Metabolic Constraints on the Evolution of Genetic Codes: Did Multiple Preaerobic’ Ecosystem Transitions Entrain Richer Dialects via Serial Endosymbiosis?

  • Rodrick Wallace
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7625)


A model derived from Tlusty’s elegant topological deconstruction suggests that multiple punctuated ecosystem resilience regime changes in metabolic free energy broadly similar to the aerobic transition enabled a punctuated sequence of increasingly complex genetic codes and protein translators. In a manner similar to the Serial Endosymbiosis effecting the Eukaryotic transition, codes and translators coevolved until the ancestor of the present narrow spectrum of protein machineries became locked-in by evolutionary path dependence at a relatively modest level of fitness reflecting a modest embedding metabolic free energy ecology. A search for evidence of a sequence of ‘preaerobic’ ecosystem shifts in metabolic free energy availability or efficiency of use might be surprisingly fruitful.


Genetic Code Morse Theory Free Energy Density Morse Function Rate Distortion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Ash, R.: Information Theory. Dover Publications, New York (1990)zbMATHGoogle Scholar
  2. 2.
    Bennett, C.: Logical depth and physical complexity. In: Herkin, R. (ed.) The Universal Turing Machine: a Half-Century Survey, pp. 227–257. Oxford University Press (1988)Google Scholar
  3. 3.
    Bos, R.: Continuous representations of groupoids. ArXiv:math/0612639 (2007)Google Scholar
  4. 4.
    Bredon, G.: Topology and Geometry. Springer, New York (1993)zbMATHGoogle Scholar
  5. 5.
    Brown, R.: From groups to groupoids: a brief survey. Bulletin of the London Mathematical Society 19, 113–134 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Buneci, M.: Representare de Groupoizi. Editura Mirton, Timisoara (2003)Google Scholar
  7. 7.
    Cannas da Silva, A., Weinstein, A.: Geometric Models for Noncommunative Algebra. American Mathematical Society, New York (1999)Google Scholar
  8. 8.
    Canfield, D., Rosing, M., Bjerrum, C.: Early anaerobic metabolisms. Philosophical Transactions of the Royal Society, B 351, 1819–1836 (2006)CrossRefGoogle Scholar
  9. 9.
    Champagnat, N., Ferriere, R., Meleard, S.: Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theoretical Population Biology 69, 297–321 (2006)zbMATHCrossRefGoogle Scholar
  10. 10.
    Cover, T., Thomas, J.: Elements of Information Theory. Wiley, New York (1991)zbMATHCrossRefGoogle Scholar
  11. 11.
    Dembo, A., Zeitouni, O.: Large Deviations and Applications, 2nd edn. Springer, NY (1988)Google Scholar
  12. 12.
    Diekmann, U., Law, R.: The dynamical theory of coevolution: a derivation from stochastic ecological processes. Journal of Mathematical Biology 34, 579–612 (1996)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Eigen, M.: Steps Toward Life: A Perspective on Evolution. Oxford University Press, New York (1996)Google Scholar
  14. 14.
    Ellis, R.: Entropy, Large Deviations, and Statistical Mechanics. Springer, New York (1985)zbMATHCrossRefGoogle Scholar
  15. 15.
    Feynman, R.: Lectures on Computation. Westview Press, New York (2000)Google Scholar
  16. 16.
    Franzosi, R., Pettini, M.: Theorem on the origin of phase transitions. Physical Review Letters 92, 060601 (2004)CrossRefGoogle Scholar
  17. 17.
    Glazebrook, J.F., Wallace, R.: Small worlds and Red Queens in the Global Workspace: An information-theoretic approach. Cognitive Systems Research 10, 333–365 (2009)CrossRefGoogle Scholar
  18. 18.
    Glazebrook, J.F., Wallace, R.: Rate distortion manifolds as models for cognitive information. Informatica 33, 309–345 (2009)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Golubitsky, M., Stewart, I.: Nonlinear dynamics and networks: the groupoid formalism. Bulletin of the American Mathematical Society 43, 305–364 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Gunderson, L.: Ecological resilience in theory and applications. Annual Reviews of Ecological Systematics 31, 425–439 (2000)CrossRefGoogle Scholar
  21. 21.
    Holling, C.: Resilience and stability of ecological systems. Annual Reviews of Ecological Systematics 4, 1–23 (1973)CrossRefGoogle Scholar
  22. 22.
    Kastner, M.: Phase transitions and configuration space topology. Reviews of Modern Physics 80, 167–187 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Khinchin, A.: Mathematical Foundations of Information Theory. Dover, New York (1957)zbMATHGoogle Scholar
  24. 24.
    Koonin, E., Senkevich, T., Dolja, V.: The ancient virus world and evolution of cells. Biology Direct (2006), doi 10.1186/1745-6150-1-29Google Scholar
  25. 25.
    Koonin, E., Novozhilov, A.: Origin and evolution of the genetic code: the universal enigma. Life 61, 99–111 (2009)Google Scholar
  26. 26.
    Landau, L., Lifshitz, E.: Statistical Physics, Part I. Elsevier, New York (2007)Google Scholar
  27. 27.
    Lee, J.: Introduction to Topological Manifolds. Springer, New York (2000)zbMATHGoogle Scholar
  28. 28.
    Matsumoto, Y.: An Introduction to Morse Theory. Translations of Mathematical Monographs, vol. 208. American Mathematical Society (2002)Google Scholar
  29. 29.
    Michel, L., Mozrymas, J.: Application of Morse Theory to the symmetry breaking in the Landau theory of the second order phase transition. In: Kramer, P., Rieckers, A. (eds.) Group Theoretical Methods in Physics: Sixth International Colloquium. Lecture Notes in Physics, vol. 79, pp. 447–461. Springer, New York (1977)CrossRefGoogle Scholar
