Skip to main content

Advertisement

SpringerLink
Log in

The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems

  • Published:
Journal of Molecular Evolution Aims and scope Submit manuscript

Abstract

In the RNA world hypothesis, RNA(-like) self-replicators are suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in such replicators, i.e., the problem of parasites. Parasites, which are replicated by catalytic replicators (catalysts), but do not replicate the others, can destroy a whole replicator system by exploitation. Recently, a theoretical study underlined complex formation between replicators—an often neglected but realistic process—as a stabilizing factor in a replicator system by demonstrating that complex formation can shift the viable range of diffusion intensity to higher values. In the current study, we extend the previous study of complex formation. Firstly, by investigating a well-mixed replicator system, we establish that complex formation gives parasites an implicit advantage over catalysts, which makes the system significantly more vulnerable to parasites. Secondly, by investigating a spatially extended replicator system, we show that the formation of traveling wave patterns plays a crucial role in the stability of the system against parasites, and that because of this the effect of complex formation is not straightforward; i.e., whether complex formation stabilizes or destabilizes the spatial system is a complex function of other parameters. We give a detailed analysis of the spatial system by considering the pattern dynamics of waves. Furthermore, we investigate the effect of deleterious mutations. Surprisingly, high mutation rates can weaken the exploitation of the catalyst by the parasite.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Notes

  1. This problem is often referred to as the error threshold or information threshold, although the problem does not necessarily exhibit threshold-like behavior (Takeuchi and Hogeweg 2007).

  2. In the genomic tag hypothesis, Maizels and Weiner (1998) suggested a tRNA-like structure as such a tag motif in ancient RNA genomes.

  3. If it were used to obtain the dynamics of the replicators, θ would cancel out in the growth term κc xx θ, and thus there would be no limitation to the growth, which is not sensible. According to numerical solutions of Eq. (5), when κ \( \gg \) b i , c xx θ suddenly becomes zero at θ = 0 (i.e., x t + y t = 1) in a singular-like manner. This behavior cannot be captured if one takes the limit of κ i → ∞ (i = x, y) because the term κ i θ appears in Eq. (5).

  4. E.g. for the replication reaction to happen, one cell must be empty, and the other must be a complex.

  5. Strictly speaking, θ = 1−x−y−2c xx −2c xy in the CA model because a complex occupies twice as much space as a single molecule, but this hardly affects the results.

  6. The template activity of parasites was 1% higher than that of the catalyst.

  7. See also footnote 8.

  8. R was set small in attempt to make β max comparable to that for R = 0. However, it turns out that a slight mutation can significantly increase β max when a parameter set allows the formation of wave patterns. An increase can be as much as 20% for D = 0.01. This increase of β max can be understood in the light of pattern dynamics of waves, which is developed later in this paper. Mutation inoculates a small number of parasites in the traveling front of waves (see Fig. 5, D = 0.1), and thereby, the parasite can split a wave in a few parts, giving rise to more waves. Thus, a slight mutation can enhance the stability of the system.

  9. In a standard predator–prey (host–parasite) system predators (parasites) can directly kill preys (host), whereas in the current model, such a direct killing does not happen. To replace a catalyst population, parasites must wait until the catalysts disappear via intrinsic decay.

  10. The following two sets of parameters were examined: (1) log10 D ∞ = −1.15 (D 2 ≈ 0.053), k 2 = 1, k 1 = 0.085, k −1 = 0.001, d = 0.00125; and (2) log10 D ∞ = −1.075 (D 2 ≈ 0.063), k 2 = 1, k 1 = 0.085, k −1 = 0.001, d = 0.015. See Füchslin et al. (2004) for the notation.

  11. Note that M max is not exactly the same as the error threshold: while the error-threshold phenomenon—or the breakdown of Darwinian optimization—happens because of the competition between the fittest and the mutants (Eigen et al. 1989; see also Takeuchi and Hogeweg 2007), M max exists because X cannot grow faster than it decays for a sufficiently large M.

