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Antisymmetry, directional asymmetry, and dynamic morphogenesis

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Abstract

Fluctuating asymmetry is the most commonly used measure of developmental instability. Some authors have claimed that antisymmetry and directional asymmetry may have a significant genetic basis, thereby rendering these forms of asymmetry useless for studies of developmental instability. Using a modified Rashevsky-Turing reaction-diffusion model of morphogenesis, we show that both antisymmetry and directional asymmetry can arise from symmetry-breaking phase transitions. Concentrations of morphogen on right and left sides can be induced to undergo transitions from phase-locked periodicity, to phase-lagged periodicity, to chaos, by simply changing the levels of feedback and inhibition in the model. The chaotic attractor has two basins of attraction-right sidedominance and left side dominance. With minor disturbance, a developmental trajectory settles into one basin or the other. With increasing disturbance, the trajectory can jump from basin to basin. The changes that lead to phase transitions and chaos are those expected to occur with either genetic change or stress. If we assume that the morphogen influences the behavior of cell populations, then a transition from phase-locked periodicity to chaos in the morphogen produces a corresponding transition from fluctuating asymmetry to antisymmetry in both morphogen concentrations and cell populations. Directional asymmetry is easily modeled by introducing a bias in the conditions of the simulation. We discuss the implications of this model for researchers using fluctuating asymmetry as an indicator of stress.

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References

  • Alekseeva, T. A., V. V. Zinichev & A. I. Zotin, 1992. Energy criteria of reliability and stability of development, pp. 159–165 in Developmental Stability in Natural Populations, edited by V. M. Zakharov & J. H. Graham. Volume 191, Acta Zoologica Fennica, Finnish Zoological Publishing Board, Helsinki.

    Google Scholar 

  • Ashby, W. R., 1956. An Introduction to Cybernetics. John Wiley and Sons, New York.

    Google Scholar 

  • Bailly, F., F. Gaill & R. Mosseri. 1991. A dynamical system for biological development: the case ofCaenorhabditis elegans. Acta Biotheoretica 39: 167–184.

    Article  CAS  PubMed  Google Scholar 

  • Bergé, P., Y. Pomeau & C. Vidal, 1984. Order Within Chaos: Towards a Deterministic Approach to Turbulence. John Wiley and Sons, New York.

    Google Scholar 

  • Cunningham, W. J., 1963. The concept of stability. American Scientist 51: 425–436.

    Google Scholar 

  • De Pomerai, D., 1990. From Gene to Animal: An Introduction to the Molecular Biology of Animal Development. 2nd Edition. Cambridge University Press, Cambridge.

    Google Scholar 

  • Devroetes, P., 1989.Dictyostelium discoideum: a model system for cell-cell interactions in development. Science 245: 1054–1058.

    Google Scholar 

  • Emlen, J. M., D. C. Freeman & J. H. Graham, 1993. Nonlinear growth dynamics and the origin of fluctuating asymmetry, pp. 77–96 in Developmental Instability: Origins and Evolutionary Significance, edited by T. Markow, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Freeman, D. C., J. H. Graham & J. M. Emlen, 1993. Developmental stability in plants: symmetries, stress, and epigenetic effects, pp. 97–119 in Developmental Instability: Origins and Evolutionary Significance, edited by T. Markow. Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Gilbert, S. F., 1991. Developmental Biology, 3rd Edition. Sinauer Associates, Sunderland, Massachusetts.

    Google Scholar 

  • Glass, L., editor, 1991. Nonlinear Dynamics of Physiological Function and Control. Chaos 1: 1-132.

  • Goldbeter, A. & J. L. Martiel, 1987. Periodic behaviour and chaos in the mechanism of intercellular communication governing aggregation ofDictyostelium amoebae, pp. 79–89 in Chaos in Biological Systems, edited by H. Degn, A. V. Holden & L. F. Olsen. Plenum Press, New York.

    Google Scholar 

  • Goodwin, B., 1971. A model of early amphibian development, pp. 417–428 in British Society of Experimental Biology Symposium 25, edited by D. D. Davies & M. Balls. Cambridge University Press, Cambridge.

