Stochastic kinetic models of chiral autocatalysis: a general tool for the quantitative interpretation of total asymmetric synthesis

A continuous time discrete state stochastic kinetic approach is used to study various chiral autocatalytic models in which the possibility of total asymmetric synthesis arises. It is shown that this approach is superior to the deterministic approaches used earlier and is able to interpret many aspects of chiral autocatalysis. First-order autocatalysis, independently of further kinetic details of the system, leads to a unique final statistical distribution of enantiomers. Higher order autocatalysis, on the other hand, leads to a final state where one of the enantiomers is in overwhelming excess over the other. Criteria are postulated to differentiate between inherently stochastic phenomena in chiral autocatalytic reactions and irreproducibility because of insufficient control of external factors.     

A few molecules can control the enantiomeric outcome. Evidence supporting absolute asymmetric synthesis using the Soai asymmetric autocatalysis

[reaction: see text] Experiments were carried out to investigate whether the Soai asymmetric autocatalysis can accomplish true absolute asymmetric synthesis. In 54 reactions, R and S enantiomeric products were obtained 27 times each. Of 25 pairs of side-by-side identical reactions, 12 afforded opposite enantiomers. In a test of the mechanistic viability of a random-chance process, it was found that a very few molecules (approximately 60 000) were sufficient to control the enantiomeric outcome of these reactions. These observations appear most consistent with asymmetric synthesis originating from the chance enantiomeric excess in a racemate.     

Kinetic aspects of non-linear effects in asymmetric synthesis,catalysis, and autocatalysis

The Kagan ML_n models developed for rationalizing non-linear effects of catalyst enantiopurity have become a valuable mechanistic tool for probing complex asymmetric catalytic reactions. This work demonstrates how these models also provide clues about reactivity that may be used for further evidence to test a mechanistic hypothesis. Special considerations for probing non-linear effects in asymmetric synthesis using stoichiometric chiral auxiliaries and in asymmetric autocatalysis are highlighted in comparison with asymmetric catalysis.     

Enantioselective synthesis utilizing enantiomorphous organic crystal of achiral benzils as a source of chirality in asymmetric autocatalysis

Chiral crystals of achiral benzils act as efficient chiral initiators of asymmetric autocatalysis to afford highly enantioenriched pyrimidyl alkanols whose absolute configurations depend upon the enantiomorph of the crystal used in conjunction with asymmetric autocatalysis with amplification of enantiomeric excess.     

Asymmetric autocatalysis of pyrimidyl alkanol and related compounds. Self-replication,amplification of chirality and implication for the origin of biological enantioenriched chirality

We discovered asymmetric autocatalysis in the enantioselective addition of diisopropylzinc to pyrimidine-5-carbaldehyde, where the product 5-pyrimidyl alkanol acts as a highly efficient asymmetric autocatalyst to afford more of itself (Soai reaction). Asymmetric autocatalysis proceeded quantitatively (>99% yield), affording itself as a near enantiomerically pure (>99.5% ee) product. An extremely low enantiomeric excess (ca. 0.00005% ee) can automultiply during three rounds of consecutive asymmetric autocatalysis to >99.5% ee by asymmetric amplification. Circularly polarized light, and inorganic and organic crystals, act as the origin of chirality to trigger asymmetric autocatalysis. Asymmetric autocatalysis has enormous power to recognize and amplify the chirality of hydrogen, carbon, oxygen, and nitrogen isotopomers. Moreover, absolute asymmetric synthesis, i.e., the formation of enantioenriched compounds without the intervention of any chiral factor, is realized by asymmetric autocatalysis. By using designed molecules based on 5-pyrimidyl alkanol, the intramolecular asymmetric control, self-replication, and improvement of chiral multifunctionalized large molecules has been developed by applying asymmetric autocatalysis.     

Enantioselective synthesis mediated by chiral crystal of achiral hippuric acid in conjunction with asymmetric autocatalysis

Enantiomorphous crystals composed of achiral hippuric acid, i.e., naturally occurring N-benzoylglycine, have been used successfully as chiral inducers in enantioselective synthesis in combination with asymmetric autocatalysis to afford the product with extremely high enantiomeric excess.     

