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Stability and selection in self-reproducing macromolecular systems

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Abstract

In this paper we develop stability criteria applicable to Eigen's model for the selection and evolution of biological macromolecules. We show that it is possible to characterize the time evolution of the macromolecular system by Lyapounov-like functionals. The Lyapounov method is used to discuss the general stability of the system and the metastable nature of the selected states are discussed.

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Literature

  • Eigen, M. 1971. “Self-Organization of Matter and the Evolution of Biological Macromolecules”.Naturwissenschaften,58, 465–523.

    Article  Google Scholar 

  • Eigen, M. and P. Schuster. 1977. “The Hypercycle; A Principle of Natural Self-Organization.”Naturwissenschaften,64, 541–565.

    Article  Google Scholar 

  • — 1978. “The Hypercycle”. (Part B)Naturwissenschaften,65, 7–41.

    Article  Google Scholar 

  • Jones, B.L., R. H. Enns and S. S. Rangnekar. 1976. “On the Theory of Selection of Coupled Macromolecular System”.Bull. Math. Biol.,38, 15–28.

    Article  MATH  Google Scholar 

  • —, 1977. “Analysis of Eigen's Equations for Selection of Biological Molecules with Fluctuating Mutation Rates”.Bull. Math. Biol.,39, 311–316; “A Model for Macromolecular Selection in Complementary Instructing Systems”.J. Math. Biol. 4, 29–34; “A Solvable Self-Reproductive Hypercycle Model for the Selection of Biological Molecules”.J. Math. Biol. 4, 187–193.

    Article  MATH  Google Scholar 

  • Nicolis, G. 1971. “Stability and Dissipative Structure in Open Systems Far From Equilibrium”.Adv. Chem. Phys.,19, 209–323.

    Google Scholar 

  • Schuster, P., K. Sigmund and R. Wolff. 1978. “Dynamical Systems Under Constant Organization I: Topological Analysis of a Family of Non-Linear Differential Equations—A Model for Catalytic Hypercycles”.Bull. Math. Biol.,40, 743–769.

    Article  MathSciNet  Google Scholar 

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  1. Department of Physics, Simon Fraser University, V5A 1S6, Burnaby, British Columbia, Canada

    B. L. Jones

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  1. B. L. Jones
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Jones, B.L. Stability and selection in self-reproducing macromolecular systems. Bltn Mathcal Biology 41, 449–460 (1979). https://doi.org/10.1007/BF02458323

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  • DOI: https://doi.org/10.1007/BF02458323

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