Сhiral and Racemic Fields Concept for Understanding of the Homochirality Origin, Asymmetric Catalysis, Chiral Superstructure Formation from Achiral Molecules, and B-Z DNA Conformational Transition

The four most important and well-studied phenomena of mirror symmetry breaking of molecules were analyzed for the first time in terms of available common features and regularities. Mirror symmetry breaking of the primary origin of biological homochirality requires the involvement of an external chiral inductor (environmental chirality). All reviewed mirror symmetry breaking phenomena were considered from that standpoint. A concept of chiral and racemic fields was highly helpful in this analysis. A chiral gravitational field in combination with a static magnetic field (Earth’s environmental conditions) may be regarded as a hypothetical long-term chiral inductor. Experimental evidences suggest a possible effect of the environmental chiral inductor as a chiral trigger on the mirror symmetry breaking effect. Also, this effect explains a conformational transition of the right-handed double DNA helix to the left-handed double DNA helix (B-Z DNA transition) as possible DNA damage.


Introduction
Curie [1] was convinced that "without asymmetric physical impact no asymmetric chemical effect arises". Modern experimental data support this criterion: asymmetric induction in asymmetric catalysis is only implemented through the asymmetric (C1 symmetry axis) key intermediate [2].
If a substrate has two or three functional groups which can be coordinated in that intermediate, A reason for this choice has not received a generally recognized explanation up to now [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These references indicate a variety of scenarios for the emergence of homochirality and therefore origin of life [16]. Various scenarios are explained by external and internal reasons existing on the primary Earth. Possible scenarios of homochirality origin include Earth and exoterrestrial origins, mirror-symmetrical and non-mirror symmetrical forces, different ampllification mechanisms leading to L-or D-amino acids and sugars, and L-amino acids excess during meteorite impact.
We believe [3,4] that a possible basis for such a ratio of configurations is the right-handed helix (P) conformation of important biomacromolecules formed from amino acids and monosaccharides. (Scheme 1). The L-D ratio of amino acid and sugar monomer configurations may merely occur where there is a right-handed helix conformation. Mutual relations of single, double and triple right-handed (P) helixes are also not accidental. The single helix (α-polypeptide) protects amino acids from racemization by hydrogen bonds between helical turns.
Thus, it is not by chance that nature has chosen the double helix structure to stabilize the righthanded conformation of DNA. In this case, the configuration error reducing factor is also important [27]. There is directionality to a right-handed helix in triple helical structures such as in fungi, mushrooms, and so on. For example, the simplest β-(1→3)-D-glucans, namely curdlan [27], lentinan [30], scleroglucan [31], xylan [32], etc., with side chains [33-38] form triple P-helices with the righthanded helical conformation. Hence, there is a triad pronounced in Scheme 1. That is why right-handed helix structures of important biomacromolecules are representatives of the regular trend in nature.
Since all natural processes occur in the open system, in previous work [39], we attemted to assess the external chiral effect on the homochirality origin on the early Earth. A possible influence of an external asymmetric inductor was analyzed for metastable (stochastic and spontaneous) reactions [39]. In this review, we continue the search for traces of the external chiral inductor, such as the chiral gravitational field, in the most studied reactions with mirror symmetry breaking. Davankov [40] suggested chirality to be an indispensable feature of different levels of matter. While evolving this idea, we [39] considered a possibility of chiral effects of various physical phenomena on chemical reactions (electric field [41], electric field (propeller effect) [42], a combination of electric and magnetic fields [4,43], magnetic field [4,39,44], circularly polarized light [45], plasma torch of meteorite impact [46,47], solar irradiation [48,49], parity violation energy difference [29], and similar effects [39]). Gravity is among such physical phenomena as asymmetric factors [39]. Basing on Barron's concept [50] of true and false chirality, we can assume that the mutual gravitational influence of a space object and its satellites is a chiral factor. In the schematic diagram ( Figure 2), we tried to summarize information on mutual gravitational impact (moving in space) of Sun, Earth, Moon, and Venus. Their mutual movements create a combination of trajectories in the form of virtual chiral helices. The image below gives a view of the chiral gravitational environment that is probably strictly individual for Earth (The Earth-Moon (ratio of masses 81/1) is a double planet system unlike other planets and satellites of the Solar system, for example, Jupiter-Europe (4·10 4 /1), Mars-Phobos (6·10 7 /1), and so on). A hypothesis about the formal similarity and possible effect of the Earth's right-handed (spin) rotation near the Moon, alongside with the right-handed Earth's orbital motion around moving Sun and right-handed helix symmetry of biomacromolecules, was published earlier [3,29,39,51]. Perhaps, all spiral movments shown in Figure 2 should be considered as a manifestation of the unified structure of the gravitational field of our Galaxy. The Milky Way Galaxy is a double snail of flat structure (Figure 3a,b) [52][53][54][55]. A symmetry plane virtually divides the Galaxy into a mirror symmetric left-handed snail -"bottom" (Figure 4c), and a right-handed snail -"top" (Figure 3d). Hence, the Milky Way may be presented as a mesostructure (an inner racemate).  In terms of symmetry, the Galaxy bears a similarity to inner racemate (for example, mesotartaric acid. It is conceivable that this mesostructure is confirmed by the anomalous rotation (counterclockwise) of Venus in the Solar system. This movement does not contradict with the complexity of the Galaxy structure. Indeed, the mirror symmetry plane divides "clockwise" and "counterclockwise" fields (Mirror reflection effect or a positive-negative photoeffect.) of the galactic space (P-and M-snails). Because the Solar system spins and moves along the right-handed trajectory [52][53][54][55] (Figure 4) in the P-snail field, Earth and other planets move identically (clockwise) with the exception of Venus.

Gravity as a Chirality Inductor
An example of the chiral environment's (chiral gravitational field?) influence is found in configurational stability (mirror symmetry breaking) of sea snail shells [56,57] (Figure 5). All collectors of sea shells (conchiologists) evidence that the opposite left-handed structure is an extreme rarity [58].
How does gravity affect symmetry of molecules? In contrast to the influence of the electromagnetic field [59], the effect of gravity on chemical reactions is difficult to verify experimentally. It was previously believed that this effect was absent or very insignificant. Another point of view appeared possible with the beginning of the space flight era.

