Stochastic Approach to Enantiomeric Excess Amplification and Chiral Symmetry Breaking

Stochastic aspects of chemical reaction models related to the Soai reactions as well as to the homochirality in life are studied analytically and numerically by the use of the master equation and random walk model. For systems with a recycling process, a unique final probability distribution is obtained by means of detailed balance conditions. With a nonlinear autocatalysis the distribution has a double-peak structure, indicating the chiral symmetry breaking. This problem is further analyzed by examining eigenvalues and eigenfunctions of the master equation. In the case without recycling process, final probability distributions depend on the initial conditions. In the nonlinear autocatalytic case, time-evolution starting from a complete achiral state leads to a final distribution which differs from that deduced from the nonzero recycling result. This is due to the absence of the detailed balance, and a directed random walk model is shown to give the correct final profile. When the nonlinear autocatalysis is sufficiently strong and the initial state is achiral, the final probability distribution has a double-peak structure, related to the enantiomeric excess amplification. It is argued that with autocatalyses and a very small but nonzero spontaneous production, a single mother scenario could be a main mechanism to produce the homochirality.Comment: 25 pages, 6 figure

Stability of racemic and chiral steady states in open and closed chemical systems

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.Comment: 25 pages, 1 figure. To appear in Physics Letters A (2008

Total Chiral Symmetry Breaking during Crystallization: Who needs a "Mother Crystal"?

Processes that can produce states of broken chiral symmetry are of particular interest to physics, chemistry and biology. Chiral symmetry breaking during crystallization of sodium chlorate occurs via the production of secondary crystals of the same handedness from a single "mother crystal" that seeds the solution. Here we report that a large and "symmetric" population of D- and L-crystals moves into complete chiral purity disappearing one of the enantiomers. This result shows: (i) a new symmetry breaking process incompatible with the hypothesis of a single "mother crystal"; (ii) that complete symmetry breaking and chiral purity can be achieved from an initial system with both enantiomers. These findings demand a new explanation to the process of total symmetry breaking in crystallization without the intervention of a "mother crystal" and open the debate on this fascinating phenomenon. We present arguments to show that our experimental data can been explained with a new model of "complete chiral purity induced by nonlinear autocatalysis and recycling".Comment: 5 pages, 4 figures, Added reference

Chirality Selection in Open Flow Systems and in Polymerization

As an attempt to understand the homochirality of organic molecules in life, a chemical reaction model is proposed where the production of chiral monomers from achiral substrate is catalyzed by the polymers of the same enatiomeric type. This system has to be open because in a closed system the enhanced production of chiral monomers by enzymes is compensated by the associated enhancement in back reaction, and the chiral symmetry is conserved. Open flow without cross inhibition is shown to lead to the chirality selection in a general model. In polymerization, the influx of substrate from the ambience and the efflux of chiral products for purposes other than the catalyst production make the system necessarily open. The chiral symmetry is found to be broken if the influx of substrate lies within a finite interval. As the efficiency of the enzyme increases, the maximum value of the enantiomeric excess approaches unity so that the chirality selection becomes complete.Comment: 8 pages, 4 figure

Complete homochirality induced by the nonlinear autocatalysis and recycling

A nonlinear autocatalysis of a chiral substance is shown to achieve homochirality in a closed system, if the back-reaction is included. Asymmetry in the concentration of two enantiomers or the enantiometric excess increases due to the nonlinear autocatalysis. Furthermore, when the back-reaction is taken into account, the reactant supplied by the decomposition of the enantiomers is recycled to produce more and more the dominant one, and eventually the homochirality is established.Comment: 4 pages, 2 figure

Chiral Crystal Growth under Grinding

To study the establishment of homochirality observed in the crystal growth experiment of chiral molecules from a solution under grinding, we extend the lattice gas model of crystal growth as follows. A lattice site can be occupied by a chiral molecule in R or S form, or can be empty. Molecules form homoclusters by nearest neighbor bonds. They change their chirality if they are isolated monomers in the solution. Grinding is incorporated by cutting and shafling the system randomly. It is shown that Ostwald ripening without grinding is extremely slow to select chirality, if possible. Grinding alone also cannot achieve chirality selection. For the accomplishment of homochirality, we need an enhanced chirality change on crystalline surface. With this "autocatalytic effect" and the recycling of monomers due to rinding, an exponential increase of crystal enantiomeric excess to homochiral state is realized.Comment: 10 pages, 5 figure

4-Chloro-2-((1R)-1-{[(R)-(2-chloro­phen­yl)(cyclo­pent­yl)meth­yl]amino}eth­yl)phenol

The title compound, C20H23Cl2NO, was prepared by condensation of (R)-1-(2-chloro­phen­yl)-1-cyclo­pentyl­methanamine with 1-(5-chloro-2-hydroxy­phen­yl)ethanone, resulting in the formation of a new chiral center. The structural analysis confirms the absolute configuration of the title compound and the formation of the (R,R) diastereoisomer. There is an intra­molecular O—H⋯N hydrogen bond which stabilizes the conformation of the mol­ecule. The mol­ecules are linked to each other through weak C—H⋯π inter­actions