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

Temporary mirror symmetry breaking and chiral excursions in open and closed systems

The reversible Frank model is capable of amplifying the initial small statistical deviations from the idealized racemic composition. This temporary amplification can be interpreted as a chiral excursion in a dynamic phase space. It is well known that if the system is open to matter and energy exchange, a permanently chiral state can be reached asymptotically, while the final state is necessarily racemic if the system is closed. In this work, we combine phase space analysis, stability analysis and numerical simulations to study the initial chiral excursions and determine how they depend on whether the system is open, semi-open or closed

(m-Phenyl­enedimethyl­ene)diammonium dichloride

The asymmetric unit of the title compound, C8H14N2 2+·2Cl−, contains one and a half of the dications and three chloride anions. The half molecule is completed by crystallographic twofold symmetry with two C atoms lying on the rotation axis. The two ammonium groups in each cation adopt a trans conformation with respect ot the benzene ring. The ammonium groups and chloride anions are involved in the formation of a three-dimensional N—H⋯Cl hydrogen-bonding network, which stabilizes the crystal packing

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

Incidence of dengue and chikungunya viruses in mosquitoes and human patients in border provinces of Vietnam

Background: Dengue virus remains a major threat in Vietnam, while chikungunya virus is expected to become one. Surveillance was conducted from 2012 to 2014 in Vietnam to assess the presence of dengue and chikungunya viruses in patients hospitalized with acute fever in five Vietnam provinces neighboring Lao PDR and Cambodia. Surveillance was extended to mosquitoes present in the vicinity of the patients' households. Results: A total 558 human serum samples were collected along with 1104 adult mosquitoes and 12,041 larvae from 2250 households. Dengue virus was found in 17 (3%) human serum samples and in 9 (0.8%) adult mosquitoes. Chikungunya virus was detected in 2 adult mosquitoes (0.18%) while no chikungunya virus was detected in humans. Differing densities of mosquito populations were found, with the highest in the Long An Province border with Cambodia. Long An Province also displayed the lowest rate of infection, despite a very high Breteau Index, high human population density and presence of the main cross border road system. The highest incidence was found in Dac Nong Province, where the Breteau and Container indices were the second lowest. Dengue virus was detected in five Aedes albopictus, three Aedes aegypti and one Culex vishnui. Chikungunya virus was detected in two Ae. aegypti. All infected mosquitoes belonged to haplotypes described in other parts of the world and a number of novel haplotypes were found among uninfected mosquitoes. Conclusions: Dengue is considered to be regularly introduced to Vietnam from Cambodia, mostly through human movement. The data reported here provides a complementary picture. Due to intensive international trade, long-distance transportation of mosquito populations may play a role in the regular importation of dengue in Vietnam through Ho Chi Minh City. It is important to decipher the movement of mosquitoes in Vietnam, not only at the Lao PDR and Cambodia borders but also through international trade routes. Mosquito surveillance programs should address and follow mosquito populations instead of mosquito species