Chiral symmetry conservation principle

We show a chiral symmetry conservation principle based on chemical kinetics using stochastic results. Suppose the chiral symmetry conservation is evoked, and our universe can be considered globally asymmetric. In that case, there are at least two mirrored asymmetric universes if all the chiral properties are strongly correlated. However, if the chiral correlations are weak or nonexistent, there are possibly Many-(Chiral-Symmetry)-Worlds. Alternatively, if our universe is only locally asymmetric, there could be a single universe with segregated chiral regions. The possible mechanisms of the primordial chiral symmetry breaking can only be found if the chiral symmetry is not truly conserved by assuming the initial racemic conditions. In that case, our universe is asymmetric and could be alone. On the other hand, if the chiral symmetry is conserved, there is no chance of finding the primordial chiral symmetry breaking. Based on this conservation (or not), it is possible to infer two opposite hypotheses, where two general scenarios about the chiral universes are possible.     

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.     

Chiral Symmetry Breaking in Peptide Systems During Formation of Life on Earth

Chiral symmetry breaking in complex chemical systems with a large number of amino acids and a large number of similar reactions was considered. It was shown that effective averaging over similar reaction channels may result in very weak effective enantioselectivity of forward reactions, which does not allow most of the known models to result in chiral symmetry breaking during formation of life on Earth. Models with simple and catalytic synthesis of a single amino acid, formation of peptides up to length five, and sedimentation of insoluble pair of substances were considered. It was shown that depending on the model and the values of the parameters, chiral symmetry breaking may occur in up to about 10% out of all possible unique insoluble pair combinations even in the absence of any catalytic synthesis and that minimum total number of amino acids in the pair is 5. If weak enantioselective forward catalytic synthesis of amino acids is present, then the number of possible variants, in which chiral symmetry breaking may occur, increases substantially. It was shown that that the most interesting catalysts have zero or one amino acid of “incorrect” chirality. If the parameters of the model are adjusted in such a way to result in an increase of concentration of longer peptides, then catalysts with two amino acids of incorrect chirality start to appear at peptides of length five. Models of chiral symmetry breaking in the presence of epimerization were considered for peptides up to length three. It was shown that the range of parameters in which chiral symmetry breaking could occur significantly shrinks in comparison to previously considered models with peptides up to length two. An experiment of chiral symmetry breaking was proposed. The experiment consists of a three-step cycle: reversible catalytic synthesis of amino acids, reversible synthesis of peptides, and irreversible sedimentation of insoluble substances.     

Space Asymmetry as a Possible Global Feature

A series of reports in the literature indicated symmetry breaking in assemblies of chiral molecules of opposite handedness. These unexpected observations could be accounted for as being generated by the “parity violation” of the nuclear weak force, combined with an autocatalytic amplification process. However, in many such cases, in particular of chiral fluids, this putative mechanism is far from providing a reasonable explanation for such discrimination. In this article it is suggested that space may have deviated a priori from absolute symmetry, a possibility which complies with observations in atoms and molecules and may even be implicated in the asymmetrical configuration of spiral galaxies. Space asymmetry can be extrapolated to a difference between the relative statistical weights of the “right” versus the “left” directions with respect to Euclidian coordinates or, analogously, to a difference between the clockwise and anticlockwise orientations in polar coordinates. The difference in weights of these directions in space is estimated to be around 1%, based on the differences observed in density values of chiral fluids and chiral crystals of NaClO₃. The implied asymmetry of time, as the conjugated fourth dimension, suggests a similar difference in magnitude of the time coordinate in a right‐handed versus left‐handed space, which is feasible for experimental verification. Chirality 25:308–311, 2013. © 2013 Wiley Periodicals, Inc.     

Selection of molecular chirality by extremely weak chiral interactions under far-from-equilibrium conditions

A general formalism for chiral symmetry breaking in far-from-equilibrium chemical systems is presented. It is pointed out that slow passage through the transition point makes the system sensitive to very weak, but systematic, chiral influences. The general implications of this process for the origin of biomolecular chirality is discussed.     

