Critical evaluation of mathematical models for the amplification of chirality

Amplification of enantiomeric excess, mirror-image symmetry breaking and kinetic proofreading in Soai reaction models with different oligomeric orders

A comprehensive kinetic analysis of three prototypical autocatalytic cycle models based on the absolute asymmetric Soai reaction is presented. The three models, which can give rise to amplification of enantiomeric excess and mirror-image symmetry breaking, vary by their monomeric, dimeric or trimeric order of the assumed catalytic species. Our numerical approach considered the entire chiral combinatorics of the diastereomeric interactions in the models as well as the multiplicity of coupled reversible reactions without applying fast equilibration or quasi-steady state approximations. For the simplest monomeric model, an extensive range of parameters was explored employing a random grid parameter scanning method that revealed the influence of the parameter values on the product distribution, the reaction-time, the attenuation or amplification of enantiomeric excess as well as on the presence or absence of mirror-image symmetry breaking. A symmetry breaking test was imposed on the three models showing that an increase in the catalytic oligomer size from one to three leads to a higher tolerance to poorer chiral recognition between the diastereoisomers and identifies the greater impact of the diastereoisomeric energy difference over an imperfect stereoselectivity in the catalytic step. This robustness is understood as a particular case of so-called kinetic proofreading in asymmetric autocatalysis.

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.

Parity violation and the evolution of biomolecular homochirality

Parity violation at the level of terrestrial biopolymers, as seen in proteins, DNAs, and RNAs, and parity violation at the level of nuclear processes, as evident in longitudinally polarized beta-particles and parity-violating energy differences (PVEDs), are discussed and their fundamental importances are emphasized. Attempts to find a causal connection between the unique homochirality of biopolymers and parity violation at the nuclear level, and speculations that the former is a consequence of the latter, are reviewed. Consideration of all lines of evidence leads to the conclusion that there is no substantiation for such a causal connection, and that the two levels of parity violation are entirely independent of each other.

Chirality amplification--the accumulation principle revisited

The chirality amplification mechanism proposed by Yamagata in 1966, relying on an Accumulation Principle which involved the parity violating energy difference (1 + epsilon) presumed to be operative at each step in the formation of a homochiral biopolymer, is briefly surveyed historically. The Accumulation Principle is then examined analytically and found to be incapable of producing a unique homochiral polymer in any realistic polymerization process. The extension of the Accumulation Principle to crystallizations which afford enantiomorphic crystals is also scrutinized and found to be misapplied and invalid.

The electroweak origin of biomolecular handedness

The parity-violating weak neutral current perturbation of the ground-state electronic energy has been calculated by ab initio methods for glycine over a range of chiral conformations, for L-alanine, L-α-aminopropionitrile, and for the peptide residue of polypeptides in the α-helix and the β-sheet conformation. It is found that L-alanine in its preferred conformation in aqueous solution and the L-peptides in the α-helix and the β-sheet conformation, have a lower ground-state energy than the corresponding D-enantiomers, because of the electroweak interaction. The enantiomer energy difference is small, of the order of 10 -14 J mol -1 , corresponding to an enantiomeric excess of 10 6 molecules of L-alanine or the L-peptide in one mole of the corresponding racemic mixture in thermodynamic equilibrium at ambient temperature. The significance of the energy difference between enantiomers arising from the electroweak interaction for the transition from racemic geochemistry to homochiral biochemistry in terrestrial evolution is discussed.

Amplification of chirality based upon the association of nucleic acid strands of opposite handedness

It is proposed that nucleotide strands of opposite handedness may strongly associate and thereby provide the key step of a mechanism for the amplification of a small enantiomeric excess in an initially near-racemic mixture of poly- or oligonucleotides. This hypothesis, if confirmed by experimentation, may have important implications for the question of the origin of biomolecular chirality. The results of preliminary NMR experiments are given, which do show evidence of a strong association between pentanucleotide RNA strands whose monomers have opposite chirality. Simple kinetic equations are solved to demonstrate the conditions under which such association can produce amplification of chirality.

