Béla Barabás

Isotope Chirality and Asymmetric Autocatalysis: A Possible Entry to Biological Chirality

Natural-abundance isotopic substitution in isotopically prochiral groups of otherwise achiral molecules can provide stochastically formed enantiomeric excesses which exceed the sensitivity threshold of sensitive asymmetric autocatalytic (Soai-type) reactions. This kind of induction of chirality should be taken into consideration in in vitro model experiments and offer a new kind of entry into primary prebiotic or early biotic enantioselection in the earliest stages of molecular evolution.

Natural Abundance Isotopic Chirality in the Reagents of the Soai Reaction

Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars–Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.

Stochastic and empirical models of the absolute asymmetric synthesis by the Soai-autocatalysis

Absolute asymmetric synthesis (AAS) is the preparation of pure (or excess of one) enantiomer of a chiral compound from achiral precursor(s) by a chemical reaction, without enantiopure chiral additive and/or without applied asymmetric physical field. Only one well-characterized example of AAS is known today: the Soai-autocatalysis. In an attempt at clarification of the mechanism of this particular reaction we have undertaken empirical and stochastic analysis of several parallel AAS experiments. Our results show that the initial steps of the reaction might be controlled by simple normal distribution (“coin tossing”) formalism. Advanced stages of the reaction, however, appear to be of a more complicated nature. Symmetric beta distribution formalism could not be brought into correspondence with the experimental observations. A bimodal beta distribution algorithm provided suitable agreement with the experimental data. The parameters of this bimodal beta function were determined by a Pólya-urn experiment (simulated by computer). Interestingly, parameters of the resulting bimodal beta function give a golden section ratio. These results show, that in this highly interesting autocatalysis two or even perhaps three catalytic cycles are cooperating. An attempt at constructing a “designed” Soai-type reaction system has also been made.

Star graph representations of chiral objects in graph theory

Planar chirality of objects is a problem with important applications in many fields of natural sciences, especially in chemistry and pharmacology. The analysis of chirality properties can be studied using n-polyominoes and planar graphs. In this paper we show that graph representations of chiral objects can be star-graphs.

On the traces of absolute enantioselective synthesis

The main goal of this communication is to show the utility of empirical approaches combined with mathematical methods in the research regarding the molecular basis of biological chirality. Preparative results (enantiomeric excesses, e.e.) obtained in asymmetric autocatalysis with (AAC) and without (AES) chiral additive were analyzed. Statistical calculations show, that AES (absolute enantioselective synthesis) experiments yield two independent groups of results with prevalence of the R‐ or S‐enantiomer. These are distributed asymmetrically in a second‐order beta distribution. Empirical calculations both on AAC and EAS enable to identify the very low (statistical) e.e.‐s amplified by AES. These initial e.e.‐s show normal distribution. Possible molecular‐level reasons of these results were controlled by quantum chemical MO calculations and compatible mechanism(s) are discussed.

Three-dimensional chiral objects and their star graph representations

Planar chirality properties can be analysed using n-polyominoes and graphs. In this paper we study graph representations of three-dimensional chiral objects and discuss the generalization of planar case. We show that graph representations of three-dimensional chiral objects can be star graphs.

Isotope chirality in long-armed multifunctional organosilicon (“Cephalopod”) molecules

Long-armed multifunctional organosilicon molecules display self-replicating and self-perfecting behavior in asymmetric autocatalysis (Soai reaction). Two representatives of this class were studied by statistical methods aiming at determination of probabilities of natural abundance chiral isotopomers. The results, reported here, show an astonishing richness of possibilities of the formation of chiral isotopically substituted derivatives. This feature could serve as a model for the evolution of biological chirality in prebiotic and early biotic stereochemistry.

Graph Theoretical and Statistical Analysis of the Impact of Soai Reaction on Natural Sciences

Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery has had an exceptional influence on several branches of natural sciences. In the present paper citations to this milestone article—556 publications of 908 scientists from Google Scholar’s database—are analyzed by graph theoretical and statistical tools. The results enable localization of the most active research groups, their priorities and the identification of the distribution of scientific disciplines influenced by the Soai reaction.

Graph Theoretical Tools in Two- and Three-Dimensional Chirality Problems

Abstract Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or 2D animals. Generalizing this idea for 3D problems we consider in the three-dimensional space R3 a Cartesian grid of the first octant consisting of n3 small unit cubic cells and define there solid animals or 3D animals. The simplest approach is to say that a 2D (or 3D) animal is chiral or achiral. One could assume that there is no other possibility. On the other hand a few scientists recognized that it is possible to measure the degree of chirality. For example F. Harary, R. W. Robinson, P. G. Mezey, A. I. Kitaigorodski, K. Mislow, J. Siegel, G. Gilat, D. Avnir, and A. Y. Meyer have made important contributions to this field. In this paper we provide a solution for quantification of the problem of chirality for 2D and 3D objects using graphs.Two-dimensional chirality problems in mathematics can be studied by so-called lattice animals or 2D animals. Generalizing this idea for 3D problems we consider in the three-dimensional space R3 a Cartesian grid of the first octant consisting of n3 small unit cubic cells and define there solid animals or 3D animals. The simplest approach is to say that a 2D (or 3D) animal is chiral or achiral. One could assume that there is no other possibility. On the other hand a few scientists recognized that it is possible to measure the degree of chirality. For example F. Harary, R. W. Robinson, P. G. Mezey, A. I. Kitaigorodski, K. Mislow, J. Siegel, G. Gilat, D. Avnir, and A. Y. Meyer have made important contributions to this field. In this paper we provide a solution for quantification of the problem of chirality for 2D and 3D objects using graphs.