A Sequential Scenario for the Origin of Biological Chirality

A sequential model is proposed regarding the origin of biological chirality. Three major stages are presumed: a symmetry breaking (prebiotic chiral disruption in enantiomeric mixtures of monomers), a chiral amplification (prebiotic increase of the chiral character of the monomers affected first by the symmetry breaking), and a chiral expansion (proto biological increase of the chiral character and spread of the chirality to molecules which were less affected by prebiotic chiralizations). As a symmetry-breaking mechanism, the model proposed by Deutsch (1991) is used, which involves a dissymmetric exposure of amino acids (AA) to ultraviolet circularly polarized light (UV-CPL) on evaporative seashores. It is presumed that the chiral amplification, up to a protobiologic significance, was influenced by a periodic overlapping of two abiotic events, a synchronization between tidal-based hydrous–anhydrous cycles, and littoral asymmetric photolysis cycles. This long-term astronomic asymmetry acted around 3.8–4.2 billion years ago and was unique to the Earth in our solar system. It is also presumed that the abiotic symmetry breaking is heterogenous, that only a few l-AAs were used in the beginning, and that the chirality expanded later to all 20 AAs based on a coevolutionary strategy of the genetic code and on a physiological relationship between AAs. In this scenario the d-chirality of pentoses in polynucleotides was attributed to both d-pentose/l-AA relationships and to a structural evolution. Received: 10 May 1996 / Accepted: 13 August 1996     

Why the wrinkling transition in partially polymerized membranes is not universal? Fractal-multifractal hierarchy

When partially polymerized membranes wrinkle they exhibit a passage from a conventional buckling (due to an instability caused by chiral symmetry breaking) at low polymerization to a local roughening (due to a frustration in the local packing of the chiral molecules composing the membrane) as a function of the polymerization of the lipids aliphatic tails. This transition was found to be non-universal and here we used neutron scattering to elucidate that this behavior is due to the onset of stretching in the membrane accompanied by a bilayer thickness variation. Close to the percolation limit this deformation is plastic similar to mutated lysozymes. We draw an analogy between this transition and echinocytes in red blood cells.     

Viewing and Inducing Symmetry Breaking at the Single‐Molecule Limit

Symmetry breaking by photons, electrons, and molecular interactions lies at the heart of many important problems as varied as the origin of homochiral life to enantioselective drug production. Herein we report a system in which symmetry breaking can be induced and measured in situ at the single‐molecule level using scanning tunneling microscopy. We demonstrate that electrical excitation of a prochiral molecule on an achiral surface produces large enantiomeric excesses in the chiral adsorbed state of up to 39%. The degree of symmetry breaking was monitored as a function of scanning probe tip state, and the results revealed that enantiomeric excesses are correlated with the intrinsic chirality in scanning probe tips themselves, as evidenced by height differences between single molecule enantiomers. While this work has consequences for the study of two‐dimensional chirality, more importantly, it offers a new method for interrogating the coupling of photons, electrons, and combinations of physical fields to achiral starting systems in a reproducible manner. This will allow the mechanism of chirality transfer to be studied in a system in which enantiomeric excesses are quantified accurately by counting individual molecules. Chirality 24:1051–1054, 2012. © 2012 Wiley Periodicals, Inc.     

