Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Chiral polymerisation and the RNA world

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as information storage and a catalyst for its own production. We note the similarities and differences in chemical mechanisms present in the systems. We review these two systems, analysing steady-states, interesting kinetics and the stability of symmetric solutions. In both systems we show that there are ranges of parameter values where some chains increase their own concentrations faster than others.

Chiral polymerisation and the RNA world

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as information storage and a catalyst for its own production. We note the similarities and differences in chemical mechanisms present in the systems. We review these two systems, analysing steady-states, interesting kinetics and the stability of symmetric solutions. In both systems we show that there are ranges of parameter values where some chains increase their own concentrations faster than others.