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Stochastic aspects of asymmetric autocatalysis and absolute asymmetric synthesis

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Abstract

The main goal of the present review is to collect in a unified framework the deterministic and stochastic models of emergence and amplification of chirality by mechanisms such as asymmetric autocatalysis and absolute asymmetric synthesis. Empirical approach and modeling have recently provided a good insight into these phenomena. Our groups in Italy and Hungary have a wide variety of expertise both in fields of experiments and modeling. In the last decade important results have been achieved, however, more experiments and more detailed deterministic and stochastic models are needed for a better understanding of details and significance of asymmetric autocatalysis and absolute asymmetric synthesis.

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References

  1. A bibliography for stochastic systems biology. http://biowiki.org/StochasticBiology

  2. Abstracts and talk materials: stochastic models for intracellular reaction networks May 11–13, 2008, University of Minnesota. http://www.ima.umn.edu/2007-2008/SW5.11-13.08/abstracts.html

  3. D. F. Anderson, G. Craciun and T.G. Kurtz, Bull. Math. Biol. (2010, epub ahead of print)

  4. Arányi P., Tóth J.: Acta Biochim. Biophys. Acad. Sci. Hung. 12, 375 (1977)

    Google Scholar 

  5. Asakura K., Kondepudi D.K., Martin R.: Chirality 10, 343 (1998)

    Article  CAS  Google Scholar 

  6. Asakura K., Ikumo A., Kurihara K., Osanai S., Kondepudi D.K.: J. Phys. Chem. A 104, 2689 (2000)

    Article  CAS  Google Scholar 

  7. Asakura K., Osanai S., Kondepudi D.K.: Chirality 13, 435 (2001)

    Article  CAS  Google Scholar 

  8. Bada J.L.: Nature 374, 594 (1995)

    Article  CAS  Google Scholar 

  9. Barabás B., Caglioti L., Faglioni F., Florini N., Lazzeretti P., Maioli M., Micskei K., Rábai G., Taddei F., Zucchi C., Pályi G.: Amer. Inst. Phys. Proc. 963, 1150 (2008)

    Google Scholar 

  10. Barabás B., Caglioti L., Micskei K., Pályi G.: Bull. Chem. Soc. Japan 82, 1372 (2009)

    Article  CAS  Google Scholar 

  11. Barabás B., Caglioti L., Zucchi C., Maioli M., Gál E., Micskei K., Pályi G.: J. Phys. Chem. B 111, 11506 (2007)

    Article  CAS  Google Scholar 

  12. Barabás B., Micskei K., Zucchi C., Pályi G.: Orig. Life Evol. Biosph. 38, 317 (2008)

    Article  CAS  Google Scholar 

  13. Barak S., Doron L.: Orig. Life Evol. Biosph. 34, 181 (2004)

    Article  Google Scholar 

  14. Baras F., Malek-Mansour M., Pearson J.E.: J. Chem. Phys. 105, 8257 (1996)

    Article  CAS  Google Scholar 

  15. Bazsa G., Beck M.T.: Acta Chim. Acad. Sci. Hung. 73, 425 (1972)

    CAS  Google Scholar 

  16. W. Bialek, arXiv:cond-mat/0005235v1 [cond-mat.soft] 2000, pp. 1–10

  17. Blackmond D.G.: Proc. Natl. Acad. Sci. USA 101, 5732 (2004)

    Article  CAS  Google Scholar 

  18. Blackmond D.G.: Tetrahedron: Asymmetry 17, 584 (2006)

    Article  CAS  Google Scholar 

  19. Borgis D., Moreau M.: Physica A 123, 109 (1984)

    Article  Google Scholar 

  20. Caglioti L., Zucchi C., Pályi G.: Chem. Today 23, 38 (2005)

    CAS  Google Scholar 

  21. Caglioti L., Hajdu C., Holczknecht O., Zékány L., Zucchi C., Micskei K., Pályi G.: Viva Origino 34, 62 (2006)

    CAS  Google Scholar 

  22. Caglioti L., Holczknecht O., Fujii N., Zucchi C., Pályi G.: Orig. Life Evol. Biosph. 36, 459 (2006)

    Article  CAS  Google Scholar 

  23. Caglioti L., Micskei K., Pályi G.: Viva Origino 35, 82 (2007)

    CAS  Google Scholar 

  24. Caglioti L., Barabás B., Faglioni F., Florini N., Lazzeretti P., Maioli M., Micskei K., Rábai G., Taddei F., Zucchi C., Pályi G.: Chimica Oggi/CHEM. TODAY 26, 24 (2008)

