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We are indebted to an anonymous reviewer for pointing out references to several of the stochastic models in Ref. 1. The referee also noted that the possible importance of the stochastic approach for autocatalytic systems was pointed out as early as 1940: M. J. Delbrück J. Chem. Phys. 1940, 8, 120
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We are indebted to an anonymous reviewer for pointing out references to several of the stochastic models in Ref. 1. The referee also noted that the possible importance of the stochastic approach for autocatalytic systems was pointed out as early as 1940: M. J. Delbrück J. Chem. Phys. 1940, 8, 120.
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A further report showing simulations of a reversible version of the original Frank model has recently been published: Mauksch, M, Tsogoeva, S. B, Wei, S, Martynova, I. M. Chirality 2007, 19, 816-825
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A further report showing simulations of a reversible version of the original Frank model has recently been published: Mauksch, M.; Tsogoeva, S. B.; Wei, S.; Martynova, I. M. Chirality 2007, 19, 816-825.
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Other reports of kinetic simulations of the Soai reaction have also provided mathematical models that are not in agreement with experimentally observed behavior, which involves stochastic formation of homochiral and heterochiral dimers. See, for example: Rivera Islas, J, Lavabre, D, Grevy, J.-M, Hernandez Lamoneda, R, Rojas Cabrera, H, Micheau, J.-C, Buhse, T. PNAS 2005, 102, 13743;
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Other reports of kinetic simulations of the Soai reaction have also provided mathematical models that are not in agreement with experimentally observed behavior, which involves stochastic formation of homochiral and heterochiral dimers. See, for example: Rivera Islas, J.; Lavabre, D.; Grevy, J.-M.; Hernandez Lamoneda, R.; Rojas Cabrera, H.: Micheau, J.-C.; Buhse, T. PNAS 2005, 102, 13743;
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for a critique of these studies, see ref 10 in Blackmond, D. G. Tetr. Asymm. 2006, 17, 584-589
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for a critique of these studies, see ref 10 in Blackmond, D. G. Tetr. Asymm. 2006, 17, 584-589.
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Enantiomeric excess in this system is defined as: ee = 100·Σ D - Σ L/Σ D+ Σ L Σ D = [D] + [DL] + [LD] + D* + 2·[DD] Σ L= [L] + [DL] + [LD] + L* + 2·[LL]
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Enantiomeric excess in this system is defined as: ee = 100·Σ D - Σ L/Σ D+ Σ L Σ D = [D] + [DL] + [LD] + D* + 2·[DD] Σ L= [L] + [DL] + [LD] + L* + 2·[LL]
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84906401041
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We are very much indebted to an anonymous referee who pointed out the relation between the network of Scheme 4 and the Onsager triangle reaction
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We are very much indebted to an anonymous referee who pointed out the relation between the network of Scheme 4 and the Onsager triangle reaction.
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41
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84906386493
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It should be noted that even with photochemical activation, the antagonistic model presented in ref 1 la does not lead inexorably to the spontaneous emergence of homochirality as suggested by the authors, but rather to a nonracemic steady-state that may in fact give a depletion rather than enhancement in ee, depending on the system's rate constants and initial ee value
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It should be noted that even with photochemical activation, the "antagonistic" model presented in ref 1 la does not lead inexorably to the "spontaneous emergence of homochirality" as suggested by the authors, but rather to a nonracemic steady-state that may in fact give a depletion rather than enhancement in ee, depending on the system's rate constants and initial ee value.
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Modelling was carried out using Copasi simulator (official test release 1). (Copyright © 2005 by Pedro Mendes, Virginia Tech Intellectual Properties, Inc. and EML Research, gGmbH. All rights reserved.) www-.copasi.org. In addition, the ordinary differential equations (ODEs) describing the reaction models depicted in Schemes 1 and 3 were solved using Gear's method, which is an implicit, stable, multi-step ODE solver. These results were also cross-validated with those obtained using the commercial software Maple. See also: Hoops. S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. Bioinformatics 2006, 22, 3067-74.
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Modelling was carried out using Copasi simulator (official test release 1). (Copyright © 2005 by Pedro Mendes, Virginia Tech Intellectual Properties, Inc. and EML Research, gGmbH. All rights reserved.) www-.copasi.org. In addition, the ordinary differential equations (ODEs) describing the reaction models depicted in Schemes 1 and 3 were solved using Gear's method, which is an implicit, stable, multi-step ODE solver. These results were also cross-validated with those obtained using the commercial software Maple. See also: Hoops. S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. Bioinformatics 2006, 22, 3067-74.
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