Gravitational Field Impact on Chemical Reactions
Analyzing an open system, we have to evaluate all possible physical inductors which may affect the system. Among the non-obvious physical factors that may affect chemical reactions is gravity. After the discovery of gravitational waves (Gravitational waves discovery (Abbott B.P. et. al. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett., 2016. 116. 061102) suggests the complex structure of the gravitational field.) the influence of this factor, especially in unstable asymmetric reactions, became more obvious. A nuclear decay has a reputation of a stable process that does not depend on external physical inductors. If an external inductor such as a gravitational field can alter the radioactive decay rate it is bound to affect the nucleus mass. Therefore, if such effect occurs, this phenomenon may be called a "mass resonator" or "mass resonance". Fischbach et al. [60][61][62] analyzed a 137 Cs decay sample onboard the Messenger spacecraft during its mission to Mercury and 54 Mn decay data during the solar flare on December 13 2006. The goal was to show the limits of a possible correlation between nuclear decay rates and solar activity. Such correlation was suggested not only on the basis of the 54 Mn decay during the solar flare but also by indications of annual and other periodic variations in the decay rates of 32 Si, 36 Cl and 226 Ra. Data from five measurements of the 137 Cs count rate over a period of approximately 5.4 years was fit to a formula which accounts for a typical exponential decrease in the count rate over time, alongside with the addition of a theoretical solar contribution varying with the Messinger -Sun distance [61]. These controversial data on nonexponential periodic decay rates drew attention and gave rise to discussion [63][64][65].
Ivanova et al. [48] observed North-South solar asymmetry and anisotropy of cosmic rays over solar polar caps. The measurements were taken onboard the Kosmos-480 satellite on April 18 1972 over a 10-h period. In particular, the flow above the south pole was an order of magnitude higher than that above the north pole. Svirzhevsky et al. [49] examined N-S solar poles asymmetry relative to the solar wind speed, plasma density, and some other solar parameters. Asymmetry between the north and south solar fields was observed in the plasma density, solar radio flux, and geomagnetic indices [66]. Consequently, N-S solar asymmetry (Figure 3a) is an additional chirality trigger alongside with chirality of the right-handed helix orbital trajectory of Earth revolving around Sun ( Figure 3c). Indeed, N-S solar asymmetric poles during the Sun's movement form a virtual double right-handed helix (Figure 3a]. Gravitation field asymmetry throughout the entire life time of the Solar system can culminate in the chiral biomacromolecules origin as well as in biological objects ( Figure 6). Nevertheless, the question of the noticeable effect of asymmetric gravity on symmetry of molecules remains unanswered. However, asymmetric gravity could affect metastable chiral reactions if assume the gravitational field affects the radioactive decay.

Stirring (Helical Flux) of the Reaction Mass as a Chirality Trigger
The formation of a conglomerate (50/50% l-and d-crystals) during crystallization of NaClO3 from a saturated aqueous solution proceeds over a short time interval. However, stirring of the NaClO3 solution (for appreciable time) leads to mirror symmetry breaking (Scheme 2). The enantiomeric direction of crystallization during stirring was ascribed to the primary crystal as a crystallization germ ('secondary' crystal nuclei) [67,68] Similar enantiomeric and racemic conglomerate crystallization was observed in stirred and unstirred 1,1´-binaphthyl melts [69,70]. The enantiomeric excess (ee up to 80%) in each stirred crystallization test varied randomly as well.
Stirring of l-and d-crystals mixture of NaClO3 (50/50%) with glass beads led to 100% l-or dcrystals, randomly, whereas stirring without glass beads left the mixture unchanged [71] (Figure 7a,c). It is interesting to note that the "stirring time to achieve 100% ee depends on the number of glass beads and the stirring rate" [72]. In attempt to explain NaClO3 crystallization data, Kondepudi et al. [66][67][68][69][70]73,74] and other researchers [75][76][77][78] attached importance to the experimental fact of stirring. To explain enantioselectivity of NaClO3 l-and d-crystals stirring with and without glass beads ( Figure  6a,c) many researchers [71,[79][80][81][82][83][84][85][86][87] argued that attrition/grinding was the key factor. There are data that argue against the role of stirring. In boiling solutions of the racemic mixture of NaClO3 crystals, stirring (without abrasion) did not bring mirror symmetry breaking [88] ( Figure  6b). However, the temperature gradient (120°C lower layer-106 C upper layer of colution in the reaction vessel) [88] led to the formation of spiral flows in the boiling solution ( Figure 6d) (shown by the snail-shaped arrows). These flows could appear destroyed while stirring, which is why the enantioenrichment did not occur (Figure 6b).
Even more obvious evidence of the effect of temperature flows of the reaction mixture on enantioselectivity is sublimation. For example, valine, racemic amino acid, was converted via sublimation into a conglomerate [89]. During continued heating, the crystals underwent substantial chirality amplification (increase of initial ee). This phenomenon occurred both in the closed and in the open system [89]. The authors observed the appearance of three sublimation regions depending on their location in the form of rings on the conical flask walls. The most enantioselective region corresponded to the enantioenrichment of the valine sublimate with ee 80% (the closed system) and ee 70% (the open system). In our opinion, the intervention of the external chiral inductor in this experiment is reasonably evident.
We believe that the rotation of the flow energy (stirring) or temperature convectional flow of the helical structure can be a reason for the emergence of enantioselectivity. This scenario can also be triggered by an external chiral field.
The possible existence of this field is evidenced by statistical experiments while studying the Viedma ripening procedure (VRP). Viedma [90] discarded any explanation of VRP by the parity violation energy difference (PVED) effect (Table 2). The experiments were performed with racemic mixtures obtained spontaneously from the same solutions and in the same competing conditions between l-and d-crystals" ("natural" or true population) [90]. Those data support Viedma's opinion that the handedness of chiral crystals remaining in the solution ( Table 2) is not random. As seen from Table 2, there is a predominance of l-crystals (in some cases up to 99.5%), alongside with a few exceptions (l-crystals 49% and 44.5%). Thus, there is quite a definite trend expressed in the predominant formation of l-crystals. According to Viedma [90] these experimental results may be explained by the "cryptochiral environment in control".
