An Extended Model for the Evolution of Prebiotic Homochirality: A Bottom-Up Approach to the Origin of Life

TL;DR

This paper presents a detailed generalized autocatalytic model for chiral polymerization, exploring the conditions under which homochirality can emerge from racemic initial states, with implications for the origin of life.

Contribution

It introduces a comprehensive model incorporating autogenic monomer formation and analyzes its dynamics, revealing critical parameters for the emergence of homochirality and the impact of polymer length.

Findings

Autogenic formation acts as a control parameter for symmetry breaking.

Homochirality is achieved only below a critical autogenic rate $\\epsilon_c$.

Net chiral asymmetry increases with maximum polymer length N.

Abstract

A generalized autocatalytic model for chiral polymerization is investigated in detail. Apart from enantiomeric cross-inhibition, the model allows for the autogenic (non-catalytic) formation of left and right-handed monomers from a substrate with reaction rates $\epsilon_L$ and $\epsilon_R$, respectively. The spatiotemporal evolution of the net chiral asymmetry is studied for models with several values of the maximum polymer length, N. For N=2, we study the validity of the adiabatic approximation often cited in the literature. We show that the approximation obtains the correct equilibrium values of the net chirality, but fails to reproduce the short time behavior. We show also that the autogenic term in the full N=2 model behaves as a control parameter in a chiral symmetry- breaking phase transition leading to full homochirality from racemic initial conditions. We study the dynamics of the N -> infinity model with symmetric ($\epsilon_L = \epsilon_R$) autogenic formation, showing that it only achieves homochirality for $\epsilon < \epsilon_c$, where $\epsilon_c$ is an N-dependent critical value. For $\epsilon \leq \epsilon_c$ we investigate the behavior of models with several values of N, showing that the net chiral asymmetry grows as tanh(N). We show that for a given symmetric autogenic reaction rate, the net chirality and the concentrations of chirally pure polymers increase with the maximum polymer length in the model. We briefly discuss the consequences of our results for the development of homochirality in prebiotic Earth and possible experimental verification of our findings.