Abstract
The Frank model for spontaneous chiral stereoselection of biomolecules is extended by taking into account the influence of electroweak effects on the rates of enantiomeric chemical reactions. Explicit analytical solutions of the respective differential 'equations are obtained, describing the behaviour of the generalized Frank model immediately after the beginning of the process, when the direction of the stereoselection is decided. The direction of the stereoselection is affected by both stochastic and deterministic factors, whose complex interrelations are examined.
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References
L. Pasteur, Leçons sur la Dissymètrie Molèculaire (Hachette, Paris, 1981).
G. Wald, Ann. N.Y. Acad. Sci. 69 (1957)352.
K. Harada, Naturwiss. 57 (1970)144.
S.F. Mason, Molecular Optical Activity and the Chiral Discrimination (Cambridge University Press, Cambridge, 1982).
W. Liu, Origins of Life 12 (1982)205.
W. Liu, Sci. Sinica 25 (1982)822.
G.F. Joyce, G.M. Visser, C.A.A. van Boeckel, J.H. van Boon, L.E. Orgel and J. van Westerenen, Nature 310 (1984)602.
R.A. Hegstrom, Nature 315 (1985)749.
L.J. Dunne, Chem. Phys. Lett. 121 (1985)17.
B. Nordèn, J.O. Liljenzin and R.K. Tokay, J. Mol. Evol. 21 (1985)364.
A. Klemm, Z. Naturforsch. 40a (1985)1231.
A.J. MacDermott, Nature 323 (1986)16.
A.G. Cairns-Smith, Chem. Britain 22 (1986)559.
J. Galloway, Nature 330 (1987)204.
D.K. Kondepudi and G.W. Nelson, Physica 125A (1984)465.
D.K. Kondepudi and G.W. Nelson, Nature 314 (1985)438.
D.K. Kondepudi, F. Moss and P.V.E. McClintock, Physica 21D (1986)296.
D.K. Kondepudi and M.J. Gao, Phys. Rev. A35 (1987)340.
D.K. Kondepudi, BioSystems 20 (1987)75.
I. Gutman and A. Klemm, Z. Naturforsch. 42a (1987)899.
S.F. Mason and G.E. Tranter, Chem. Phys. Lett. 94 (1983)34.
S.F. Mason and G.E. Tranter, J, Chem. Soc. Chem. Commun. (1983)117.
S.F. Mason and G.E. Tranter, Mol. Phys. 53 (1984)1091.
G.E. Tranter, Mol. Phys. 56 (1985)825.
S.F. Mason and G.E. Tranter, Proc. Roy. Soc. (London) A397 (1985)45.
G.E. Tranter, Nature 318 (1985)172.
G.E. Tranter, Chem. Phys. Lett. 115 (1985)286.
G.E. Tranter, Chem. Phys. Lett. 120 (1985)93.
G.E. Tranter, Chem. Phys. Lett. 121 (1985)339.
G.E. Tranter, J. Chem. Soc. Chem. Commun. (1986)60.
K. Tennakone, Chem. Phys. Lett. 105 (1984)444.
S.F. Mason, Nature 314 (1985)400.
V. Babović, I. Gutman and S. Jokić, Z. Naturforsch. 42a (1987)1024.
I. Gutman, V. Babović and S. Jokić, Chem. Phys. Lett. 144 (1988)187.
I. Gutman, V. Babović and S. Jokić, J. Serb. Chem. Soc. 53 (1988)129.
L.D. Barron, Chem. Soc. Rev. 15 (1986)189.
J.H. Brewster, J. Chem. Educ. 63 (1986)667.
R. Janoschek, Naturwiss. Rundschau 39 (1986)327.
G.E. Tranter, Nachr. Chem. Tech. Lab. 34 (1986)866.
F.C. Frank, Biochim. Biophys. Acta 11 (1953)459.
F.F. Seelig, J. Theor. Biol. 31 (1971)355.
F.F. Seelig, J. Theor. Biol. 32 (1971)93.
F.F. Seelig, J. Theor. Biol. 34 (1972)197.
D.W. Rein, R.A. Hegstrom and P.G.H. Sandars, Phys. Lett. 71A (1979)499.
R.A. Hegstrom, D.W. Rein and P.G.H. Sandars, J. Chem. Phys. 73 (1980)2329.
J.L. Lopes,Gauge Field Theories (Pergamon, Oxford, 1981).
M. Quack, Chem. Phys. Lett. 132 (1986)147.
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received by the Publisher 20 September 1989
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Gutman, I. Factors determining the direction of the stereoselection process in the generalized Frank model. J Math Chem 3, 343–355 (1989). https://doi.org/10.1007/BF01169016
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DOI: https://doi.org/10.1007/BF01169016