To our knowledge, a thorough statistical analysis of changes in left-handed or right-handed chirality of reaction products, depending on the direction of reaction mixture stirring (clockwise or counterclockwise), has not been undertaken (there is an opinion that the stirring direction is not important in VRP expirements [76]). In addition, the nature and origin of this cryptochiral environment's effect have not been discussed [81][82][83][84][85][86][87][88][89]91]. About the same statistical likelihood of random (stochastic) signs of chirality is observed even with the same rotation direction (also, stochastic distribution of the enantiomer outcome was observed in crystallization under cooling [92]).
NaClO3 crystallization and similar dissolution-crystallizations are metastable processes [93,94]. Therefore, even a small energy of the spiral flow during mixing can affect chirality as an inductor or trigger. It explains well the influence of product enantiopurity on the number of glass beads and the stirring rate [72]. It resembles a search of resonance such as the action of the ultrasonic radiation field (20 KHz) on enantiopurity of the product during threonine crystallization (5(D)→70-87(D)%ee) [95].
Indeed, Figure 7 shows that the maximal enantioenrichment of NaClO3 crystallization occurs in the time corridor of 20-24 h of stirring at a speed of 600 rpm (rotation per minute) and with 4 g of glass balls (data from Reference [72]). This result is likely to be a reflection of a search of resonance with some external chiral inductor. The shaded area in this figure is the possible resonance region. Moreover, chiral enrichment vectors are the same in time but are manifested as stochastically (random) reactions, while enantioselectivity vectors are not the same for different enantiomers ( Figure 8).
The results given in Table 2 also testify to the vector of predominant "natural" enantioselectivity. A striking case of a literally "mechanistic" embodiment of stirring in the chiral effect can be demonstrated by the example of antracene polymerization into a chiral nanofiber structure ( Figure 9) [96].  An average diameter of the rotational helix flux of the reaction solution as a result of stirring and the supermolecular polyantracene helix cannot be directrly interdependent because of the incompatibility of helix sizes (the ratio of the diameter of the helices is ~5·10 9 -1 nm). Therefore, chirality of the reaction product could appear apparently only due to an external chiral inductor as a resonator or the rotation flux of the reaction mixture as a trigger.
Low temperature can also be a stabilization factor of chirality. Mirror symmetry breaking occurred upon low temperature spontaneous crystallization of achiral macrocyclic imines [97]. An absolute asymmetric synthesis was also carried out with a chiral reagent from chiral crystals with axial chirality [98]. Crystalline 1 was melted at 120°C and then gradually solidified by lowering the temperature to 110°C with vigorous stirring. Reactions (1) and (2) proceeded as 'frozen chirality' [98] at a low temperature ("frozen chirality") [92]. Low temperature monitoring data for the reaction (2) are given in Table 3. There are other examples of axially chiral reagents with "frozen chirality" at a low temperature [99]. Crystallization of racemic axially chiral pyrimidinethione led to the chiral product with up to 91% ee at a high temperature only [100].
Strong temperature stabilization of axial chirality suggests the existence of a chirality resonator. A similar assumption can be made in analyzing a dependence of the helicity sign from temperature. The helicity dependence from temperature was vividly exemplified by experimenting with poly {(S)-3,7-dimethyloctyl-3-methylbutulsilylene} 3 [101] (Scheme 3). Also, a similar P↔M transition was observed for other polysilylenes and analogous polymers at different temperatures, with various solvents and varying other reaction conditions [102][103][104][105][106][107].
Reactions (3) and (4) resulted in helical products with different signs. When analyzing the differences in the energy of these product conformations, it was shown that small amount of energy (~1/600 of the ambient energy) is only distinguished P-and M-helices in these deuterated polyisocyanates [108][109][110][111]. Therefore, it is quite possible that even a weak external inductor may be capable of affecting the chiral conformation of helical nanostructures. This assumption should be verified with special care, for example, in the case of the P↔M conversion of DNA (see Section 8).
A possible existence of the chiral environmental inductor is also evidenced by asymmetric reactions of achiral molecules adsorbed on the surface of metals [112][113][114][115]. Ernst rightly noted that product's chirality depends not only on the surface structure but also on the molecules orientation ( Figure 10) [116]. Chirality in this case can occur, apart from under the action of the chiral surface structure, under the impact of the adsorbing molecule orientation. The environmental chiral inductor in turn can contribute to this chiral orientation. Problematical chirality of metal surfaces suggests that the chiral orientation is the main factor that provides enantioselectivity of the reaction of adsorbed achiral molecules.

Chiral and Racemic Field in Asymmetric Catalysis and Nonlinear Effects
Racemic compounds can also exist in solution, e.g., in ongoing reactions. The formation of racemic intermediates of a reaction is observed in catalytic asymmetric reactions. The use of nonenantiopure chiral auxiliaries as asymmetric catalysts sometimes causes a deviation from the proportional linearity to ee of a catalytic reaction product (nonlinear effect NLE) in asymmetric catalysis [117] (Figure 11). Scheme 4 shows two models for explaining nonlinear еffects: Kagan's and Noyori's models [118]. According to both models racemates and homochiral dimers function as real actors of the reaction mechanism. However, both schemes do not take into account the specifics of the reaction and substrate to predict the NLE occurance.   A racemic (heterochiral) complex was formffed where X = SMe3 or t-Bu (Scheme 6). The use of fenchols with X = H and X = CH3 in the reaction (5) resulted in (-)-NLE while fenchols with X = SMe3 and X-t-Bu catalyzed this reaction with a linear relationship. Thus, the emergence or absence of (-)-NLE in the reaction (5) depends only on the structure of ligands. Therefore, in this case, the (-)-NLE emergence is formally defined by Kagan-Noyori models.
Chen et al. [120] discovered a substrate dependence of the nonlinear effect in diethylzinc addition to aromatic aldehydes over chiral auxiliary 5.
Reactions with electron-donating substituents on the aromatic ring of aldehyde exhibited a greater (+)-NLE than those with electron-withdrawing substituents. These data contradict with the Noyori-Kagan models. The observed substrate dependence can be explained by a reaction of aldehydes with diastereomeric homo-and hetero-chiral dimers of 6 via different pathways.
