Temporary mirror symmetry breaking and chiral excursions in open and closed systems

Spontaneous Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models

To explore abiotic theories related to the origin of biomolecular homochirality, we analyze two entirely reversible kinetic models composed of an enantioselective autocatalysis with limited stereoselectivity that is coupled to an enantiomeric mutual inhibition (Frank-like models). The two models differ in their autocatalytic steps in respect to the formation of monomer species in one model and of dimer species in the other. While fully reversible and running in a closed system, spontaneous mirror symmetry breaking (SMSB) gives rise to transient chiral excursions, even when starting from a strictly achiral situation. Before the SMSB, the two models differ in the main dissipative processes. At the SMSB, the entropy production rate reaches its maximum in both models. Here it is the enantioselective autocatalysis with retention of the winner enantiomer that dominates. During the terminal phase, the enantioselective autocatalysis with inversion prevails, while the entropy production rate vanishes, thus fulfilling the conditions of microscopic reversibility. SMSB does not occur if the autocatalytic rate constant is too strong or too weak. However, when the autocatalysis is relatively weak, the temporary chiral excursions last for long periods of time and could be the starting point of a cascade of asymmetric reactions. The realism of such Frank-like models is discussed from the viewpoint of their relevance to prebiotic chemistry.

On the asymmetric autocatalysis of aldol reactions: The case of 4-nitrobenzaldehyde and acetone. A critical appraisal with a focus on theory

Under neutral conditions, spontaneous mirror symmetry breaking has been occasionally reported for aldol reactions starting from achiral reagents and conditions. Chiral induction might be interpreted in terms of autocatalysis exerted by chiral mono-aldol or bis-aldol products as source of initial enantiomeric excesses, which may account for such experimental observations. We describe here a thorough Density Functional Theory (DFT) study on this complex and otherwise difficult problem, which provides some insights into this phenomenon. The picture adds further rationale to an in-depth analysis by Moyano et al, who showed the isolation and characterization of bis-aldol adducts and their participation in a complex network of reversible steps. However, the lack of enantiodiscrimination (ees vanish rapidly in solution) suggests, according to the present results, a weak association in complexes formed by the catalysts and substrates. The latter would also be consistent with almost flat transition states having similar heights for competitive catalyst-bound transition structures (actually, we were unable to locate them at the level explored). Overall, neither autocatalysis as once conjectured nor mutual inhibition of enantiomers appears to be operating mechanisms. Asymmetric amplification in early stages harnessing unavoidable enantiomeric imbalances in reaction mixtures of chiral products represents a plausible interpretation.

Model of complex chiral drug metabolic systems and numerical simulation of the remaining chirality toward analysis of dynamical pharmacological activity

In this study, systems of complicated pathways involved in chiral drug metabolism were investigated. The development of chiral drugs resulted in significant improvement in the remedies available for the treatment of various severe sicknesses. Enantiopure drugs undergo various biological transformations that involve chiral inversion and thus result in the generation of multiple enantiomeric metabolites. Identification of the specific active substances determining a given drug׳s efficacy among such a mixture of different metabolites remains a challenge. To comprehend this complexity, we constructed a mathematical model representing the complicated metabolic pathways simultaneously involving chiral inversion. Moreover, this model is applied to the metabolism of thalidomide, which has recently been revived as a potentially effective prescription drug for a number of intractable diseases. The numerical simulation results indicate that retained chirality in the metabolites reflects the original chirality of the unmetabolized drug, and a higher level of enantiomeric purity is preserved during spontaneous degradation. In addition, chirality remaining after equilibration is directly related to the rate constant not only for chiral inversion but also for generation and degradation. Furthermore, the retention of chirality is quantitatively predictable using this combination of kinetic parameters. Our simulation results well explain the behavior of thalidomide in the practical biological experimental data. Therefore, this model promises a comprehensive understanding of dynamic metabolic systems involving chiral drugs that express multiple enantiospecific drug efficacies.

Stochastic mirror symmetry breaking: theoretical models and simulation of experiments

This chapter provides a review of recently elaborated mathematical models for explaining the salient features of two experimental studies selected for their relevance to the problem of stochastic mirror symmetry breaking and amplification. The first experiment modeled treats the phenomena of mirror symmetry breaking via the autocatalytic crystallization of the glycine and α-amino acid system at the air-water interface. The second experiment deals with the lattice-controlled generation of homochiral oligopeptides, which we model based on a kinetic scheme for copolymerization in a closed reaction system. Since the fundamental paradigm of mutual inhibition lies at the core of both these models, we review how the final asymptotic states in the Frank model depend crucially on whether the system is open or closed, and emphasize the importance of temporary chiral excursions, which can and do arise in more complex reaction schemes during their approach to chemical equilibrium in closed systems.

Autocatalyses

Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. With the notion of autocatalysis covering a large variety of mechanistic realizations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form.