Absolute asymmetric synthesis driven by circularly polarized light

Circularly polarized light (CPL) is an inherently chiral entity and is regarded as one of the possible deterministic signals that led to the evolution of homochirality in earth. Thus, CPL as an external physical field has been widely used in a technique known as absolute asymmetric synthesis, because a product enriched in one enantiomer is formed from racemic precursor molecules without the intervention of a chiral catalyst. In this review, we retrospect the historical research of CPL-induced absolute asymmetric synthesis, including chiral organic molecules, helical polymers, supramolecular assemblies, noble metal nanostructures. However, based on these results, we concluded that the chiral photon-matter interaction is very faint due to the arrangement of molecular bonds giving rise to chiral features, is over a smaller distance than the helical pitch of CPL, leading extremely small enantiomeric excess for product. Therefore, we highlight the recently emerged technology called superchiral field, in which the superchiral far-field and near-field could enhance the dissymmetry of optical field and near-field, respectively. In sum, we hope this review could bring some enlightenment to researchers and further improve the enantioselectivity of CPL-induced absolute asymmetric synthesis.     

Chiral discrimination of cryptochiral saturated quaternary and tertiary hydrocarbons by asymmetric autocatalysis

Chiral discrimination of saturated hydrocarbons has been very difficult to establish, or has not been possible at all. The first chiral discrimination of cryptochiral 5-ethyl-5-propylundecane 1, that is, (n-butyl)ethyl(n-hexyl)(n-propyl)methane, a chiral saturated quaternary hydrocarbon, which is known to exhibit practically no detectable value of optical rotation between 280 and 580 nm, has been accomplished by asymmetric autocatalysis of pyrimidyl alkanol. The absolute configuration of 1 has been determined. In the presence of (R)- or (S)-1, the reaction between pyrimidine-5-carbaldehyde and diisopropylzinc affords (S)- and (R)-pyrimidyl alkanol with 91-97% ee, respectively. Thus, asymmetric autocatalysis serves as a powerful tool for the chiral discrimination of saturated hydrocarbons.     

Principles for designing an achiral receptor promoting asymmetric autocatalysis with amplification of chirality

The idea that an achiral receptor can promote asymmetric autocatalysis with amplification of chirality is presented and discussed in the light of two models, dubbed ACM1 and ACM2, corresponding to the autocatalytic versions of the classical Kagan and Noyori models for non-linear effects in asymmetric catalysis. The chiral amplifications produced by the two models have been investigated. The results suggest that an achiral receptor working according to the ACM1 model presents distinct advantages over the ACM2 counterpart, both in terms of elegance of design and performance.     

Enantioselective synthesis of near enantiopure compound by asymmetric autocatalysis triggered by asymmetric photolysis with circularly polarized light

Right- and left-handed circularly polarized light (CPL) has been proposed as one of the origins of homochirality of biomolecules. However, the enantiomeric excess induced by CPL has been only very low (<2% ee). We found the unprecedented example of asymmetric autocatalysis triggered directly by a chiral physical factor, that is, right- and left-handed CPL, leading to a near enantiopure compound. Asymmetric photolysis of racemic pyrimidyl alkanol by r-CPL irradiation followed by asymmetric autocatalysis affords (R)-pyrimidyl alkanol with >99.5% ee. On the other hand, irradiation with l-CPL affords (S)-pyrimidyl alkanol with >99.5% ee. Thus, chiral physical power, such as CPL, in conjunction with asymmetric autocatalysis, provides a highly enantioenriched compound.     

Enantioselective synthesis induced by chiral crystal composed of DL-serine in conjunction with asymmetric autocatalysis

Asymmetric autocatalysis initiated by chiral crystals containing racemic DL-serine was achieved. P- and M-crystals of DL-serine acted as the source of chirality of asymmetric autocatalysis to afford highly enantioenriched (>99.5% ee) (S)- and (R)-pyrimidylalkanols after the amplification of ee. This is the first example of the usage of the crystal, which contains the same number of D- and L-enantiomers as an origin of chirality in enantioselective synthesis.     

Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle

The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations.     