Several BINOLate-titanium complexes (e.g., 7 -reaction (7)) were synthesized at a low temperature and characterized by crystallography X-ray crystallography. It was shown that (-)-NLE was only observed in stoichiometric experiments ( Figure 12). Catalytic experiments replicated the proportional linearity of the ee product and the ee catalyst [122].  Catalytic reactions were run with 20 mol% of (BINOLate)Ti(O-i-Pr)2 and 80 mol% of titanium tetraisopropoxide. The stoichiometric reaction were performed using 100 mol% of (BINOLate)Ti(O-i-Pr)2.
Such a difference between the stoichiometric and catalytic experiments is true if homochiral dimers catalyze the reaction path to enantiomerically pure products (no NLE). The stoichiometric reaction results in non-enantiomerically pure products. Given the observed difference the NLE formation mechanism remains unclear. The heterochiral dimer was shown to be significantly more stable than homochiral dimers [123]. It is safe to assume that the concentration of homochiral dimers is higher in the stochiometric experiments than in the catalytic ones. On the basis of this ratio, we may hypothesize a more pronounced role of homochiral dimers (C2-symmetrical) in the occurance of (-)-NLE during the stochiometric experiments.
The assumption about the leading role of C2 -symmetric homochiral dimers in the appearance of (-)-NLE gained experimental justification in other reactions. For example, pronounced (-)-NLE was observed in Friedel-Crafts alkylation of pyrrole with chalcones (8) catalyzed by C2-symmetric chiral dinuclear zinc catalyst 8 [124] and in the hetero-Diels-Alder reaction of Danishefsky's diene and aromatic aldehydes (9) over BINOLate-Zn complex 9 [125]. Thus, the deviation from the linearity in favor of the racemic product ((-)-NLE) occurs in case aromatic substrates in reactions catalyzed by homochiral C2-symmetric dimeres in situ formed from dialkylzinc. This observation resembles catalytic reactions of aromatic substrates under the action of C2-symmetric chiral catalysts that occur with anomalous low ee, i.e., an almost racemic product. Addition of diethylzinc to trifluoromethyl ketones (aromatic) over С2-symmetric chiral auxiliaries (10) pertains to such reactions (Table 4) [126].  It can be seen that all complexes with C2-symmetric ligands in the reaction (10) lead to racematelike products.
Addition of diethylzinc to aromatic aldehydes (11) in the presence of chiral auxiliaries manifests other interesting features: differences in enantioselectivity of C2and C1-symmetric chiral auxiliaries of similar structures are sometimes greater than an order of magnitude (Table 5).
The catalytic cycle of this reaction in the presence of asymmetric (C1) ligands 16-18 was suggested on the basis of a calorimetric study of kinetics [133]. The decrease in enantioselectivity in the reaction (11) over C2-symmetric chiral auxiliaries can be explained on the grounds of a similar catalytic cycle (Scheme 7) [134].  (11), in accordance with the mechanism, can proceed with the formation of a product of low optical purity, in accordance to the experiment.
The deviation from the linearity to a racemic product ((-)-NLE) was observed not only in the reactions of dialkylzinc addition to aromatic substrates catalyzed by homochiral dimers on the basis of zinc. Remarkable (-)-NLEs were observed in reactions (12) and (13) Thus, all reactions with (-)-NLE occur on the basis of aromatic substrates under the action of C2symmetric chiral complexes. A similar effect was mentioned above for the reactions over in situ formed catalysts with the dialkylzinc participation. The deviation from the linearity with the formation of the low ee product in asymmetric catalytic reactions occurs where there is an abnormally low ee product in the presence of C2-symmetric chiral complexes as compared to C1 complexes of similar structure [2].
Noticeable distinctions between enantioselectivities of identical catalysts with ligands having a similar structure but different symmetry (C2-21,26,27 and C1-28) were observed in reactions (14) and (15) (14) and (15)  Thus, simple aromatic substrates (acetophenone, etc.) exhibit similar behavior with respect to C2 or C2 inductor (catalysts). These monofunctional substrates which coordinate with a catalyst by the reacting group (single-point coordination) only receive stereospecific information directly from the asymmetric catalyst. A racemic field formed by the π → π * coordination of aromatic substrates (Scheme 7) can induce a decrease in enantioselectivity. A stage of intermediate complexing with C2symmetric ligand may be responsible for the product ee reduction. This mechanism, perhaps, is similar to the mechanism of the (-)-NLE occurrence established for aromatic substrates.
Since asymmetric induction occurs at the catalyst-substrate stage, symmetry of this intermediate determines enantioselectivity. If the substrate has two or three functional groups, the chiral C2symmetric catalyst loses C2 symmetry at the stage of coordination with such substrate. Indeed, hydrogenation of amino acid precursors on C2-symmetric chiral complexes (three-point coordination) involves the formation of the C1 (asymmetric) intermediate [2].
All asymmetric reactions on chiral metal complexes as catalysts support this concept [2]. The experimental data are entirely consistent with Curie-Pasteur's doctrine: only asymmetric factors are responsible for products with asymmetric carbon atoms [1].
A similar situation is observed in asymmetric reactions over chiral organocatalysts.   Figure 14 shows two possible favoured and two disfavoured intermediates which are different from the viewpoint of an approach of the reagents to C2 33 (a front or rear approach). Both favoured-1 and favoured-2 intermediates, alongside with those disfavoured-1 and disfavoured-2, are formed as a result of the reactants coordination with different side nitrogen atoms of C2-symmetrical 33. Therefore, they are similar in terms of the structure and symmetry of both 1 and 2 favoured or disfavoured 1 and 2 key intermediates (C2 symmetry of 33 and C1 symmetry of key intermediates).
Thus, all the above-mentioned reactions of asymmetric catalysis proceed by the standard scheme: asymmetric catalyst (an asymmetry inductor) -asymmetric product. C2 chiral catalysts (a C2 chiral metallocomplex and a C2 chiral organocatalyst) lose C2 symmetry of the key intermediate that determines asymmetric induction. Therefore, asymmetric catalytic reactions run in the asymmetric field and do not occur in the chiral field (asymmetry-(C1), chirality-(C1, C2, Cn, D2).

