The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems

Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System

We review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma’s crystal grinding systems and the APED model. We include a few new results based on asymptotic analysis of the APED system.

Evolutionary Approach to Biological Homochirality

We study a very simple linear evolutionary model based on distribution of protocells by total enantiomeric excess and without any mutual inhibition and show that such model can produce two species with values of total enantiomeric excess in each of the species approaching $$\pm 1$$ ± 1 when there is a global $$L\leftrightarrow D$$ L ↔ D symmetry. We then consider a scenario when there is a small external global asymmetry factor, like weak interaction, and show that only one of the species remains in such a case, and that is the one, which is more efficient in replication. We perform an estimate of the time necessary to reach homochirality in such a model and show that reasonable assumptions lead to an estimate of around 300 thousand years plus or minus a couple of orders of magnitude. Despite this seemingly large time to reach homochirality, the model is immune to racemization because amino acids in the model follow the lifespan of the protocells rather than the time needed to reach homochirality. We show that not needing mutual inhibition in such evolutionary model is due to the difference in the topology of the spaces in which considered model and many known models of biological homochirality operate. Bifurcation-based models operate in disconnected zero-dimensional space (the space is just two points with enantiomeric excess equal $$-1$$ - 1 and $$1$$ 1 ), whereas considered evolutionary model (in its continuous representation) operates in one-dimensional connected space, that is the whole interval between $$-1$$ - 1 and $$1$$ 1 of total enantiomeric excess. We then proceed with the analysis of the replication process in non-homochiral environment and show that replication errors (the probability to attach an amino acid of wrong chirality) result in a smooth decrease of replication time when total enantiomeric excess of the replicated structure moves away from zero. We show that this decrease in replication time is sufficient for considered model to work.

Duplex Formation and the Origins of Homochirality

The roots of biological homochirality remain unknown despite decades of study. A commonly proposed path includes an initial small enantiomeric excess that was amplified over time, but a satisfactory source of the excess and a plausible amplification process have yet to be described. We propose here a route to oligonucleotide homochirality from unactivated racemic sources based upon the facts that duplex structures are inherently homochiral and their synthesis from strands of complementary string nucleotide subunits is both uncommonly rapid and exergonic. Simulations employing available kinetic and thermochemical data in an iterated sequence of three equilibria in dry/wet cycles running from unactivated and racemic RNA monomers through oligonucleotides to duplex structures have shown that the exceptional association rate distorts the otherwise simple equilibrium string and overcomes the severe kinetic and stoichiometric barriers to the pairing of the statistically scant homochiral fractions. The simulations reveal widespread deracemization and the full conversion of racemic monomers to populations of L- and D-duplexes in a succession of growth in which the initially formed duplexes are replaced over time with increasingly larger descendants. This claim is open to experimental testing.

Factors in Protobiomonomer Selection for the Origin of the Standard Genetic Code

Natural selection of specific protobiomonomers during abiogenic development of the prototype genetic code is hindered by the diversity of structural, spatial, and rotational isomers that have identical elemental composition and molecular mass (M), but can vary significantly in their physicochemical characteristics, such as the melting temperature T_m, the T_m:M ratio, and the solubility in water, due to different positions of atoms in the molecule. These parameters differ between cis- and trans-isomers of dicarboxylic acids, spatial monosaccharide isomers, and structural isomers of α-, β-, and γ-amino acids. The stable planar heterocyclic molecules of the major nucleobases comprise four (C, H, N, O) or three (C, H, N) elements and contain a single -C=C bond and two nitrogen atoms in each heterocycle involved in C-N and C=N bonds. They exist as isomeric resonance hybrids of single and double bonds and as a mixture of tautomer forms due to the presence of -C=O and/or -NH₂ side groups. They are thermostable, insoluble in water, and exhibit solid-state stability, which is of central importance for DNA molecules as carriers of genetic information. In M-T_m diagrams, proteinogenic amino acids and the corresponding codons are distributed fairly regularly relative to the distinct clusters of purine and pyrimidine bases, reflecting the correspondence between codons and amino acids that was established in different periods of genetic code development. The body of data on the evolution of the genetic code system indicates that the elemental composition and molecular structure of protobiomonomers, and their M, T_m, photostability, and aqueous solubility determined their selection in the emergence of the standard genetic code.