    Google Scholar 

  25. L. Caglioti, K. Micskei, G. Pályi: Chirality (2009, in press)

  26. X. Cai, Z. Xu, J. Chem. Phys. 126 (2007) 074102 (10 pages)

  27. Calvin M.: Molecular evolution. OUP, Oxford (1969)

    Google Scholar 

  28. T. Carletti, D. Fanelli, Europhys. Lett. 77, 18005 (2007) (6 pages)

  29. Castillo-Garit J.A., Marrero-Ponce Y., Torrens F., Rotondo R.: J. Mol. Graph. Model. 26, 32 (2007)

    Article  CAS  Google Scholar 

  30. Chen X., Ling A.: Chin. Phys. Lett. 24, 2509 (2007)

    Article  CAS  Google Scholar 

  31. P. Csermely, Weak links: stabilizers of complex systems from proteins to social networks? THE FRONTIERS COLLECTION, Series Editors: D. Dragoman, M. Dragoman, A.C. Elitzur, M.R. Silverman, J. Tuszynski, H.D. Zeh, (Springer, 2006)

  32. Csikja R., Tóth J.: Enformatika. Int. J. Appl. Math. Comput. Sci. 4, 728 (2007)

    Google Scholar 

  33. Delbrück M.: J. Chem. Phys. 8, 120 (1940)

    Article  Google Scholar 

  34. Eggenberger F., Pólya G.: Zeit. Angew. Math. Mech. 3, 279 (1923)

    Article  Google Scholar 

  35. Eigen M., Schuster P.: The hypercycle: a principle of natural self-organization. Springer, Berlin, Heidelberg, New York (1979)

    Google Scholar 

  36. Engel M.H., Nagy B.: Nature 296, 837 (1982)

    Article  CAS  Google Scholar 

  37. English B.P., Min W., Oijen A.M., Lee K.T., Luo G., Sun H., Cherayil B.J., Kou S.C., Xie X.S.: Nat. Chem. Biol. 2, 87 (2006)

    Article  CAS  Google Scholar 

  38. Érdi P., Sipos T., Tóth J.: Magyar Kém. Folyóirat 79, 97 (1973)

    Google Scholar 

  39. Érdi P., Tóth J.: Mathematical models of chemical reactions. Theory and applications of deterministic and stochastic models. Princeton University Press, Princeton (1989)

    Google Scholar 

  40. P. Érdi, J. Tóth, V. Hárs, in Colloquia Mathematica Societatis János Bolyai, (Szeged, Hungary, 1979) Qualitative theory of differential equations, ed. by M. Farkas (North-Holland and János Bolyai Mathematical Society: Budapest, 1981), Vol. 30, pp. 205

  41. Feher G., Weissman M.: Proc. Natl. Acad. Sci. USA 70, 870 (1973)

    Article  CAS  Google Scholar 

  42. Frank F.C.: Biochim. Biophys. Acta 11, 459 (1953)

    Article  CAS  Google Scholar 

  43. Frankowicz M., Malek-Mansour M., Nicolis G.: Physica 125, 237 (1984)

    Article  Google Scholar 

  44. Frankowicz M., Kawczyński A.L.: Pol. J. Chem. 71, 467 (1997)

    CAS  Google Scholar 

  45. Gadgil Ch., Lee Ch.H., Othmer H.G.: Bull. Math. Biol. 67, 901 (2005)

    Article  CAS  Google Scholar 

  46. B. Gaveau, M. Moreau, J. Tóth, in Variational and extremum principles in macroscopic systems, Chap. 15, eds. by S. Sieniutycz, H. Farkas, (Elsevier, 2005), p. 315

