Chirality fluctuations

Interestingly, it has also been proposed that chiral fluctuations are responsible for the anomalous normal-state properties of the metallic cuprates (Wen et al. 1989, Y. Chen et al, 1989, Nagaosa and Lee 1990, 1991) in particular, Nagaosa and Lee (1991) predicted the... 

Phase transitions frcnn chiral nonatics to chiral smectics, or to blue or evm to isotropic phases can be connected to chirality-induced pretransMonal effects which often exist at more than lOX above or below the transition tempoature. Thus measuremrats of ORD have bera performed, where an enormous enhancemrat of the rotation [37] has been found. This effect can be related [38] to chiral fluctuations within the phase. The handedness of the effect induced is determined by the sign of (n Vxn), the term which introduces the chiral interaction in continuum theory. 

Because the time scale of the Raman scattering event ( 3.3 x 10-14s for a vibration with wavenumber shift 1000 cm-1 excited in the visible) is much shorter than that of the fastest conformational fluctuations in biomolecules, the ROA spectrum is a superposition of snapshot spectra from all the distinct chiral conformers present in the sample. Together with the dependence of ROA on chirality, this leads to an enhanced sensitivity to the dynamic aspects of biomolecular structure. The two-group model provides a qualitative explanation since it predicts ROA intensities that depend on absolute chirality in the form of a sin x dependence... 

Another attempt to explain the homochirality of biomolecules is based on autocatalysis. The great advantage of asymmetric catalysis is that the catalyst and the chiral product are identical and thus do not need to be separated (Buschmann et al., 2000). The racemic mixture must have been affected by a weak perturbation in order that autocatalysis, which acts as an amplifier of enantioselectivity, could have led to only one of the two enantiomeric forms. This perturbation could have been due to the slight energy difference of the enantiomers referred to above, or to statistical fluctuations. 

Thus, the model predicts that thermal fluctuations in the tilt and curvature change the way that the tubule radius scales with chiral elastic constant— instead of r oc (THp) 1, the scaling has an anomalous, temperature-dependent exponent. This anomalous exponent might be detectable in the scaling of tubule radius as a function of enantiomeric excess in a mixture of enantiomers or as a function of chiral fraction in a chiral-achiral mixture. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

The circumstances producing an e.e. on the early Earth could well have been capture and amplification of one of the fluctuational mechanisms outlined above, although present evidence favors the meteoric infall of chiral molecules synthesized in interstellar dust douds. The total flux of organics on the early Earth, delivered to Earth both by way of comets and other bolides, and synthesized by terrestrial mechanisms... 

The continuous availability of trillions of independent microreactors greatly multiplied the initial mixture of extraterrestrial organics and hydrothermal vent-produced chemicals into a rich variety of adsorbed and transformed materials, including lipids, amphiphiles, chiral metal complexes, amino add polymers, and nudeo-tide bases. Production and chiral amplification of polypeptides and other polymeric molecules would be induced by exposure of absorbed amino adds and organics to dehydration/rehydration cydes promoted by heat-flows beneath a sea-level hydro-thermal field or by sporadic subaerial exposure of near-shore vents and surfaces. In this environment the e.e. of chiral amino adds could have provided the ligands required for any metal centers capable of catalyzing enantiomeric dominance. The auto-amplification of a small e.e. of i-amino adds, whether extraterrestrially delivered or fluctuationally induced, thus becomes conceptually reasonable. 

In the absence of any chiral factors, the probability of the formation of S- and 77-enantiomers is 1 to 1. However, the numbers of the resulting two enantiomers are not exactly the same in almost all cases. Mislow197 described the inevitability of small enantiomeric enrichment in absolute asymmetric synthesis. According to the statistics, it is expected that a fluctuation in the ratio of the S- and 77-enantiomers becomes more and more likely as the numbers in the enantiomer mixture become smaller198. Thus, if the asymmetric autocatalysis is initiated without adding any chiral substance, small fluctuations of enantiomers produced in the initial stage could be enhanced by consecutive asymmetric autocatalytic reaction of pyrimidyl alkanol with amplification of chirality. 

Small fluctuations in the ratio of the two enantiomers are considered to be present in racemic mixtures of chiral molecules [14,101]. We thought that, when a reaction system involves asymmetric autocatalysis with amplification of ee, the initial small fluctuation of ee in racemic mixtures that arises from the reaction of achiral reactants can produce an enantiomerically enriched product. We anticipated that when z-P Zn was treated with pyrimidine-5-carbaldehydes without adding any chiral substance, extremely slight enan-tioenrichment would be induced statistically in the initially formed zinc alkoxide of the alkanol, and that the subsequent amplification of chirality by asymmetric autocatalysis would produce the pyrimidyl alkanol with detectable enantioenrichment (Scheme 19). 

Fluctuations are inherent to any experimental chemical system. Even if these fluctuations are infinitesimally small, they are sufficient to drive the system away from an unstable state. The optically active state is characterized by two equivalent options starting from an unstable racemic situation, the system can evolve into either an R configuration or into an S one. However, each individual experiment remains unpredictable as to which of the optically active states the system will move towards. For a large number of experiments an equal and random distribution between R and S dominance is expected if the initial conditions do not involve any preferences. Due to this unpredictability of the chiral configuration, the phenomenon of mirror-symmetry breaking introduces another element of stochastic behavior into chemical reactions different from that occurring in clock reactions [38,39]. 

Such spontaneous generation of chiral asymmetry must be distinguished from occasional large fluctuations in the ee that can be also observed in asymmetric reactions. These processes generally correspond to a Gaussian distribution of the ee around zero, while symmetry breaking results in a bi-modal probability distribution around the two optically active situations, and basically no racemic result is observed. 

During classical asymmetric synthesis, the amplitude of these fluctuations are expected to decrease during the course of the reaction because more and more chiral molecules are formed and eeeXp declines. However, in the presence of chiral autocatalysis, the small ee caused by such fluctuations can be amplified. In such cases, the system is likely to be most sensitive in the initial stage of reaction when the concentration of chiral molecules is still small. If the autocatalytic species are concentrated they can be either in a racemic or optically active state but if they are highly diluted, as at the beginning of the reaction, statistical fluctuations can become significant so that the state... 

Of course, the probability is small that at any instant, the enantiomeric mixture at equilibrium is exactly equimolar the absence of observable chirality phenomena, such as optical activity, is the result of rapid cancelations of random statistical fluctuations of activity in the time domain of observation. In other words, although, at any instant, the mixture (with a high degree of probability) has an excess of one enantiomer or the other, under measurement conditions, it effectively contains an equal number of enantiomeric molecules. When 10,000,000 dissymmetric [i.e., chiral] molecules are produced under conditions which favor neither enantiomorph, there is an even chance that the product will contain an excess of more than 0.021 % of one enantiomorph or the other. It is practically impossible for the product to be absolutely optically inactive [12],... 

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