Hiroyuki Hyuga

Complete homochirality induced by nonlinear autocatalysis and recycling

The nonlinear autocatalysis of the 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 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 of the dominant enantiomer, and eventually homochirality is established.

Deformation of Vesicles under the Influence of Strong Electric Fields II

The deformation of vesicles with conducting membranes in external electric fields has been studied in the framework of the perturbation theory. A simple model for dynamics of deformation is proposed, and the results of numerical calculations for typical combinations of the vesicle size and the electric field are presented. When the conductivity inside a spherical vesicle is larger than that of the exterior medium, the deformations, both static and dynamic, are prolate and, otherwise, they are oblate.

Chirality Selection in Crystallization

A cluster growth model is proposed to study chiral symmetry breaking in stirred crystallization from an achiral element. Achiral monomers are assumed to coagulate to form chiral clusters from dimer...

Homochirality proliferation in space

To understand the chirality selection in the biological organic system, a simple lattice model of chemical reaction with molecular diffusion is proposed and studied by Monte Carlo simulations. In addition to a simple stochastic process of conversion between an achiral reactant A and chiral products, R and S molecules, a nonlinear autocatalysis is incorporated by enhancing the reaction rate from A to R (or S), when A is surrounded by more than one R (or S) molecules. With this nonlinear autocatalysis, the chiral symmetry between R and S is shown to be broken in a dense system. In a dilute solution with a chemically inactive solvent, molecular diffusion accomplishes chirality selection, provided that the initial concentration is higher than the critical value.

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.

Rate Equation Approaches to Amplification of Enantiomeric Excess and Chiral Symmetry Breaking

Theoretical models and rate equations relevant to the Soai reaction are reviewed. It is found thatin production of chiral molecules from an achiral substrate autocatalytic processes can induce either enantiomericexcess (ee) amplification or chiral symmetry breaking. The former means that the final ee value islarger than the initial value but is dependent upon it, whereas the latter means the selection of a uniquevalue of the final ee, independent of the initial value. The ee amplification takes place in an irreversiblereaction such that all the substrate molecules are converted to chiral products and the reaction comes toa halt. Chiral symmetry breaking is possible when recycling processes are incorporated. Reactionsbecome reversible and the system relaxes slowly to a unique final state. The difference between thetwo behaviors is apparent in the flow diagram in the phase space of chiral molecule concentrations. Theee amplification takes place when the flow terminates on a line of fixed points (or a fixed line),whereas symmetry breaking corresponds to the dissolution of the fixed line accompanied by the appearanceof fixed points. The relevance of the Soai reaction to the homochirality in life is also discussed.

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 a directed random walk model. For systems with a recycling back reaction, 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, 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.

Steady-state deformation of a vesicle in alternating electric fields

Abstract Steady-state deformation of a vesicle with a membrane of arbitrary conductance in an alternating electric field is discussed. A simple formula is obtained for the elongation modulus of the vesicle as a function of the frequency of the applied field. The dependences of this modulus on the conditions in the medium and the membrane characteristics are illustrated in detail. Experimental applicability to the extraction of information on the characteristics of a vesicle are discussed.

Selection of Crystal Chirality: Equilibrium or Nonequilibrium?

To study the solution growth of crystals composed of chiral organic molecules, a spin-one Ising lattice gas model is proposed. The model turns out to be equivalent to the Blume–Emery–Griffiths model, which shows an equilibrium chiral symmetry breaking at low temperatures. The kinetic Monte Carlo simulation of crystal growth, however, demonstrates that Ostwald ripening is a very slow process with a characteristic time proportional to the system size: The dynamics is nonergodic. It is then argued that by incorporating grinding dynamics, homochirality is achieved in a short time, independent of the system size. Grinding limits cluster sizes to a certain range independent of system size and at the same time keeps the supersaturation so high that population numbers of average-sized clusters grow. If numbers of clusters for two types of enantiomers differ by chance, the difference is amplified exponentially and the system rapidly approaches the homochiral state. Relaxation time to the final homochiral state is ...

The Dynamical Casimir Effect for an Oscillating Dielectric Model.

Dynamical Casimir effects caused by a moving mirror and a varying dielectric medium are studied in the effective Hamiltonian approach. The explicit form of the effective Hamiltonian for the uniform, step-wise, and time-dependent dielectric model is derived in addition to that for the moving mirror model. The resonant properties of induced photons for both models are considered and it is found that in contrast to the moving mirror case, the inter-mode transition for the dielectric case is suppressed between the odd-odd levels and between the even-even levels. The effects of dissipation are also taken into account by the master equation. For numerical analyses, a convenient method to integrate the time evolution is proposed.