interscience, New York.Google Scholar
  58. Ouweneel, W.J., 1976, Developmental genetics and homeosis, Adv. Gen., 18: 179.CrossRefGoogle Scholar
  59. Ouweneel, W.J., 1969, Morphology and development of loboidophthalmoptera, a homeotic strain in Drosophila melanogaster, Wilhelm Roux’s Archives, 164: 1.CrossRefGoogle Scholar
  60. Postlethwait, J.H., 1974, Development of the temperature sensitive homeotic mutant eyeless ophthalmoptera of Drosophila melanogaster, Dev. Biol., 36: 212.CrossRefGoogle Scholar
  61. Postlethwait, J.H., and Schneiderman, H.A., 1974, Developmental genetics of Drosophila imaginal discs, Ann. Rev. Genetics, 7: 381.CrossRefGoogle Scholar
  62. Reinhardt, C., Hodgkin, N.M., and Bryant, P.J., 1977, Wound healing in imaginal discs of Drosophila. I. Scanning electron microscopy of normal and healing wing discs, Dev. Biol., 60: 238.CrossRefGoogle Scholar
  63. Roberts, P., 1964, Mosaics involving aristapedia, a homeotic mutant Drosophila melanogaster, Genetics, 49: 593.Google Scholar
  64. Rose, S.M., 1962, Tissue-arc control of regeneration in the amphibian limb, Symp. Soc. Study Develop. Growth, 20: 153.Google Scholar
  65. Russell, M., 1978, A spherical coordinate model of positional information, 20th Annual Drosophila Conference.Google Scholar
  66. Sander, K., 1977, Current understanding of cytoplasmic control centers, in: “Insect Embryology,” S.W. Visscher, ed., Montana State University Press.Google Scholar
  67. Sattinger, D.H., 1972, Topics in stability and bifurcation theory, in: “Lecture Notes in Mathematics. Vol. 309,” Springer-Verlag, Heidelberg.Google Scholar
  68. Schubiger, G., 1971, Regeneration, duplication and transdetermination in fragments of the leg disc of Drosophila melanogaster, Dev. Biol., 67: 286.CrossRefGoogle Scholar
  69. Schubiger, G., and Schubiger, M., 1978, Distal transformation in Drosophila leg imaginal disc fragments, Dev. Biol., 67: 286.CrossRefGoogle Scholar
  70. Sengel, P., 1953, Sur 11 induction d’une zone pharyngienne chez la planaire d’eau douce Dugesia lugubris. Schm., Arch. d’Anat. Mier., 42: 57.Google Scholar
  71. Slack, J., 1980, A serial threshold theory of regeneration, J. Theor. Biol. 82: 105.MathSciNetCrossRefGoogle Scholar
  72. Slack, J., and Savage, S., 1978a, Regeneration of reduplicated limbs in contravention of the complete circle rule, Nature, 271: 760.ADSCrossRefGoogle Scholar
  73. Slack, J., and Savage, S., 1978b, Regeneration of mirror symmetrical limbs in the axolotl, Cell, 14: 1.CrossRefGoogle Scholar
  74. Stern, C., 1968, Developmental genetics of pattern, in: “Genetic Mosaics and Other Essays,” Harvard University Press, Cambridge, Mass.Google Scholar
  75. Stocum, D.L., 1978, Regeneration of symmetrical hindlimbs in larval salamanders, Science, 200: 790.ADSCrossRefGoogle Scholar
  76. Stocum, D.L., 1975, Regulation after proximal or distal transposition of limb regeneration blastemas and determination of the proximal boundary of the regenerate, Dev. Biol., 45: 112.CrossRefGoogle Scholar
  77. Strub, S., 1977, Development potential of the cells of the male foreleg disc of Drosophila, Wilhelm Roux’s Archives, 181: 309.CrossRefGoogle Scholar
  78. Swett, F.H., 1977, Determination of limb axes, Quart. Rev. Biol., 12: 322.Google Scholar
  79. Swett, F.H., 1924, Exceptions to Bateson’s rules of mirror symmetry, Anat. Rec., 28: 63.CrossRefGoogle Scholar
  80. Tank, P.W., and Holder, N.,. 1978, The effect of healing time on the proximodistal organization of double-half forelimb regenerates in the axolotl, Abystoma mexicanum, Dev. Biol., 66: 72.CrossRefGoogle Scholar
  81. Tokunaga, C., 1978, Genetic mosaic studies of pattern formation in Drosophila melanogaster, with special reference to the pre- pattern hypothesis, jln: “Results and Problems of Cell Differentiation, Genetic Mosaics and Cell Differentiation, Vol. 9,” A. Gehring, ed. Springer-Verlag, Heidelberg, New York.Google Scholar
  82. Turing, A.M., 1952, The chemical basis of morphogenesis, Philos. Trans. R. Soc. London, Ser. B., 237: 37.ADSCrossRefGoogle Scholar
  83. Van der Meer, J.M., and Ouweneel, W.J., 1974, Differentiation capacities of the dorsal mesothoracic (haltere) disc of Drosophila melanogaster. II. Regeneration and duplication, Wilhelm Roux’s Archives, 174: 361.CrossRefGoogle Scholar
  84. Weiss, P., 1939, “Principles of Development,” Holt, Reinhart and Winston, New York.Google Scholar
  85. Winfree, A.T., 1980, “The Geometry of Biological Time. Biomathematics Vol. 8,” Springer-Verlag, Heidelberg, New York.Google Scholar
  86. Wolpert, L., 1971, Positional information and pattern formation, in: “Current Topics in Developmental Biology, Vol. 6,” A.A. Moscana and A. Monroy, ed., Academic Press, New York.Google Scholar
  87. Wolpert, L., 1969, Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol., 25: 1.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • Stuart A. Kauffman
    • 1
  1. 1.Department of Biochemistry and BiophysicsUniversity of Pennsylvania School of MedicinePhiladelphiaUSA

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