Symmetry-breaking in Chiral Polymerisation

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 righthanded 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 monomer 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 steadystate solutions described above.

Prebiotic Homochirality as a Critical Phenomenon

“…The constants p = 1 2 (1 + f ) and q = 1 2 (1 − f ) are given in terms of the fidelity of enzymatic reactions f , an adjustable parameter. As demonstrated by Kondepudi and Nelson (Kondepudi and Nelson, 1983) and many others (Sandars, 2003;Wattis and Coveney, 2005 Gayathri and Rao, 2005;Avetisov and Goldanskii, 1993), auto-catalytic networks show a tendency to bifurcate toward homochirality for values above critical, f c . The specific value of f c is model-dependent.…”

Mechanically Induced Homochirality in Nucleated Enantioselective Polymerization

“…In other words, a cross-inhibition mechanism has, by itself, a strict deracemizing tendency. [2][3][4][5][6][7]29 The absence of cross-inhibition in our model thus implies that SMSB and the subsequent amplification to large values of ee must rely solely on the purely homochiral processes alone:…”

“…In related models, the polymers may grow to arbitrary lengths and the chiral polymers of all lengths, from the dimer on upwards, can act catalytically in the breakdown of the achiral source into chiral monomers. 5 The role of external white noise on such polymerization networks including spatial extent has also been explored 6,7 to model random environmental disturbances. Another variation on this theme 9 gives rise to homochiral states in dimerization, but without invoking the enantiomeric cross inhibition, allowing instead for reversibility in all the reaction steps.…”

Asymmetric Spatiotemporal Evolution of Prebiotic Homochirality

“…As has been thoroughly discussed in the literature [18,24,30,34], the dynamical system defined by the polymerization equations for a given value of N shows a bifurcation behavior at a certain critical value of f , f c . The specific value of f c depends on the choice made for the enzymatic enhancements C L(R) and on the ratio of reaction rates k I /k S , but the behavior is qualitatively the same.…”