We analyze a recent proposal for spontaneous mirror symmetry breaking based on the coupling of first-order enantioselective autocatalysis and direct production of the enantiomers that invokes a critical role for intrinsic reaction noise. For isolated systems, the racemic state is the unique stable outcome for both stochastic and deterministic dynamics when the system is in compliance with the constraints dictated by the thermodynamics of chemical reaction processes. In open systems, the racemic outcome also results for both stochastic and deterministic dynamics when driving the autocatalysis unidirectionally by external reagents. Nonracemic states can result in the latter only if the reverse reactions are strictly zero: these are kinetically controlled outcomes for small populations and volumes, and can be simulated by stochastic dynamics. However, the stability of the thermodynamic limit proves that the racemic outcome is the unique stable state for strictly irreversible externally driven autocatalysis. These findings contradict the suggestion that the inhibition requirement of the Frank autocatalytic model for the emergence of homochirality may be relaxed in a noise-induced mechanism.

1.
Biochirality: Origins, Evolution and Molecular Recognition
, edited by
P.
Cintas
(
Springer-Verlag
,
Heidelberg
,
2013
).
2.

Systems capable of SMSB yield large net chiral excesses, mostly in the vicinity of homochirality, as common non-thermodynamic states.3 In closed systems with relatively high exergonic transformations, prolonged chiral excursions, i.e., kinetically controlled chiral outcomes, are possible.4 Final stationary chiral states are possible in either open or in closed systems prevented from coming into thermodynamic equilibrium with their surroundings; see, for example, Refs. 5 and 6.

3.
J. M.
Ribó
,
C.
Blanco
,
J.
Crusats
,
Z.
El-Hachemi
,
D.
Hochberg
, and
A.
Moyano
, “
Absolute asymmetric synthesis in enantioselective autocatalytic reaction networks
,”
Chem. Eur. J.
20
,
17250
(
2014
).
4.
J.
Crusats
,
D.
Hochberg
,
A.
Moyano
, and
J. M.
Ribó
, “
Frank model and spontaneous emergence of chirality in closed systems
,”
ChemPhysChem
10
(
12
),
2123
(
2009
).
5.
C.
Blanco
,
J. M.
Ribó
,
J.
Crusats
,
Z.
El-Hachemi
,
A.
Moyano
, and
D.
Hochberg
, “
Mirror symmetry breaking with limited enantioselective autocatalysis and temperature gradients
,”
Phys. Chem. Chem. Phys.
15
,
1546
(
2013
).
6.
C.
Blanco
,
J.
Crusats
,
Z.
El-Hachemi
,
A.
Moyano
,
D.
Hochberg
, and
J. M.
Ribó
, “
Spontaneous emergence of chirality in the limited enantioselective model: Autocatalytic cycle driven by an external reagent
,”
ChemPhysChem
14
,
2432
2440
(
2013
).
7.
A.
Guijarro
and
M.
Yus
,
The Origin of Chirality in the Molecules of Life
(
RSC Publishing
,
Cambridge
,
2009
).
8.
V.
Avetisov
and
V.
Goldanskii
, “
Mirror symmetry breaking at the molecular level
,”
Proc. Natl. Acad. Sci. U. S. A.
93
,
11435
(
1996
).
9.
F. C.
Frank
, “
On spontaneous asymmetric synthesis
,”
Biochim. Biophys. Acta
11
,
459
463
(
1953
).
10.
K.
Soai
,
T.
Shibata
,
H.
Morioka
, and
K.
Choji
, “
Asymmetric autocatalysis and amplification of enantiomeric excess of a chiral molecule
,”
Nature (London)
378
,
767
(
1995
).
11.
D. G.
Blackmond
, “
Asymmetric autocatalysis and its implications for the origin of homochirality
,”
Proc. Natl. Acad. Sci. U. S. A.
101
,
5732
(
2004
).
12.
D. G.
Blackmond
, “
“If pigs could fly” chemistry: A tutorial on the principle of microscopic reversibility
,”
Angew. Chem., Int. Ed.
48
,
2648
(
2009
).
13.
J. M.
Ribó
and
D.
Hochberg
, “
Competitive exclusion principle in ecology and absolute asymmetric synthesis in chemistry
,”
Chirality
27
,
722
727
(
2015
).
14.
F.
Jafarpour
,
T.
Biancalani
, and
N.
Goldenfeld
, “
Noise-induced mechanism for biological homochirality of early life self-replicators
,”
Phys. Rev. Lett.
115
,
158101
(
2015
).
15.
D. G.
Blackmond
, “
The origin of biological homochirality
,” in
The Origin of Life
, edited by
D.
Deamer
and
J.W.
Szostak
(
Cold Spring Harbor Laboratory Press
,
2010
).
16.
W. H.
Mills
, “
Some aspects of stereochemistry
,”
J. Soc. Chem. Ind., London
51
,
750
759
(
1932
).
17.
K.
Mislow
, “
Absolute asymmetric synthesis: A commentary
,”
Collect. Czech. Chem. Commun.
68
,
849
864
(
2003
).
18.
N. G.
van Kampen
,
Stochastic Processes in Physics and Chemistry
(
Elsevier
,
Amsterdam
,
2007
).
19.
D. T.
Gillespie
, “
Stochastic simulation of chemical kinetics
,”
Annu. Rev. Phys. Chem.
58
,
35
55
(
2007
).
20.
J.
Puchalka
and
A. M.
Kierzek
, “
Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks
,”
Biophys. J.
86
,
1357
1372
(
2004
).
21.
P.
Erdí
and
G.
Lente
,
Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications
,
Springer Series in Synergetics
(
Springer
,
New York
,
2014
).
22.