    Google Scholar 

  • Govind, C. K. & J. Pearce, 1986. Differential reflex activity determines claw and closer muscle asymmetry in developing lobsters. Science 233: 354–356.

    PubMed  Google Scholar 

  • Govind, C. K. & J. Pearce, 1992. Mechanoreceptors and minimal reflex activity determining claw laterality in developing lobsters. Journal of Experimental Biology 171: 149–162.

    Google Scholar 

  • Graham, J. H., D. C. Freeman & J. M. Emlen, 1993. Developmental instability: a sensitive indicator of populations under stress, pp. 136–158 in Environmental Toxicology and Risk Assessment, ASTM STP 1179, edited by G. Landis, J. Hughes & M. A. Lewis. American Society for Testing and Materials, Philadelphia.

    Google Scholar 

  • Graham, J. H., K. Roe & T. West. Effects of lead and benzene on the developmental stability ofDrosophila melanogaster. Ecotoxicology (in press).

  • Grassberger, P. & I. Procaccia, 1983. Measuring the strangeness of strange attractors. Physical Review Letters 50: 346–369.

    Article  Google Scholar 

  • Hummel, K. P. & D. B. Chapman, 1959. Visceral asymmetry and associated anomalies in the mouse. Journal of Heredity 50: 9–13.

    Google Scholar 

  • Layton, W. M., Jr., 1976. Random determination of a developmental process. Journal of Heredity 67: 336–338.

    PubMed  Google Scholar 

  • Leary, R. F. & F. W. Allendorf, 1989. Fluctuating asymmetry as an indicator of stress: implications for conservation biology. Trends in Ecology and Evolution 4: 214–217.

    Article  Google Scholar 

  • Lewis, J., J. M. Slack & L. Wolpert, 1977. Thresholds in development. Journal of Theoretical Biology 65: 579–590.

    Article  CAS  PubMed  Google Scholar 

  • Lewontin, R. C., 1986. Gene, organism, and environment, pp. 273–285 in Evolution from Molecules to Men, edited by D. S. Bendall. Cambridge University Press, New York.

    Google Scholar 

  • Markert, C. L. & R. M. Petters, 1978. Manufactured hexaparental mice show that adults are derived from three embryonic cells. Science 202: 56–58.

    CAS  PubMed  Google Scholar 

  • Mather, K., 1953. Genetical control of stability in development. Heredity 7: 297–336.

    Google Scholar 

  • Maynard-Smith, J., 1960. Continuous, quantized and modal variation. Proceedings of the Royal Society 152: 397–409.

    Article  Google Scholar 

  • McKenzie, J. A. & G. M. Clarke, 1988. Diazanon resistance, fluctuating asymmetry and fitness in the Australian sheep blowfly,Lucilia cuprina. Genetics 120: 213–220.

    CAS  PubMed  Google Scholar 

  • McKenzie, J. A., P. Batterham & L. Baker, 1990. Fitness and asymmetry modification as an evolutionary process: A study in the Australian sheep blowfly,Lucilia cuprina andDrosophila melanogaster, pp. 57–73 in Ecological and Evolutionary Genetics of Drosophila, edited by J. S. F. Barker. Plenum Press, New York.

    Google Scholar 

  • McKenzie, J. A. & K. O'Farrell, 1993. Modification of developmental instability and fitness: malathion-resistance in the Australian sheep blowfly,Lucilia cuprina, pp. 67–76 in Developmental Instability: Origins and Evolutionary Significance, edited by T. Markow. Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Meinhardt, H., 1982. Models of Biological Pattern Formation. Academic Press, New York.

    Google Scholar 

  • Morgan, M. J. & M. C. Corballis, 1978. On the biological basis of human laterality. II The mechanism of inheritance. Behavioral and Brain Sciences 2: 270–277.

    Google Scholar 

  • Olsen, L. F. & H. Degn, 1977. Chaos in an enzymatic reaction. Nature 267: 177–178.

    Article  CAS  PubMed  Google Scholar 

  • Osgood, D. W., 1978. Effects of temperature on the development of meristic characters inNatrix fasciata. Copeia 1978: 33–47.

