Sensitivity of Time-Dependent Bifurcation Processes and the Origin of Biomolecular Chirality.

I consider the case of a symmetry-breaking bifurcation of steady states, in a system containing noise. If the bifurcation parameter lambda increases slowly through the critical point of the bifurcation, an extremely small symmetry-breaking perturbation can effectively select the direction of bifurcation. If dlambda/dt = gamma, then for a wide range of parameters, the number of standard deviations of selectivity is given by the simple expression(UNFORMATTED TABLE OR EQUATION FOLLOWS)N_sigma = Wg ( {epsilonover 2})^ {-{1over 2}} ( {Vgammaover pi}) ^{-{1over 4}},eqno(0.1) (TABLE/EQUATION ENDS)where g is the size of the perturbation, epsilon the size of the noise, and W and V are respectively the coefficients of g and lambdaalpha (alpha is the system variable) in the bifurcation equation. These results are applied to chemical systems which break chiral symmetry, with reference to the question of the origin of biomolecular chirality. Calculations of parity-violating molecular effects resulting from the weak force, and capable of affecting chemical reaction rates, have been reported. Estimates of differences in reaction rates for L- and D-molecules resulting from these effects range from 1 part in 10^{17 }, for weak neutral current effects, to 1 part in 10^{11}, for beta-radiolysis. Considering likely conditions in the prebiotic oceans, selection of biomolecular chirality by beta-radiolysis seems entirely plausible, while selection by weak neutral current effects seems marginally plausible.