Connections Between Mathematical Models of Prebiotic Evolution and Homochirality

  • Celia BlancoEmail author
  • Irene A. Chen
Part of the Nucleic Acids and Molecular Biology book series (NUCLEIC, volume 35)


The evolutionary dynamics of prebiotic replicators and the amplification kinetics leading to homochirality share certain features and properties, such as the emergence of a certain type that achieves high abundance. The study of replicator dynamics and the study of the origin of homochirality have both seen numerous advances, both theoretical and experimental, in the last decades. Experimental models formulated in these fields are quite different one from the other, and these fields have traditionally been viewed as separate undertakings. However, despite differences in formalisms, it is remarkable that mathematical descriptions used to explain the behavior of replicating entities can be transformed into the mathematical descriptions of models leading to enantiomeric symmetry breaking. Thus two important phenomena during the origin of life, the selection of replicators and the origin of biological homochirality, share similar dynamics.


  1. Amedjkouh M, Brandberg M (2008) Asymmetric autocatalytic Mannich reaction in the presence of water and its implication in prebiotic chemistry. Chem Commun 44:3043–3045CrossRefGoogle Scholar
  2. Avalos M, Babiano R, Cintas P, Jimenez JL, Palacios JC, Barron LD (1998) Absolute asymmetric synthesis under physical fields: facts and fictions. Chem Rev 98:2391–2404CrossRefPubMedGoogle Scholar
  3. Avetisov V, Goldanskii V (1996) Mirror symmetry breaking at the molecular level. Proc Natl Acad Sci U S A 93:11435–11442CrossRefPubMedPubMedCentralGoogle Scholar
  4. Bargueno P, De Tudela RP, Miret-Artes S, Gonzalo I (2011) An alternative route to detect parity violating energy differences through Bose-Einstein condensation of chiral molecules. Phys Chem Chem Phys 13:806–810CrossRefPubMedGoogle Scholar
  5. Barron LD (1981) Optical-activity and time-reversal. Mol Phys 43:1395–1406CrossRefGoogle Scholar
  6. Barron LD (1986) True and false chirality and absolute asymmetric-synthesis. J Am Chem Soc 108:5539–5542CrossRefGoogle Scholar
  7. Bartel DP, Szostak JW (1993) Isolation of new ribozymes from a large pool of random sequences. Science 261:1411–1418CrossRefGoogle Scholar
  8. Blackmond DG (2009) “If pigs could fly” chemistry: a tutorial on the principle of microscopic reversibility. Angew Chem Int Ed 48:2648–2654CrossRefGoogle Scholar
  9. Blackmond DG (2010) The origin of biological homochirality. Cold Spring Harb Perspect Biol 2:a002147CrossRefPubMedPubMedCentralGoogle Scholar
  10. Blackmond DG, Matar OK (2008) Re-examination of reversibility in reaction models for the spontaneous emergence of homochirality. J Phys Chem B 112:5098–5104CrossRefPubMedGoogle Scholar
  11. Blanco C, Stich M, Hochberg D (2011) Temporary mirror symmetry breaking and chiral excursions in open and closed systems. Chem Phys Lett 505:140–147CrossRefGoogle Scholar
  12. Blanco C, Crusats J, El-Hachemi Z, Moyano A, Hochberg D, Ribo JM (2013a) Spontaneous emergence of chirality in the limited enantioselectivity model: autocatalytic cycle driven by an external reagent. Chemphyschem 14:2432–2440CrossRefPubMedGoogle Scholar
  13. Blanco C, Ribo JM, Crusats J, El-Hachemi Z, Moyano A, Hochberg D (2013b) Mirror symmetry breaking with limited enantioselective autocatalysis and temperature gradients: a stability survey. Phys Chem Chem Phys 15:1546–1556CrossRefPubMedGoogle Scholar
