Advertisement

Journal of Biological Physics

, Volume 13, Issue 4, pp 87–94 | Cite as

Applications of differential geometry to molecular genetics

  • A. M. Findley
  • S. P. McGlynn
  • G. L. Findley
Article

Abstract

A mathematical formalism is presented in which changes in information content of an evolving DNA (deoxyribonucleic acid) molecule may be described. The basic construct is a 65-dimensional differentiable manifold (the informational space-time manifold) in a coordinate structure such that the manifold points represent (i) the number of each codon type in a DNA molecule, and (ii) the evolutionary time of that DNA. It is shown that this manifold cannot be Euclidean but must be taken, at least conditionally, to be Riemannian. Evolutionary motions in the informational space-time manifold are initially postulated to be geodesics, and evolutionary equations-of-motion are elaborated. These equations are governed by an evolutionary field which is produced by the intrinsic structure of the manifold. The concept of genetic cosmology is introduced, and a manifold in which the evolutionary field is weak and depends only upon the evolutionary time is investigated. The nature of empirical input into genetic cosmology is discussed.

Keywords

Polymer Manifold Codon Evolutionary Time Information Content 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beyer, W.A.; Stein, M.L.; Smith, T.F.; Ulam, S.A. 1974.Math. Biosci. 19, 9–25.Google Scholar
  2. Birge, E.A. 1981.Bacterial and Bacteriophage Genetics, An Introduction, Springer-Verlag, New York.Google Scholar
  3. Dayhoff, M.O. 1972Atlas of Protein Sequence and Structure, Natl. Biomed. Res. Found., Washington, DC.Google Scholar
  4. Dobzhansky, T.; Ayala, F.J.; Stebbins, G.L.; Valentine, J.W. 1977.Evolution, Freeman, San Francisco, pp. 68–72.Google Scholar
  5. Eisenhart, L.P. 1926.Riemannian Geometry, Princeton Univ. Press, Princeton, NJ.Google Scholar
  6. Findley, A.M.; Findley, G.L. 1982.Int. J Quantum Chem., Quantum Biol. Symo. 9, 59–63.Google Scholar
  7. Findley, A.M.; Findley, G.L. 1984a.Int. J. Quantum Chem., Quantum Biol. Symp. 11, 109–116.Google Scholar
  8. Findley, A.M.; Findley, G.L. 1984b. In:Colloquium in Biological Sciences, New York Acad. Sci., NY, pp. 537–540.Google Scholar
  9. Findley, A.M.; Findley, G.L. McGlynn, S.P. 1982a.J. Theor. Biol. 97, 299–318.Google Scholar
  10. Findley, A.M.; McGlynn, S.P.; Findley, G.L. 1986.The Geometry of Genetics, Wiley-Interscience, New York, in press.Google Scholar
  11. Findley, G.L. 1978.A Riemannian-Geometric Realization of Molecular Genetics, Ph. D. Thesis, Louisiana State University, Baton Rouge.Google Scholar
  12. Findley, G.L.; McGlynn, S.P. 1979a.Int. J. Quantum Chem., Quantum Biol. Symp. 6, 313–327.Google Scholar
  13. Findley, G.L.; McGlynn, S.P. 1979b. In:Group Theoretical Methods in Physics. (W. Beiglbock, A. Böhm and E. Takasugi, eds.), Springer-Verlag, Berlin, pp. 71–72.Google Scholar
  14. Findley, G.L.; McGlynn, S.P. 1980.Int. J. Quantum Chem., Quantum Biol. Symp. 7, 277–281.Google Scholar
  15. Findley, G.L.; McGlynn, S.P. 1981.Int. J. Quantum Chem., Quantum Biol. Symp. 8, 455–461.Google Scholar
  16. Findley, G.L.; Findley, A.M.; McGlynn, S.P. 1982b.Proc. Natl. Acad. Sci. USA 79, 7061–7065.Google Scholar
  17. Fitch, W.M.; Margoliash, E. 1967.Science 155, 279–284.Google Scholar
  18. Margoliash, E. 1975.Adv. Chem. Phys. 29, 191–252.Google Scholar
  19. Sanger, F.; Air, G.M.; Barrell, B.G.; Brown, N.L.; Coulson, A.R.; Fiddes, J.C.; Hutchinson, C.A., III; Slocombe, P.M.; Smith, M. 1977.Nature 265, 687–695.Google Scholar
  20. Stent, G. S.; Calendar, R. 1978.Molecular Genetics, An Introductory Narrative, 2nd ed., Freeman, San Francisco.Google Scholar
  21. Watson, J.D. 1976.Molecular Biology of the Gene, 3rd ed., Benjamin, Menlo Park, CA.Google Scholar
  22. Watson, J.D.; Crick, F.H.C. 1953.Nature 171, 964–969.PubMedGoogle Scholar
  23. Wu, T.T.; Fitch, W.M.; Margoliash, E. 1974.Ann. Rev. Biochem. 43, 539–566.Google Scholar

Copyright information

© New Forums Press, Inc. 1985

Authors and Affiliations

  • A. M. Findley
    • 1
  • S. P. McGlynn
    • 2
  • G. L. Findley
    • 1
    • 2
  1. 1.Department of ChemistryNew York UniversityNew York
  2. 2.Department of ChemistryLouisiana State UniversityBaton Rouge

Personalised recommendations