Quantum mechanical considerations on the algebraic structure of central molecular chirality

The chiral algebra of tetrahedral molecules, derived from Fischer's projections, is discussed in the framework of quantum mechanics. A "quantum chiral algebra" is obtained whose operators, acting as rotations or inversions, commute with the Hamiltonian of the system. It is shown that energy and chirality eigenstates are strictly related through the Heisenberg relations, while chirality operators "conserve" parity eigenstates.     

Nonhanded chirality in octahedral metal complexes

Chiral molecules can either be handed (i.e., "shoes") or nonhanded ("potatoes"). The only chiral ligand partition for tetrahedral metal complexes (or for a tetrahedral carbon atom such as that found in amino acids and other chiral biological molecules) is the fully unsymmetrical degree 6 partition (1(4)), which leads to handed metal complexes of the type MABCD with a lowest-degree chirality polynomial consisting of the product of all six possible linear factors of the type (s(i)-s(j)) where 1 < or = i,j < or = 4. The lowest-degree chiral ligand partitions for octahedral metal complexes are the degree 6 partitions (31(3)) and (2(3)) leading to handed chiral metal complexes of the types fac-MA(3)BCD and cis-MA(2)B(2)C(2). The form of the lowest-degree chirality polynomial for the (31(3)) chiral ligand partition of the octahedron resembles that of the (1(4)) chiral ligand partition of the tetrahedron, likewise with four different ligands. However, the form of the lowest-degree chirality polynomial for the (2(3)) chiral ligand partition of the octahedron corresponds to the square of the chirality polynomial of the (1(3)) chiral ligand partition of the polarized triangle, which likewise has three different ligands. Ligand partitions for octahedral metal complexes such as (2(2)1(2)), (21(4)), and (1(6)), which are less symmetrical than the lowest-degree chiral ligand partitions (31(3)) and (2(3)), lead to chiral octahedral metal complexes which are nonhanded. In such complexes, pairs of enantiomers can be interconverted by simple ligand interchanges without ever going through an achiral intermediate.     

Algebraic structure of central molecular chirality starting from Fischer projections

The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and inversions is identified. The result can be generalized to chains of connected tetrahedrons.     

Fundamental symmetry aspects of chirality

Physical systems which exhibit distinguishable enantiomers under space inversion are not necessarily chiral. A new definition of chirality is proposed that enables true and false chirality to be distinguished. Although spatial enantiomorphism is sufficient to guarantee chirality in a stationary object, enantiomorphous systems are not necessarily chiral when motion is involved. Only a truly chiral influence can induce absolute asymmetric synthesis in a reaction mixture at thermodynamic equilibrium, but false chirality might suffice if equilibrium is not attained. Parity violation lifts only the degeneracy of enantiomers of truly chiral systems, the true enantiomers (i.e. strictly degenerate) being interconverted by space inversion together with charge conjugation. The time-independence of optical activity arising from parity violation is contrasted with the time-dependence of that arising from spontaneous parity breaking.     

Speciation and gene flow between snails of opposite chirality

Left-right asymmetry in snails is intriguing because individuals of opposite chirality are either unable to mate or can only mate with difficulty, so could be reproductively isolated from each other. We have therefore investigated chiral evolution in the Japanese land snail genus Euhadra to understand whether changes in chirality have promoted speciation. In particular, we aimed to understand the effect of the maternal inheritance of chirality on reproductive isolation and gene flow. We found that the mitochondrial DNA phylogeny of Euhadra is consistent with a single, relatively ancient evolution of sinistral species and suggests either recent “single-gene speciation” or gene flow between chiral morphs that are unable to mate. To clarify the conditions under which new chiral morphs might evolve and whether single-gene speciation can occur, we developed a mathematical model that is relevant to any maternal-effect gene. The model shows that reproductive character displacement can promote the evolution of new chiral morphs, tending to counteract the positive frequency-dependent selection that would otherwise drive the more common chiral morph to fixation. This therefore suggests a general mechanism as to how chiral variation arises in snails. In populations that contain both chiral morphs, two different situations are then possible. In the first, gene flow is substantial between morphs even without interchiral mating, because of the maternal inheritance of chirality. In the second, reproductive isolation is possible but unstable, and will also lead to gene flow if intrachiral matings occasionally produce offspring with the opposite chirality. Together, the results imply that speciation by chiral reversal is only meaningful in the context of a complex biogeographical process, and so must usually involve other factors. In order to understand the roles of reproductive character displacement and gene flow in the chiral evolution of Euhadra, it will be necessary to investigate populations in which both chiral morphs coexist.     