Spontaneous Chiral Ordering of Achiral Molecules in Liquid Crystals
A common feature of achiral molecules involved in chiral ordering is the ability to bind to each other due to π -π * staking, hydrogen bonds or hydrophobic interactions. Linked by those bonds, they shift relative to each other around the central axis on the right or left screw. This synchronization of achiral molecules in chiral superstructures occurs in smectic (lamellar) or nematic liquid crystal (LC) phases. Numerous studies [158][159][160][161][162][163][164][165] of these nanostructures with a "banana", "hat" or crown-like shape show that a ratio of layers with chiral superstructures of different signs in the LC phase is 50:50% or so. It is viewed in photomicrographs as chiral domains (dark/bright spots of equal areas) between slightly uncrossed polarizers. Therefore, the definition of such spontaneous crystallization of achiral molecules as "mirror symmetry breaking" [158][159][160][161][162][163][164][165] can only refer to one individual domain or monolayer with superstructures of similar chirality. Since the ratio of domains of different signs is close to racemic, this definition is not correct for crystallization of the entire mass of molecules.
Thus, the formation of chiral superstructures from achiral molecules in LC and distribution of these chiral structures of different signs in the LC matrix is strikingly similar to the formation of chiral crystals from achiral inorganic compounds/salt molecules (Section 4). For example, a similar pattern of the equal ratio (l/d = 1:1) of chiral inorganic crystals is observed in deposits of quartz [166][167][168][169] ( Figure 15) as well as in the formation of a conglomerate (a mixture of l-and d-crystals) during NaClO3 crystallization (Scheme 2). Powdering of natural chiral quartz crystals blends left-and right-handed domains [166][167][168][169]. Chiral surfaces of centric calcite (CaCO3,) were observed as well [170][171][172]. Asymmetric crystals of gypsum (CaSO4·2H2O) were also found [173] and used for asymmetric adsorption [174]. It is believed that natural processes of nucleation and growth of these crystals last for a very long time under the influence of the chiral environment.
Crystallization of achiral molecules in LC and crystallization of quartz and other minerals and salts (see Scheme 8) in nature are likely to proceed according to the laws same as of chirality occurrence. This regularity was also confirmed in the conditions of a standard organic reaction (19) (Figure 16) [175]. Achiral molecules crystallize in the LC matrix with an approximately equal area of domains of chiral superstructures with different chirality signs. It is difficult to measure the exact ratio of superstructures with different signs of chirality using a polarizing microscope technique (domains) or scanning electron microscopy (twisted ribbons). Therefore, the (1:1) ratio (a racemic mixture) can be assumed valid on the grounds of many publications [158][159][160][161][162][163][164][165].
Spontaneous formation of chiral nanostructures from achiral molecules in the LC matrix has a high inertia depending on heating or cooling to reach a certain temperature. For example, a paradoxal situation may arise when chiral domains of different chirality signs can be formed at the same temperature depending on its achievement by heating or cooling (Figures 17 and 18) [57,176].

43
Similar effects were observed in the ongoing formation of other chiral superstructures from achiral molecules [57,[177][178][179][180]. The dependence of chiral nanostructures from various mesophase temperatures of LC (maximal order) suggests that this regularity is of general nature. The temperature inertia of the formation of chiral superstructures is comparable with the time inertia of crystallization of calcite, gypsum or quartz in nature.
Mineo et al. [57] suggested that chiral superstructures on the basis of "achiral porphyrin-based molecules 42 can be induced and controlled by means of a weak asymmetric thermal gradient" or "asymmetric heat flow." It can be considered as evidence of "very weak forces having an important role in natural chiral selective processes" [57]. May it be regarded as a manifestation of resonance with the external chiral field?
Another feature of the reaction of the chiral superstructure formation from achiral molecules is a dependence of the conformation of P or M helical structures from irradiation of different energy. The ratio of P↔M enantiomeres was found to be reproducible depending on irradiation [158,162] ( Figure 19). If enantiomers are an energy equivalent, the ratio of enantiomers should be random and nonreproducible. The reproducibility of M→P ratio UV and the opposite P→M sequence after Vis irradiation ( Figure 19) could result from the action of the external chiral inductor as a chiral trigger.
Another strange feature of crystallization of achiral molecules in the LC phase was found during crystallization of pyridinum-tailored antracene 44 [181] in the presence of iodine and other pseudo-halogen anions with a similar anionic radius.

44
A specific role of the anionic radius to form chiral supromolecular assemblies from achiral molecule 44 testifies to the influence of the helix pitch size in the ongoing formation of a helix structure. An external chiral inductor may also be responsible for this experimental data. It is difficult to explain a similar sensitivity of the organic helical framework to the metallic core radius by internal reasons [182].
An extremely interesting effect was observed in a supamolecular self-assembly of achiral tetraphenylethylene 45 (Figures 20 and 21 Hence, 45 with the even number of carbon atoms in alkyl chains was produced by right-handed superstructures, whereas the odd number led to the left-handed supramolecular structure ( Figure 21). No physical rationale for this phenomenon has been discussed. We believe that a possible explanation for this effect may be the influence of an external chiral inductor as a resonator.   [148,164].  As can be seen, symmetry (C2, C4) of corresponding chiral superstructures coincides with symmetry of the underlying achiral molecules (46,45,48). Crown-shaped molecule 49 with 12 peripheral alkyl chains (C3) form single columns with 12-fold triple helices (C3) (Figure 25) [186,187]. Asymmetric molecule 47 (C1 symmetry axis) with the center of gravity in the side chain forms a helix from the linear sequence of these molecules (tail to head) with C1 symmetry (Figure 23).
Thus, the centers of gravity (symmetry) of achiral molecules and relevant chiral superstructures are similar. This coincidence could be possible evidence of the gravitational influence in the construction of chiral ensembles from achiral molecules.