  12. Suppose β = 1 is tolerable, and the next examined value β = 2 is not tolerable, but the third examined value β = 1.5 is tolerable. Then, it might be that β = 2 is tolerable if the initial condition is taken from the system with β = 1.5 instead from that with β = 1.

References

  • Allee WC (1931) Animal aggregations: a study in general sociology. University of Chicago Press, Chicago

    Google Scholar 

  • Altmeyer S, Füchslin RM, McCaskil JS (2004) Folding stabilizes the evolution of catalysts. Artif Life 10:23–38

    Article  PubMed  Google Scholar 

  • Bartel DP (1998) Re-creating an RNA replicase. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 2nd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 143–162

    Google Scholar 

  • Boerlijst MA, Hogeweg P (1991a) Selfstructuring and selection: spiral waves as a substrate for prebiotic evolution. In: Langton CG, Taylor C, Farmer JD, Rasmussen S (eds) Artificial Life II. Addison Wesley, Massachusetts, pp. 255–276

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

    Google Scholar 

  • Bresch C, Niesert V, Harnasch D (1980) Hypercycles, parasites and packages. J Theor Biol 85:399–405

    Article  PubMed  CAS  Google Scholar 

  • Campos PRA, Fontanari JF, Stadler PF (2000) Error propagation in the hypercycle. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 61:2996–3002

    PubMed  CAS  Google Scholar 

  • Cesh TR (1986) A model for the RNA-catalyzed replication of RNA. Proc Natl Acad Sci USA 83:4360–4363

    Article  Google Scholar 

  • Chen IA, Hanczyc MM, Sazani PL, Szostak JW (2006) Protocells: genetic polymers inside membrane vesicles. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 3rd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 57–88

    Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • De Boer RJ, Pagie L (2005) GRIND Ver 2.05. http://www.theory.bio.uu.nl/rdb/software.html

  • Eigen M (1971) Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465–523

    Article  PubMed  CAS  Google Scholar 

  • Eigen M, Schuster P (1979) The hypercycle—a principle of natural selforganization. Springer–Verlag, Berlin

    Google Scholar 

  • Eigen M, McCaskill J, Schuster P (1989) The molecular quasi-species. Adv Chem Phys 75:149–263

    Article  CAS  Google Scholar 

  • Füchslin RM, Altmeyer S, McCaskill JS (2004) Evolutionary stabilization of generous replicases by complex formation. Eur Phys J B 38:103–110

    Article  Google Scholar 

  • García-Tejedor A, Morán F, Montero F (1987) Influence of the hypercyclic organization on the error threshold. J Theor Biol 127:393–402

    Article  Google Scholar 

  • Gesteland RF, Cech TR, Atkins JF (eds) (2006) The RNA world, 3rd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor

    Google Scholar 

  • Gilbert W (1986) The RNA world. Nature 319:618

    Article  Google Scholar 

  • Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434

    Article  CAS  Google Scholar 

  • Hanczyc MM, Dorit RL (1998) Experimental evolution of complexity: in vitro emergence of intermolecular ribozyme interactions. RNA 4:268–275

    PubMed  CAS  Google Scholar 

  • Hogeweg P, Takeuchi N (2003) Multilevel selection in models of prebiotic evolution: compartments and spatial self-organization. Orig Life Evol Biosph 33:375–403

    Article  PubMed  CAS  Google Scholar 

  • Huynen MA, Hogeweg P (1994) Pattern generation in molecular evolution: exploitation of the variation in RNA landscapes. J Mol Evol 39:71–9

    Article  PubMed  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 

  • Joyce GF (1983) The instability of the autogen. J Mol Evol 19:192–194

    Article  PubMed  CAS  Google Scholar 

  • Joyce GF (1987) Nonenzymatic template-directed synthesis of informational macromolecules. Cold Spring Harb Symp Quant Biol 52:41–51

    PubMed  CAS  Google Scholar 

  • Joyce GF (1998) Appendix 3: reactions catalyzed by RNA and DNA enzymes. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 2nd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 687–690

