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Mathematical Models of Prebiotic Replication of Informational Molecules

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Genesis - In The Beginning

Part of the book series: Cellular Origin, Life in Extreme Habitats and Astrobiology ((COLE,volume 22))

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Abstract

The origin of life is a fascinating problem for both theorists and experimentalists. In this chapter, we review some major mathematical ideas (quasispecies, the error threshold and ways around it, hypercycles, and recent work on the transition from chemical kinetics to replicator dynamics) and relevant experimental contexts. Such models are ideal launch points for mutually informative collaborations in this highly interdisciplinary field.

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References

  • Adami C, Ofria C, Collier TC (2000) Evolution of biological complexity. Proc Natl Acad Sci 97(9):4463–4468

    Article  PubMed  CAS  Google Scholar 

  • Altmeyer S, McCaskill JS (2001) Error threshold for spatially resolved evolution in the quasispecies model. Phys Rev Lett 86:5819–5822

    Article  PubMed  CAS  Google Scholar 

  • Anderson JP, Daifuku R, Loeb LA (2004) Viral error catastrophe by mutagenic nucleosides. Annu Rev Microbiol 58:183–205

    Article  PubMed  CAS  Google Scholar 

  • Anet FAL (2004) The place of metabolism in the origin of life. Curr Op Chem Biol 8(6):654–659

    Article  CAS  Google Scholar 

  • Bartel DP, Szostak JW (1993) Isolation of a new ribozymes from a large pool of random sequences. Science 261:1411–1418

    Article  Google Scholar 

  • Boerlijst MC, Hogeweg P (1991) Spiral wave structure in pre-biotic evolution: hypercycles stable against parasites. Phys D: Nonlinear Phenomena 48(1):17–28

    Article  Google Scholar 

  • Crick FHC (1963) On the genetic code: deductions about the general nature of the code are drawn from results of biochemical experimentation. Science 8:461–464

    Article  Google Scholar 

  • Crick FHC (1968) The origin of the genetic code. J Mol Biol 38(3):367–379

    Article  PubMed  CAS  Google Scholar 

  • Crotty S, Cameron CE, Andino R (2004) RNA virus error catastrophe: direct molecular test by using ribavirin. Proc Natl Acad Sci U S A 98(12):6895–6900

    Article  Google Scholar 

  • Domingo E, Holland JJ (1997) RNA virus mutations and fitness for survival. Annu Rev Microbiol 51:151–178

    Article  PubMed  CAS  Google Scholar 

  • Doudna JD, Szostak JW (1989) RNA-catalyzed synthesis of complementary-strand RNA. Nature 339:519–522

    Article  PubMed  CAS  Google Scholar 

  • Eigen M (1971) Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 33a:465–523

    Article  Google Scholar 

  • Eigen M (1977) The hypercycle: a principle of natural self-organization; Part A: emergence of the hypercycle. Naturwissenschaften 64:541–565

    Article  PubMed  CAS  Google Scholar 

  • Eigen M (1993) The origin of genetic information: viruses as models. Gene 135:37–47

    Article  PubMed  CAS  Google Scholar 

  • Eigen M (2002) Error catastrophe and antiviral strategy. Proc Natl Acad Sci U S A 99(21):13374–13376

    Article  PubMed  CAS  Google Scholar 

  • Eigen M, Schuster P (1978a) The hypercycle: a principle of natural self-organization; Part B: The abstract hypercycle. Naturwissenschaften 65:7–41

    Article  Google Scholar 

  • Eigen M, Schuster P (1978b) The hypercycle: a principle of natural self-organization; Part C: The realistic hypercycle. Naturwissenschaften 65:341–369

    Article  CAS  Google Scholar 

  • Eigen M, Winkler-Oswatitsch R (1981a) Transfer RNA: the early adaptor. Naturwissenschaften 68:217–228

    Article  PubMed  CAS  Google Scholar 

  • Eigen M, Winkler-Oswatitsch R (1981b) Transfer RNA, an early gene? Naturwissenschaften 68:282–292

