Spatial dynamics of homochiralization

Abstract

The emergence and spreading of chirality on the early Earth is considered by studying a set of reactiondiffusion equations based on a polymerization model. It is found that effective mixing of the early oceans is necessary to reach the present homochiral state. The possibility of introducing mass extinctions and modifying the emergence rate of life is discussed.

Homochirality and the Need for Energy

“…This behavior seems to be quite general and independent of the detailed chemistry, and have now been obtained by various groups (Saito and Hyuga 2004;Brandenburg and Multamäki 2004;Multamäki and Brandenburg 2005;Hochberg and Zorzano 2006;Gleiser 2007;Giaquinta and Hochberg 2008;Gleiser and Walker 2009). Initially, the diffusion does not have much time to operate: in the initially racemic mixture some local systems bifurcate to one configuration, and some other bifurcate to the opposite one, while the total system remains globally racemic.…”

“…multiple objects) that will be globally racemic for sufficiently large systems. This propagation of the asymmetry can be enhanced by the advection phenomenon: adding mechanical motions able to stir the system will perturb the interfaces and increase the transport speed of compounds inside the system, leading thus much faster to one unique configuration in all space locations (Brandenburg and Multamäki 2004;Multamäki and Brandenburg 2005). The effects of noise, which corresponds to a stochastic loss of chirality in random locations, can however offset this effect either partially or completely (Gleiser 2007;Gleiser and Walker 2009).…”

“…This behavior seems to be quite general and independent of the detailed chemistry, and have now been obtained by various groups. [41][42][43][44][45][46] Initially, the diffusion does not have much time to operate: in the initially racemic mixture some local systems bifurcate to one configuration, and some other bifurcate to the opposite one, while the total system remains globally racemic. These different regions are initially well separated and will then spread by simple diffusion into the still racemic regions.…”

Mathematical Models of the Homochiralisation of Crystals by Grinding

“…This model and generalisations of it have been analysed by Sandars [25], Brandenburg et al [5,6], Multimaki & Brandenburg [19], Wattis & Coveney [32,33], Gleiser & Walker [11], Gleiser et al [12]. Typically a classic pitchfork bifurcation is found when the fidelity (f ) of the autocatalysis over the cross-catalysis is increased.…”

“…Sandars assumes the growth rates of chains are linear and not catalysed; the other mechanism required to produce a symmetry-breaking bifurcation to a chiral state is cross-inhibition, by which chains of opposite handednesses interact and prevent either from further growth. These mechanisms are summarised by This model and generalisations of it have been analysed by Sandars ( 2003 ), Brandenburg et al ( 2005a , b ), Multimaki and Brandenburg ( 2005 ), Wattis and Coveney ( 2005a , b ), Gleiser and Walker ( 2008 ), Gleiser et al ( 2008 ), Coveney and Wattis ( 2006 ). Typically a classic pitchfork bifurcation is found when the fidelity ( f ) of the autocatalysis over the cross-catalysis is increased.…”