Neutral currents in weak interactions and molecular asymmetry

Weak interactions are parity violating forces, i.e. they differentiate between mirror images. Therefore it is a very attractive hypothesis to invoke weak interactions in explaining the origin of molecular asymmetry. It is, however, not clear whether weak interactions may operate between electrons and/or between electrons and protons? For these types of interactions so called neutral currents are needed. Recent experiments with muon neutrinos at CERN gave some evidence for the existence of neutral currents. Thus we may suppose that parity violating forces are active in molecules. In the first part of this paper a very elementary theory of weak interactions is outlined with special reference to the discovery of neutral currents. In the second part we show how weak interactions may differentiate between mirror image molecules. The asymmetrically distributed static charges in chiral molecules represent a helical potential field. This potential field may exert an effect on the orbital electrons and therefore coupling of spins and momenta occurs. Thus the enantiomers are parity transformed images not only as geometrical bodies, but their orbital electrons are parity transformed too as "a helical electron gas". Weak interactions will differentiate between L and D forms because their orbital electrons have a nonzero spin polarization with respect to their velocity.     

Chiral symmetry breaking in nonlinear autocatalytic reactions and the effect of external noise

A mathematical model based on difference equations is presented to show that minute chiral perturbations are sufficient for spontaneous breaking ofL, D symmetry in nonlinear autocatalytic reactions. The effect of noise on rate constants is analysed and it was noted that, below a critical noise level, the influence of the chiral perturbation results selection of the biased isomer with certainty.Sumanasekara Chair in Natural Sciences.     

Spontaneous chiral symmetry breaking in early molecular networks

Background  

An important facet of early biological evolution is the selection of chiral enantiomers for molecules such as amino acids and sugars. The origin of this symmetry breaking is a long-standing question in molecular evolution. Previous models addressing this question include particular kinetic properties such as autocatalysis or negative cross catalysis.     

Universal dissymmetry and the origin of biomolecular chirality

Handed systems are distributed over four general domains. These span the fundamental particles, the molecular enantiomers, the crystal enantiomorphs, and the spiral galaxies. The characterisation of the molecular enantiomers followed from the identification of the crystal enantiomorphs and revealed a chiral homogeneity in the biomolecules of the organic world. The origin of the homogeneity has been variously ascribed to a universal dissymmetric force, from Pasteur, or to a chance choice of the initial enantiomer perpetuated by the stereoselection of diastereomer production with recycling, from Fischer's "key and lock" hypothesis. The classical chiral fields identified by Curie require a particular time or location on the Earth's surface for a determinate molecular enantioselection, as do the weak charged current agencies of the non-classical weak interaction. The weak neutral current of the electroweak interaction provides a constant and uniform chiral agency which favours both the L-series of amino acids and polypeptides and the parent aldotriose of the D-series of sugars. The enantiomeric bias of the electroweak interaction is small at the molecular level: it may become significant either as a trigger-perturbation guiding the transition from a metastable autocatalytic racemic process to one of the two constituent enantiomeric reaction channels, or by cumulative amplification in a large chirally-homogeneous aggregate of enantiomer units.     

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.

     

Cytoskeletal symmetry breaking in animal cells

Symmetry breaking is a crucial step in structure formation and function of all cells, necessary for cell movement, cell division, and polarity establishment. Although the mechanisms of symmetry breaking are diverse, they often share common characteristics. Here we review examples of nematic, polar, and chiral cytoskeletal symmetry breaking in animal cells, and analogous processes in simplified reconstituted systems. We discuss the origins of symmetry breaking, which can arise spontaneously, or involve amplification of a pre-existing external or internal bias to the whole cell level. The underlying mechanisms often involve both chemical and mechanical processes that cooperate to break symmetry in a robust manner, and typically depend on the shape, size, or properties of the cell’s boundary.     

Morphological and chiral symmetry breaking in reaction-diffusion systems

Morphological and chiral symmetry breaking in reaction-diffusion systems is considered on the basis of the theory of imperfect codimension-two bifurcations. A new type of pattern selection with two triggers is elucidated: (1) morphologically asymmetric structures displaying optical activity can probably be originated from initially racemic and homogeneous conditions when chiral interaction, having the characteristic strength delta (such as electroweak interaction and circularly polarized light) as well as external field, having the characteristic strength eta (such as gravitational field and electrostatic field) are considered; (2) the selective sensitivity of molecular chirality and morphological asymmetry is omicron(delta 1/3) and omicron(eta 1/3), respectively; the sensitivity of mode-mode interaction between chiral polarization and concentration vector is omicron(delta 2/3) or omicron(eta 2/3), respectively. The relation of these conclusions to the life problem is discussed briefly.     

