Mirror symmetry breaking as a problem in dynamic critical phenomena

Hochberg, David; Zorzano, María Paz

doi:10.1103/physreve.76.021109

Cited by 15 publications

(25 citation statements)

References 31 publications

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“…In the latter case, the racemic state is unstable, and an initial small perturbation is sufficient to tip the system over into one of its equally likely stable chiral states. These crucial fluctuations are actually intrinsic to the reacting and diffusing system itself and need not be put in by hand [7,8]. In contrast to the Frank model, the final chiral states are not homochiral, but rather are composed of an unequal proportion of the two enantiomers, with one of them having the larger concentration.…”

Section: Introductionmentioning

confidence: 93%

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

Giaquinta

Hochberg

2008

Physica D: Nonlinear Phenomena

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Section: Introductionmentioning

confidence: 93%

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

Giaquinta

Hochberg

2008

Physica D: Nonlinear Phenomena

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“…32 This is so because first, the total number of molecules is conserved by our reaction scheme, hence so is the total concentration n = a + d + l. Second, the total chiral matter χ = d + l is a fast degree of freedom relative to the enantiomeric excess θ. 33 Simulations of the fully reversible scheme Eqs. (A1) and (A2) using the Gillespie algorithm 19 confirm that χ approaches a stable fixed point value surrounded by small Gaussian fluctuations (see Fig.…”

Section: Appendix A: Probability Distribution For the Enantiomeric Exmentioning

confidence: 99%

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

Stich

Ribó

Blackmond

et al. 2016

The Journal of Chemical Physics

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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. Published by AIP Publishing. [http://dx

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“…On the other hand, ribozyme-driven catalyst experiments [28] have inspired theories based on polymerization and chiral inhibition that minimize [10,14,29] or do not include at all [12,30] autocatalysis. Further extensions accounting for both intrinsic noise [15,31] and diffusion [32][33][34][35] build further upon Frank's work.…”

Section: B Biological Homochirality: a Symmetry-breaking Problemmentioning

confidence: 99%

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality

Jafarpour

Biancalani

Goldenfeld³

2017

Phys. Rev. E

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The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition. DOI: 10.1103/PhysRevE.95.032407 Homochirality, the single-handedness of all biological amino acids and sugars, is one of two major universal features of life on Earth. The other is the canonical genetic code. Their universality transcends all categories of life, up to and including the three domains, and thus requires an explanation that transcends the idiosyncrasies of individual organisms and particular environments. The only universal process common to all life is, of course, evolution, and so it is natural to seek an explanation for biological homochirality in these terms, just as has been done to account for the universality and error-minimization aspects of the genetic code [1]. This paper is just such an attempt, using the simplest and most general commonly accepted attributes of living systems.The origin of biological homochirality has been one of the most debated topics since its discovery by Louis Pasteur in 1848 [2]. There are those who argue that homochirality must have preceded the first chemical systems undergoing Darwinian evolution, and there are those who believe homochirality is a consequence of life, but not a prerequisite [3]. There are even those who argue that homochirality is a consequence of underlying asymmetries from the laws of physics, invoking complicated astrophysical scenarios for the origin of chiral organic molecules [4] or even the violation of parity from the weak interactions [5,6]! In fact, explanations that are based on physical asymmetries can only predict an enantiomeric excess of one handedness over another, and not the 100% effect observed in nature [7]. * Corresponding author: fjafarpo@purdue.eduThe most influential class of theories for biological homochirality rest on an idea of F.C. Frank's, in which there is a kinetic instability of a racemic (50% right handed and 50% left handed) mi...

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Mirror symmetry breaking as a problem in dynamic critical phenomena

Cited by 15 publications

References 31 publications

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

Necessary conditions for the emergence of homochirality via autocatalytic self-replication

Noise-induced symmetry breaking far from equilibrium and the emergence of biological homochirality

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