  14. Bomze IM, Burger R (1995) Stability by mutation in evolutionary games. Games Econ Behav 11:146–172CrossRefGoogle Scholar
  15. Chapman RN (1931) Animal ecology, with special reference to insects. McGraw-Hill, New YorkGoogle Scholar
  16. Chen IA, Nowak MA (2012) From prelife to life: how chemical kinetics become evolutionary dynamics. Acc Chem Res 45:2088–2096CrossRefPubMedPubMedCentralGoogle Scholar
  17. Cintas P (2016) Homochirogenesis and the emergence of lifelike structures. Chirality in supramolecular assemblies. Wiley, New YorkGoogle Scholar
  18. Collet A, Gabard J, Jacques J, Cesario M, Guilhem J, Pascard C (1981) Synthesis and absolute-configuration of chiral (C-3) cyclotriveratrylene derivatives – crystal-structure of (M)-(-)-2,7,12-triethoxy-3,8,13-tris-[(R)-1-methoxycarbonylethoxy]-10,15-dihydro-5h-tribenzo[a,D,G]-cyclononene. J Chem Soc Perkin Trans 1:1630–1638CrossRefGoogle Scholar
  19. Crick FHC (1968) Origin of genetic code. J Mol Biol 38:367CrossRefPubMedGoogle Scholar
  20. Crusats J, Hochberg D, Moyano A, Ribo JM (2009) Frank model and spontaneous emergence of chirality in closed systems. ChemPhysChem 10:2123–2131CrossRefPubMedGoogle Scholar
  21. Eigen M, Schuster P (1977) Hypercycle – principle of natural self-organization. A. Emergence of hypercycle. Naturwissenschaften 64:541–565CrossRefPubMedGoogle Scholar
  22. El-Hachemi Z, Crusats J, Ribo JM, McBride JM, Veintemillas-Verdaguer S (2011) Metastability in supersaturated solution and transition towards chirality in the crystallization of NaClO3. Angew Chem Int Ed 50:2359–2363CrossRefGoogle Scholar
  23. Ertem G, Ferris JP (1996) Synthesis of RNA oligomers on heterogeneous templates. Nature 379:238–240CrossRefPubMedGoogle Scholar
  24. Feringa BL, Van Delden RA (1999) Absolute asymmetric synthesis: the origin, control, and amplification of chirality. Angew Chem Int Ed 38:3419–3438CrossRefGoogle Scholar
  25. Ferris JP, Ertem G (1992) Oligomerization of ribonucleotides on montmorillonite – reaction of the 5′-phosphorimidazolide of adenosine. Science 257:1387–1389CrossRefPubMedGoogle Scholar
  26. Ferris JP, Ertem G (1993) Montmorillonite catalysis of RNA oligomer formation in aqueous-solution – a model for the prebiotic formation of RNA. J Am Chem Soc 115:12270–12275CrossRefPubMedGoogle Scholar
  27. Ferris JP, Hill AR, Liu RH, Orgel LE (1996) Synthesis of long prebiotic oligomers on mineral surfaces. Nature 381:59–61CrossRefPubMedGoogle Scholar
  28. Frank FC (1953) On spontaneous asymmetric synthesis. Biochim Biophys Acta 11:459–463CrossRefPubMedGoogle Scholar
  29. Guijarro A, Yus M (2009) The origin of chirality in the molecules of life: a revision from awareness to the current theories and perspectives of this unsolved problem. Royal Society of Chemistry, CambridgeGoogle Scholar
  30. Hadeler KP (1981) Stable polymorphisms in a selection model with mutation. SIAM J Appl Math 41:1–7CrossRefGoogle Scholar
  31. Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge, New York, NYCrossRefGoogle Scholar
  32. Hofbauer J, Schuster P, Sigmund K (1979) A note on evolutionary stable strategies and game dynamics. J Theor Biol 81:609–612CrossRefPubMedGoogle Scholar
  33. Islas JR, Lavabre D, Grevy JM, Lamoneda RH, Cabrera HR, Micheau JC, Buhse T (2005) Mirror-symmetry breaking in the Soai reaction: a kinetic understanding. Proc Natl Acad Sci U S A 102:13743–13748CrossRefPubMedPubMedCentralGoogle Scholar