  47. Gánti T.: The principles of life. Oxford University Press, Oxford (2003)

    Book  Google Scholar 

  48. D.T. Gillespie, S. Lampoudi, L.R. Petzold, J. Chem. Phys. 126, 034302 (2007) (9 pages)

    Google Scholar 

  49. Goss P.J.E., Peccoud J.: Proc. Natl. Acad. Sci. USA 95, 6750 (1998)

    Article  CAS  Google Scholar 

  50. Goutsias J.: Biophys. J. 92, 2350 (2007)

    Article  CAS  Google Scholar 

  51. Gridnev I.D., Serafimov J.M., Quiney H., Brown J.M.: Org. Biomol. Chem. 1, 3811 (2003)

    Article  CAS  Google Scholar 

  52. Guldberg C.M., Waage P.: Études sur les affinités chimiques. Brøgger & Christei, Christiania (1867)

    Google Scholar 

  53. Gutman I., Todorović D., Vućković M.: Chem. Phys. Lett. 216, 447 (1993)

    Article  CAS  Google Scholar 

  54. Hanusse P.: Compt. Rend. 277, 93 (1973)

    CAS  Google Scholar 

  55. Hellander A., Loetstedt P.: J. Comp. Phys. 227, 100 (2007)

    Article  CAS  Google Scholar 

  56. Hochberg D., Zorzano M.-P.: Chem. Phys. Lett. 431, 185 (2006)

    Article  CAS  Google Scholar 

  57. Hochstim A.R.: Orig. Life Evol. Biosph. 6, 317 (1975)

    Article  CAS  Google Scholar 

  58. Á. Horváth, Multimodality of discrete distributions with applications, (MSc thesis), ELTE TTK, Budapest, 1985 (in Hungarian)

  59. Hou Z., Xin H.: Huaxue Jinzhan 18, 142 (2007)

    Google Scholar 

  60. Iosifescu M., Tăutu P.: Stochastic processes and applications in biology and medicine, Vol. 1.: Theory, Vol. 2: Models. Springer, Editura Academiei, Berlin, Heidelberg, New York and Bucure sti (1973)

    Google Scholar 

  61. Jia Y., Li J.-R.: Phys. Rev. E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics) 53, 5764 (1996)

    CAS  Google Scholar 

  62. K. Kaneko, Phys. Rev. E 68, 031909 (2003) (5 pages)

  63. Kawasaki T., Harada Y., Suzuki K., Tobita T., Florini N., Pályi G., Soai K.: Org. Lett. 10, 4085 (2008)

    Article  CAS  Google Scholar 

  64. Kawasaki T., Shimizu M., Nishiyama D., Ito M., Ozawa H., Soai K.: Chem. Commun. 29, 4396 (2009)

    Article  CAS  Google Scholar 

  65. Kawasaki T., Matsumura Y., Tsutsumi T., Suzuki K., Ito M., Soai K.: Science 324, 492 (2009)

    Article  CAS  Google Scholar 

  66. Keszthelyi L.: Orig. Life Evol. Biosph. 14, 375 (1984)

    Article  CAS  Google Scholar 

  67. Keszthelyi L.: Quart. Rev. Biophys. 28, 473 (1995)

    Article  CAS  Google Scholar 

  68. Keszthelyi L.: Orig. Life Evol. Biosph. 31, 249 (2001)

    Article  CAS  Google Scholar 

  69. Szabó-Nagy A., Keszthelyi L.: Proc. Natl. Acad. Sci. USA 96, 4252 (1999)

    Article  Google Scholar 

  70. Kondepudi D.K., Culha M.: Chirality 10, 238 (1998)

    Article  CAS  Google Scholar 

  71. Kondepudi D.K., Nelson G.W.: Phys. Rev. Lett. 50, 1023 (1983)

    Article  CAS  Google Scholar 

  72. Kondepudi D.K., Nelson G.W.: Nature 314, 438 (1985)

    Article  CAS  Google Scholar 

  73. Kondepudi D.K., Asakura K.: Acc. Chem. Res. 34, 946 (2001)

    Article  CAS  Google Scholar 

  74. Kou S.C., Cherayil B.J., Min W., English B.P., Xie X.S.: J. Phys. Chem. B 109, 19068 (2005)

    Article  CAS  Google Scholar 

  75. Kramers H.A.: Physica 7, 284 (1940)

    Article  CAS  Google Scholar 

  76. Kurtz T.G.: J. Chem. Phys. 57, 2976 (1972)

    Article  CAS  Google Scholar 

  77. Kvenvolden K.A., Lawless J., Pering K., Peterson E., Flores J., Ponnamperuma C., Kaplan I.R., Moore C.: Nature 228, 923 (1970)

