Network Theory in Prebiotic Evolution

  • Sara Imari WalkerEmail author
  • Cole Mathis
Part of the Nucleic Acids and Molecular Biology book series (NUCLEIC, volume 35)


One of the most challenging aspect of origins of life research is that we do not know precisely what life is. In recent years, the use of network theory has revolutionized our understanding of living systems by permitting a mathematical framework for understanding life as an emergent, collective property of many interacting entities. So far, complex systems science has seen little direct application to the origins of life, particularly in laboratory science. Yet, networks are important mathematical descriptors in cases where the structure of interactions matters more than counting individual component parts—precisely what we envision happens as matter transitions to life. Here, we review a few notable examples of the use of network theory in prebiotic evolution, and discuss the promise of systems approaches to origins of life. The end goal is to develop a statistical mechanics useful to origins of life—that is, one that deals with interactions of system components (rather than merely counting them) and is therefore equipped to model life as an emergent phenomena.


  1. Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47–97. Scholar
  2. Alon U (2003) Biological networks: the tinkerer as an engineer. Science 301(5641):1866–1867. Scholar
  3. Andersen JL, Andersen T, Flamm C, Hanczyc MM, Merkle D, Stadler PF (2013) Navigating the chemical space of HCN polymerization and hydrolysis: guiding graph grammars by mass spectrometry data. Entropy 15(10):4066–4083. Scholar
  4. Andersen JL, Flamm C, Merkle D, Stadler PF (2017) An intermediate level of abstraction for computational systems chemistry. Philos Trans R Soc A Math Phys Eng Sci 375(2109):20160354. Scholar
  5. Arita M (2004) The metabolic world of Escherichia coli is not small. Proc Natl Acad Sci U S A 101(6):1543–1547. Scholar
  6. Ashkenasy G, Ghadiri MR (2004) Boolean logic functions of a synthetic peptide network. J Am Chem Soc 126(36):11140–11141. Scholar
  7. Ashkenasy G, Jagasia R, Yadav M, Ghadiri MR (2004) Design of a directed molecular network. Proc Natl Acad Sci U S A 101(30):10872–10877. Scholar
  8. Barabasi A-L (2009) Scale-free networks: a decade and beyond. Science 325(5939):412–413. Scholar
  9. Barabási A-L (2016) Network science. Cambridge University Press, CambridgeGoogle Scholar
  10. Barabasi L, Albert R (1999) Emergence of scaling in random networks. Science 286:509–513. Scholar
  11. Barabási A-L, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5(2):101–113. Scholar
  12. Bianconi G, Barabási A-L (2000) Competition and multiscaling in evolving networks. Europhys Lett 54(May):436–442. Scholar
  13. Boccaletti S, Bianconi G, Criado R, del Genio CI, Gómez-Gardeñes J, Romance M, Sendiña-Nadal I, Wang Z, Zanin M (2014) The structure and dynamics of multilayer networks. Phys Rep 544(1):1–122. Scholar
  14. Cairns-Smith AG (1986) Clay minerals and the origin of life. Cambridge University Press, New YorkGoogle Scholar
  15. Clauset A, Shalizi CR, Newman MEJ (2009) Power-law distributions in empirical data. SIAM Rev 51(4):661–703. Scholar
  16. Cohen R, Erez K, Ben-Avraham D, Havlin S (2001) Breakdown of the Internet under intentional attack. Phys Rev Lett 86(16):3682–3685. Scholar
  17. Cronin L, Walker SI (2016) Beyond prebiotic chemistry: what dynamic network properties allow the emergence of life? Science 352(6290):1174–1175. Scholar
  18. Davies PCW, Walker SI (2016) The hidden simplicity of biology. Rep Prog Phys 79(10):102601. Scholar
  19. Dinsdale EA, Edwards RA, Hall D, Angly F, Breitbart M, Brulc JM, Furlan M et al (2008) Functional metagenomic profiling of nine biomes. Nature 452(7187):629–632. Scholar
  20. Eigen M (1971) Self-organisation of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465–523CrossRefPubMedGoogle Scholar
  21. Eigen M, Schuster P (1978) The hypercycle. a principle of natural self-organisation. Part C: the realistic hypercycle. Naturwissenschaften 65(2):341–369. Scholar
  22. Erdös P, Rényi A (1959) On random graphs. Publ Math 6:290–297. Scholar