  34. Iwamoto K (2003) Spontaneous appearance of chirally asymmetric steady states in a reaction model including Michaelis-Menten type catalytic reactions. Phys Chem Chem Phys 5:3616–3621CrossRefGoogle Scholar
  35. Kondepudi DK, Nelson GW (1983) Chiral symmetry-breaking in non-equilibrium systems. Phys Rev Lett 50:1023–1026CrossRefGoogle Scholar
  36. Lotka AJ (1920) Undamped oscillations derived from the law of mass action. J Am Chem Soc 42:1595–1599CrossRefGoogle Scholar
  37. Lotka AJ (1925) Elements of physical biology. Williams and Wilkins, BaltimoreGoogle Scholar
  38. Lotka AJ (1932) Contribution to the mathematical theory of capture: I. Conditions for capture. Proc Natl Acad Sci U S A 18:172–178CrossRefPubMedPubMedCentralGoogle Scholar
  39. Manapat M, Ohtsuki H, Burger R, Nowak MA (2009) Originator dynamics. J Theor Biol 256:586–595CrossRefPubMedGoogle Scholar
  40. Mauksch M, Tsogoeva SB, Martynova IM, Wei SW (2007a) Evidence of asymmetric autocatalysis in organocatalytic reactions. Angew Chem Int Ed 46:393–396CrossRefGoogle Scholar
  41. Mauksch M, Tsogoeva SB, Wei SW, Martynova IM (2007b) Demonstration of spontaneous chiral symmetry breaking in in asymmetric Mannich and Aldol reactions. Chirality 19:816–825CrossRefPubMedGoogle Scholar
  42. Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge, New YorkCrossRefGoogle Scholar
  43. Miller SL (1953) A production of amino acids under possible primitive earth conditions. Science 117:528–529CrossRefGoogle Scholar
  44. Mislow K (2003) Absolute asymmetric synthesis: a commentary. Collect Czechoslov Chem Commun 68:849–864CrossRefGoogle Scholar
  45. Monnard PA, Deamer DW (2001) Nutrient uptake by protocells: a liposome model system. Orig Life Evol Biosph 31:147–155CrossRefPubMedGoogle Scholar
  46. Monnard PA, Deamer DW (2002) Membrane self-assembly processes: steps toward the first cellular life. Anat Rec 268:196–207CrossRefPubMedGoogle Scholar
  47. Myrgorodska I, Meinert C, Martins Z, D’hendecourt LL, Meierhenrich UJ (2015) Molecular chirality in meteorites and interstellar ices, and the chirality experiment on board the ESA cometary rosetta mission. Angew Chem Int Ed 54:1402–1412CrossRefGoogle Scholar
  48. Noorduin WL, Izumi T, Millemaggi A, Leeman M, Meekes H, Van Enckevort WJP, Kellogg RM, Kaptein B, Vlieg E, Blackmond DG (2008) Emergence of a single solid chiral state from a nearly racemic amino acid derivative. J Am Chem Soc 130:1158CrossRefPubMedGoogle Scholar
  49. Noorduin WL, Vlieg E, Kellogg RM, Kaptein B (2009) From Ostwald ripening to single chirality. Angew Chem Int Ed 48:9600–9606CrossRefGoogle Scholar
  50. Nowak MA, Ohtsuki H (2008) Prevolutionary dynamics and the origin of evolution. Proc Natl Acad Sci U S A 105:14924–14927CrossRefPubMedPubMedCentralGoogle Scholar
  51. Nowak MA, Komarova NL, Niyogi P (2001) Evolution of universal grammar. Science 291:114–118CrossRefPubMedGoogle Scholar
  52. Ohtsuki H, Nowak MA (2009) Prelife catalysts and replicators. Proc R Soc B Biol Sci 276:3783–3790CrossRefGoogle Scholar
  53. Orgel LE (1968) Evolution of genetic apparatus. J Mol Biol 38:381CrossRefPubMedGoogle Scholar
  54. Orgel LE (1992) Molecular replication. Nature 358:203–209CrossRefPubMedGoogle Scholar
  55. Page KM, Nowak MA (2002) Unifying evolutionary dynamics. J Theor Biol 219:93–98CrossRefPubMedGoogle Scholar
  56. Plasson R, Kondepudi DK, Bersini H, Commeyras A, Asakura K (2007) Emergence of homochirality in far-from-equilibrium systems: mechanisms and role in prebiotic chemistry. Chirality 19:589–600CrossRefPubMedGoogle Scholar