    Article  CAS  Google Scholar 

  78. Laurenzi I.J.: J. Chem. Phys. 113, 3315 (2000)

    Article  CAS  Google Scholar 

  79. Le Guennec P.: J. Math. Chem. 23, 429 (1998)

    Article  CAS  Google Scholar 

  80. Lente G.: J. Phys. Chem. A 108, 9475 (2004)

    Article  CAS  Google Scholar 

  81. Lente G.: J. Phys. Chem. A 109, 11058 (2005)

    Article  CAS  Google Scholar 

  82. Lente G.: J. Phys. Chem. A 110, 12711 (2006)

    Article  CAS  Google Scholar 

  83. Lente G.: Phys. Chem. Chem. Phys. 9, 6134 (2007)

    Article  CAS  Google Scholar 

  84. Lente G.: React. Kinet. Catal. Lett. 95, 13 (2008)

    Article  CAS  Google Scholar 

  85. Lente G., Ditrói T.: J. Phys. Chem. B 113, 7237 (2009)

    Article  CAS  Google Scholar 

  86. Lindblad P., Degn H.: Acta Chim. Scand. 21, 791 (1967)

    Article  CAS  Google Scholar 

  87. Maioli M., Micskei K., Zucchi C., Caglioti L., Pályi G.: J. Math. Chem. 43, 1505 (2008)

    Article  CAS  Google Scholar 

  88. Marion G., Mao X., Renshaw E., Liu J.: Phys. Rev. E 66, 051915 (2002)

    Article  CAS  Google Scholar 

  89. Markó L.: Diss. Savariensis 24, 1 (1998)

    Google Scholar 

  90. Martinek T.A., Varga T., Balázsik K., Szöllősi G., Fülöp F., Bartók M.: J. Catal. 255, 296 (1998)

    Article  CAS  Google Scholar 

  91. Mason S.F.: Nature 311, 19 (1984)

    Article  CAS  Google Scholar 

  92. Matsuura T., Koshima H.: J. Photochem. Photobiol. C: Photochem. Rev. 6, 7 (2005)

    Article  CAS  Google Scholar 

  93. Medgyessy P.: Decomposition of superpositions of distribution functions. Publishing House of the Hungarian Academy of Sciences, Budapest (1961)

    Google Scholar 

  94. Mezey P.: A global approach to molecular chirality. In: Mezey, P. (eds) New developments in molecular chirality, pp. 257. Kluver, Dordrecht (1991)