Not necessarily organic compounds or salts solely participate in the formation of chiral superstructures. Singh et al. [188] observed that cubic nanocrystals (~13.4 nm) of magnetite Fe3O4 as dipoles self-assembled into arrays of helical superstructures. Fe3O4 dipoles are oriented along the applied magnetic field (H = 700g). The chains of single magnetite particles aggregated as the solvent evaporated ( Figure 26). Examples of self-assembly of one-dimensional Fe3O4 nanocube belts can be seen in Figure 27. The authors concluded that "there was no intrinsic preference for helices of either handedness; each experiment began with the nucleation of either right-or left-handed helices with equal probability". At the same time, chiral arrays during a single experiment retained the identical handedness. Double or triple helices were observed during some experiments (Figure 28a,b). Figure  28c,d also shows chirality inversion cases in some single experiments (denoted by arrows). Consequently, chirality was preserved during the experiments, except for some cases of partial inversion which reduced enantioselectivity. Whereas crystallization of chiral superstructures from achiral molecules in LC can be compared with NaClO3 crystallization without stirring (Scheme 2 top), chiral arrays of Fe3O4 nanoparticles in the magnetic field can be compared with NaClO3 crystallization with stirring (Scheme 2, bottom). Indeed, the images (Figures 27 and 28a) show domains with homochiral superstructures (single handedness). A comparison to NaClO3 crystallization with stirring implies a presence of a hypothetical chiral inductor. Hence, the magnetic field alone cannot be a chiral inductor in the formation of the chiral order of magnetite crystals. It is believed that a combination of the magnetic field only with another field [189] (electrical or gravitational) can be an asymmetric inductor.
A number of nanotubes were synthesized (BN, WS2, MoS2, NbSe2, NiCl2, SiO2, TiO2, MoO3, and V2O5) [189]. Celik-Aktas et al. [190] studing boron nitride nanotubes by transmission electron microscopy (TEM), observed "regular, zigzag, dark and bright spots on the side walls of the nanotubes." These spots moved in a regular fashion around the tube. Basing on this evidence, the authors [191,192] suggested a double-helix structural model (Figure 29) "as a result of a stronger wall-wall interaction associated with the ionic bonding in boron nitride". However, stabilization of the righthanded helix structure (Figure 29) is opposite to that of the left-handed. It is possible that the preference of right-handed helix symmetry can be explained as the result of an external chiral inductor (chiral environment).  [191][192][193].
The sharp turning point of the BN nanotube at an angle of about 30-40° ( Figure 29) [190][191][192][193] is extremely similar to the inversion point of the chirality sign of the magnetite nanocrystals selfassembly (Figure 28c,d). Therefore, it can be assumed that this BN point is the turning point of the transition of the right-handed helix to the left-handed one (or the contrary).

Chiral Field (Chiral Memory) and Racemic Field
An example of the chiral field existence can be an enantioselective reaction (21) of prochiral substrate hydrogenation on an achiral catalyst in the cholesteric liquid crystal (ChLC) [189]. ChLC + H 2 (21) The temperature maximum of hydrogenation enantioselectivity (ee = 16% at 60-70 C) coincides with the temperature maximum of ChLC (cholesteryl tridecanoate) helical ordering. Mirror symmetry breaking in this case is contrary to common sense. Indeed, molecule sizes of α-acetamidocinnamic acid and the RhCl(PPh3)3 catalyst are much smaller than the ChLC helical pitch (300-400 nm). Therefore, asymmetric induction at the stage of coordination of substrate and catalyst molecules cannot only occur under the influence of ChLC helical chirality. A possible explanation of mirror symmetry breaking in this experiment is the effect of the chiral field on individual molecules of the substrate and catalyst [194,195]. Indeed, it was shown by the method of induced circular dichroism that helical ordering was built by achiral reactant molecules as well as from achiral Wilkinson's catalyst molecules in the conditions of the hydrogenation reaction in the ChLC medium. Thus, the chiral structure of the key intermediate in this reaction was provided by the action of the chiral field [194,195].
A strong chiral field was shown to exist between two flat aromatic "pincers" (tweezers) [196,197] separated by some kind of a more or less rigid "teter" with a chiral moiety as a chirality inductor. Porphyrin or metalloporphyrin groups at the chain ends with the chiral inductor in the middle of this host molecule, for example 50, can be used as tweezers [198][199][200][201]. The length of the chain the inductor and porphyrin group separating can exceed 13 single and double bonds 173 . In the absence of a chiral inductor, such structure is used to study molecular chirality of chiral bidentate guest molecules by circular dichroism of metalloporphyrin hosts as a sensor of chirality [202][203][204][205][206][207]. End porphyrin groups can be located at a considerable distance from each other in formulations such as dibenzo-30-crown-10 skeleton 51 [208]. There is an assumption that tweezer's architecture of 51 lead to the mesostructure formation. Mmirror symmetry of N-atoms in 51 is realized through the π-π * interaction of porphirin groups. This structure provides a strong racemic field between flat porphirin groups. Chirality of self-assembled achiral porphyrins (imprinted chirality) in host-chiral guest structures persists after a removal of the chiral guestinductor which caused this chirality [209]. This is a new example of chiral memory.
A property of silica gel to retain information ("remember"it) about complex or chiral molecules dissolved in it during molding was noticed long ago [210][211][212][213]. After their removal, silica gel could selectively adsorb these molecules or enantiomers. This selectivity of silica gel could be attributed individually to silylium ions [214]. However, the experimental variety of the ability to memorize structural information, which is characteristic of different gels, allows us to attribute this property to physical gels [215][216][217][218][219][220][221][222][223].