    Article  PubMed  CAS  Google Scholar 

  • Eigen M, McCaskill J, Schuster P (1988) Molecular quasi-species. J Phys Chem 92:6881–6891

    Article  CAS  Google Scholar 

  • Ekland EH, Bartel DP (1995) The secondary structure and sequence optimization of an RNA ligase ribozyme. Nucleic Acids Res 23(16):3231–3238

    Article  PubMed  CAS  Google Scholar 

  • Ertem G, Ferris JP (1996) Synthesis of RNA oligomers on heterogeneous templates. Nature 379:238–240

    Article  PubMed  CAS  Google Scholar 

  • Ferris JP, Ertem G (1992) Oligomerization of ribonucleotides on montmorillonite: reaction of the 5′-phosphorimidazolide of adenosine. Science 257(5075):1387–1389

    Article  PubMed  CAS  Google Scholar 

  • 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(26):12270–12275

    Article  PubMed  CAS  Google Scholar 

  • Ferris JP, Hill AR, Liu R, Orgel LE (1996) Synthesis of long prebiotic oligomers on mineral surfaces. Nature 381:59–61

    Article  PubMed  CAS  Google Scholar 

  • Fontana W, Buss LW (1994) What would be conserved if “the tape were played twice”? Proc Natl Acad Sci U S A 91:757–761

    Article  PubMed  CAS  Google Scholar 

  • Fontana W, Wagner GP, Buss LW (1994) Beyond digital naturalism. Artif Life 1:211–227

    Article  Google Scholar 

  • Freeland SJ, Hurst LD (1998) The genetic code is one in a million. J Mol Evol 47:238–248

    Article  PubMed  CAS  Google Scholar 

  • Freeland SJ, Knight RD, Landweber LF, Hurst LD (2000) Early fixation of an optimal genetic code. Mol Biol Evol 17:511–518

    PubMed  CAS  Google Scholar 

  • Gago S, Elena SF, Flores R, Sanjuan R (2009) Extremely high mutation rate of a hammerhead viroid. Science 323:1308

    Article  PubMed  CAS  Google Scholar 

  • Gould SJ (1989) Wonderful life. Norton, New York

    Google Scholar 

  • Grande-Perez A, Sierra S, Castro MG, Domingo E, Lowenstein PR (2002) Molecular indetermination in the transition to error catastrophe: systematic elimination of lymphocytic choriomeningitis virus through mutagenesis does not correlate linearly with large increases in mutant spectrum complexity. Proc Natl Acad Sci U S A 99(20):12938–12943

    Article  PubMed  CAS  Google Scholar 

  • Green R, Szostak JW (1992) Selection of a ribozyme that functions as a superior template in a self-copying reaction. Science 258(5090):1910–1915

    Article  PubMed  CAS  Google Scholar 

  • Guerrier-Takada C, Gardiner K, Marsh T, Pace N, Altman S (1983) The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme. Cell 35:849–857

    Article  PubMed  CAS  Google Scholar 

  • Hagenbuch P, Kervio E, Hochgesand A, Plutowski U, Richert C (2005) Chemical primer extension: efficiently determining single nucleotides in DNA. Angew Chem Int Ed 44:6588–6592

    Article  CAS  Google Scholar 

  • Hager AJ, Szostak JW (1997) Isolation of novel ribozymes that ligate AMP-activated RNA substrates. Chem Biol 4(8):607–617

    Article  PubMed  CAS  Google Scholar 

  • Harris K (2009) On the dynamics of prebiotic evolution. A.B. honors thesis, Harvard University, http://brauer.harvard.edu/theses/senior/harris/harris.pdf

  • Hayden EJ, Lehman N (2006) Self-assembly of a group I intron from inactive oligonucleotide fragments. Chem Biol 13(8):909–918

    Article  PubMed  CAS  Google Scholar 

  • Hayden EJ, Riley CA, Burton AS, Lehman N (2005) RNA-directed construction of structurally complex and active ligase ribozymes through recombination. RNA 11:1678–1687

