A Necessary and Sufficient Condition in the Model of Kondepudi and Nelson for the Breaking of Chiral Symmetry

Abstract

The setting is a system containing achiral reactants which form a chiral compound. In 1983, Kondepudi and Nelson proposed a model for the breaking of chiral symmetry. The present article reduces the conditions for bifurcation to a single condition which is shown to be both necessary and sufficient. A number of other papers on this topic also propose models for the breaking of chiral symmetry. These are shown to be essentially special cases of the model of Kondepudi and Nelson, with the same necessary and sufficient condition. The central question of this line of research is: in a racemic mixture of a chiral compound, could an excess of one enantiomer over the other develop on its own? Our answer is yes, if and only if a certain simple condition is satisfied. This answer should prove useful in further research, both theoretical and experimental, into the origin of life.

Spontaneous emergence of enantioenriched chiral aldol reaction products from Achiral precursors in solution and origin of biological homochirality of sugars: a first-principles study

“…An important feature of the Frank model (Scheme 1) is the absence of SMSB below a certain threshold value for the product of reactant concentrations. 77 This is due to reversibility, and could be operative also in model of Scheme 4: when decay rate of monomeric autocatalyst is faster than reaction velocity of linearly autocatalytic step divided by concentration of enantiomeric autocatalyst, 77 b the Frank model produces no SMSB event. However, please note that this limitation holds, irrespective of whether reactants are provided initially in stoichiometric ratios, or not.…”