Values for the constants in the introductory simulations in Figure 1 of Ref. 14 are not given. The first paragraph of the text and Fig. 1(a) in Ref. 14 incorrectly attributes the reaction D + L → 2A to Frank’s model (see explanation in Footnote [4] of that work).

23.
R.
Wegscheider
, “
Über simultane Gleichgewichte und die Beziehung zwischen Thermodynamic und Reaktionskinetic homogener systeme
,”
Z. Phys. Chem.
39
,
257
303
(
1902
).
24.
A. N.
Gorban
and
G. S.
Yablonsky
, “
Extended detailed balance for systems with irreversible reactions
,”
Chem. Eng. Sci.
66
,
5388
(
2011
).
25.
D. G.
Blackmond
and
O. K.
Matar
, “
Re-examination of reversibility in reaction models for the spontaneous emergence of homochirality
,”
J. Phys. Chem. B
112
,
5098
5104
(
2008
).
26.
L.
Onsager
, “
Reciprocal relations in irreversible processes I
,”
Phys. Rev.
37
,
405
(
1931
);
L.
Onsager
, “
Reciprocal relations in irreversible processes II
,”
Phys. Rev.
38
,
2265
(
1931
).
27.

For driven catalysis, the external reagents lead to two independent dimensionless variables g, u, compared to one variable in the undriven case.

28.
D. G.
Blackmond
,
C. R.
McMillan
,
S.
Ramdeehul
,
A.
Schorm
, and
J. M.
Brown
, “
Origins of asymmetric amplification in autocatalytic Alkylzinc additions
,”
J. Am. Chem. Soc.
123
,
10103
10104
(
2001
).
29.
R.
Plasson
,
D. K.
Kondepudi
,
H.
Bersini
,
A.
Commeyras
, and
K.
Asakura
, “
Emergence of homochirality in far-from-equilibrium systems: Mechanisms and role in prebiotic chemistry
,”
Chirality
19
,
589
600
(
2007
).
30.
C. W.
Gardiner
,
Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
, 2nd ed. (
Springer-Verlag
,
Berlin
,
1997
).
31.
H.
Risken
,
The Fokker-Planck Equation, Methods of Solution and Applications
, 2nd ed. (
Springer
,
Berlin
,
1989
).
32.
See http://link.aps.org/supplemental/10.1103/PhysRevLett.115.158101 for further details, and the references therein.
33.
D.
Hochberg
and
M.-P.
Zorzano
, “
Mirror symmetry breaking as a problem in dynamic critical phenomena
,”
Phys. Rev. E
76
,
0211109
(
2007
).
34.
H.
Hochstadt
, in
The Functions of Mathematical Physics
(
Dover
,
New York
,
1986
), Chap. 4.
35.
J. M.
Ribó
and
D.
Hochberg
, “
Stability of racemic and chiral steady states in open and closed chemical systems
,”
Phys. Lett. A
373
,
111
122
(
2008
).
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