    Article  PubMed  CAS  Google Scholar 

  • Hill AR Jr, Orgel LE (1993) The limits of template-directed synthesis with nucleoside-5′-phosophoro(2-methyl)imidazolides. Orig Life Evol Biosph 23:285–290

    Article  PubMed  CAS  Google Scholar 

  • Horn RA, Johnson CR (1991) Matrix analysis. Cambridge University Press, New York

    Book  Google Scholar 

  • Huang M-M, Arnheim N, Goodman MF (1992) Extension of base mispairs by Taq DNA polymerase: implications for single nucleotide discrimination in PCR. Nucleic Acids Res 20(17):4567–4573

    Article  PubMed  CAS  Google Scholar 

  • Hutton TJ (2007) Evolvable self-reproducing cells in a two-dimensional artificial chemistry. Artif Life 13(1):11–30

    Article  PubMed  Google Scholar 

  • Ichida JK, Horhota A, Zou K, McLaughlin LW, Szostak JW (2005a) High fidelity TNA synthesis by Therminator polymerase. Nucleic Acids Res 33(6):5219–5225

    Article  PubMed  CAS  Google Scholar 

  • Ichida JK, Zou K, Horhota A, Yu B, McLaughlin LW, Szostak JW (2005b) An in vitro selection system for TNA. J Am Chem Soc 127(9):2802–2803

    Article  PubMed  CAS  Google Scholar 

  • Jackson SE (1998) How do small single-domain proteins fold? Fold Des 3:R81–R91

    Article  PubMed  CAS  Google Scholar 

  • Jaeger L, Wright MC, Joyce GF (1999) A complex ligase ribozyme evolved in vitro from a group I ribozyme domain. Proc Natl Acad Sci U S A 96(26):14712–14717

    Article  PubMed  CAS  Google Scholar 

  • James KD, Ellington AD (1997) Surprising fidelity of template-directed chemical ligation of oligonucleotides. Chem Biol 4(8):595–605

    Article  PubMed  CAS  Google Scholar 

  • Johnston WK, Unrau PJ, Lawrence MS, Glasner ME, Bartel DP (2001) RNA-catalyzed RNA polyme­rization: accurate and general RNA-templated primer extension. Science 292:1319–1325

    Article  PubMed  CAS  Google Scholar 

  • Kim D-E, Joyce GF (2004) Cross-catalytic replication of an RNA ligase ribozyme. Chem Biol 11(11):1505–1512

    Article  PubMed  CAS  Google Scholar 

  • Krasilnikova MM, Mirkin SM (2004) Replication stalling at Friedrich’s ataxia (GAA) n repeats in vivo. Mol Cell Biol 24(6):2286–2295

    Article  PubMed  CAS  Google Scholar 

  • Kruger K, Grabowski PJ, Zaug AJ, Sands J, Gottschling DE, Cech TR (1982) Self-splicing RNA: autoexcision and autocyclization of the ribosomal RNA intervening sequence of Tetrahymena. Cell 31:147–157

    Article  PubMed  CAS  Google Scholar 

  • Kun A, Santos M, Szathmary E (2005) Real ribozymes suggest a relaxed error threshold. Nat Genet 37(9):1008–1011

    Article  PubMed  CAS  Google Scholar 

  • Lawless JG, Yuen GU (1979) Quantification of monocarboxylic acids in the Murchison carbonaceous meteorite. Nature 282:396–398

    Article  CAS  Google Scholar 

  • Lee DH, Granja JR, Martinez JA, Severin K, Ghadiri MR (1996) A self-replicating peptide. Nature 382:525–528

    Article  PubMed  CAS  Google Scholar 

  • Lincoln TA, Joyce GF (2009) Self-sustained replication of an RNA enzyme. Science 323(5918):1229–1232

    Article  PubMed  CAS  Google Scholar 

  • Manapat ML, Ohtsuki H, Burger R, Nowak MA (2009) Originator dynamics. J Theor Biol 256:586–595