    Google Scholar 

  • Joyce GF, Orgel LE (2006) Progress toward understanding the origins of the RNA world. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 3rd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 23–56

    Google Scholar 

  • Joyce GF, Schwartz AW, Miller SL, Orgel LE (1987) The case for an ancestral genetic system involving simple analogues of the nucleotides. Proc Natl Acad Sci USA 84:4398–4402

    Article  PubMed  CAS  Google Scholar 

  • Kaneko K, Ikegami T (1992) Homeochaos: dynamic stability of a symbiotic network with population dynamics and evolving mutation rates. Physica D 56:406–429

    Article  Google Scholar 

  • Károlyi G, Péntrek A, Scheuring I, Tél T, Toroczkail Z (2000) Chaotic flow: the physics of species coexistence. Proc Natl Acad Sci USA 97:13661–13665

    Article  PubMed  Google Scholar 

  • Ke A, Doudna JA (2006) Catalytic strategies of self-cleaving ribozymes: relics of an RNA world. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 3rd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 109–131

    Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Küppers B (1983) Molecular theory of evolution: outline of a physico-chemical theory of the origin of life. Springer–Verlag, Berlin

    Google Scholar 

  • Kuznetsov YA (1999) CONTENT Ver 1.5. http://www.math.uu.nl/people/kuznet/CONTENT/

  • Lehman N (2003) A case for the extreme antiquity of recombination. J Mol Evol 56:770–777

    Article  PubMed  CAS  Google Scholar 

  • Maizels N, Weiner AM (1998) The genomic tag hypothesis: what molecular fossils tell us about the evolution of tRNA. In: Gesteland RF, Cech TR, Atkins JF (eds) The RNA world, 2nd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp. 79–111

    Google Scholar 

  • Maynard Smith J (1979) Hypercycles and the origin of life. Nature 280:445–446

    Article  Google Scholar 

  • McCaskill JS, Füchslin RM, Altmeyer S (2001) The stochastic evolution of catalysts in spatially resolved molecular systems. Biol Chem 382:1343–1363

    Article  PubMed  CAS  Google Scholar 

  • Michod R (1983) Population biology of the first replicators: the origin of genotype, phenotype and organism. Am Zool 23:5–14

    CAS  Google Scholar 

  • Muller HJ (1966) The gene material as the initiator and the organizing basis of life. Am Nat 100:493–517

    Article  Google Scholar 

  • Nuño JC, Andrade MA, Montero F (1993) Non-uniformities and superimposed competition in a model of an autocatalytic network formed by error-prone self-replicative species. Bull Math Biol 55:417–449

    Google Scholar 

  • Orgel LE (2004) Prebiotic chemistry and the origins of the RNA world. Crit Rev Biochem Mol Biol 39:99–23

    Article  PubMed  CAS  Google Scholar 

  • Orr HA (2000) The rate of adaptation in asexuals. Genetics 155:961–968

    PubMed  CAS  Google Scholar 

  • Pace NR, Marsh TL (1985) RNA catalysis and the origin of life. Orig Life 16:97–116

    Article  CAS  Google Scholar 

  • Pagie L, Hogeweg P (1999) Colicin diversity: a result of eco-evolutionary dynamics. J Theor Biol 196:251–261

    Article  PubMed  CAS  Google Scholar 

  • Pagie L, Hogeweg P (2000) Individual-and population-based diversity in restriction modification systems. Bull Math Biol 62:759–774

    Article  PubMed  CAS  Google Scholar 

  • Santos M, Zintzaras E, Szathmáry E (2004) Recombination in primeval genomes: a step forward but still a long leap from maintaining a sizable genome. J Mol Evol 59:507–519

    Article  PubMed  CAS  Google Scholar 

  • Savill NJ, Rohani P, Hogeweg P (1997) Self-reinforcing spatial patterns enslave evolution in a host-parasitoid system. J Theor Biol 188:11–20

