Applied Biochemistry and Microbiology

, Volume 46, Issue 7, pp 671–687 | Cite as

Metabolic engineering in silico

  • V. A. Likhoshvai
  • T. M. Khlebodarova
  • M. T. Ree
  • N. A. Kolchanov
Article

Abstract

This review briefs on the main directions in the field of mathematical modeling of metabolic processes aimed at a rational design of genetically modified organisms. The class of generalized Hill functions is described, and their application to modeling of nonlinear processes in Escherichia coli metabolic systems is illustrated by several examples. A model for the pyrimidine biosynthesis in E. coli, taking into account the nonlinear effects of a negative allosteric regulation of enzyme activities involved in the control of the subsequent stages by the end products of synthesis, is considered. It has been shown that the model displays its own continuous oscillation mode of functioning with a period of approximately 50 min, which is close to the duration of E. coli cell cycle. The need in considering the nonlinear effects in the models as essential elements in the function of metabolic systems far from equilibrium is discussed.

Key words

mathematical modeling metabolic engineering generalized Hill functions regulation Escherichia coli 

Abbreviations

MTO

model of target objects

GHF

generalized Hill function

AKB

α-ketobutyrate

APRT

adenine phosphoribosyltransferase

ATCase

aspartate transcarbamoylase

CAASP

carbamoyl aspartate

CAP

carbamoyl phosphate

CPSase

carbamoyl phosphate synthetase

CTPase

cytosine triphosphate synthetase

DAHPS(Trp)