    Google Scholar 

  95. Mezey, P. (eds): New developments in molecular chirality. Kluver, Dordrecht (1991)

    Google Scholar 

  96. Michaelis L., Menten M.L.: Biochem. Z. 49, 333–369 (1913)

    CAS  Google Scholar 

  97. Micskei K., Maioli M., Zucchi C., Caglioti L., Pályi G.: Tetrahedron: Asymmetry 17, 2960 (2006)

    Article  CAS  Google Scholar 

  98. Micskei K., Póta G., Caglioti L., Pályi G.: J. Phys. Chem. A 110, 5982 (2006)

    Article  CAS  Google Scholar 

  99. Micskei K., Rábai G., Gál E., Caglioti L., Pályi G.: J. Phys. Chem. B 112, 9196 (2008)

    Article  CAS  Google Scholar 

  100. Mills W.H.: J. Soc. Chem. Ind. 51, 750 (1932)

    Article  CAS  Google Scholar 

  101. Nagypál I., Epstein I.R.: J. Phys. Chem. 90, 6285 (1986)

    Article  Google Scholar 

  102. Nagypál I., Epstein I.R.: J. Chem. Phys. 80, 6925 (1988)

    Article  Google Scholar 

  103. Ornstein G.E., Uhlenbeck L.S.: Phys. Rev. 36, 823 (1930)

    Article  Google Scholar 

  104. Országh I., Beck M.T.: Magyar Kém. Folyóirat 86, 248 (1980)

    Google Scholar 

  105. Pasteur L.: Compt. Rend. 26, 535 (1848)

    Google Scholar 

  106. L. Pál, Arxiv preprint cond-mat/0407106, (2004)

  107. Pályi, G., Zucchi, C., Caglioti, L. (eds): Advances in bioChirality. Elsevier, Amsterdam (1999)

    Google Scholar 

  108. Pályi, G., Zucchi, C., Caglioti, L. (eds): Progress in biological chirality. Elsevier, Oxford (GB) (2004)

    Google Scholar 

  109. Pályi G., Micskei K., Zékány L., Zucchi C., Caglioti L.: Magy. Kém. Lapja 60, 17 (2005)

    Google Scholar 

  110. Pearson K.: Proc. Roy. Soc. (Lond) 60, 489 (1897)

    Article  Google Scholar 

  111. X. Peng, W. Zhou, Y. Wang, J. Chem. Phys. 126, 224109 (2007) (9 pages)

  112. Pineda M., Imbihl R., Schimansky-Geier L., Zülicke Ch.: J. Chem. Phys. 124, 044701 (2006)

    Article  CAS  Google Scholar 

  113. Pizzarello S., Hang Y., Becker L., Poreda R.J., Nieman R.A., Cooper G., Williams M.: Science 293, 2236 (2001)

    Article  CAS  Google Scholar 

  114. Plasson R., Bersini H., Commeyras A.: Proc. Natl. Acad. Sci. USA 101, 16733 (2004)

    Article  CAS  Google Scholar 

  115. Pólya G.: Math. Ann. 84, 149 (1921)

    Article  Google Scholar 

  116. Póta G., Stedman G.: ACH-Models Chem. 131, 229 (1994)

    Google Scholar 

  117. Qian H.: Biophys. Chem. 105, 585 (2003)

    Article  CAS  Google Scholar 

  118. Qian H., Elson E.L.: Biophys. Chem. 101–102, 565 (2002)

    Article  Google Scholar 

  119. Qian H., Saffarian S., Elson E.L.: Proc. Natl. Acad. Sci. USA 99, 10376 (2002)

    Article  CAS  Google Scholar 

  120. Reddy V.T.N.: J. Statist. Phys. 13, 61 (1975)

    Article  Google Scholar 

  121. Renyi A.: MTA Alk. Mat. Int. Közl. 2, 83–101 (1953)

    Google Scholar 

  122. Saito Y., Sugimori T., Hyuga H.: J. Phys. Soc. Jpn. 76, 044802 (2007)

    Article  CAS  Google Scholar 

  123. Samoilov M., Plyasunov S., Arkin A.P.: Proc. Natl. Acad. Sci. USA 102, 2310 (2005)

    Article  CAS  Google Scholar 

  124. Sato I., Omiya D., Tsukiyama K., Ogi Y., Soai K.: Tetrahedron: Asymmetry 12, 1965 (2001)

    Article  CAS  Google Scholar 

  125. Sato I., Omiya D., Igarashi H., Kato K., Ogi Y., Tsukiyama K., Soai K.: Tetrahedron: Asymmetry 14, 975 (2003)

    Article  CAS  Google Scholar 

  126. Schaad L.J.: J. Amer. Chem. Soc. 85, 3588 (1963)

    Article  CAS  Google Scholar 

  127. Schnell S., Chappell M.J., Evans N.D., Roussel M.R.: Compt. Rend. Biol. 329, 51 (2006)

    Article  CAS  Google Scholar 

  128. Schnell S., Maini K.: Math. Comput. Model. 35, 137 (2002)

    Article  Google Scholar 

  129. El-Fayyoumi Shaimaa, M.H. Todd, Abstracts of papers, 232nd National Meeting, San Francisco, United States, Sept. 10–14, 2006

  130. Shao J., Liu L.: J. Phys. Chem. A 111, 9570 (2007)

    Article  CAS  Google Scholar 

  131. Shibata T.: World Sci. Lect. Notes Complex Syst. 3, 203 (2005)

    Article  CAS  Google Scholar 

  132. Sipos T., Tóth J., Érdi P.: React. Kinet. Catal. Lett. 1, 113 (1974)

    Article  CAS  Google Scholar 

  133. Soai K., Shibata T., Morioka H., Choji K.: Nature 378, 767 (1995)

    Article  CAS  Google Scholar 

  134. Soai K., Shibata T., Sato I.: Acc. Chem. Res. 33, 382 (2000)

    Article  CAS  Google Scholar 

  135. Soai K., Sato I., Shibata T.: Chem. Record 1, 321 (2001)

    Article  CAS  Google Scholar 

  136. Soai K.: Viva Origino 30, 186 (2002)

    CAS  Google Scholar 

  137. Soai K., Sato I., Shibata T., Komiya S., Hayashi M., Matsueda Y., Imamura H., Hayase T., Morioka H., Tabira H., Yamamoto Y., Kowata Y.: Tetrahedron: Asymmetry 14, 185 (2003)

