%0 Book Section %1 statphys23_0578 %A Sugimori, T. %A Saito, Y. %A Hyuga, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K back distribution equation homochirality master probability reaction recycling soai statphys23 topic-4 %T Stochastic Approach to Enantiomeric Excess Amplification and Chiral Symmetry Breaking %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=578 %X For some organic molecules two kind of stereostructures that are mutually mirror symmetric are possible to exist, and they are called enantiomers. Two enantiomers are chiral like the left- and the right-hand which cannot be overlapped by translational and rotational transformations. Since their physical properties are mostly the same, there should be an equal amount of both enantiomers in the production started from achiral substrates. In nature, on the other hand, it has long been known that the chiral symmetry in life is broken. all proteins consist of the left-handed L-amino acids and nearly all sugars belong to the right-handed D-series. Ideas explaining the origin of homochirality are categorized in two groups;it is brought by some external advantage factor for one chirality to the other, or it happens by accident. In both cases, however, the degree of excess of one enantiomer to the other is expected very small, and the amplification of enantiomeric excess (ee) is indispensable. Recently, chemical reaction systems which show ee amplification through autocatalysis are found by K. Soai and his group. Starting from a completely achiral initial state, the final state with a finite ee is obtained but the ee value is stochastic following a probability distribution with a double-peak structure. We study stochastic aspects of the chiral symmetry breaking analytically and numerically by the use of the master equation and a directed random walk model. For systems with a recycling back reaction in addition to autocatalytic processes, a unique final probability distribution is obtained by means of detailed balance conditions. Especially, with a nonlinear autocatalysis the distribution is found to have a double-peak structure, indicating the chiral symmetry breaking. The problem is further analyzed by examining eigenvalues and eigenfunctions of the master equation. In the case without recycling, 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. In this case, directed random walk model is found useful. 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. For the Soai reaction, however, spontaneous production is moderate to produce both enantiomers and the ee value achived has a broad distribution with peaks at incomplete chirality. Ref: Y. Saito, T. Sugimori, H. Hyuga; J. Phys. Soc. Jpn 76 (2007) 044802.

@incollection{statphys23_0578, abstract = {For some organic molecules two kind of stereostructures that are mutually mirror symmetric are possible to exist, and they are called enantiomers. Two enantiomers are chiral like the left- and the right-hand which cannot be overlapped by translational and rotational transformations. Since their physical properties are mostly the same, there should be an equal amount of both enantiomers in the production started from achiral substrates. In nature, on the other hand, it has long been known that the chiral symmetry in life is broken. all proteins consist of the left-handed L-amino acids and nearly all sugars belong to the right-handed D-series. Ideas explaining the origin of homochirality are categorized in two groups;it is brought by some external advantage factor for one chirality to the other, or it happens by accident. In both cases, however, the degree of excess of one enantiomer to the other is expected very small, and the amplification of enantiomeric excess (ee) is indispensable. Recently, chemical reaction systems which show ee amplification through autocatalysis are found by K. Soai and his group. Starting from a completely achiral initial state, the final state with a finite ee is obtained but the ee value is stochastic following a probability distribution with a double-peak structure. We study stochastic aspects of the chiral symmetry breaking analytically and numerically by the use of the master equation and a directed random walk model. For systems with a recycling back reaction in addition to autocatalytic processes, a unique final probability distribution is obtained by means of detailed balance conditions. Especially, with a nonlinear autocatalysis the distribution is found to have a double-peak structure, indicating the chiral symmetry breaking. The problem is further analyzed by examining eigenvalues and eigenfunctions of the master equation. In the case without recycling, 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. In this case, directed random walk model is found useful. 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. For the Soai reaction, however, spontaneous production is moderate to produce both enantiomers and the ee value achived has a broad distribution with peaks at incomplete chirality. Ref: Y. Saito, T. Sugimori, H. Hyuga; J. Phys. Soc. Jpn 76 (2007) 044802.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Sugimori, T. and Saito, Y. and Hyuga, H.}, biburl = {https://www.bibsonomy.org/bibtex/23c93a7fef164bd1f603f1949841c932f/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {298a35662374274d747502aa68fe96cb}, intrahash = {3c93a7fef164bd1f603f1949841c932f}, keywords = {back distribution equation homochirality master probability reaction recycling soai statphys23 topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:24.000+0200}, title = {Stochastic Approach to Enantiomeric Excess Amplification and Chiral Symmetry Breaking}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=578}, year = 2007 }