Symmetry-breaking in chiral polymerisation

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Wattis, Jonathan A.D. and Coveney, Peter V. (2005) Symmetry-breaking in chiral polymerisation. Origins of Life and the Evolution of the Biosphere, 35 (3). pp. 243-273. ISSN 0169-6149

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Abstract

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.