Autocatalytic networks with translation

Bulletin of Mathematical Biology

Volumn 58, Issue 5, 1996, Pages 877-905

  Happel, Robert ^a   Hecht, Robert ^a   Stadler, Peter F ^a,b  

^a UNIVERSITY OF VIENNA   (Austria)

^b SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030237287     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02459488     Document Type: Article

References (60)

1. Arneodo, A., P. Coullet, J. Peyraud, and C. Tresser. 1992. Strange attractors in Volterra equations for species competition. J. Math. Biol. 14, 153-157.
2. Arneodo, A., P. Coullet, and C. Tresser. 1980. Occurrence of strange attractors in three-dimensional Volterra equations. Phys. Lett. A 79, 259-263.
3. Bauer, G. J. 1989. Traveling waves of in vitro evolving RNA. Proc. Natl. Acad. Sci. U.S.A. 86, 7937-4179.
4. Biebricher, C. K., M. Eigen, W. C. Gardiner, Jr., and R. Luce. 1983. Kinetics of RNA replication. Biochemistry 22, 2544-2599.
5. Biebricher, C. K., M. Eigen, W. C. Gardiner, Jr., and R. Luce. 1984. Kinetics of RNA replication: competition and selection among self-replicating RNA species. Biochemistry 23, 6550-6560.
6. Biebricher, C. K., M. Eigen, W. C. Gardiner, Jr., and R. Luce. 1985. Kinetics of RNA replication: plus-minus asymmetry and double strand formation. Biochemistry 24, 3186-3194.
7. Cech, T. 1986. RNA as an enzyme. Sci. Am. 11, 76-84.
8. Cech, T. R. 1988. Conserved sequences and structures of group I introns: building an active site for RNA catalysis - a review. Gene 73, 259-271.
9. Doudna, J., S. Couture, and J. Szostak. 1991. A multi-subunit ribozyme that is a catalyst of and a template for complementary-strand RNA synthesis. Science 251, 1605-1608.
10. Doudna, J., N. Usman, and J. Szostak. 1993. Ribozyme-catalyzed primer extension by trinucleotides: a model for the RNA-catalyzed replication of RNA. Biochemistry 32, 2111-2115.
11. Eigen, M. 1971. Self-organization of matter and the evolution of macromolecules. Naturwiss. 58, 465-523.
12. Eigen, M. and P. Schuster. 1977. The hypercycle: A. Emergence of the hypercycle. Naturwiss. 64, 541-565.
13. Eigen, M. and P. Schuster. 1978a. The hypercycle: B. The abstract hypercycle. Naturwiss. 65, 7-41.
14. Eigen, M. and P. Schuster. 1978b. The hypercycle: C. The realistic hypercycle. Naturwiss. 65, 341-369.
15. Eigen, M. and P. Schuster. 1979. The Hypercycle. New York: Springer-Verlag.
16. Eigen, M., P. Schuster, K. Sigmund, and R. Wolff. 1980. Elementary step dynamics of catalytic hypercycles. BioSystems 13, 1-22.
17. Famulok, M., J. Nowick, and J. Rebek, Jr. 1992. Self-replicating systems. Act. Chim. Scand. 46, 315-324.
18. Fenichel, N. 1978. Geometric singular perturbation theory for ordinary differential equations. J. Diff. Eqs. 31, 53-98.
19. Gesteland, R. and J. Atkins (Eds). 1993. The RNA World. Cold Spring Harbor, NY: Cold Spring Harbor Laboratory Press.
20. Gilpin, M. E. 1978. Spiral chaos in a predator pray system. Amer. Nat. 133, 306-308.
21. Gordon, K. H. 1995. Were RNA replication and translation directly coupled in the RNA (+ protein?) world? J. Theor. Biol. 173, 179-193.
22. Guerrier-Takada, C. and S. Altman. 1984. Catalytic activity of an RNA molecule prepared by transcription in vitro. Science 223, 285-286.
23. Happel, R. 1994. Dynamics of autocatalytic reaction networks: replication with translation. Master's thesis, University of Vienna.
24. Happel, R. and P. Stadler. 1995. Autocatalytic replication in a CSTR and constant organization. Santa Fe Institute preprint 95-07-062.
25. Hecht, R. 1994. Replicator networks with intermediates. Ph.D. thesis, University of Vienna.
26. Henry, D. 1978. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, Vol. 84. Berlin: Springer-Verlag.
27. Hirsch, M. W. and S. Smale. 1974. Differential Equations, Dynamical Systems, and Linear Algebra. Orlando, FL: Academic Press.
28. Hofbauer, J. 1981. On the occurrence of limit cycles in Volterra-Lotka equations. Nonlinear Anal. 5, 1003-1007.