    Article  Google Scholar 

  • Ozernyuk, N. D., V. I. Dyomin, E. A. Prokofyev & I. M. Androsova, 1992. Energy homeostasis and developmental stability, pp. 167–175 in Developmental Stability in Natural Populations, edited by V. M. Zakharov and J. H. Graham. Volume 191, Acta Zoologica Fennica, Finnish Zoological Publishing Board, Helsinki.

    Google Scholar 

  • Palmer, A. R. & C. Strobeck, 1986. Fluctuating asymmetry: measurement, analysis, patterns. Annual Review of Ecology and Systematics 17: 391–421.

    Article  Google Scholar 

  • Palmer, A. R. & C. Strobeck, 1992. Fluctuating asymmetry as a measure of developmental stability: implications of non-normal distributions and power of statistical tests, pp. 57–72 in Developmental Stability in Natural Populations, edited by V. M. Zakharov and J. H. Graham. Volume 191, Acta Zoologica Fennica, Finnish Zoological Publishing Board, Helsinki.

    Google Scholar 

  • Parisi, J., B. Röhricht, J. Peinke & O. E. Rössler, 1987. Turbulent morphogenesis of a prototype model reaction-diffusion system, pp. 91–95 in Chaos in Biological Systems, edited by H. Degn, A. V. Holden & L. F. Olsen. Plenum Press, New York.

    Google Scholar 

  • Pearson, J. E. & W. Horsthemke, 1989. Turing instabilities with nearly equal diffusion coefficients. Journal of Chemistry and Physics 90: 1588–1599.

    Article  CAS  Google Scholar 

  • Ransom, R., 1981. Computers and Embryos: Models in Developmental Biology. John Wiley and Sons, New York.

    Google Scholar 

  • Reeve, E. C. R., 1960. Some genetic tests on asymmetry of sternopleural chaeta number inDrosophila. Genetical Research 1: 151–172.

    Article  Google Scholar 

  • Saunders, P. T., 1980. An Introduction to Catastrophe Theory. Cambridge University Press, Cambridge.

    Google Scholar 

  • Saunders, P. T. & C. Kubal, 1989. Bifurcations and the epigenetic landscape, pp. 16–30 in Theoretical Biology: Epigenetic and Evolutionary Order from Complex Systems, edited by B. Goodwin & P. Saunders. Edinburgh University Press, Edinburgh.

    Google Scholar 

  • Savageau, M. A., 1989. Are there rules governing patterns of gene regulation?, pp. 42–66 in Theoretical Biology: Epigenetic and Evolutionary Order from Complex Systems, edited by B. Goodwin & P. Saunders. Edinburgh University Press, Edinburgh.

    Google Scholar 

  • Shaw, R., 1985. The Dripping Faucet as a Model Chaotic System. Aerial Press, Santa Cruz.

    Google Scholar 

  • Smale, S., 1974. A mathematical model of two cells via Turing's equation. Lectures on Mathematics in the Life Sciences 6: 15–26.

    Google Scholar 

  • Soulé, M. & J. Cuzin-Roudy, 1982. Allomeric variation. 2. Developmental instability of extreme phenotypes. American Naturalist 120: 765–768.

    Article  Google Scholar 

  • Sternberg, P. W., 1991. Control of cell lineage and cell fate during nematode development, pp. 177–225 in Current Topics in Developmental Biology, Volume 25, edited by H. R. Bode. Academic Press, New York.

    Google Scholar 

  • Sugihara, G. & R. M. May, 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344: 734–741.

    Article  CAS  PubMed  Google Scholar 

  • Sulston, J. E., E. Schierenberg, J. G. White & J. N. Thomson, 1983. The embryonic cell lineage of the nematodeCaenorhabditis elegans. Developmental Biology 100: 64–119.

    Article  CAS  PubMed  Google Scholar 

  • Thom, R., 1972. Structural Stability and Morphogenesis. Benjamin, New York.