Bulky melamine-based Zn-porphyrin tweezer as a CD probe of molecular chirality

The transfer of chirality from a guest molecule to an achiral host is the subject of significant interest especially when, upon chiral induction, the chiroptical response of the host/guest complex can effectively report the absolute configuration (AC) of the guest. For more than a decade, dimeric metalloporphyrin hosts (tweezers) have been successfully applied as chirality probes for determination of the AC for a wide variety of chiral synthetic compounds and natural products. The objective of this study is to investigate the utility of a new class of melamine-bridged Zn-porphyrin tweezers as sensitive AC reporters. A combined approach based on an experimental CD analysis and a theoretical prediction of the prevailing interporphyrin helicity demonstrates that these tweezers display favorable properties for chiral recognition. Herein, we discuss the application of the melamine-bridged tweezer to the chiral recognition of a diverse set of chiral guests, such as 1,2-diamines, α-amino-esters and amides, secondary alcohols, and 1,2-amino-alcohols. The bulky periphery and the presence of a rigid porphyrin linkage lead, in some cases, to a more enhanced CD sensitivity than that reported earlier with other tweezers.     

A novel spectroscopic probe for molecular chirality

Recent advances in developing sum frequency generation (SFG) as a novel spectroscopic probe for molecular chirality are reviewed. The basic principle underlying the technique is briefly described, in comparison with circular dichroism (CD). The significantly better sensitivity of the technique than CD is pointed out, and the reason is discussed. Bi-naphthol (BN) and amino acids are used as representatives for two different types of chiral molecules; the measured chirality in their electronic transitions can be understood by two different molecular models, respectively, that are extensions of models developed earlier for CD. Optically active or chiral SFG from vibrational transitions are weaker, but with the help of electronic-vibrational double resonance, the vibrational spectrum of a monolayer of BN has been obtained. Generally, optically active SFG is sufficiently sensitive to be employed to probe in-situ chirality of chiral monolayers and thin films.     

Biological significance of molecular chirality in energy balance and metabolism

Summary In biological electron transport the spin, and thus the magnetic property of electrons, is neglected. Furthermore, no attention is paid to the fact that the great majority of biologically important molecules are chiral, and during excitation a magnetic moment is induced in them. It is shown, both theoretically and experimentally, that the magnetic moment of the electron and the magnetic transition moment of the optically active molecules may interact. The main consequences of such an interaction are a higher probability of the occurrence of optically active molecules in triplet states, and the polarization of transported electrons.Note: The term chirality has been introduced byKelvin (Robert Boyle Lecture May 16, 1893, printed in Baltimore Lectures Appendix H p. 439, 1904). He wrote: I call any geometrical figure, or any group of points chiral, and say it has chirality, if its image in a plane mirror can not be brought to coincide with itself.     

Transition state chirality and role of the vicinal hydroxyl in the ribosomal peptidyl transferase reaction

The ribosomal peptidyl transferase is a biologically essential catalyst responsible for protein synthesis. The reaction is expected to proceed through a transition state approaching tetrahedral geometry with a specific chirality. To establish that stereospecificity, we synthesized two diastereomers of a transition state inhibitor with mimics for each of the four ligands around the reactive chiral center. Preferential binding of the inhibitor that mimics a transition state with S chirality establishes the spatial position of the nascent peptide and the oxyanion and places the amine near the critical A76 2'-OH group on the P-site tRNA. Another inhibitor series with 2'-NH 2 and 2'-SH substitutions at the critical 2'-OH group was used to test the neutrality of the 2'-OH group as predicted if the hydroxyl functions as a proton shuttle in the transition state. The lack of significant pH-dependent binding by these inhibitors argues that the 2'-OH group remains neutral in the transition state. Both of these observations are consistent with a proton shuttle mechanism for the peptidyl transferase reaction.     

Memory of chirality in reactions involving monoradicals

Abstract

The effects of memory of chirality (MoC) in reactions involving monoradical species are reviewed here. Reactions involving a nonracemic chiral starting material bearing a single stereogenic element such as a chiral center or chiral axis directly involved in the new bond formation are discussed. These reactions lead to a nonracemic product via an intermediate susceptible to rapid racemization. Memory of chirality has been observed in cyclic radicals, aryl, ester/amide substituted acyclic radicals, and benzylic radicals at temperatures up to 130?°C.     

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

Summary 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.     

Olfactory discrimination among sex pheromone stereoisomers: chirality recognition by pink hibiscus mealybug males

Our previous field studies suggested that the two chiral centers in the sex pheromone of pink hibiscus mealybug, Maconellicoccus hirsutus, could elicit different male responses. The chiral center in the acid moiety of the pheromone seemed to be more critical than the alcohol portion of the pheromone molecule for attractiveness. The objective of the current study was to test this hypothesis by deploying stereoisomeric blends in pheromone traps. Captures of male M. hirsutus showed that pheromone with the naturally occurring (R)-maconelliyl (S)-2-methylbutanoate and (R)-lavandulyl (S)-2-methylbutanoate [R-S configuration] was most attractive and that pheromone with the unnatural S-S configuration was less attractive. In addition, the RS-R blend (containing R-R and S-R stereoisomers) yielded captures of male M. hirsutus that were comparable to blank controls, and an inhibitory effect was observed when R-R and S-R were combined with naturally occurring R-S blend. These results suggest a unique chirality recognition mechanism; olfactory discrimination among different pheromone stereoisomers depends upon both asymmetric centers. The S configuration on the acid moiety elicits attraction, whereas the R configuration induces inhibition. However, the attractive activity shows some degree of tolerance toward chirality change in the alcohol portion of the pheromone molecules.     