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A minor structural variation in this type molecules may dramatically disturb helical columnar superstructures built on the basis of these molecules. The structure and properties variability of these helical columnar aggregates may be related to the gel structure as well as π-π * stacking and Hbonding. It is believed that the gel formation leads to reaction medium structuring. Together with ππ * stacking [227,228], H-bonding [229], and donor-acceptor interaction [230], this structuring facilitates the chiral information transfer. Polymers 54 and 55 form co-gels with the N,N'-bis(octadecyl)L(D)-Boc-glutamic gelator [218]. Supramolecular chirality of polymers 54 and 55 follows the chirality type of the gelator. Helicity of the polymer assemblies can be memorized even after a removal of gelator molecules. Reaction mixture structuring by means of physical gel and π-π * stacking or H-bonding relationships of interacting molecules is necessary for displaying chiral memory in the formation of chiral superstructures. These relations and the chiral memory effect were observed for self-assembly of molecules 56 [231] and 57 [216], and other aromatic molecules in the presence of
Numerous examples of the chiral memory effect have been observed in polymerization [236][237][238][239][240][241][242][243]. Polymerization creates higher-order structural ordering than the structural arrangement by gel. Therefore, π-π * stacking, in addition to structural ordering during polymerization, creates conditions for the emergence of chiral memory. The chiral memory effect in polymerization of oligomers is also observed with the participation of hydrogen bonding [244]. It is also possible that other factors may contribute to chiral structuring of the medium during polymerization, e.g., vicinal chirality ( Figure 30) [245]. Chiral effects are known to have only a small energy barrier (see, e.g., reactions (3) and (4) with the P-M transition) [107][108][109][110][111]). Therefore, for example, the P-M conversion occurs when the temperature changes within 30°C [101][102][103][104][105][106][107][108][109][110][111]. The chiral field effect may be compared with the chiral effect of other fields or inductors. An example is the chiral effect of ultrasound radiation on chiral amplification [95] in crystallization. It is of interest that the chiral memory motif is also observed in chirality amplification during porphyrin self-assembling [246].
A racemic field is misappreciated in comparison with a chiral field. Perhaps, a reason for this is a kinetic dependence, in which an asymmetric reaction (without an asymmetric inductor) produces the same number of "right" and "left" products. With a high energy of this reaction, the racemic field may not be noticed. Therefore, the comparison between the racemic field and the chiral field can be valid only for not high-energy reactions such as crystallization [247]. Thomas and Tor [248] synthesized a novel 1.10-phenanthroline ligand with branched multifunctional dentritic groups. When an octahedral metal ion self-assembled with these ligands two enantiomers, ∆ and Λ, were formed ( Figure 31). This can apparently be considered as an example of racemic field impact.
A colourless crystal of helical [Cu4Cl4(ally)4]∞ was formed after neat triallylamine (ally) addition to copper (I) chloride at ambient temperature [249] (Figure 32). Out of the five crystallizations three resulted in the predominantly P-helix and two in the predominantly M-helix. Those examples can be considered as a manifestation of the stochastic action of the chiral fieid ( Figure 32) as well as the racemic field ( Figure 31).  These cases demonstrate an analogy with crystallization of sodium chlorate (Scheme 2) and the stochastic helicity formation (Section 6).
There is abundant evidence that a collection of right-and left-handed enantiomers possesses other physical properties than a collection of pure enantiomers [39]. It is reflected in tighter packing (more than 4% denser) or higher melting points of racemates than those of their enantiomers (Wallach's rule) [250][251][252]. Also, data on solubility and some other physical properties show that racemates tend to be slightly more stable than pure enantiomers. The simplest explanation of Wallach's phenomenon is associated with a difference in hydrogen bonding energies of "true" racemates and pure enantiomers [253][254][255][256][257][258][259][260]. Opponents of this concept validity believe that "true" racemates and pure enantiomers with analogous H-bonding are not rare in occurrence [261][262][263][264][265][266]. The discussion is complicated by the fact that there are the examples of anti-Wallach's rule [267]. Therefore, the cause of Wallach's phenomenon has not been completely understood up to now. Some researchers designated Wallach's rule as "mutually exclusive binding" in "true" racemates [268].
Thus, the differences in the physical properties of racemate and enantiomer crystals as well as mirror symmetry breaking or conservation in crystallization of sodium chlorate (Scheme 2) or dendritic complexes ( Figure 31) and triallylamine complexes (Figure 32) suggest the existence of a racemic field alongside with a chiral field. It is possible that the existence of mirror symmetry in the form of a racemic field is global (mirror symmetry space). After all, our Galaxy has a mesostructure ( Figure 3).
There are direct evidences of sophisticated structures of racemates. For example, collagen peptides form tight ridges-in-grooves packing of right-and left-handed triple helices ( Figure 33) [269].
It seems there is a force which provides an energy advantage for the synthesis of a denser racemate structure. The difference between racemic and chiral fields could explain this experimental observation. Racemic compounds exist in solution as well (Scheme 4). According to Kagan and Noyori's models racemates and homochiral dimers function as real actors in catalytic asymmetric reactions with nonlinear effects (see Section 5).

B-Z DNA Conformational Transition
Having a seemingly stable molecular structure, the DNA molecule is a vulnerable object. For example, there are more than a hundred of oxidative damages of the DNA molecular structure. Alongside with the structural damages, the DNA molecule may be subject to conformational distortions (Table 7) [276]. All these conformations of canonical B-DNA (right-handed double helix) lead to genetic instability and genetic diseases [277][278][279][280][281][282][283]. From this viewpoint, the conversion of right-handed B-DNA into left-handed Z-DNA attracts widespread attention.  [284] presented a schematic structure (Figure 34) of B-and Z-DNA molecules after the inversion point. The base pairs in Z-DNA are directed opposite (arrows) from those in B-DNA.
It is unlikely that a transition of right-handed B-DNA into left-handed Z-DNA shown in Table  7 occurs linearly without changing the angle of the DNA thread. It is known that the angle between the polymer helices of opposite senses is about 130° (Figure 35) [285,286], which has been confirmed by other experimental data (see Figure 28 c,d).  Lee et al. [287] calculated a free energy difference between B-DNA and Z-DNA which is 0.9 kcal/mol per dinucleotide unit. The low energy of this transition was confirmed by the influence of relatively weak chemical factors on this transition. Indeed, ions, especially cations, strongly affect B-Z DNA transitions [288,289]. This influence can be explained by reducing phosphate-phosphate interactions between phosphate groups on opposite strands. Phosphate groups got closer to each other in Z-DNA than in B-DNA (7.7 Å in Z-DNA compared to 11.7 Å in B-DNA) [290]. Therefore, cations clustering around the negatively charged phosphate group affected B-DNA and Z-DNA in a different manner. It is not surprising that ions with higher valencies appeared more effective than monovalent ions [291][292][293]. The agents that change the dielectric constant of water (or alcohol) were found to stabilize Z-DNA [294][295][296]. Small molecules affected B↔Z equilibrium as well [297,298]. The B-Z DNA transition was also influenced by Co, Mn, Ru and Pt complexes [299][300][301]. Nevertheless, chiral metal complexes failed to convert B-DNA to Z-DNA (see also [302][303][304][305][306]).