    Article  PubMed  CAS  Google Scholar 

  • Scheuring I, Czárán T, Szabó P, Károlyi G, Toroczkai Z (2003) Spatial models of prebiotic evolution: soup before pizza? Orig Life Evol Biosph 33:319–355

    Article  PubMed  CAS  Google Scholar 

  • Segel LA (1984) Modeling dynamic phenomena in molecular and cellular biology. Cambridge University Press, Cambridge

    Google Scholar 

  • Segré D, Ben-Eli D, Lancet D (2000) Compositional genomes: prebiotic information transfer in mutually catalytic noncovalent assemblies. Proc Natl Acad Sci USA 97:4112–4117

    Article  PubMed  Google Scholar 

  • Sharp PA (1985) On the origin of RNA splicing and introns. Cell 42:397–400

    Article  PubMed  CAS  Google Scholar 

  • Stadler BMR, Stadler PF (2004) Molecular replicator dynamics. Adv Complex Syst 59:507–519

    Google Scholar 

  • Stadler BMR, Stadler PF, Schuster P (2000) Dynamics of autocatalytic replicator networks based on higher-order ligation reactions. Bull Math Biol 62:1061–1086

    Article  PubMed  CAS  Google Scholar 

  • Steitz TA, Moore PB (2003) RNA, the first macromolecular catalyst: the ribosome is a ribozyme. Trends Biochem Sci 28:411–418

    Article  PubMed  CAS  Google Scholar 

  • Szabó P, Scheruing I, Czárán T, Szathmáry E (2002) In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity. Nature 420:340–343

    Article  PubMed  Google Scholar 

  • Szathmáry E (2006) The origin of replicators and reproducers. Philos Trans R Soc Lond B Biol Sci 361:1761–1776

    Article  PubMed  Google Scholar 

  • Szathmáry E, Demeter L (1987) Group selection of early replicators and the origin of life. J Theor Biol 128:463–486

    Article  PubMed  Google Scholar 

  • Takeuchi N, Hogeweg P (2007) Error-threshold exists in fitness landscapes with lethal mutants. BMC Evol Biol 7:15

    Article  PubMed  Google Scholar 

  • Takeuchi N, Poorthuis PH, Hogeweg P (2005) Phenotypic error threshold; additivity and epistasis in RNA evolution. BMC Evol Biol 3:9

    Article  Google Scholar 

  • Van Ballegooijen WM, Boerlijst MC (2004) Emergent trade-offs and selection for outbreak frequency in spatial epidemics. Proc Natl Acad Sci USA 101:18246–18250

    Article  PubMed  Google Scholar 

  • Van Nimwegen E, Crutchfield JP (2001) Optimizing epochal evolutionary search: population-size dependent theory. J Mach Learn Res 45:77–114

    Article  Google Scholar 

  • White HB III (1976) Coenzymes as fossils of an earlier metabolic state. J Mol Evol 7:101–104

    Article  PubMed  CAS  Google Scholar 

  • Zaher HS, Unrau PJ (2007) Selection of an improved RNA polymerase ribozyme with superior extension and fidelity. RNA 13:1017–1026

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

We express our gratitude to the associate editor Dr. N. Lehman and the three anonymous reviewers for their constructive criticisms on our manuscript. The research was supported by NWO exact sciences 612.060.522.

Author information

Authors and Affiliations

  1. Theoretical Biology/Bioinformatics Group, Utrecht University, Utrecht, The Netherlands

    Nobuto Takeuchi & Paulien Hogeweg

  2. Theoretische Biologie/Bioinformatica, Padualaan 8, 3584CH, Utrecht, The Netherlands

    Nobuto Takeuchi

Authors
  1. Nobuto Takeuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paulien Hogeweg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nobuto Takeuchi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takeuchi, N., Hogeweg, P. The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems. J Mol Evol 65, 668–686 (2007). https://doi.org/10.1007/s00239-007-9044-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00239-007-9044-6

Keywords

Search

Navigation