    Article  PubMed  Google Scholar 

  • Manapat ML, Chen IA, Nowak MA (2010) The basic reproductive ratio of life. J Theor Biol 263(3):317–327

    Article  PubMed  Google Scholar 

  • Mansy SS, Szostak JW (2009) Reconstructing the emergence of cellular life through the synthesis of model protocells. Cold Spring Harb Symp Quant Biol 74:47–54

    Article  PubMed  CAS  Google Scholar 

  • Mansy SS, Schrum JP, Krishnamurthy M, Tobe S, Treco DA, Szostak JW (2008) Template-directed synthesis of a genetic polymer in a model protocell. Nature 454:122–125

    Article  PubMed  CAS  Google Scholar 

  • Mendelman LV, Petruska J, Goodman MC (1990) Base mispair extension kinetics: comparison of DNA polymerase alpha and reverse transcriptase. J Biol Chem 265:2338–2346

    PubMed  CAS  Google Scholar 

  • Miller SL, Urey HC (1959) Organic compound synthesis on the primitive Earth: several questions about the origin of life have been answered, but much remains to be studied. Science 130(3370):245–251

    Article  PubMed  CAS  Google Scholar 

  • Mirkin EV, Mirkin AM (2007) Replication fork stalling at natural impediments. Microbiol Mol Biol Rev 71(1):13–35

    Article  PubMed  CAS  Google Scholar 

  • Monnard PA, Deamer DW (2001) Nutrient uptake by protocells: a liposome model system. Orig Life Evol Biosph 31(1):147–155

    Article  PubMed  CAS  Google Scholar 

  • Monnard PA, Deamer DW (2002) Membrane self-assembly processes: steps toward the first cellular life. Anat Rec 268:196–207

    Article  PubMed  CAS  Google Scholar 

  • Nowak MA, Ohtsuki H (2008) Prevolutionary dynamics and the origin of evolution. Proc Natl Acad Sci U S A 105(39):14924–14927

    Article  PubMed  CAS  Google Scholar 

  • Ofria C, Wilke CO (2004) Avida: a software platform for research in computational evolutionary biology. Artif Life 10(2):191–229

    Article  PubMed  Google Scholar 

  • Ohtsuki H, Nowak MA (2009) Prelife catalysts and replicators. Proc R Soc B 279:3783–3790

    Article  Google Scholar 

  • Orgel L (1992) Molecular replication. Nature 358:203–209

    Article  PubMed  CAS  Google Scholar 

  • Orgel L (2004) Prebiotic chemistry and the origin of the RNA world. Crit Rev Biochem Mol Biol 39:99–123

    Article  PubMed  CAS  Google Scholar 

  • Perrino FW, Loeb LA (1989) Differential extension of 3′ mispairs is a major contribution to the high fidelity of calf thymus DNA polymerase-alpha. J Biol Chem 264:2898–2905

    PubMed  CAS  Google Scholar 

  • Powner MW, Gerland B, Sutherland JD (2009) Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions. Nature 459:239–242

    Article  PubMed  CAS  Google Scholar 

  • Pross A (2004) Causation and the origin of life: metabolism or replication first? Orig Life Evol Biosph 34:3307–3321

    Article  Google Scholar 

  • Quer J, Huerta R, Novella IS, Tsimring L, Domingo E, Holland JJ (1996) Reproducible nonlinear population dynamics and critical points during replicative competitions of RNA virus quasispecies. J Mol Biol 264:465–471

    Article  PubMed  CAS  Google Scholar 

  • 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(1):57–74

    Article  PubMed  CAS  Google Scholar 

  • Rajamani S, Ichida JK, Antal T, Treco DA, Leu K, Nowak MA, Szostak JW, Chen IA (2010) Effect of stalling after mismatches on the error catastrophe in non-enzymatic nucleic acid replication. J Am Chem Soc 132(16):5880–5885

    Article  PubMed  CAS  Google Scholar 

  • Ricardo A, Carrigan MA, Olcott AN, Benner SA (2004) Borate minerals stabilize ribose. Science 303(5655):196