Xu et al. [307] first reported that the (P) and (M) helicene 60 helix molecule ( Figure 36) displayed structural selectivity in binding to DNA. The circular dichroism (CD) spectra of the (P)-60/Z-DNA mixture showed the 70% decrease in intensity of CD whereas no change occurred in binding of (P)-60 to B-DNA. No discrimination was seen in the CD spectra of the (M)-60/B-DNA and (M)-60/Z-DNA mixture. There was only the 20% decrease in CD intensity. This observation allows a very important and fundamental conclusion: an external chiral inductor can affect B-Z DNA conformations or their equilibrium. The influence of this inductor is apparently not related to the chemical interaction. Optically active hexahelicen and its derivatives are known for their huge optical rotational ability (CD activity and chiral field). Therefore, their effect on chiral conformations of DNA is due to a greater degree of the helicene chiral field.
Apart from the above-mentioned chiral inductors, complex structures containing large aromatic ensembles can exert a discriminatory effect on DNA. Doi et al. [310]

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An analysis of the discriminatory ability of irradiations and electromagnetic fields to initiate DNA degradation shows that almost each of them exerts impact on DNA, alone or jointly with some other factors. For example, a magnetic field with an extremely low frequency can induce a DNA double-strand break (the most potent form of DNA damage and genomic instability) [312]. A similar effect was observed for DNA marker exposure under a pulsed magnetic field (25 Hz) [313]. The pulsed magnetic field increased a spontaneous genomic DNA degradation in this case. The pulsed magnetic field enhanced the cell-killing effect of UV radiation [314].
Impact of the electromagnetic field on DNA obeys the same pattern as that of the magnetic field. It appears that a stable electromagnetic field does not affect DNA. These are only low frequency electromagnetic fields that exert a genotoxic effect on DNA [315]. For example, 50 Hz low frequency electromagnetic fields enhanced cell proliferation and DNA damage [316]. Genotoxic effects were observed in human fibroblasts after intermittent exposure to 50 Hz electromagnetic fields [317] (see also [318,319]). Regretfully, a combination of two factors (ionizing radiation and a presence of organic salts) is required to protect DNA from damage. Zheng and Sanche [320] marked that organic salts were efficient in protecting DNA from damage by electrons of 1 eV to 60 keV. The authors suggest that anions of organic salts create additional electric fields within the DNA groove which protect the molecule (see also [321]). Therefore, usually, a low frequency electromagnetic or a low frequency magnetic field (alone or in combination with other factors) can affect DNA; however, some scientists disagree with this opinion [322,323].
Investigations of the static magnetic field effect on DNA have led to less definite conclusions. Li et al. [324] showed that a "magnetic field could potentiate the activity of oxidant radicals" and could bring about "both stabilizing and destabilizing effects to DNA". According to Ruiz-Gomez et al. [325] the magnetic field effect on DNA is not certain. Aydin et al. [326] believe that a low intensity static magnetic field may trigger genomic instability. "But this genotoxic effect of the magnetic field, however, is minimized in living organisms due to the presence of protectic cellular responses" [327] (see, however [328]).
This assumption has sound grounds. It is now known that each type of DNA damage corresponds to a certain repair mechanism in a living cell such as nucleotide excision repair, base excision repair, mismatch repair, and so on [329]. It is logical to assume that impact of a stable factor of the Earth's magnetic field over millions of years of evolution has led to the development of a living cell protective mechanism, alongside with a corresponding DNA repair mechanism. However, since the pulsed magnetic field is not found in nature, DNA has no protective mechanism from it. Probably, that is why the static magnetic field has little effect on DNA and the cell in vivo whereas the pulsated magnetic field affects DNA and the cell radically [320][321][322]330]. According to the same logic we can suggest that periodic long-term gravitational pulsations (lunar tides), as a common phenomenon on Earth, have a protective mechanism against DNA damage (corresponding DNA repair mechanism) whereas static gravitation is uncommon for living organisms on Earth. Indeed, gravitational impact on the Moon (by Earth) has no pulsation. This impact is constant because only one side of the Moon faces the Earth. Therefore, living organisms may have difficulties with the B-Z DNA transition as there is no protection from static gravity.

Conclusion
An obvious advantage of the right-handed helical structure of the most important biological macromolecules is possible evidence of the existence of an external chiral inductor with similar symmetry.
Effects of chiral and racemic fields as possible inductors and conductors of the corresponding influence explain chemical processes with mirror symmetry breaking or retention.
It is possible that the mirror symmetry effect of a racemic field generates additional energy for material objects. This effect may probably explain the mesostructure of galaxies or the formation of chiral crystals of different signs in equal proportions in Earth's deposits. Also, this effect may account for the difference in the physical properties of racemic and enantiomeric crystals (Wallach's rule) or spontaneous chiral ordering of achiral molecules in the form of domains of different chirality signs in approximately equal proportions. The physical basis of mirror symmetry breaking and mirror symmetry retention effects can be found in stochastic chemical reactions running by two routes: with the formation either of racemic or chiral products.
External inductor's impact on these reactions and processes has been also discussed. This influence corresponds to the mesostructure of our Galaxy as a source of chiral and racemic gravitational fields. The fields can serve as a chiral (chiral environment) or racemic inductor and trigger.
These fields, in turn, can affect all biological processes in living organisms. This is especially relevant for Z-DNA areas of native DNA damage with the left-handed conformational conversion. Indeed, there are mechanisms in Nature that protect DNA from destructive factors (mismatch repair, nucleotide or base excision repair, oxidative defects repair, and so on). It is highly likely that Nature has a corresponding DNA repair mechanism against DNA conformational damage caused by the pulsed gravitational field of Earth (Moon tides). Changing of this status quo in lunar settlements (stable gravity and zero magnetic field) can be dangerous for living organisms. Indeed, it is possible that DNA molecules (especially Z-DNA fragments) in organisms placed in the other chiral gravitational environment could behave via a different mechanism and become more vulnerable. Moreover, the corresponding DNA repair mechanism will function in a different manner.