The effect of parity violation on kinetic models of enantioselective autocatalysis

A detailed analysis of enantioselective autocatalytic reaction models is carried out using both deterministic and stochastic approaches. The models include the small differences between the total energies of enantiomers (DeltaE(PV) approximately 10(-13) J mol(-1)) that arise due to parity violation. Different possible orders of autocatalysis are considered, and the reasons why the predictions of the stochastic and deterministic approaches are different under certain conditions are explored. The continuous time discrete state (CDS) stochastic approach is clearly superior to the deterministic approach. It is concluded that the small difference between enantiomers caused by DeltaE(PV) cannot be amplified under conditions reasonable for the generation of biological chirality. It also seems highly unlikely that biological chirality was determined by any intrinsic difference between enantiomers.     

不对称自催化反应

不对称自催化反应是指由不对称反应生成的手性产物自身作为催化剂的反应过程。不对称自催化具有手性自动放大、反应活性较高、产物处理较易、反应体系连续等特点,是不对称化学的一个新的领域。不对称自催化反应结合手性放大作用,使人们对手性起源有了新的认识。自1990年代以来该方面的探索和研究取得令人注目的重大突破。本文综述了近年来不对称自催化反应的新进展。     

Enantioselective synthesis without discrete optically active additives

By an adaptation of the asymmetric autocatalysis reactions of Soai, it was found that small enantiomeric excesses may be amplified to an arbitrary extent. When this process was applied 48 times to reactions in the absence of discrete optically active additives, all ultimately afforded substantial optical activity in the product. However, observations strongly suggest that most (and likely all) of these reactions are not true examples of absolute asymmetric synthesis. Rather, the ultimate optical activity arises from optically active impurities. Trace amounts of optically active materials may dominate the outcome of reactions involving asymmetric autocatalysis, and in the presence of opposite chiral influences a single enantiomer tends to take over a reaction. The possible implications of these observations to the origin of biological homochirality are noted.     

Reflections on spontaneous asymmetric synthesis by amplifying autocatalysis

Spontaneous generation of chirality was observed in the course of studying the mechanism of asymmetric autocatalysis by NMR in ZnR2 alkylation of pyrimidin-5-aldehydes. A systematic study was carried out in order to discover its origins. Even in clean fresh non-glass reaction vessels spontaneous ee was clearly observed, and was not dependent on any single reaction parameter. For comparison it was demonstrated that enantiomerically pure Zn alkoxide catalyst could control the configuration of the reaction product even when present at below micromolar concentrations. The high propensity of the Soai reaction system to produce an enantiomerically enriched product without initial bias is suggested to result from stochastic effects. These are especially important in autocatalysis because all the final products can be derived by breeding from a small number of initial events. The statistical excess of one enantiomer in that set is sufficient to generate a measurable ee in the product. The process is aided by the requirement for dimerisation before the product is an active catalyst. An enumeration that rationalises these observations is provided.     

Reliable phase stability analysis for asymmetric models

A deterministic technique for reliable phase stability analysis is described for the case in which asymmetric modeling (different models for vapor and liquid phases) is used. In comparison to the symmetric modeling case, the use of multiple thermodynamic models in the asymmetric case adds an additional layer of complexity to the phase stability problem. To deal with this additional complexity we formulate the phase stability problem in terms of a new type of tangent plane distance function, which uses a binary variable to account for the presence of different liquid and vapor phase models. To then solve the problem deterministically, we use an approach based on interval analysis, which provides a mathematical and computational guarantee that the phase stability problem is correctly solved, and that thus the global minimum in the total Gibbs energy is found in the phase equilibrium problem. The new methodology is tested using several examples, involving as many as eight components, with NRTL as the liquid phase model and a cubic equation of state as the vapor phase model. In two cases, published phase equilibrium computations were found to be incorrect (not stable).     

Role of the isopropyl group in asymmetric autocatalytic zinc alkylations

The amplifying asymmetric autocatalysis discovered by Soai and co-workers is dependent on the unique steric properties of the isopropyl group.     

Achiral Inorganic Gypsum Acts as an Origin of Chirality through Its Enantiotopic Surface in Conjunction with Asymmetric Autocatalysis

Achiral inorganic gypsum (CaSO₄⋅2 H₂O) triggers the asymmetric autocatalysis of pyrimidyl alkanol on its two‐dimensional enantiotopic faces to give highly enantioenriched alkanol products with absolute configurations corresponding to the respective enantiotopic surfaces. This is the first example of highly enantioselective synthesis on the enantiotopic surface of an achiral mineral.