  23. Filisetti A, Graudenzi A, Serra R, Villani M, Füchslin RM, Packard N, Kauffman SA, Poli I (2012) A stochastic model of autocatalytic reaction networks. Theory Biosci 131(2):85–93. Scholar
  24. Gisiger T (2001) Scale invariance in biology: coincidence or footprint of a universal mechanism? Biol Rev Camb Philos Soc 76(2). Arizona State University Libraries:S1464793101005607. doi:
  25. Gleiss PM, Stadler PF, Wagner A, Fell D a (2001) Relevant cycles in chemical reaction networks. Adv Complex Syst 4(02n03):207–226. Scholar
  26. Goldenfeld N, Biancalani T, Jafarpour F (2017) Universal biology and the statistical mechanics of early life. Philos Trans R Soc A 375(2109):20160341. Scholar
  27. Goldford JE, Hartman H, Smith TF, Segrè D (2017) Remnants of an ancient metabolism without phosphate. Cell 168(6):1126–1134.e9. Scholar
  28. Handorf T, Ebenhöh O, Heinrich R (2005) Expanding metabolic networks: scopes of compounds, robustness, and evolution. J Mol Evol 61(4):498–512. Scholar
  29. Hordijk W, Steel M (2004) Detecting autocatalytic, self-sustaining sets in chemical reaction systems. J Theor Biol 227(4):451–461. Scholar
  30. Hordijk W, Steel M (2017) Chasing the tail: the emergence of autocatalytic networks. BioSystems 152:1–10. Scholar
  31. Hordijk W, Kauffman SA, Steel M (2011) Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems. Int J Mol Sci 12(5):3085–3101. Scholar
  32. Hordijk W, Steel M, Kauffman S (2012) The structure of autocatalytic sets: evolvability, enablement, and emergence. Acta Biotheor 60(4):379–392. Scholar
  33. Hordijk W, Hasenclever L, Gao J, Mincheva D, Hein J (2014) An investigation into irreducible autocatalytic sets and power law distributed catalysis. Nat Comput 13(3):287–296. Scholar
  34. Jeong H, Albert R, Ottval ZN, Barabási AL (2000) The large scale organization of metabolic networks. Nature 407(6804):651–654CrossRefPubMedGoogle Scholar
  35. Kamimura A, Kaneko K (2010) Reproduction of a protocell by replication of a minority molecule in a catalytic reaction network. Phys Rev Lett 105(26):1–4. Scholar
  36. Kaneko K, Yomo T (2002) On a kinetic origin of heredity: minority control in a replicating system with mutually catalytic molecules. J Theor Biol 214(4):563–576. Scholar
  37. Kauffman S (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, New YorkGoogle Scholar
  38. Kim H, Davies P, Walker SI (2015) New scaling relation for information transfer in biological networks. J R Soc Interface 12(113):20150944. Scholar
  39. Kim H, Smith H, Mathis C, Raymond J, Walker SI (2018) Universal scaling across biochemical networks on earth. bioRxiv.
  40. Kuppers B-O (1990) Information and the origin of life. MIT Press, Cambridge, MAGoogle Scholar
  41. Larhlimi A, Blachon S, Selbig J, Nikoloski Z (2011) Robustness of metabolic networks: a review of existing definitions. BioSystems 106(1):1–8. Scholar
  42. Lifson S (1997) On the crucial stages in the origin of animate matter. J Mol Evol 44(1):1–8. Scholar
  43. Mathis C, Bhattacharya T, Walker SI (2017a) The emergence of life as a first-order phase transition. Astrobiology 17(3):266–276. Scholar
  44. Mathis C, Ramprasad S, Walker S, Lehman N (2017b) Prebiotic RNA network formation: a taxonomy of molecular cooperation. Life 7(4):38. Scholar
  45. Maynard Smith J, Szathmáry E (1995) The major transitions in evolution. Oxford University Press, OxfordGoogle Scholar
  46. Milo R (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827. Scholar
  47. Montañez R, Medina MA, Solé RV, Rodríguez-Caso C (2010) When metabolism meets topology: reconciling metabolite and reaction networks. BioEssays 32(3):246–256. Scholar
  48. Newman MEJ (2004) Analysis of weighted networks. Phys Rev E Stat Nonlinear Soft Matter Phys 70(5 2):1–9. Scholar
  49. Nghe P, Hordijk W, Kauffman SA, Walker SI, Schmidt FJ, Kemble H, Yeates JAM, Lehman N (2015) Prebiotic network evolution: six key parameters. Mol BioSyst 11(12):3206–3217. Scholar
  50. Nowak MA, Ohtsuki H (2008) Prevolutionary dynamics and the origin of evolution. Proc Natl Acad Sci U S A 105(39):14924–14927. Scholar
  51. Ogata H, Goto S, Sato K, Fujibuchi W, Bono H, Kanehisa M (1999) KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Res 27(1):29–34. Scholar
  52. Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi A-L (2002) Hierarchical organization of modularity in metabolic networks. Science 297(5586):1551–1555. Scholar
  53. Raymond J, Segre D (2006) The effect of oxygen on biochemical networks and the evolution of complex life. Science 311(5768):1764–1767. Scholar
  54. Schrodinger E (1944) What is life? Cambridge University PressGoogle Scholar
  55. Schütte M, Skupin A, Segrè D, Ebenhöh O (2010) Modeling the complex dynamics of enzyme-pathway coevolution. Chaos 20(4):1–12. Scholar
  56. Segre D, Ben-Eli D, Lancet D (2000) Compositional genomes: prebiotic information transfer in mutually catalytic noncovalent assemblies. Proc Natl Acad Sci U S A 97(8):4112–4117. Scholar
  57. Segré D, Ben-Eli D, Deamer DW, Lancet D (2001) The lipid world. Orig Life Evol Biosph 31(1–2):119–145. Scholar
  58. Sessions AL, Doughty DM, Welander PV, Summons RE, Newman DK (2009) The continuing puzzle of the great oxidation event. Curr Biol 19(14):R567–R574. Scholar
  59. Shock EL, Boyd ES (2015) Principles of geobiochemistry. Elements 11(6):395–401CrossRefGoogle Scholar
  60. Smith E, Morowitz H (2016) The origin and nature of life on earth: the emergence of the fourth geosphere. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  61. Sole RV, Munteanu A (2004) The large-scale organization of chemical reaction networks in astrophysics. EPL (Europhys Lett) 68(2):170CrossRefGoogle Scholar
  62. Sousa FL, Hordijk W, Steel M, Martin WF (2015) Autocatalytic sets in E. coli metabolism. J Syst Chem 6(1):4. Scholar
  63. Sterelny K (2015) Universal biology. Br Soc Philos Sci 48(4):587–601CrossRefGoogle Scholar
  64. Vaidya N, Manapat ML, Chen IA, Xulvi-Brunet R, Hayden EJ, Lehman N (2012) Spontaneous network formation among cooperative RNA replicators. Nature 491(7422):72–77. Scholar
  65. Vaidya N, Walker SI, Lehman N (2013) Recycling of informational units leads to selection of replicators in a prebiotic soup. Chem Biol 20(2):241–252. Scholar
  66. Vasas V, Szathmary E, Santos M (2010) Lack of evolvability in self-sustaining autocatalytic networks constraints metabolism-first scenarios for the origin of life. Proc Natl Acad Sci U S A 107(4):1470–1475. Scholar
  67. Vasas V, Fernando C, Santos M, Kauffman S, Szathmáry E (2012) Evolution before genes. Biol Direct 7(1):1. Scholar
  68. Wagner A (1998) The large-scale structure of metabolic networks: a glimpse of life’s origin? Wiley Periodicals 8(1): 15–19Google Scholar
  69. Wagner A, Fell DA (2001) The small world inside large metabolic networks. Proc R Soc B Biol Sci 268(1478):1803–1810. Scholar
  70. Walker SI (2017) Origins of life: a problem for physics, a key issues review. Rep Prog Phys 80(9):092601. Scholar
  71. Walker SI, Davies PCW (2013) The algorithmic origins of life. J R Soc Interface 10(79):20120869. Scholar
  72. Walker SI, Kim H, Davies PCW (2016) The informational architecture of the cell. Philos Trans R Soc A Math Phys Eng Sci 374(2063).
  73. Wang RS, Saadatpour A, Albert R (2012) Boolean modeling in systems biology: an overview of methodology and applications. Phys Biol 9(5):055001. Scholar
  74. Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  75. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442CrossRefPubMedGoogle Scholar
  76. West GB (1999a) The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284(5420):1677–1679. Scholar
  77. West GB (1999b) The origin of universal scaling laws in biology. Phys A Stat Mech Appl 263(1–4):104–113. Scholar
  78. Wynveen A, Fedorov I, Halley JW (2014) Nonequilibrium steady states in a model for prebiotic evolution. Phys Rev E 89(2):22725. Scholar
  79. Yockey H (2005) Information theory, evolution and the origin of life. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beyond Center for Fundamental Concepts in ScienceArizona State UniversityTempeUSA
  2. 2.School of Earth and Space Exploration, Arizona State UniversityTempeUSA
  3. 3.ASU-SFI Center for Biosocial Complex Systems, Arizona State UniversityTempeUSA
  4. 4.Blue Marble Space Institute for ScienceSeattleUSA
  5. 5.Department of PhysicsArizona State UniversityTempeUSA

Personalised recommendations