Molecular chirality and the origin of life

In the living systems L-amino acids and D-sugars are found with almost no exceptions. Although all the molecular chirality must have been established prior to the emergence of life, the origin of the asymmetry of molecules is still an unsolved problem. The time of appearance of the asymmetry of molecules, therefore, was quite problematic during chemical evolution.Since Pasteur's discovery in 1848, a large number of works for solving this problem have been carried out on the basis of mathematics, physics or chemistry. All the proposals which put forth for breaking the symmetry are still considered to be too weak to explain the cause of obtaining the chiral purity as a result of the symmetry breaking of molecules. In order to expand our scope, new sources of the symmetry breaking of molecules should be considered.In this article, some approaches to the achiral-chiral transition are reviewed, which will give an idea for the origin of asymmetry of molecules.     

Induction and memory of chirality in porphyrin hetero-aggregates: the role of the central metal ion

The anionic H2TPPS porphyrin and its copper derivative, CuTPPS, form in aqueous solution hetero-aggregates with the cationic H2T4 porphyrin and its copper derivative, CuT4. In the presence of poly-L-glutamate, at pH 4.0, a CD signal appears in the Soret region of the spectrum, indicating that the polypeptide has induced chirality into the structure of the aggregates. These species exhibit remarkable inertness due to the strength and number of the coulombic interactions between the anionic and the cationic porphyrins. This property allows them to preserve the chiral structure, even when the matrix changes or loses its chiral conformation, demonstrating that these aggregates are capable of memorizing the chiral information. The remarkable properties of the title systems may find various applications (chiral amplification, discrimination, and separation) that, on the other hand, require a more strict control of the aggregate dimension. Here, we show that the central copper of these macrocycles is crucial for determining the aggregate dimension.     

Molecular dynamics and free energy studies of chirality specificity effects on aminobenzo[a]quinolizine inhibitors binding to DPP-IV

The aminobenzo[a]quinolizines were investigated as a novel class of DPP-IV inhibitors. The stereochemistry of this class plays an important role in the bioactivity. In this study, the mechanisms of how different configuration of three chiral centers of this class influences the binding affinity were investigated by molecular dynamics simulations, free energy decomposition analysis. The S configuration for chiral center 3* is decisive for isomers to maintain high bioactivity; the chirality effect of chiral center 2* on the binding affinity is largely dependent, while the S configuration for chiral center 2* is preferable to R configuration for the bioactivity gain; the effect of chiral center 11b* on the binding affinity is insignificant. The chirality specificity for three chiral centers is responsible for distinction of two van der Waals contacts with Tyr547 and Phe357, and of H-bonding interactions with Arg125 and Glu206. Particularly, the Arg125 to act as a bridge in the H-bonding network contributes to stable H-bonding interactions of isomer in DPP-IV active site.

Effect of phosphatidylcholine vesicle size on chirality induction and chiral discrimination

The effect of the size of phosphatidylcholine (PC) vesicles on the induction of chirality and chiral discrimination was examined. Three kinds of vesicles formed with l-dimyristoyl, l-dipalmitoyl, or egg yolk PCs induced circular dichroisms (CDs) with the sign and intensity of the Cotton effect different from those of monomeric PCs. The CD intensity of the vesicles increased with a decrease in the vesicle size. Furthermore, the helicity of heterohelicene derivatives in a rapid equilibrium between right-handed (P) and left-handed (M) enantiomers was biased toward the M enantiomer side in l-PC vesicles, implying chiral discrimination by the vesicles. The extent of the bias toward the M enantiomer increased with an increase in vesicle size. Both the chirality induction and chiral discrimination were enhanced in a low-fluidity gel phase in comparison with those in a high-fluidity liquid-crystalline phase for every kind of vesicle of every size examined.     

Fundamentals of chirality,resolution, and enantiopure molecule synthesis methods

The chirality of molecules is a concept that explains the interactions in nature. We may observe the same formula but different organizations revolving around the chiral center. Since Pasteur's meticulous observation of sodium ammonium tartrate crystals' structure, scientists have discovered many features of chiral molecules. The number of newly approved single enantiomeric drugs increases every year and takes place in the market. Thus, separation or resolution methods of racemic mixtures are of continued importance in the efficacy of drugs, installation of affordable production processes, and convenient synthetic chemistry practice. This article presents the asymmetric synthesis approaches and the classification of direct resolution methods of chiral molecules.     

Spiral galaxies as enantiomers: Chirality,an underlying feature in chemistry and astrophysics

Spiral galaxies are axisymmetric objects showing 2D chirality when projected onto a plane. Features in common with tetrahedral molecules are pointed out, in particular the existence of a preferred chiral modality for genetic galaxies as in amino acids and sugars. Environmental effects can influence the intrinsic chirality of originally isolated stellar systems so that a progressive loss of chirality is recognized in the Hubble morphological sequence of galaxies. © 2005 Wiley‐Liss, Inc. Chirality