    Article  CAS  Google Scholar 

  138. Soai K., Shibata T., Sato I.: Bull. Chem. Soc. Jpn. 77, 1063 (2004)

    Article  CAS  Google Scholar 

  139. K. Soai, T. Kawasaki, ed. by K. Mikami, L. Lautens New frontiers in asymmetric catalysis (Wiley, Hoboken, 2007), p. 259

  140. Soai K., Kawasaki T.: Top. Curr. Chem. 284, 1 (2008)

    Article  CAS  Google Scholar 

  141. K. Soai, T. Kawasaki, in Organometallic Chirality, eds. by G. Pályi, C. Zucchi, L. Caglioti (Accad. Nazl. Sci. Lett. Arti - Mucchi Editore, Modena, 2008), p. 107

  142. Soai K., Kawasaki T.: Chem. Today 27(6, Supplement), 3 (2009)

    CAS  Google Scholar 

  143. Stéfanini M.O., McKane A.J., Newman T.J.: Nonlinearity 18, 1575 (2005)

    Article  Google Scholar 

  144. Todorović D., Gutman I., Radulović M.: Chem. Phys. Lett. 372, 464 (2003)

    Article  CAS  Google Scholar 

  145. Togashi Y., Kaneko K.: Phys. Rev. Lett. 86, 2459 (2001)

    Article  CAS  Google Scholar 

  146. Togashi Y., Kaneko K.: J. Phys. Soc. Jpn. 72, 62 (2003)

    Article  CAS  Google Scholar 

  147. Togashi Y., Kaneko K.: Phys. Rev. E 70, 020901 (2004)

    Article  CAS  Google Scholar 

  148. Togashi Y., Kaneko K.: Physica D 205, 87 (2005)

    Article  CAS  Google Scholar 

  149. Tóth J.: React. Kinet. Catal. Lett. 18, 169 (1981)

    Article  Google Scholar 

  150. Tóth J.: J. Math. Chem. 25, 393 (1999)

    Article  Google Scholar 

  151. Tóth J., Török T.L.: React. Kinet. Catal. Lett. 13, 167 (1980)

    Article  Google Scholar 

  152. Tranter G.E.: Nature 318, 172 (1985)

    Article  CAS  Google Scholar 

  153. Turner T.E., Schnell S., Burrage K.: Comput. Biol. Chem. 28, 165 (2004)

    Article  CAS  Google Scholar 

  154. Van Hessem D.: J. Proc. Control. 2006, 225 (2006)

    Article  CAS  Google Scholar 

  155. H. Wagner, M. Moller, K. Prank, J. Chem. Phys. 125, 174104 (2006) (11 pages)

  156. H.-Y. Wang, H. Qian, J. Math. Phys. 48, 013303 (2007) (15 pages)

    Google Scholar 

  157. E. Weinan, D. Liu, E. Vanden-Eijnden, J. Chem. Phys. 126, 137102 (2007) (3 pages)

    Google Scholar 

  158. Wilhelmy L.: Poggendorff’s Ann. Phys. Chem. 81, 413 (1850)

    Article  Google Scholar 

  159. Zheng Q., Ross J.: J. Chem. Phys. 94, 3644 (1991)

    Article  CAS  Google Scholar 

  160. Xie X.S., Trautman J.K.: Ann. Rev. Phys. Chem. 49, 441 (1998)

    Article  CAS  Google Scholar 

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  1. Department of Stochastics, Budapest University of Technology and Economics, Egry J. u. 1., 1111, Budapest, Hungary

    B. Barabás

  2. Department of Analysis, Budapest University of Technology and Economics, Egry J. u. 1., 1111, Budapest, Hungary

    J. Tóth

  3. Laboratory for Chemical Kinetics, Eötvös Loránd University, Pázmány P. sétány 1/A, 1117, Budapest, Hungary

    J. Tóth

  4. Department of Chemistry, University of Modena and Reggio Emilia, Via Campi 183, 41100, Modena, Italy

    G. Pályi

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Barabás, B., Tóth, J. & Pályi, G. Stochastic aspects of asymmetric autocatalysis and absolute asymmetric synthesis. J Math Chem 48, 457–489 (2010). https://doi.org/10.1007/s10910-010-9680-8

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