    Article  PubMed  CAS  Google Scholar 

  • Rohatgi R, Bartel DP, Szostak JW (1996a) Kinetic and mechanistic analysis of nonenzymatic, template-directed oligoribonucleotide ligation. J Am Chem Soc 118(14):3332–3339

    Article  PubMed  CAS  Google Scholar 

  • Rohatgi R, Bartel DP, Szostak JW (1996b) Nonenzymatic, template-directed ligation of oligoribonucleotides is highly regioselective for the formation of 3′-5′ phosphodiester bonds. J Am Chem Soc 118(14):3340–3344

    Article  PubMed  CAS  Google Scholar 

  • Sawai H, Orgel LE (1975) Oligonucleotide synthesis catalyzed by the Zn2+ ion. J Am Chem Soc 97:3532–3533

    Article  PubMed  CAS  Google Scholar 

  • Schultes EA, Bartel DP (2000) One sequence, two ribozymes: implications for the emergence of new ribozyme folds. Science 289(5478):448–452

    Article  PubMed  CAS  Google Scholar 

  • Sievers D, von Kiedrowski G (1994) Self-replication of complementary nucleotide-based oligomers. Nature 369:221–224

    Article  PubMed  CAS  Google Scholar 

  • Sole RV, Macia J, Fellermann H, Munteanu A, Sardanyes J, Valverde S (2009) Models of protocell replication. In: Rasmussen S, Bedau MA, Chen L, Deamer D, Krakauer DC, Packard NH, Stadler PF (eds) Protocells: bridging nonliving and living matter. MIT Press, Cambridge

    Google Scholar 

  • Szabo P, Scheuring I, Czaran T, Szathmary E (2002) In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity. Nature 420:340–343

    Article  PubMed  CAS  Google Scholar 

  • Thompson CJ, McBride JL (1974) On Eigen’s theory of the self-organization of matter and the evolution of biological macromolecules. Math Biosci 21:127

    Article  Google Scholar 

  • Vaidya N, Lehman N (2009) One RNA plays three roles to provide catalytic activity to a group I intron lacking an endogenous internal guide sequence. Nucleic Acids Res 37(12):3981–3989

    Article  PubMed  CAS  Google Scholar 

  • Vignuzzi M, Stone JK, Arnold JJ, Cameron CE, Andino R (2006) Quasispecies diversity determines pathogenesis through cooperative interactions within a viral population. Nature 439(7074):344–348

    Article  PubMed  CAS  Google Scholar 

  • Wachtershauser G (1988) Before enzymes and templates: theory of surface metabolism. Microbiol Rev 52(4):452–484

    PubMed  CAS  Google Scholar 

  • Weisstein EW (2007) Vitalism theory—from Eric Weisstein’s world of chemistry. Accessed at http://scienceworld.wolfram.com/chemistry/VitalismTheory.html on 14 Jan 2009

  • Wilke CO, Wang JL, Ofria C, Lenski RE, Adami C (2001) Evolution of digital organisms at high mutation rates leads to survival of the flattest. Nature 412:331–333

    Article  PubMed  CAS  Google Scholar 

  • Wochner A, Attwater J, Coulson A, Holliger P (2011) Ribozyme-catalyzed transcription of an active ribozyme. Science 332(6026):209–212

    Article  PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. UC Berkeley Mathematics Department, Berkeley, CA, 94720, USA

    Kelley Harris

  2. FAS Center for Systems Biology, Harvard University, 52 Oxford Street, Cambridge, MA, 02138, USA

    Irene A. Chen

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  1. Kelley Harris
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  2. Irene A. Chen
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Correspondence to Kelley Harris .

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Editors and Affiliations

  1. University of Jerusalem, Mevo Hadas 20, Efrat, 90435, Israel

    Joseph Seckbach

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Harris, K., Chen, I.A. (2012). Mathematical Models of Prebiotic Replication of Informational Molecules. In: Seckbach, J. (eds) Genesis - In The Beginning. Cellular Origin, Life in Extreme Habitats and Astrobiology, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2941-4_4

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