Models for chiral amplification in spontaneous mirror symmetry breaking

Zusammenfassung

It is an empirical fact that there is an absolute chiral imbalance (or mirror symmetry breaking) in all known biological systems, where processes crucial for life such as replication, imply chiral supramolecular structures, sharing the same chiral sign (homochirality). These chiral structures are proteins, composed of amino acids found as the left-handed enantiomers (L); and DNA, and RNA polymers and sugars, composed of right-handed (R) monocarbohydrates. Based on the fact that a perfect racemic mixture is chemically impossible to achieve on purely statistical grounds alone, we can assume the presence of an unavoidable tiny enantiomeric excess even in a ’perfect’ racemic mixture. Then, in principle, the origin and evolution of biological homochirality and Spontaneous Mirror Symmetry Breaking (SMSB) in chemical and biological systems could be theoretically explained by a model in which a tiny imbalance of one enantiomer was amplified, and the most likely path for this is by autocatalytic reactions. Our main purpose here is to test the ability of some different autocatalytic models to amplify a tiny initial enantiomeric excess, ee0, even lower than the expected inherent imbalance (i.e., using ee0 < eest). Then, in this context, we introduce and study the most basic known autocatalytic system leading to chiral amplification- the Frank model - and its ability to amplify the initial small statistical deviations from the idealized racemic composition. Depending on the conditions, this amplification can be just temporary, and it can be interpreted as a chiral excursion in a dynamic phase space. These chiral excursions can be studied through a combination of phase space analysis, stability analysis and numerical simulations in order to determine how they depend on whether the system is open, semi-open or closed. Also the emergence of homochirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non- nantioselective autocatalyses, which cannot lead to SMSB in closed systems. Since biological homochirality of living systems involves large macromolecules, the ability to amplify (and transmit to the entire system) those small initial enantiomeric excesses is studied for two different kinetic models of chiral polymerization and copolymerization in systems closed to matter and energy flow, and the results from fitting the copolymerization model to the experimental data on chiral amplification of oligopeptides are shown. Finally, both a chemical equilibrium model of template-controlled copolymerization and a probabilistic approach are presented for describing the outcome of the experimental induced desymmetrization scenarios recently proposed by Lahav and co-workers; these chiral amplification mechanisms proceed through racemic β-sheet controlled polymerization operative in both surface crystallites as well as in solution. In this case, the symmetry breaking arises from combinatorics, not from spontaneous (bifurcation) phenomena. These stochastic/statistical/combinatorial effects are not due to the inherent tiny chiral fluctuations present in all real chemical systems, but are due rather to the random occlusion of host and guest amino acids by the chiral sites of the template: the mechanisms proposed here work even for ideally racemic mixtures.