  30. 30.
    Milnor, J.: Morse Theory. Annals of Mathematical Studies. Princeton University Press, Princeton (1963)zbMATHGoogle Scholar
  31. 31.
    Pettini, M.: Geometry and Topology in Hamiltonian Dynamics. Springer, New York (2007)zbMATHCrossRefGoogle Scholar
  32. 32.
    Pielou, E.: Mathematical Ecology. Wiley, New York (1977)Google Scholar
  33. 33.
    Ringel, G., Young, J.: Solutions of the Heawood map-coloring problem. Proceedings of the National Academy of Sciences 60, 438–445 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton (1970)zbMATHGoogle Scholar
  35. 35.
    Rodin, S., Rodin, A.: On the origin of the genetic code: signatures of its primordial complementarity in tRNAs and aminoacyl-tRNA synthetases. Heredity 100, 341–355 (2008)CrossRefGoogle Scholar
  36. 36.
    Rose, K.: Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proceedings of the IEEE 86, 2210–2239 (1998)CrossRefGoogle Scholar
  37. 37.
    Sarshar, N., Wu, X.: On rate-distortion models for natural images and wavelet coding performance. IEEE Transactions on Image Processing 3, 87–93 (2007)MathSciNetGoogle Scholar
  38. 38.
    Shmulevich, I., Dougherty, E.: Genomic Signal Processing. Princeton University Press, Princeton (2007)zbMATHGoogle Scholar
  39. 39.
    Skierski, M., Grundland, A., Tuszynski, J.: Analysis of the three-dimensional time dependent Landau-Ginzburg equation and its solutions. Journal of Physics A (Math. Gen.) 22, 3789–3808 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Stewart, I., Golubitsky, M., Pivato, M.: Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM Journal of Applied Dynamical Systems 2, 609–646 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Stewart, I.: Networking opportunity. Nature 427, 601–604 (2004)CrossRefGoogle Scholar
  42. 42.
    Sun, F., Ceataeno-Anolles, G.: Evolutionary patterns in the sequence and structure of transfer RNA: a window into early translation and the genetic code. PLOSone 3(7), 32799 (2008)Google Scholar
  43. 43.
    Tlusty, T.: A model for the emergence of the genetic code as a transition in a noisy information channel. Journal of Theoretical Biology 249, 331–342 (2007)CrossRefGoogle Scholar
  44. 44.
    Tlusty, T.: A simple model for the evolution of molecular codes driven by the interplay of accuracy, diversity and cost. Physical Biology 5, 016001; Casting polymer nets to optimize noisy molecular codes. Proceedings of the National Academy of Sciences 105, 8238–8243 (2008)Google Scholar
  45. 45.
    Tlusty, T.: Personal communication (2010)Google Scholar
  46. 46.
    Ueno, Y., Yamada, K., Yoshida, N., Maruyama, S., Isozaki, Y.: Evidence for microbial methanogenesis in the early Archaean era. Nature 440, 516–519 (2006)CrossRefGoogle Scholar
  47. 47.
    Van Valen, L.: A new evolutionary law. Evolutionary Theory 1, 1–30 (1973)Google Scholar
  48. 48.
    Vetsigian, K., Wose, C., Goldenfield, N.: Collective evolution and the genetic code. Proceedings of the National Academy of Sciences 103, 10696–10701 (2006)CrossRefGoogle Scholar
  49. 49.
    Villarreal, L., Witzany, G.: Viruses are essential agents within the roots and stem of the tree of life. Journal of Theoretical Biology 262, 698–710 (2010)CrossRefGoogle Scholar
  50. 50.
    Wallace, R., Wallace, R.G.: On the spectrum of prebiotic chemical systems: an information-theoretic treatment of Eigen’s Paradox. Origins of Life and Evolution of Bioshperes 38, 419–455 (2008)CrossRefGoogle Scholar
  51. 51.
    Wallace, R., Wallace, D.: Punctuated Equilibrium in Statistical Models of Generalized Coevolutionary Resilience: How Sudden Ecosystem Transitions Can Entrain Both Phenotype Expression and Darwinian Selection. In: Priami, C. (ed.) Transactions on Computational Systems Biology IX. LNCS (LNBI), vol. 5121, pp. 23–85. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  52. 52.
    Wallace, R., Wallace, D.: Code, Context, and Epigenetic Catalysis in Gene Expression. In: Priami, C., Back, R.-J., Petre, I. (eds.) Transactions on Computational Systems Biology XI. LNCS (LNBI), vol. 5750, pp. 283–334. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  53. 53.
    Wallace, R.: Metabolic constraints on the eukaryotic transition. Origins of Life and Evolution of Biospheres 39, 165–176 (2009)CrossRefGoogle Scholar
  54. 54.
    Weinstein, A.: Groupoids: unifying internal and external symmetry. Notices of the American Mathematical Association 43, 744–752 (1996)zbMATHGoogle Scholar
  55. 55.
    Wilson, K.: Renormalization group and critical phenomena. I Renormalization group and the Kadanoff scaling picture. Physical Review B 4, 3174–3183 (1971)zbMATHGoogle Scholar
  56. 56.
    Witzany, G.: Noncoding RNAs: persistent viral agents as modular tools for cellular needs. Annals of the New York Academy of Sciences 1178, 244–267 (2009)CrossRefGoogle Scholar
  57. 57.
    Zhu, R., Rebirio, A., Salahub, D., Kauffmann, S.: Studying genetic regulatory networks at the molecular level: delayed reaction stochastic models. Journal of Theoretical Biology 246, 725–745 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rodrick Wallace
    • 1
  1. 1.Division of EpidemiologyThe New York State Psychiatric InstituteUSA

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