Determining the Diastereoselectivity of the Formation of Dipeptidonucleotides by NMR Spectroscopy

Proteins are composed of l‐amino acids, but nucleic acids and most oligosaccharides contain d‐sugars as building blocks. It is interesting to ask whether this is a coincidence or a consequence of the functional interplay of these biomolecules. One reaction that provides an opportunity to study this interplay is the formation of phosphoramidate‐linked peptido RNA from amino acids and ribonucleotides in aqueous condensation buffer. Here we report how the diastereoselectivity of the first peptide coupling of the peptido RNA pathway can be determined in situ by NMR spectroscopy. When a racemic mixture of an amino acid ester was allowed to react with an 5′‐aminoacidyl nucleotide, diastereomeric ratios of up to 72 : 28 of the resulting dipeptido nucleotides were found by integration of ³¹P‐ or ¹H‐NMR peaks. The highest diastereomeric excess was found for the homochiral coupling product d‐Ser‐d‐Trp, phosphoramidate‐linked to adenosine 5′‐monophosphate with its d‐ribose ring. When control reactions with an N‐acetyl amino acid and valine methyl ester were run in organic solvent, the diastereoselectivity was found to be lower, with diastereomeric ratios≤62 : 38. The results from the exploratory study thus indicate that the ribonucleotide residue not only facilitates the coupling of lipophilic amino acids in aqueous medium but also the formation of a homochiral dipeptide. The methodology described here may be used to search for other stereoselective reactions that shed light on the origin of homochirality.

Chiral Symmetry Breaking in Large Peptide Systems

Chiral symmetry breaking in far from equilibrium systems with large number of amino acids and peptides, like a prebiotic Earth, was considered. It was shown that if organic catalysts were abundant, then effective averaging of enantioselectivity would prohibit any symmetry breaking in such systems. It was further argued that non-linear (catalytic) reactions must be very scarce (called the abundance parameter) and catalysts should work on small groups of similar reactions (called the similarity parameter) in order to chiral symmetry breaking have a chance to occur. Models with 20 amino acids and peptide lengths up to three were considered. It was shown that there are preferred ranges of abundance and similarity parameters where the symmetry breaking can occur in the models with catalytic synthesis / catalytic destruction / both catalytic synthesis and catalytic destruction. It was further shown that models with catalytic synthesis and catalytic destruction statistically result in a substantially higher percentage of the models where the symmetry breaking can occur in comparison to the models with just catalytic synthesis or catalytic destruction. It was also shown that when chiral symmetry breaking occurs, then concentrations of some amino acids, which collectively have some mutually beneficial properties, go up, whereas the concentrations of the ones, which don't have such properties, go down. An open source code of the whole system was provided to ensure that the results can be checked, repeated, and extended further if needed.

Mirror Symmetry Breaking in Liquids and Their Impact on the Development of Homochirality in Abiogenesis: Emerging Proto-RNA as Source of Biochirality?

Recent progress in mirror symmetry breaking and chirality amplification in isotropic liquids and liquid crystalline cubic phases of achiral molecule is reviewed and discussed with respect to its implications for the hypothesis of emergence of biological chirality. It is shown that mirror symmetry breaking takes place in fluid systems where homochiral interactions are preferred over heterochiral and a dynamic network structure leads to chirality synchronization if the enantiomerization barrier is sufficiently low, i.e., that racemization drives the development of uniform chirality. Local mirror symmetry breaking leads to conglomerate formation. Total mirror symmetry breaking requires either a proper phase transitions kinetics or minor chiral fields, leading to stochastic and deterministic homochirality, respectively, associated with an extreme chirality amplification power close to the bifurcation point. These mirror symmetry broken liquids are thermodynamically stable states and considered as possible systems in which uniform biochirality could have emerged. A model is hypothesized, which assumes the emergence of uniform chirality by chirality synchronization in dynamic “helical network fluids” followed by polymerization, fixing the chirality and leading to proto-RNA formation in a single process.

Parity Violation Energy of Biomolecules - V: Protein Metal Centers

The parity-violation difference between mirror images of chiral metal centers found in naturally occurring proteins and enzymes is computed at the Dirac-Hartree-Fock level, for both equilibrium and transition state configurations. The systems, selected on the likelihood of yielding high parity violation energies based on atomic mass and coordination geometry, are extracted from: type I Blue Copper Protein active site, Zn and Cd Carbon Anhydrase, Ni Acetyl-Coenzyme-A Synthase, and Mo based CO-Dehydrogenase. Our values provide an approximate upper limit to possible parity-violation effects in biological systems based on static effects.