Evolution of homochirality by epimerization of random peptide chains. A stochastic model

A cyclic process is described which is constituted of polymerization, epimerization, and hydrolysis steps. During the first cycle peptides with random sequences are formed from racemic amino acids. A small portion of these peptides have substructures with a terminal residue linked to a homochiral sequence of optical antipodes. In such a substructure the terminal residue is assumed to invert into its mirror image so that a thermodynamically favourable epimeric stucture with continuous homochirality is formed. In the hydrolysis step the peptides are split back to monomeric units with retention of configuration. Due to stochastic differences between L- and D-substructures a net excess of one of the enantiomers results. This excess enhances the probability of the formation of substructures having the dominant configuration in the next cycle. It is shown by probabilistic considerations and computer simulations that this mechanism generates an autocatalytic growth of one of the enantiomers which finally results in homochiral populations of amino acids. The number of cycles necessary to attain homochirality depends on the number of residues of the substructure, on the chain length distribution of the polymers and on the total number of amino acid units.