279 research outputs found
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
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
An Extended Model for the Evolution of Prebiotic Homochirality: A Bottom-Up Approach to the Origin of Life
A generalized autocatalytic model for chiral polymerization is investigated
in detail. Apart from enantiomeric cross-inhibition, the model allows for the
autogenic (non-catalytic) formation of left and right-handed monomers from a
substrate with reaction rates and , respectively. The
spatiotemporal evolution of the net chiral asymmetry is studied for models with
several values of the maximum polymer length, N. For N=2, we study the validity
of the adiabatic approximation often cited in the literature. We show that the
approximation obtains the correct equilibrium values of the net chirality, but
fails to reproduce the short time behavior. We show also that the autogenic
term in the full N=2 model behaves as a control parameter in a chiral symmetry-
breaking phase transition leading to full homochirality from racemic initial
conditions. We study the dynamics of the N -> infinity model with symmetric
() autogenic formation, showing that it only achieves
homochirality for , where is an N-dependent
critical value. For we investigate the behavior of
models with several values of N, showing that the net chiral asymmetry grows as
tanh(N). We show that for a given symmetric autogenic reaction rate, the net
chirality and the concentrations of chirally pure polymers increase with the
maximum polymer length in the model. We briefly discuss the consequences of our
results for the development of homochirality in prebiotic Earth and possible
experimental verification of our findings
Generation of Absolute Controlled Crystal Chirality by the Removal of Crystal Water from Achiral Crystal of Nucleobase Cytosine
Fluctuation Induced Homochirality
We propose a new mechanism for the achievment of homochirality in life
without any autocatalytic production process. Our model consists of a
spontaneous production together with a recycling cross inhibition in a closed
system.
It is shown that although the rate equations for this system predict no
chiral symmetry breaking, the stochastic master equation predicts complete
homochirality. This is because the fluctuation induced by the discreteness of
population numbers of participating molecules plays essential roles. This
fluctuation conspires with the recyling cross inhibition to realize the
homochirality.Comment: 13 pages, 6 figure
Homochirality and the need of energy
The mechanisms for explaining how a stable asymmetric chemical system can be
formed from a symmetric chemical system, in the absence of any asymmetric
influence other than statistical fluctuations, have been developed during the
last decades, focusing on the non-linear kinetic aspects. Besides the absolute
necessity of self-amplification processes, the importance of energetic aspects
is often underestimated. Going down to the most fundamental aspects, the
distinction between a single object -- that can be intrinsically asymmetric --
and a collection of objects -- whose racemic state is the more stable one --
must be emphasized. A system of strongly interacting objects can be described
as one single object retaining its individuality and a single asymmetry; weakly
or non-interacting objects keep their own individuality, and are prone to
racemize towards the equilibrium state. In the presence of energy fluxes,
systems can be maintained in an asymmetric non-equilibrium steady-state. Such
dynamical systems can retain their asymmetry for times longer than their
racemization time.Comment: 8 pages, 7 figures, submitted to Origins of Life and Evolution of
Biosphere
Toward homochiral protocells in noncatalytic peptide systems
The activation-polymerization-epimerization-depolymerization (APED) model of
Plasson et al. has recently been proposed as a mechanism for the evolution of
homochirality on prebiotic Earth. The dynamics of the APED model in
two-dimensional spatially-extended systems is investigated for various
realistic reaction parameters. It is found that the APED system allows for the
formation of isolated homochiral proto-domains surrounded by a racemate. A
diffusive slowdown of the APED network such as induced through tidal motion or
evaporating pools and lagoons leads to the stabilization of homochiral bounded
structures as expected in the first self-assembled protocells.Comment: 10 pages, 5 figure
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