The bulletin of mathematical biophysics

, Volume 22, Issue 3, pp 227–255 | Cite as

A quantum-theoretic approach to genetic problems

  • Robert Rosen
Article

Abstract

A quantum-theoretic picture of the transfer of genetic information is described. The advantage of such an approach is that a number of genetic effects appear to be explicable on the basis of general microphysical laws, independent of any specific model (such as DNA-protein coding) for the transmission of genetic information. It is assumed that the genetic information is carried by a family of numerical observables belonging to a specific microphysical system; it is shown that a single observable is theoretically sufficient to carry this information. The various types of structure that this observable can possess are then described in detail, and the possible genetic effects which can airse from each such structure are discussed. For example, it is shown how the assumption that the genetic observable possesses degenerate eigenvalues may lead to a theory of allelism. To keep the treatment self-contained, the basic quantum-theoretical principles to be used are discussed in some detail. Finally, the relation of the present approach to current biochemical ideas and to earlier quantum-theoretic treatments of genetic systems is discussed.

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Literature

  1. Benzer, S. and E. Freese. 1958. “Induction of Specific Mutations with 5-Bromouracil.”Proc. Nat. Acad. Sci.,44, 112–119.CrossRefGoogle Scholar
  2. Chayen, J. 1959. “The Quantitative Cytochemistry of DNA and its Significance in Cell Physiology and Heredity.”Experimental Cell Ressearch, Supplement #6, 115–131.Google Scholar
  3. Friedrichs, K. O. 1948. “On the Perturbation of Continuous Spectra.”Comm. on Applied Math. 1, 361–406.MATHMathSciNetGoogle Scholar
  4. Goldschmidt, R. 1955.Theoretical Genetics. Berkeley: The University of California Press.Google Scholar
  5. Jacob, F. and E. L. Wollman. 1957. “Genetic Aspects of Lysogeny.”The Chemical Basis of Heredity (ed. W. D. McElroy and B. Glass), 468–500.Google Scholar
  6. Kadison, R. V. 1958. “Theory of Operators, Part II. Operator Algebras.”Bull. Am. Math. Soc. 64 (Number 3, Part II), 61–85.MATHMathSciNetCrossRefGoogle Scholar
  7. von Neumann, J. 1955.Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press.MATHGoogle Scholar
  8. Rashevsky, N. 1959. “Suggestions for a Possible Approach to Molecular Biology.”Bull. Math. Biophys. 21, 309–326.MathSciNetGoogle Scholar
  9. Riesz, F. and B. Sz.-Nagy 1955.Functional Analysis. New York: Frederick Ungar Publishing Co.MATHGoogle Scholar
  10. Rosen, R. 1959a. “The DNA-Protein Coding Problem.”Bull. Math. Biophys. 21, 71–95.CrossRefGoogle Scholar
  11. — 1959b. “A Relational Theory of Biological SystemsH”,21, 109–127.MathSciNetCrossRefGoogle Scholar
  12. — 1959c. “Some Further Comments on the DNA Protein Coding Problem.”,21, 289–297.Google Scholar
  13. — 1959d. “On a Logical Paradox Implicit in the Notion of a Self-Reporoducing Automaton.”,21, 387–394.MathSciNetGoogle Scholar
  14. Schrodinger, E. 1944.What is Life? Cambridge: Cambridge University Press.Google Scholar
  15. Segal, I. E. 1947. “Postulates for General Quantum Mechanics.”Annals of Math. 48, 930–948.MATHCrossRefGoogle Scholar
  16. Segal, I. E. 1955.A Mathematical Approach to Elementary Particles and their Fields. Mimeographed Lecuture Notes, The University of Chicago.Google Scholar

Copyright information

© University of Chicago 1960

Authors and Affiliations

  • Robert Rosen
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicagoUSA

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