29. Hofbauer, J. 1986. Saturated equilibria, permanence, and stability for ecological systems. In Proceedings of the Second Autumn Course on Mathematical Ecology, Trieste, Italy.
30. Hofbauer, J., J. Mallet-Paret, and H. L. Smith. 1991. Stable periodic solutions for the hypercycle system. J. Dyn. Diff. Eqs. 3, 423-436.
31. Hofbauer, J. and K. Sigmund. 1988. Dynamical Systems and the Theory of Evolution. Cambridge: Cambridge University Press.
32. Knobloch, H. and B. Aulbach. 1984. Singular perturbations and integral manifolds. J. Math. Phys. Sci. 18, 415-424.
33. Murray, J. 1984. Asymptotic Analysis. New York: Springer.
34. Orgel, L. 1992. Molecular replication. Nature 358, 203-209.
35. O'Malley, J. R. E. 1991. Singular Perturbation Methods for Ordinary Differential Equations. New York: Springer-Verlag, 1991.
36. Rebek, Jr., J. 1994. Synthetic self-replicating molecules. Sci. Am. 271, 48-57.
37. Schlögl, F. 1972. Chemical reaction models for non-equilibrium phase transitions. Z. Phys. 253, 147-161.
38. Schnabl, W., P. F. Stadler, C. Forst, and P. Schuster. 1991. Full characterization of a strange attractor. Phys. D 48, 65-90.
39. Schneider, K. R. 1987. Singularly perturbed autonomous differential systems. In Dynamical Systems and Environmental Models, H. Bothe, W. Ebeling, A. Kurzhanski and M. Peschel (Eds). Berlin: VEB-Verlag.
40. Schuster, P. 1986. Mechanisms of molecular evolution. In Self-Organization, S. Fox (Ed), pp. 57-91. Chicago, IL: Aldnine Press.
41. Schuster, P. and K. Sigmund. 1983. Replicator dynamics. J. Theor. Biol. 100, 533-538.
42. Schuster, P. and K. Sigmund. 1985. Dynamics of evolutionary optimization. Ber. Bunsen-Gesellsch. Phys. Chem. 89, 668-682.
43. Schuster, P., K. Sigmund, and R. Wolff. 1978. Dynamical systems under constant organisation I. Topologigal analysis of a family of non-linear differential equations - a model for catalytic hypercycles. Bull. Math. Biol. 40, 743-769.
44. Smith, J. M. and E. Szathmary. 1995. The Major Transitions in Evolution. Oxford: W. H. Freeman.
45. Novick, J. S., Q. Feng, and T. Tjivikua. 1991. Kinetic studies and modeling of a self-replicating system. J. Am. Chem. Soc. 113, 8831-8838.
46. Spiegelman, S. 1971. An approach to the experimental analysis of precellular evolution. Quart. Rev. Biophys. 4, 213-251.
47. Stadler, B. M. R. and P. F. Stadler. 1991. Dynamics of small autocatalytic reaction networks III: monotonous growth functions. Bull. Math. Biol. 53, 469-485.
48. Stadler, P. F. 1991. Complementary replication. Math. Biosci. 107, 83-109.
49. Stadler, P. F., W. Fontana, and J. H. Miller. 1993. Random catalytic reaction networks. Phys. D 63, 378-392.
50. Stadler, P. F. and J. C. Nuño. 1994. The influence of mutation on autocatalytic reaction networks. Math. Biosci. 122, 127-160.
51. Stadler, P. F., W. Schnabl, C. V. Forst, and P. Schuster. 1995. Dynamics of autocatalytic reaction networks II: analytically treatable special cases. Bull. Math. Biol. 57, 21-61.
52. Stadler, P. F. and P. Schuster. 1990. Dynamics of autocatalytic reaction networks I: bifurcations, permanence and exlusion. Bull. Math. Biol. 52, 485-508.
53. Stadler, P. F. and P. Schuster. 1992. Mutation in autocatalytic networks - an analysis based on perturbation theory. J. Math. Biol. 30, 597-631.
54. Streissler, C. 1992. Autocatalytic networks under diffusion. Ph.D. thesis, University of Vienna.
55. Tichonov, A. 1952. Systems of differential equations with a small parameter at the derivatives. Mat. Sbornik 31, 575-586.
56. 3. J. Physique 45, 837.
57. Vance, R. R. 1978. Predation and resource partitioning in one predator - two pray model communities. Amer. Nat. 112, 787-813.
58. von Kiedrowski, G. 1993. Minimal replicator theory I: parabolic versus exponential growth. Bioorganic Chemistry Frontiers, Vol. 3, pp. 115-146. Berlin: Springer-Verlag.
59. Weinberger, E. 1991. Spatial stability analysis of Eigen's quasispecies model and the less than five membered hypercycle under global population regulation. Bull. Math. Biol. 53, 623-638.
60. Westheimer, F. H. 1986. Polyribonucleic acids as enzymes, news and views. Nature 319, 534-536.