Parity violation and the origins of biomolecular handedness

The violation of parity by the weak interactions ensures that enantiomeric chiral molecules have inequivalent energies, one being inherently stabilized with respect to the other. These parity-violating energy differences have been calculated for a number of fundamental biomolecules including a series of alpha-amino acids, polypeptide structures, and a representative of the sugar series together with its variation over a possible prebiotic reaction path leading to alpha-amino acids. In each case the natural enantiomer found in terrestrial biochemistry was shown to be intrinsically stabilized and preferred over its unnatural enantiomer. The significance of these results in accounting for the prebiotic origins of the terrestrial biomolecular homochirality is discussed and the possible consequences of parity-violating energy differences in mineral catalysts during the prebiotic era considered.

New estimates of asymmetric decomposition of racemic mixtures by natural beta-radiation sources

The Vester-Ulbricht hypothesis suggests that the chirality of biological molecules originates from the beta-radiolysis of prebiotic racemic mixtures. Despite the inconclusiveness of past investigations, recent calculations have shown that beta particles, because of their helicity, radiolyse L- and D-enantiomers at slightly different rates, the asymmetry, AR, being predicted to be 10(-11) (new experimental tests, give /AR/ < 2 x 10(-9)). Before this, the size of the radiolysis-induced chiral polarization, eta R (eta triple bond (nL - nD)/(nL + nD) where nL and nD are the numbers of L and D molecules present), was estimated for different values of AR; according to Keszthelyi et al., if /AR/ approximately 10(-11), /eta R/ can never exceed the chiral polarization, /eta F/, produced by statistical fluctuations, thus invalidating the V-U hypothesis. Here we re-examine the major assumptions on which these calculations were based and find that several overly restrictive conditions were imposed, which, when relaxed, allow the condition /eta R/ > /eta F/, in accordance with the V-U hypothesis.

Origins of biomolecular handedness

Classical mechanisms proposed for the transition from racemic geochemistry to homochiral biochemistry in terrestrial evolution generally ascribe to chance the particular handed choice of the L-amino acids and the D-sugars by self-replicating systems. The parity-violating weak neutral current interaction gives rise to an energy difference between a chiral molecule and its mirror-image isomer, resulting in a small stabilization of the L-amino acids and the L-peptides in the alpha-helix and the beta-sheet conformation relative to the corresponding enantiomer. The energy difference suffices to break the chiral symmetry of autocatalytic racemic reaction sequences in an open non-equilibrium system.

Chiral selection in poly(C)-directed synthesis of oligo(G)

Theories of the origin of optical asymmetry in living systems place fundamental importance on the amplification of optical asymmetry by an autocatalytic process. The replication of a polynucleotide is one obvious choice for such an autocatalytic growth mechanism. If an optically homogeneous polynucleotide could replicate by directing the polymerization of monomers of the same handedness, while excluding monomers of the opposite handedness, its chiral descendants would come to dominate what was once an achiral environment. Recently, two highly efficient template-directed reaction systems have been developed for the oligomerization of activated guanosine mononucleotides (Fig. 1) on a poly(C) template. The synthesis of L-guanosine 5'-mononucleotide makes it possible to study chiral selection in these systems. We report here that poly(C)-directed oligomerization of activated guanosine mononucleotides proceeds readily if the monomers are of the same optical handedness as the template, and is indeed far less efficient if the monomers are of the opposite handedness. However, in template-directed reactions with a racemic mixture, monomers of the opposite handedness to the template are incorporated as chain terminators at the 2'(3') end of the products. This inhibition raises an important problem for many theories of the origin of life.

Beta decay and the origin of biological chirality: new experimental results

The proposed connection between the parity-violating handedness of beta particles in radioactive decay and the sign (L) of biological chirality (the Vester-Ulbricht [V-U] hypothesis) is being investigated by measuring the theoretically predicted asymmetry in the formation of triplet positronium in amino acid enantiomers by low energy positrons under reversal of the helicity of the positrons. We find the asymmetry in leucine to be (0.8 +/- 1.0) X 10(-4), i.e. consistent with the theoretical prediction of 10(-6) to 10(-7). The apparatus is now sensitive enough to test the predicted asymmetry in optically active molecules which have heavy atoms at their chiral centers. The connection between these results and asymmetry in radiolysis by beta-decay electrons is made, and the implications of our limits for the V-U hypothesis discussed. Although the above limits are 10(6) times lower than direct measurements of radiolysis, they are still not small enough to allow us to rule out the V-U hypothesis.