Chiral Oscillations and Spontaneous Mirror Symmetry Breaking in a Simple Polymerization Model

William Bock,Enrique Peacock-López

doi:10.3390/sym12091388

Abstract

The origin of biological homochirality—defined as the preference of biological systems for only one enantiomer—has widespread implications in the study of chemical evolution and the origin of life. The activation—polymerization—epimerization—depolymerization (APED) model is a theoretical model originally proposed to describe chiral symmetry breaking in a simple dimerization system. It is known that the model produces chiral and chemical oscillations for certain system parameters, in particular, the preferential formation of heterochiral polymers. In order to investigate the effect of higher oligomers, our model adds trimers, tetramers, and pentamers. We report sustained oscillations of all chemical species and the enantiomeric excess for a wide range of parameter sets as well as the periodic chiral amplification of a small initial enantiomeric excess to a nearly homochiral state.

Highlights

The origin of biological homochirality has attracted researchers’ attentions for decades
Using Stich et al.’s bifurcation analysis of the minimal APED model as a platform, we present our bifurcation analysis of several system parameters to determine how general is the appearance of oscillations in the expanded model
We have expanded the minimal APED model to include trimers, tetramers, and pentamers and have studied the range of parameter sets leading to chiral oscillations

Summary

Introduction

The origin of biological homochirality has attracted researchers’ attentions for decades. In one influential polymerization model, only the longest homochiral polymers catalyze the formation of chiral monomers, and mutual antagonism takes the form of enantiomeric cross inhibition, whereby the addition of a wrong-handed monomer to a growing chain halts elongation of that chain [6] Many variations of this model have since been proposed [7,8], including one in which homochirality arises in concert with the emergence of life [9]. Plasson et al.’s report searches for the monotonic emergence of chiral states, they note that oscillations of all chemical species, and the enantiomeric excess, occur when heterochiral dimers are strongly preferred These oscillations are the focus of Stich et al.’s report, which performs a comprehensive bifurcation analysis and finds that oscillations occur for a wide range of parameter sets [12].

The Expanded APED Model

Trimer Model

Tetramer and Pentamer Models

Minimum Initial Enantiomeric Excess

Conclusions