Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

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.…”

Absolute Asymmetric Synthesis in Enantioselective Autocatalytic Reaction Networks: Theoretical Games, Speculations on Chemical Evolution and Perhaps a Synthetic Option

“…However, in a closed system the stability analysis of LES has demonstrated that the system parameters yielding such a SMSB can occur only through violations of the micro-reversibility principle. [31] The stability analysis of LES shows that SMSB can only occur when the rate of the backward reaction in (9) is faster than the backward reaction of the enantioselective autocatalysis (7); however, for autocatalytic exponential growth the forward reaction in (7) must be faster than that for (9), that is, reactions (7) and (9) The system leads to SMSB despite the significant contributions of the non-enantioselective autocatalysis and of the homochiral dimerization reactions. Yield and ee total are calculated by assuming, and such as occurs in the Soai reaction, that in the separation method the oligomers of products/catalysts revert back to the monomeric species (R and S).…”

“…[39c] The system corresponds basically to that shown in Scheme 4: there is continuous matter transfer between the two temperature regions, with the enantioselective autocatalysis (7) compartmentalized in the low temperature region and the non-enantioselective autocatalysis (9) in the higher temperature one. This allows one to fulfill the general condition for SMSB in the LES model, [31] that is, that the backward reaction of (9) must have, and without violation of the micro-reversibility principle, a rate constant higher than that of the backward reaction of (7), and with the opposite trend holding for the forward reaction rates. A reasonable chemical scenario for this model can be imagined by assuming that the autocatalytic reactions (7) and (9) are promoted by immobilized catalysts located in different temperature regions (see the Supporting Information).…”

Stability of racemic and chiral steady states in open and closed chemical systems

“…In the case of the limited enantioselectivity model, no dimer formation is originally contemplated, and mirror symmetry breaking is mathematically possible because the needed inhibition is provided by the reverse symmetric catalysis step [24]. In spite of this, the symmetry breaking condition g < g crit , determined from the pure stability analysis, cannot be achieved on thermodynamic grounds [24], as has also been pointed out recently [26].…”

“…This scenario, corresponding to the reaction steps Eqs. (1,2,3), is termed limited enantioselectivity [13,24]. As there is no dimerization in this model, we are to solve Eqs.…”