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Bulletin of Mathematical Biology

, Volume 38, Issue 1, pp 15–28 | Cite as

On the theory of selection of coupled macromolecular systems

  • B. L. Jones
  • R. H. Enns
  • S. S. Rangnekar
Article

Abstract

In this paper we examine a set of nonlinear rate equations (devised by M. Eigen (1971)) which describe the process of selection in a collection of self-reproducing, macromolecular information carriers. We construct exact solutions to the equations for the case of constant rate parameters and constant error distributions. The solutions allow the direct assessment of the effect of mutations on the “selective value” parameters discussed by Eigen as well as the distribution of the molecular species selected in steady state. In addition we show that the selection process may be characterized by an extremal principle.

Keywords

Molecular Species Extremal Principle Perturbation Result Macromolecular Species Constant Rate Parameter 
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Literature

  1. Bellman, R. 1970.Introduction to Matrix Analysis. New York: McGraw-Hill.Google Scholar
  2. Eigen, M. 1971. “Self-Organization of Matter and the Evolution of Biological Macromolecules.”Naturwiss.,58, 465–523.CrossRefGoogle Scholar
  3. Morse P. M. and H. Feshbach. 1953.Methods of Theoretical Physics. New York: McGraw-Hill.Google Scholar
  4. Sokolnikoff, I. S. and R. M. Redheffer. 1966.Mathematics of Physics and Modern Engineering. New York: McGraw-Hill.Google Scholar

Copyright information

© Society for Mathematical Biology 1976

Authors and Affiliations

  • B. L. Jones
    • 1
  • R. H. Enns
    • 1
  • S. S. Rangnekar
    • 1
  1. 1.Department of PhysicsSimon Fraser UniversityBurnaby

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