    Google Scholar 

  • Thom, R., 1989. An inventory of Waddingtonian concepts, pp. 1–7 in Theoretical Biology: Epigenetic and Evolutionary Order from Complex Systems, edited by B. Goodwin & P. Saunders. Edinburgh University Press, Edinburgh.

    Google Scholar 

  • Timofeéf-Ressovsky, N. W., 1934. Über den Einfluss des gentypischen Milieus und der Aussenbedingungen auf die Realisation des Genotyps. Nachrichten Göttingen Gesell. Math. Physik. Kl (6) 1: 53–104.

    Google Scholar 

  • Turing, A., 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B 237: 37–72.

    Google Scholar 

  • Van Valen, L., 1962. A study of fluctuating asymmetry. Evolution 16: 125–142.

    Article  Google Scholar 

  • Van Valen, L., 1978. The control of handedness. Behavioral and Brain Sciences 2: 320.

    Article  Google Scholar 

  • Vastano, J. A., J. E. Pearson, W. Horsthemke & H. L. Swinney, 1987. Chemical pattern formation with equal diffusion coefficients. Physics Letters A. 124(6,7): 320–324.

    Article  CAS  Google Scholar 

  • Waddington, C., 1940. Organizers and Genes. Cambridge University Press, Cambridge.

    Google Scholar 

  • Waddington, C., 1957. The Strategy of the Genes. Allen and Unwin, London.

    Google Scholar 

  • West, B. J., 1987. Fractals, intermittancy and morphogenesis, pp. 305–314 in Chaos in Biological Systems, edited by H. Degn, A. V. Holden & L. F. Olsen. Plenum Press, New York.

    Google Scholar 

  • West, B. J., 1990. Fractal Physiology and Chaos in Medicine. World Scientific, Singapore.

    Google Scholar 

  • Whitney, C. A., 1990. Random Processes in Physical Systems: An Introduction to Probability-based Computer Simulations. John Wiley and Sons, New York.

    Google Scholar 

  • Wodzicki, T. J. & S. Zajaczkowski, 1989. Auxin waves in cambium and morphogenetic information in plants, pp. 45–64 in Signals in Plant Development, edited by J. Krekule and F. Seidová. Academic Publishing, The Hague.

    Google Scholar 

  • Wolf, S. D., W. K. Silk & R. E. Plant, 1986. Quantitative patterns of leaf expansion: comparison of normal and malformed growth inVitis vinifera cv Ruby Red. American Journal of Botany 73: 832–846.

    Article  Google Scholar 

  • Yuge, M. & K. Yamana, 1989. Regulation of the dorsal axial structures in cell-deficient embryos ofXenopus laevis. Development, Growth, and Differentiation 31: 315–324.

    Article  Google Scholar 

  • Zakharov, V. M., 1987. Animal Asymmetry: A Population-Phenogenetic Approach. Nauka, Moscow. (in Russian)

    Google Scholar 

  • Zakharov, V. M., 1989. Future prospects for population phenogenetics. Soviet Science Reviews F Physiology and General Biology 4: 1–79.

    Google Scholar 

  • Zakharov, V. M. & J. H. Graham, editors, 1992. Developmental Stability in Natural Populations. Volume 191, Acta Zoologica Fennica, Finnish Zoological Publishing Board, Helsinki.

  • Zeeman, C., 1989. A new concept of stability, pp. 8–15 in Theoretical Biology: Epigenetic and Evolutionary Order from Complex Systems, edited by B. Goodwin & P. Saunders. Edinburgh University Press, Edinburgh.

    Google Scholar 

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Authors and Affiliations

  1. Department of Biology, Berry College, 30149, Mt. Berry, GA, USA

    John H. Graham

  2. Department of Biological Sciences, Wayne State University, 48202, Detroit, MI, USA

    D. Carl Freeman

  3. US Fish and Wildlife, Building 204, Naval Station, 98115, Seattle, WA, USA

    John M. Emlen

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  1. John H. Graham
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  2. D. Carl Freeman
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Graham, J.H., Freeman, D.C. & Emlen, J.M. Antisymmetry, directional asymmetry, and dynamic morphogenesis. Genetica 89, 121–137 (1993). https://doi.org/10.1007/BF02424509

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