A stochastic chiral amplification model

Todorović, D. M.; Gutman, Iván; Radulović, M. M.

doi:10.1016/s0009-2614(03)00449-4

Cited by 17 publications

(14 citation statements)

References 20 publications

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“…(27) will yield a racemic solution, as will the first variation in k −2 appearing in the list Eq. (28). The latter four values will however yield chiral solutions; see Figs.…”

Section: Reaction Rates In Three Space Dimensionsmentioning

confidence: 92%

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

Giaquinta

Hochberg

2008

Physica D: Nonlinear Phenomena

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“…(27) will yield a racemic solution, as will the first variation in k −2 appearing in the list Eq. (28). The latter four values will however yield chiral solutions; see Figs.…”

Section: Reaction Rates In Three Space Dimensionsmentioning

confidence: 92%

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

Giaquinta

Hochberg

2008

Physica D: Nonlinear Phenomena

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“…28 Since then, theoretical models of chemical ''chiral bifurcation'' have been amended by Mason 29 and others. [30][31][32][33] A significant problem that still remains, is the need to find an actual concrete chemical reaction that would follow kinetics described by Frank's (or similar) model, while remaining relevant from the standpoint of prebiotic chemistry. One of the few chemical processes recognized to follow the principles of ''chiral bifurcation,'' i.e., a microscopic chiral fluctuation leads, through an autocatalytic loop, to the conversion of achiral substrate into a macroscopic excess of chiral product, is transformation of pyrimidine-5-carbaldehyde to pyrimidyl alcohol.…”

Section: Vortex-induced Chiral Bifurcation In Unbiological Systemsmentioning

confidence: 99%

Vortex‐induced chiral bifurcation in aggregating insulin

Dzwolak

2010

Chirality

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Chiral symmetry breaking occurs during vortex-assisted crystallization of several simple compounds leading to a stochastically determined emergence of an enantiomeric excess of one chiral isomer. This article summarizes recent developments in studies of a similar phenomenon observed in agitated solutions of aggregating insulin, when a phase transition-precipitation of insoluble amyloid fibrils from solutions of the native protein-is coupled to a conformational transition of the native alpha-helical structure into aggregated beta-sheets. In contrast to the previously known cases of chiral bifurcation, the substrate is built of L-amino acids and, therefore, chirally biased. However, under certain conditions, insulin forms fibrils with superstructural chiral features that are independent of the left-handedness of amino acid residues, as revealed by the sign of extrinsic Cotton effect induced in amyloid-bound achiral dye-thioflavin T. The inherent chiral bias of the protein results in a diastereomeric relationship between the two optical isomers of amyloid superstructures and the fact that relative probability of formation of either isomer is temperature dependent. As the formation of amyloid fibrils in vivo is associated with several degenerative disorders such as Alzheimer's disease, this newly observed phenomenon may have important implications in the context of structural basis of biological activity of misfolded proteins.

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“…This model has been the subject of more studies than can be cited here, but only a few of them had explicit stochastic elements [62,64,[67][68][69][70][71][72][73][74][75][76][77][78][79][80]84]. The non-CDS studies [62,64,67−70] have already been discussed.…”

Section: The Frank Modelmentioning

confidence: 99%

“…Turning now to stochastic non-CDS approaches to kinetics, Todorović et al [62] investigated a slightly modified version of the classic Frank model [63]. Rather than considering the effect of individual molecules, the rate constants in the stochastic model were assumed to show stochastic fluctuations.…”

mentioning

confidence: 99%

“…In contrast, the parting time, defined as the moment at which the enantiomeric excess attains 1% of its limit for the first time, was a linear, decreasing function of the logarithm of the magnitude of the fluctuations in the rate constants. The drawback of this approach is that it assumes uncorrelated fluctuations in the values of rate constants which should be enantiomeric mirror-image pairs and the origin of these fluctuations, which remained unspecified in the original work [62], may only be external. Consequently, this is a description of irreproducibility rather than inherent stochastic nature.…”

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confidence: 99%

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The Role of Stochastic Models in Interpreting the Origins of Biological Chirality

Lente

2010

Symmetry

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This review summarizes recent stochastic modeling efforts in the theoretical research aimed at interpreting the origins of biological chirality. Stochastic kinetic models, especially those based on the continuous time discrete state approach, have great potential in modeling absolute asymmetric reactions, experimental examples of which have been reported in the past decade. An overview of the relevant mathematical background is given and several examples are presented to show how the significant numerical problems characteristic of the use of stochastic models can be overcome by non-trivial, but elementary algebra. In these stochastic models, a particulate view of matter is used rather than the concentration-based view of traditional chemical kinetics using continuous functions to describe the properties system. This has the advantage of giving adequate description of single-molecule events, which were probably important in the origin of biological chirality. The presented models can interpret and predict the random distribution of enantiomeric excess among repetitive experiments, which is the most striking feature of absolute asymmetric reactions. It is argued that the use of the stochastic kinetic approach should be much more widespread in the relevant literature.

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A stochastic chiral amplification model

Cited by 17 publications

References 20 publications

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

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

Vortex‐induced chiral bifurcation in aggregating insulin

The Role of Stochastic Models in Interpreting the Origins of Biological Chirality

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