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.     

Generation of molecular chiral asymmetry through stirred crystallization

In our earlier work we established that stirred crystallization of achiral compounds that crystallize in enantiomeric forms result in spontaneous chiral symmetry breaking. The asymmetry thus spontaneously generated is confined to the solid state. In this article, we present a case in which the crystal enantiomeric excess (CEE) can be converted to molecular enantiomeric excess (EE) through a solid state reaction which relates the enantiomeric form of the crystal to the enantiomeric form of the product. Such a process not only provides a means of detecting the CEE generated in stirred crystallization but it is also a means through which chiral asymmetry generated spontaneously is "propagated" to generate chiral compounds with enantiomeric excess.     

Role of latent heat in chiral symmetry breaking transition in the crystallization of 1,1'-binaphthyl

The influence of latent heat dissipated by the crystallization of 1,1'-binaphthyl in its supercooled molten state on the chiral symmetry breaking transition was investigated. Temperature change in the crystallization system was monitored by infrared thermocamera. Temperature rise due to the dissipation of latent heat in the growing front of polycrystalline aggregate was about 2 degrees C in an unstirred crystallization system. The melting point of racemic mixture and racemic compound of 1,1'-binaphthyl is 145 degrees C and 158 degrees C, respectively. The latent heat generated by the crystallization could thus change the crystallization behavior when the initial temperature of the melt was slightly lower than 145 degrees C. The temperature change in both unstirred and stirred crystallization systems was monitored. In the stirred crystallization system, even in the case when the initial temperature of the melt was about 2 degrees C lower than 145 degrees C, the temperature rose by about 4 degrees C immediately after the onset of crystallization. This indicates that the role of stirring as the critical parameter for the chiral symmetry breaking transition is not only to clone the chiral crystals but also to enhance the dissipation of latent heat due to secondary nucleation.     

Intramolecular Enantiomerism in S(+)2,2‐dimethyl ‐1,3‐dioxolane‐4‐methanol: The Interpretation of Raman Optical Activity Intensity

A bond polarizability algorithm was developed and applied to interpret the Raman optical activity (ROA) intensity. It is demonstrated that for the chiral molecule such as S(+)2,2‐dimethyl‐1,3‐dioxolane‐4‐methanol there exists approximate (or symmetry breaking) mirror reflection that reverses the signs of the differential bond polarizabilities of the pair bond coordinates that are related to each other by the mirror reflection, just like that between the right and left enantiomers. The magnitude difference of the differential bond polarizabilities of the pair bond coordinates becomes smaller as they are farther away from the asymmetric atom. Hence, that the asymmetric atom (center) plays a central role in ROA is confirmed from a spectroscopic viewpoint. Meanwhile, the concept of intramolecular enantiomerism is proposed. Chirality 27:820–825, 2015. © 2015 Wiley Periodicals, Inc.     

Dissipative structures and amplification of enantiomeric excess (an experimental point of view)

Various mathematical models have been proposed to account for the origin of chiral molecules in biological systems. Most of these models invoke non-linear phenomena, and are based on the general concept of dissipative structures. These theoretical models define the fundamental criteria which must be obeyed by the experimental systems that we have investigated. Our initial approach to this problem was an extensive search of the literature data in order to select a few systems or experimental situations which would satisfy the criteria defined by the theoretical models. For these reasons, we carried out a study of the possibility of stereospecific autocatalysis in the asymmetric polymerisation of benzofuran. Similarly, the formation of spatial dissipative structures by coupling of a transport process with an interfacial reaction was investigated as a simple experimental example of symmetry breaking.