  57. Pressman A, Blanco C, Chen IA (2015) The RNA world as a model system to study the origin of life. Curr Biol 25:R953–R963CrossRefPubMedGoogle Scholar
  58. Rajamani S, Vlassov A, Benner S, Coombs A, Olasagasti F, Deamer D (2008) Lipid-assisted synthesis of RNA-like polymers from mononucleotides. Orig Life Evol Biosph 38:57–74CrossRefPubMedGoogle Scholar
  59. Ribo JM, Hochberg D (2008) Stability of racemic and chiral steady states in open and closed chemical systems. Phys Lett A 373:111–122CrossRefGoogle Scholar
  60. Ribo JM, Hochberg D (2015) Competitive exclusion principle in ecology and absolute asymmetric synthesis in chemistry. Chirality 27:722–727CrossRefPubMedGoogle Scholar
  61. Saito Y, Hyuga H (2004) Complete homochirality induced by nonlinear autocatalysis and recycling. J Phys Soc Jpn 73:33–35CrossRefGoogle Scholar
  62. Saito Y, Hyuga H (2005) Chirality selection in open flow systems and in polymerization. J Phys Soc Jpn 74:1629–1635CrossRefGoogle Scholar
  63. Sawai H, Orgel LE (1975) Oligonucleotide synthesis catalyzed by Zn2+ ion. J Am Chem Soc 97:3532–3533CrossRefPubMedGoogle Scholar
  64. Shibata T, Yamamoto J, Matsumoto N, Yonekubo S, Osanai S, Soai K (1998) Amplification of a slight enantiomeric imbalance in molecules based on asymmetric autocatalysis: the first correlation between high enantiomeric enrichment in a chiral molecule and circularly polarized light. J Am Chem Soc 120:12157–12158CrossRefGoogle Scholar
  65. Siegel JS (1998) Homochiral imperative of molecular evolution. Chirality 10:24–27CrossRefGoogle Scholar
  66. Sievers D, Von Kiedrowski G (1994) Self-replication of complementary nucleotide-based oligomers. Nature 369:221–224CrossRefPubMedGoogle Scholar
  67. Soai K, Shibata T, Morioka H, Choji K (1995) Asymmetric autocatalysis and amplification of enantiomeric excess of a chiral molecule. Nature 378:767–768CrossRefGoogle Scholar
  68. Stadler PF, Schuster P (1992) Mutation in autocatalytic reaction networks – an analysis based on perturbation-theory. J Math Biol 30:597–632CrossRefPubMedGoogle Scholar
  69. Viedma C (2005) Chiral symmetry breaking during crystallization: complete chiral purity induced by nonlinear autocatalysis and recycling. Phys Rev Lett 94:065504CrossRefPubMedGoogle Scholar
  70. Viedma C, Cintas P (2011) Homochirality beyond grinding: deracemizing chiral crystals by temperature gradient under boiling. Chem Commun 47:12786–12788CrossRefGoogle Scholar
  71. Viedma C, Noorduin WL, Ortiz JE, De Torres T, Cintas P (2011) Asymmetric amplification in amino acid sublimation involving racemic compound to conglomerate conversion. Chem Commun 47:671–673CrossRefGoogle Scholar
  72. Volterra V (1926) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Mem Accad Naz Lincei 2:31–113Google Scholar
  73. Weissbuch I, Leiserowitz L, Lahav M (2005) Stochastic “mirror symmetry breaking” via self-assembly, reactivity and amplification of chirality: relevance to abiotic conditions. In: Walde P (ed) Prebiotic chemistry: from simple amphiphiles to protocell models, vol 259. Springer, Berlin, pp 123–165CrossRefGoogle Scholar
  74. Woese CR, Dugre DH, Dugre SA, Kondo M, Saxinger WC (1966) On fundamental nature and evolution of genetic code. Cold Spring Harb Symp Quant Biol 31:723CrossRefPubMedGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Chemistry and BiochemistryUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Program in Biomolecular Sciences and EngineeringUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations