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Life’s Attractors

Understanding Developmental Systems Through Reverse Engineering and In Silico Evolution

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Evolutionary Systems Biology

Part of the book series: Advances in Experimental Medicine and Biology ((volume 751))

Abstract

We propose an approach to evolutionary systems biology which is based on reverse engineering of gene regulatory networks and in silico evolutionary simulations. We infer regulatory parameters for gene networks by fitting computational models to quantitative expression data. This allows us to characterize the regulatory structure and dynamical repertoire of evolving gene regulatory networks with a reasonable amount of experimental and computational effort. We use the resulting network models to identify those regulatory interactions that are conserved, and those that have diverged between different species. Moreover, we use the models obtained by data fitting as starting points for simulations of evolutionary transitions between species. These simulations enable us to investigate whether such transitions are random, or whether they show stereotypical series of regulatory changes which depend on the structure and dynamical repertoire of an evolving network. Finally, we present a case study—the gap gene network in dipterans (flies, midges, and mosquitoes)—to illustrate the practical application of the proposed methodology, and to highlight the kind of biological insights that can be gained by this approach.

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Notes

  1. 1.

    Italicized concepts are explained in the glossary, Table 5.1.

References

  1. Alberch P (1982) Developmental constraints in evolutionary processes. In: Bonner JT (ed) Evolution and development. Springer, Heidelberg, pp 313–332

    Google Scholar 

  2. Alberch P (1991) From genes to phenotype: dynamical systems and evolvability. Genetica 84:5–11

    PubMed  CAS  Google Scholar 

  3. Aldana M, Balleza E, Kauffman S, Resendiz O (2007) Robustness and evolvability in genetic regulatory networks. J Theor Biol 245:433–448

    PubMed  Google Scholar 

  4. Arthur W (2004) Biased embryos and evolution. Cambridge University Press, Cambridge

    Google Scholar 

  5. Arthur W (2011) Evolution: a developmental approach. Wiley, Chichester

    Google Scholar 

  6. Ashyraliyev M, Fomekong-Nanfack Y, Kaandorp JA, Blom JG (2009) Systems biology: parameter estimation for biochemical models. FEBS J 276:889–902

    Google Scholar 

  7. Ashyraliyev M, Siggens K, Janssens H, Blom J, Akam M, Jaeger J (2009) Gene circuit analysis of the terminal gap gene huckebein. PLoS Comp Biol 5:e1000548

    Google Scholar 

  8. Banga JR (2008) Optimization in computational systems biology. BMC Syst Biol 2:47

    PubMed  Google Scholar 

  9. Bergmann A, Siegal ML (2003) Evolutionary capacitance as a general feature of complex gene networks. Nature 424:549–552

    Google Scholar 

  10. Ciliberti S, Martin OC, Wagner A (2007) Innovation and robustness in complex regulatory gene networks. Proc Natl Acad Sci USA 104:13591–13596

    PubMed  CAS  Google Scholar 

  11. Ciliberti S, Martin OC, Wagner A (2007) Robustness can evolve gradually in complex regulatory gene networks with varying topology. PLoS Comp Biol 3:e15

    Google Scholar 

  12. Cotterell J, Sharpe J (2010) An atlas of gene regulatory networks reveals multiple three-gene mechanisms for interpreting morphogen gradients. Mol Syst Biol 6:425

    PubMed  Google Scholar 

  13. Crombach A, Hogeweg P (2008) Evolution of evolvability in gene regulatory networks. PLoS Comp Biol 4:e10000112

    Google Scholar 

  14. Crombach A, Wotton KR, Cicin-Sain D, Ashyraliyev M, Jaeger J (2012). Efficient reverse-engineering of a developmental gene regulatory network. PLoS Computational Biology (in print)

    Google Scholar 

  15. Davidson EH, Erwin DH (2006) Gene regulatory networks and the evolution of animal body plans. Science 311:796–800

    PubMed  CAS  Google Scholar 

  16. Davidson EH, Levine MS (2008) Properties of developmental gene regulatory networks. Proc Natl Acad Sci USA 105:20063–20066

    PubMed  CAS  Google Scholar 

  17. Davis GK, Patel NH (2002) Short, long and beyond: molecular and embryological approaches to insect segmentation. Ann Rev Entomol 47:669–699

    CAS  Google Scholar 

  18. Draghi J, Parsons TL, Wagner GP, Plotkin JB (2010) Mutational robustness can facilitate adaptation. Nature 463:353–355

    PubMed  CAS  Google Scholar 

  19. Eldredge N, Gould SJ (1972) Punctuated equilibria: an alternative to phyletic gradualism. In: Schopf TJM (ed) Models in Paleobiology. Freeman, Cooper and Company, San Francisco, pp 82–115

    Google Scholar 

  20. Fomekong-Nanfack Y, Kaandorp JA, Blom J (2007) Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster. Bioinformatics 23:3356–3363

    PubMed  CAS  Google Scholar 

  21. Fontana W (2002) Modelling ‘evo-devo’ with RNA. BioEssays 24:1164–1177

    PubMed  CAS  Google Scholar 

  22. François P, Hakim V, Siggia ED (2007) Deriving structure from evolution: metazoan segmentation. Mol Syst Biol 3:154

    PubMed  Google Scholar 

  23. Fujimoto K, Ishihara S, Kaneko K (2008) Network evolution of body plans. PLoS ONE 3:e2772

    PubMed  Google Scholar 

  24. García Solache MA, Jaeger J, Akam M (2010) A systematic analysis of the gap gene system in the moth midge Clogmia albipunctata. Dev Biol 344:306–318

    PubMed  Google Scholar 

  25. Gilbert SF (2010) Developmental biology, 9th edn. Sinauer Associates, Sunderland

    Google Scholar 

  26. Gilbert SF, Epel D (2009) Ecological developmental biology: integrating epigenetics, medicine, and evolution. Sinauer Associates, Cambridge

    Google Scholar 

  27. Gjuvsland AB, Plahte E, Omholt SW (2007) Threshold-dominated regulation hides genetic variation in gene expression networks. BMC Syst Biol 1:57

    PubMed  Google Scholar 

  28. Goentoro LA, Reeves GT, Kowal CP, Martinelli L, Schüpbach T, Shvartsman SY (2006) Quantifying the gurken morphogen gradient in Drosophila oogenesis. Dev Cell 11:263–272

    PubMed  CAS  Google Scholar 

  29. Goltsev Y, Hsiong W, Lanzaro G, Levine M (2004) Different combinations of gap repressors for common stripes in Anopheles and Drosophila embryos. Dev Biol 275:435–446

    PubMed  CAS  Google Scholar 

  30. Goodwin BC (1982) Development and evolution. J Theor Biol 97:43–55

    PubMed  CAS  Google Scholar 

  31. Goodwin BC, Kauffman SA, Murray JD (1993) Is morphogenesis an intrinsically robust process? J Theor Biol 163:135–144

    PubMed  CAS  Google Scholar 

  32. Hecker M, Lambeck S, Toepfer S, van Someren E, Guthke R (2009) Gene regulatory network inference: data integration in dynamic models – a review. BioSystems 96:86–103

    PubMed  CAS  Google Scholar 

  33. Hendrikse JL, Parsons TE, Hallgrmsson B (2007) Evolvability as the proper focus of evolutionary developmental biology. Evol Dev 9:393–401

    PubMed  Google Scholar 

  34. Hogeweg P (2002) Computing an organism: on the interface between informatic and dynamic processes. BioSystems 64:97–109

    PubMed  Google Scholar 

  35. Hogeweg P (2011) The roots of bioinformatics in theoretical biology. PLoS Comp Biol 7:e1002021

    CAS  Google Scholar 

  36. Hoyos E, Kim K, Milloz J, Barkoulas M, Pénigault JB, Munro E, Félix MA (2011) Quantitative variation in autocrine signaling and pathway crosstalk in the Caenorhabditis vulval network. Curr Biol 21:527–538

    PubMed  CAS  Google Scholar 

  37. Jaeger J (2010) The gap gene network. Cell Mol Life Sci 68:243–274

    PubMed  Google Scholar 

  38. Jaeger J, Monk NAM (2010) Reverse engineering of gene regulatory networks. In: Lawrence ND, Girolami M, Rattray M, Sanguinetti G (eds) Learning and inference in computational systems biology. MIT, Cambridge, pp 9–34

    Google Scholar 

  39. Jaeger J, Reinitz J (2006) On the dynamic nature of positional information. BioEssays 28:1102–1111

    PubMed  CAS  Google Scholar 

  40. Jaeger J, Surkova S, Blagov M, Janssens H, Kosman D, Kozlov KN, Manu, Myasnikova E, Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J (2004) Dynamic control of positional information in the early Drosophila embryo. Nature 430:368–371

    PubMed  CAS  Google Scholar 

  41. Jaeger J, Blagov M, Kosman D, Kozlov KN, Manu, Myasnikova E, Surkova S, Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J (2004) Dynamical analysis of regulatory interactions in the gap gene system of Drosophila melanogaster. Genetics 167:1721–1737

    PubMed  CAS  Google Scholar 

  42. Jaeger J, Sharp DH, Reinitz J (2007) Known maternal gradients are not sufficient for the establishment of gap domains in Drosophila melanogaster. Mech Dev 124:108–128

    PubMed  CAS  Google Scholar 

  43. Jaeger J, Irons D, Monk N (2008) Regulative feedback in pattern formation: towards a general relativistic theory of positional information. Development 135:3175–3183

    PubMed  CAS  Google Scholar 

  44. Jaeger J, Irons D, Monk N (2011) The inheritance of process: causality and chance in evolution. J Exp Zool B (Mol Dev Evol) (in review)

    Google Scholar 

  45. Jaqaman K, Danuser G (2006) Linking data to models: data regression. Nat Rev Mol Cell Biol 7:813–819

    PubMed  CAS  Google Scholar 

  46. de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comp Biol 9:67–103

    Google Scholar 

  47. Kanodia JS, Rikhy R, Kim Y, Lund VK, DeLotto R, Lippincott-Schwartz J, Shvartsman SY (2009) Dynamics of the dorsal morphogen gradient. Proc Natl Acad Sci USA 106:21707–21712

    PubMed  CAS  Google Scholar 

  48. Karlebach G, Shamir R (2008) Modelling and analysis of gene regulatory networks. Nat Rev Genet 9:770–780

    CAS  Google Scholar 

  49. Kashtan N, Alon U (2005) Spontaneous evolution of modularity and network motifs. Proc Natl Acad Sci USA 102:13773–13778

    PubMed  CAS  Google Scholar 

  50. Kashtan N, Noor E, Alon U (2007) Varying environments can speed up evolution. Proc Natl Acad Sci USA 104:13711–13716

    PubMed  CAS  Google Scholar 

  51. Kashtan N, Mayo AE, Kalisky T, Alon U (2009) An analytically solvable model for rapid evolution of modular structure. PLoS Comp Biol 5:e1000355

    Google Scholar 

  52. Kauffman S (2004) A proposal for using the ensemble approach to understand genetic regulatory networks. J Theor Biol 230:581–590

    PubMed  Google Scholar 

  53. Kauffman S, Levin S (1987) Towards a general theory of adaptive walks on rugged landscapes. J Theor Biol 128:11–45

    PubMed  CAS  Google Scholar 

  54. Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22:437–467

    PubMed  CAS  Google Scholar 

  55. Kauffman SA (1974) The large scale structure and dynamics of gene control circuits. J Theor Biol 44:167–190

    PubMed  CAS  Google Scholar 

  56. Kauffman SA (1993) The origins of order: self organization and selection in evolution. Oxford University Press, Oxford

    Google Scholar 

  57. Kirschner M, Gerhart J (1998) Evolvability. Proc Natl Acad Sci USA 95:8420–8427

    PubMed  CAS  Google Scholar 

  58. Ma W, Lai L, Ouyang Q, Tang C (2006) Robustness and modular design of the Drosophila segment polarity network. Mol Syst Biol 2:70

    PubMed  Google Scholar 

  59. Ma W, Trusina A, El-Samad H, Lim WA, Tang C (2009) Defining network topologies that can achieve biochemical adaptation. Cell 138:760–773

    PubMed  CAS  Google Scholar 

  60. Manu, Surkova S, Spirov AV, Gursky V, Janssens H, Kim AR, Radulescu O, Vanario-Alonso CE, Sharp DH, Samsonova M, Reinitz J (2009) Canalization of gene expression and domain shifts in the Drosophila blastoderm by dynamical attractors. PLoS Comp Biol 5:e1000303

    CAS  Google Scholar 

  61. Manu, Surkova S, Spirov AV, Gursky V, Janssens H, Kim AR, Radulescu O, Vanario-Alonso CE, Sharp DH, Samsonova M, Reinitz J (2009) Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation. PLoS Biol 7:e1000049

    PubMed  CAS  Google Scholar 

  62. Maynard Smith J, Burian R, Kauffman S, Alberch P, Campbell J, Goodwin B, Lande R, Raup D, Wolpert L (1985) Developmental constraints and evolution. Quart Rev Biol 60:265–287

    Google Scholar 

  63. Mjolsness E, Sharp DH, Reinitz J (1991) A connectionist model of development. J Theor Biol 152:429–453

    PubMed  CAS  Google Scholar 

  64. Müller GB (2007) Evo-devo: extending the evolutionary synthesis. Nat Rev Genet 8:943–949

    PubMed  Google Scholar 

  65. Müller GB (2010) Epigenetic innovation. In: Pigliucci M, Müller GB (eds) Evolution: the extended synthesis. MIT, Cambridge, pp 307–332

    Google Scholar 

  66. Müller GB, Newman SA (2005) The innovation triad: an evodevo agenda. J Exp Zool B (Mol Dev Evol) 304:487–503

    Google Scholar 

  67. Munteanu A, Solé RV (2008) Neutrality and robustness in evo-devo: emergence of lateral inhibition. PLoS Comp Biol 4:e10000226

    Google Scholar 

  68. Nahmad M, Glass L, Abouheif E (2008) The dynamics of developmental system drift in the gene networks underlying wing polyphenism in ants: a mathematical model. Evol Dev 10:360–374

    PubMed  Google Scholar 

  69. van Nimwegen E, Crutchfield JP (2000) Metastable evolutionary dynamics: crossing fitness barriers or escaping via neutral paths? Bull Math Biol 62:799–848

    PubMed  Google Scholar 

  70. van Nimwegen E, Crutchfield JP, Huynen M (1999) Neutral evolution of mutational robustness. Proc Natl Acad Sci USA 96:9716–9720

    PubMed  Google Scholar 

  71. Noble D (2006) The music of life: biology beyond genes. Oxford University Press, Oxford

    Google Scholar 

  72. O’Malley MA (2012) Evolutionary systems biology: historical and philosophical perspectives on an emerging synthesis. In: Soyer O (ed) Evolutionary systems biology. Springer, Berlin

    Google Scholar 

  73. Oster G, Alberch P (1982) Evolution and bifurcation of developmental programs. Evolution 36:444–459

    Google Scholar 

  74. Oyama S (2000) The ontogeny of information: developmental systems and evolution, 2nd edn. Duke University Press, Durham

    Google Scholar 

  75. Oyama S, Griffiths PE, Gray RD (eds) (2001) Cycles of contingency: developmental systems and evolution. MIT, Cambridge

    Google Scholar 

  76. Perkins TJ, Jaeger J, Reinitz J, Glass L (2006) Reverse engineering the gap gene network. PLoS Comp Biol 2:e51

    Google Scholar 

  77. Pigliucci M (2008) Is evolvability evolvable? Nat Rev Genet 9:75–82

    PubMed  CAS  Google Scholar 

  78. Pigliucci M (2010) Genotype-phenotype mapping and the end of the ‘genes as blueprint’ metaphor. Phil Trans Roy Soc B 365:557–566

    CAS  Google Scholar 

  79. Reinitz J, Sharp DH (1995) Mechanism of eve stripe formation. Mech Dev 49:133–158

    PubMed  CAS  Google Scholar 

  80. Reinitz J, Mjolsness E, Sharp DH (1995) Cooperative control of positional information in Drosophila by bicoid and maternal hunchback. J Exp Zool 271:47–56

    PubMed  CAS  Google Scholar 

  81. Richardson MK, Chipman AD (2003) Developmental constraints in a comparative framework: a test case using variations in phalanx number during amniote evolution. J Exp Zool B (Mol Dev Evol) 296:8–22

    Google Scholar 

  82. Robert JS (2004) Embryology, epigenesis, and evolution: taking development seriously. Cambridge University Press, Cambridge

    Google Scholar 

  83. Rockman MV (2008) Reverse engineering the genotype-phenotype map with natural genetic variation. Nature 456:738–744

    PubMed  CAS  Google Scholar 

  84. Salazar-Ciudad I (2006) Developmental constraints vs. variational properties: how pattern formation can help to understand evolution and development. J Exp Zool B (Mol Dev Evol) 306:107–125

    Google Scholar 

  85. Salazar-Ciudad I (2006) On the origins of morphological disparity and its diverse developmental bases. BioEssays 28:1112–1122

    PubMed  Google Scholar 

  86. Salazar-Ciudad I (2010) Morphological evolution and embryonic developmental diversity in metazoa. Development 137:531–539

    PubMed  CAS  Google Scholar 

  87. Salazar-Ciudad I, Jernvall J (2002) A gene network model accounting for development and evolutiion of mammalian teeth. Proc Natl Acad Sci USA 99:8116–8120

    PubMed  CAS  Google Scholar 

  88. Salazar-Ciudad I, Jernvall J (2004) How different types of pattern formation mechanisms affect the evolution of form and development. Evol Dev 6:6–16

    PubMed  Google Scholar 

  89. Salazar-Ciudad I, Jernvall J (2010) A computational model of teeth and the developmental origins of morphological variation. Nature 464:583–586

    PubMed  CAS  Google Scholar 

  90. Salazar-Ciudad I, Garcia-Fernández J, Solé R (2000) Gene networks capable of pattern formation: from induction to reaction-diffusion. J Theor Biol 205:587–603

    PubMed  CAS  Google Scholar 

  91. Salazar-Ciudad I, Newman SA, Solé RV (2001) Phenotypic and dynamical transitions in model genetic networks I. Emergence of patterns and genotype-phenotype relationships. Evol Dev 3:84–94

    CAS  Google Scholar 

  92. Salazar-Ciudad I, Solé RV, Newman SA (2001) Phenotypic and dynamical transitions in model genetic networks II. Application to the evolution of segmentation mechanisms. Evol Dev 3:95–103

    CAS  Google Scholar 

  93. Salazar-Ciudad I, Jernvall J, Newman SA (2003) Mechanisms of pattern formation in development and evolution. Development 130:2027–2037

    PubMed  CAS  Google Scholar 

  94. Sharp DH, Reinitz J (1998) Prediction of mutant expression patterns using gene circuits. BioSystems 47:79–90

    PubMed  CAS  Google Scholar 

  95. Shen-Orr SS, Milo R, Mangan S, Alon U (2002) Network motifs in the transcriptional regulation network of Escherichia coli. Nat Genet 31:64–68

    PubMed  CAS  Google Scholar 

  96. Siegal ML, Bergmann A (2002) Waddington’s canalization revisited: developmental stability and evolution. Proc Natl Acad Sci USA 99:10528–10532

    PubMed  CAS  Google Scholar 

  97. Stauber M, Taubert H, Schmidt-Ott U (2000) Function of bicoid and Hunchback homologs in the basal cyclorrhaphan fly Megaselia (phoridae). Proc Natl Acad Sci USA 97:10844–10849

    PubMed  CAS  Google Scholar 

  98. Stauber M, Prell A, Schmidt-Ott U (2002) A single hox3 gene with composite Bicoid and zerknüllt expression characteristics in non-cyclorrhaphan flies. Proc Natl Acad Sci USA 99:274–279

    PubMed  CAS  Google Scholar 

  99. Stauber M, Lemke S, Schmidt-Ott U (2008) Expression and regulation of Caudal in the lower cyclorrhaphan fly Megaselia. Dev Genes Evol 218:81–87

    PubMed  CAS  Google Scholar 

  100. Stern DL, Orgogozo V (2009) Is genetic evolution predictable? Science 323:746–751

    PubMed  CAS  Google Scholar 

  101. Strogatz SH (2000) Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry and engineering. Perseus Books, New York

    Google Scholar 

  102. Struhl G, Johnston P, Lawrence PA (1992) Control of Drosophila body pattern by the hunchback morphogen gradient. Cell 69:237–249

    PubMed  CAS  Google Scholar 

  103. Surkova S, Kosman D, Kozlov K, Manu, Myasnikova E, Samsonova AA, Spirov A, Vanario-Alonso CE, Samsonova M, Reinitz J (2008) Characterization of the Drosophila segment determination morphome. Dev Biol 313:844–862

    PubMed  CAS  Google Scholar 

  104. Surkova S, Myasnikova E, Janssens H, Kozlov KN, Samsonova AA, Reinitz J, Samsonova M (2008) Pipeline for acquisition of quantitative data on segmentation gene expression from confocal images. Fly 2:1–9

    Google Scholar 

  105. Thom R (1988) Structural stability and morphogenesis. Westview Press, Boulder

    Google Scholar 

  106. ten Tusscher KH, Hogeweg P (2011) Evolution of networks for body plan patterning; interplay of modularity, robustness and evolvability. PLoS Comp Biol 7:e1002208

    Google Scholar 

  107. Waddington CH (1942) Canalization of development and the inheritance of acquired characters. Nature 150:563–565

    Google Scholar 

  108. Wagner A (1996) Does evolutionary plasticity evolve? Evolution 50:1008–1023

    Google Scholar 

  109. Wagner A (2005) Robustness and evolvability in living systems. Princeton University Press, Princeton

    Google Scholar 

  110. Wagner A (2011) The origins of evolutionary innovations: a theory of transformative change in living systems. Oxford University Press, Oxford

    Google Scholar 

  111. Wagner GP (1988) The significance of developmental constraints for phenotypic evolution by natural selection. In: de Jong G (ed) Population genetics and evolution. Springer, Berlin, pp 222–229

    Google Scholar 

  112. Wagner GP, Altenberg L (1996) Complex adaptations and the evolution of evolvability. Evolution 50:967–976

    Google Scholar 

  113. Webster G, Goodwin BC (1996) Form and transformation: generative and relational principles in biology. Cambridge University Press, Cambridge

    Google Scholar 

  114. West-Eberhard MJ (2003) Developmental plasticity and evolution. Oxford University Press, Oxford

    Google Scholar 

  115. Wiegmann BM, Trautwein MD, Winkler IS, Barr NB, Kim JW, Lambkin C, Bertone MA, Cassel BK, Bayless KM, Heimberg AM, Wheeler BM, Peterson KJ, Pape T, Sinclair BJ, Skevington JH, Blagoderov V, Caravas J, Narayanan Kutty S, Schmidt-Ott U, Kampmeier GE, Thompson FC, Grimaldi DA, Beckenbach AT, Courtney GW, Friedrich M, Meier R, Yeates DK (2011) Episodic radiations in the fly tree of life. Proc Natl Acad Sci USA 108:5690–5695

    PubMed  CAS  Google Scholar 

  116. Wilkins AS (2001) The evolution of developmental pathways. Sinauer Associates, Sunderland

    Google Scholar 

  117. Wilkins AS (2007) Between “design” and “bricolage”: genetic networks, levels of selection, and adaptive evolution. Proc Natl Acad Sci USA 104:8590–8596

    PubMed  CAS  Google Scholar 

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Acknowledgements

We would like to acknowledge Karl Wotton and Mónica García-Solache for creating the quantitative data sets mentioned in Sect. 4. We thank Damjan Cicin-Sain for designing computational tools and databases that were essential for data processing and quantification. Analyses and models based on those data will be published elsewhere. We are grateful to David Irons and Nick Monk for letting us use their phase portraits of the toggle switch model, shown in Figs. 5.2 and 5.3. Finally, we thank all members of the Jaeger Lab at the CRG for discussions, constructive criticism, and useful feedback on the manuscript.

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  1. EMBL/CRG Research Unit in Systems Biology, Centre de Regulació Genòmica (CRG), and Universitat Pompeu Fabra (UPF), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain

    Johannes Jaeger & Anton Crombach

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  1. Johannes Jaeger
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Correspondence to Johannes Jaeger .

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  1. University of Exeter, Prince of Wales Road, Exeter, EX4 4SB, Devon, United Kingdom

    Orkun S. Soyer

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Jaeger, J., Crombach, A. (2012). Life’s Attractors. In: Soyer, O. (eds) Evolutionary Systems Biology. Advances in Experimental Medicine and Biology, vol 751. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3567-9_5

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