Spontaneous appearance of chirally asymmetric steady states in a reaction model including Michaelis–Menten type catalytic reactions

Iwamoto, Kazutoshi

doi:10.1039/b303363e

Cited by 18 publications

(18 citation statements)

References 39 publications

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“…For the sake of simplicity, the description of the catalytic cycle is limited to a minimal Michaelis–Menten mechanism characterized by a constant K m =( k c + k r )/ k f . This choice is justified because it is the easiest way to portray a catalytic step in a realistic manner and, moreover, such a hypothesis has been formerly applied to describe the alkylation of chalcone and benzaldehyde with dialkylzinc …”

Section: Resultsmentioning

confidence: 98%

Nonlinear Effects in Asymmetric Synthesis: A Practical Tool for the Discrimination between Monomer and Dimer Catalysis

et al. 2016

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Nonlinear effects in asymmetric synthesis are identified by a nonlinear relationship between the enantiomeric excess of the product versus that of the chiral catalyst. Such information is not always sufficient to reveal if the active catalyst acts in its monomeric or dimeric form. Numerical simulations of two kinetic models including monomer and dimer catalysis with a Michaelis–Menten‐type reaction mechanism suggest that the nonlinear effects are mainly sensitive to an analogue of the Michaelis–Menten constant as well as to the diastereomeric energy difference between homochiral and heterochiral catalyst dimers. A practical monomer–dimer discrimination table is presented showing that the influence of the initial catalyst enantiomeric excess and the catalytic charge on the product enantiomeric excess and on the reaction half‐time together with the assessment of the kinetic order of the prochiral substrate are sufficient to assess whether the active catalyst acts in its monomeric or dimeric form.

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Section: Resultsmentioning

confidence: 98%

Nonlinear Effects in Asymmetric Synthesis: A Practical Tool for the Discrimination between Monomer and Dimer Catalysis

et al. 2016

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“…In some models, 17,34,35 the direct non-autocatalyzed reaction can be totally neglected compared to this one.…”

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confidence: 97%

“…In some models, the two steps of mutual destruction and elimination can be replaced by a direct continuous elimination of both chiral compounds from the system. 35 All these reactions can be reversible 32 (with the obvious exception of the matter flow itself), but can also be described as irreversible. 34 The original model of Frank is the simplest instance of this general class of systems: only autocatalyzed synthesis of the chiral compound, and irreversible reactions are present together with an implicit (but present) flow of matter.…”

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confidence: 99%

Emergence of homochirality in far‐from‐equilibrium systems: Mechanisms and role in prebiotic chemistry

et al. 2007

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Since the model proposed by Frank (Frank FC, Biochem Biophys Acta 1953;11:459-463), several alternative models have been developed to explain how an asymmetric non-racemic steady state can be reached by a chirally symmetric chemical reactive system. This paper explains how a stable non-racemic regime can be obtained as a symmetry breaking occurring in a far-from-equilibrium reactive system initiated with an initial imbalance. Departing from the variations around the original Frank's model that are commonly described in the literature, i.e. open-flow systems of direct autocatalytic reactions, we discuss recent developments emphasizing both an active recycling of components and an autocatalytic network of simple reactions. We will present our APED model as the most natural realization of such thermodynamic openness and non-equilibrium, of recycling and of network autocatalysis, each of these in prebiotic conditions. The different experimental and theoretical models in the literature will be classified according to mechanism. The place and role of such self-structured networks responsible for the presence of homochirality in the primitive Earth will be detailed.

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“…In those cases, a fast exploration around the computed values, using bifurcation diagrams, could be enough to find SMSB. Additionally, this procedure can be used to build phase diagrams such as the ones shown in references [25,26].…”

Section: Computer Experimentsmentioning

confidence: 99%

Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

Montoya

Cruz

Ágreda

2019

Life

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The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.

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Spontaneous appearance of chirally asymmetric steady states in a reaction model including Michaelis–Menten type catalytic reactions

Cited by 18 publications

References 39 publications

Nonlinear Effects in Asymmetric Synthesis: A Practical Tool for the Discrimination between Monomer and Dimer Catalysis

Nonlinear Effects in Asymmetric Synthesis: A Practical Tool for the Discrimination between Monomer and Dimer Catalysis

Emergence of homochirality in far‐from‐equilibrium systems: Mechanisms and role in prebiotic chemistry

Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

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