tryptophansensitive 3-deoxy-D-arabinoheptulonate-7-phosphate synthetase

3DDAH7P

3-deoxy-D-arabinoheptulonate-7-phosphate

DHOase

dihydroorotate dehydrogenase

DOROA

dihydroorotate

E4P

erythrose-4-phosphate

Lac

lactate

LDHA

NAD(P)-dependent lactate dehydrogenase 2

NDK

nucleoside diphosphate kinase

OMP

orotidine monophosphate

OMPase

orotidine monophosphate decarboxylase

OPTase

orotate phosphoribosyl transferase

OROA

orotate

Ox

oxalate

PEP

phosphoenolpyruvate

PFL1

pyruvate formate lyase

Pyr

pyruvate

RDREDase

ribonucleoside diphosphate reductase

RNTPRase

ribonucleoside triphosphate reductase

Trp

tryptophan

UMP kinase

uridine monophosphate kinase

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References

  1. 1.
    Bailey, J.E., Science, 1991, vol. 252, pp. 1668–1675.PubMedGoogle Scholar
  2. 2.
    Cameron, D.C. and Tong, I.T., Appl. Biochem. Biotechnol., 1993, vol. 38, pp. 105–140.PubMedGoogle Scholar
  3. 3.
    Koffas, M., Roberge, C., Lee, K., and Stephanopoulos, G., Annu. Rev. Biomed. Eng., 1999, vol. 1, pp. 535–557.PubMedGoogle Scholar
  4. 4.
    Stephanopoulos, G., Metab. Eng., 1999, vol. 1, no. 1, pp. 1–11.PubMedGoogle Scholar
  5. 5.
    Harris, L.M., Desai, R.P., Welker, N.E., and Papoutsakis, E.T., Biotechnol. Bioeng., 2000, vol. 67, pp. 1–11.PubMedGoogle Scholar
  6. 6.
    Barkovich, R. and Liao, J.C., Metab. Eng., 2001, vol. 3, pp. 27–39.PubMedGoogle Scholar
  7. 7.
    Nielsen, J., Appl. Microbiol. Biotechnol., 2001, vol. 55, pp. 263–283.PubMedGoogle Scholar
  8. 8.
    Thykaer, J. and Nielsen, J., Metab. Eng., 2003, vol. 5, no. 1, pp. 56–69.PubMedGoogle Scholar
  9. 9.
    Leuchtenberger, W., Huthmacher, K., and Drauz, K., Appl. Microbiol. Biotechnol., 2005, vol. 69, pp. 1–8.PubMedGoogle Scholar
  10. 10.
    Raab, R.M., Tyo, K., and Stephanopoulos, G., Adv. Biochem. Eng. Biotechnol., 2005, vol. 100, pp. 1–17.PubMedGoogle Scholar
  11. 11.
    Ikeda, M., Appl. Microbiol. Biotechnol., 2006, vol. 69, no. 6, pp. 615–626.PubMedGoogle Scholar
  12. 12.
    Wendisch, V.F., Bott, M., and Eikmanns, B.J., Curr. Opin. Microbiol., 2006, vol. 9, pp. 268–274.PubMedGoogle Scholar
  13. 13.
    Kern, A., Tilley, E., Hunter, I.S., Legisa, M., and Glieder, A., J. Biotechnol., 2007, vol. 129, pp. 6–29.PubMedGoogle Scholar
  14. 14.
    Sprenger, G.A., Appl. Microbiol. Biotechnol., 2007, vol. 75, pp. 739–749.PubMedGoogle Scholar
  15. 15.
    Kim, T.Y., Sohn, S.B., Kim, H.U., and Lee, S.Y., Biotechnol. J., 2008, vol. 3, pp. 612–623.PubMedGoogle Scholar
  16. 16.
    Nielsen, J., J. Bacteriol., 2003, vol. 185, pp. 7031–7035.PubMedGoogle Scholar
  17. 17.
    Stephanopoulos, J., Alper, H., and Moxley, J., Nat. Biotechnol., 2004, vol. 22, no. (10, pp. 1261–1267.PubMedGoogle Scholar
  18. 18.
    Bailey, J.E., Biotechnol. Prog., 1998, vol. 14, pp. 8–20.PubMedGoogle Scholar
  19. 19.
    Hatzimanikatis, V. and Liao, J.C., Biotechnol. Bioeng., 2002, vol. 79, pp. 504–508.PubMedGoogle Scholar
  20. 20.
    Domach, M.M., Leung, S.K., Cahn, R.E., Cocks, G.G., and Shuler, M.L., Biotechnol. Bioeng., 1984, vol. 26, pp. 203–216.PubMedGoogle Scholar
  21. 21.
    Ataai, M.M. and Shuler, M.L., Biotechnol. Bioeng., 1985, vol. 27, pp. 1027–1035.PubMedGoogle Scholar
  22. 22.
    Peretti, S.W. and Bailey, J.E., Biotehcnol. Bioeng., 1986, vol. 28, no. 11, pp. 1672–1689.Google Scholar
  23. 23.
    Shu, J., and Shuler, L.M., Biotechnol. Bioeng., 1989, vol. 33, no. 9, pp. 1117–1126.PubMedGoogle Scholar
  24. 24.
    Hatzimanikatis, V., Emmerling, M., Sauer, U., and Bailey, J.E., Biotechnol. Bioeng., 1998, vol. 58, pp. 154–161.PubMedGoogle Scholar
  25. 25.
    Wiecheri, W., J. Biotechnol., 2002, vol. 94, no. 1, pp. 37–63.Google Scholar
  26. 26.
    Gadkar, K.G., Doyle, F.J., III, Edwards, J.S., and Mahadevan, R., Biotecnol. Bioeng., 2005, vol. 89, pp. 243–251.Google Scholar
  27. 27.
    Visser, D., Schmid, J.W., Mauch, K., Reuss, M., and Heijnen, J.J., Metab. Eng., 2004, vol. 6, pp. 378–390.PubMedGoogle Scholar
  28. 28.
    Krömer, J.O., Wittmann, C., Schröoder, H., and Heinzle, E., Metab. Eng., 2006, vol. 8, pp. 353–369.PubMedGoogle Scholar
  29. 29.
    Nikerel, I.E., Van Winden, W.A., Van Gulik, W.M., and Heijnen, J.J., BMC Bioinformatics, 2006, vol. 7, p. 540.PubMedGoogle Scholar
  30. 30.
    Van Dien, S.J., Iwatani, S., Usuda, Y., and Matsui, K.T., J. Biosci. Bioeng., 2006, vol. 102, pp. 34–40.PubMedGoogle Scholar
  31. 31.
    Vital-Lopez, F.G., Armaou, A., Nikolaev, E.V., and Maranas, C.D., Biotechnol. Prog., 2006, vol. 22, no. 6, pp. 1507–1517.PubMedGoogle Scholar
  32. 32.
    Young, J.D., Henne, K.L., Morgan, J.A., Konopka, A.E., and Ramkrishna, D., Biotechnol. Bioeng., 2008, vol. 100, no. 3, pp. 5452–559.Google Scholar
  33. 33.
    Varma, A. and Palsson, B.O., Appl. Environ. Mecrobiol., 1994, vol. 60, no. 10, pp. 3724–3731.Google Scholar
  34. 34.
    Varma, A. and Palsson, B.O., Biotechnol. Bioeng., 1994, vol. 43, no. 4, pp. 275–285.PubMedGoogle Scholar
  35. 35.
    Varma, A. and Palsson, B.O., Biotechnol. Bioeng., 1995, vol. 45, no. (1), pp. 69–79.PubMedGoogle Scholar
  36. 36.
    Pramanik, J. and Keasling, J.D., Biotechnol. Bioeng., 1997, vol. 56, no. 4, pp. 398–421.PubMedGoogle Scholar
  37. 37.
    Ibarra, R.U., Edwards, J.S., and Palsson, B.O., Nature, 2002, vol. 420, pp. 186–189.PubMedGoogle Scholar
  38. 38.
    Reed, J.L., Vo, T.D., Schilling, C.H., and Palsson, B.O., Genome Biol., 2003, vol. 4, no. 9, p. R54.PubMedGoogle Scholar
  39. 39.
    Nazipova, N.N., El’kin, Yu.E., Panyukov, V.V., and Drozdov-Tikhomirov, L.N., Matem. Biol. Bioinform., 2007, vol. 2, pp. 98–119.Google Scholar
  40. 40.
    Llaneras, F. and Pico, J., J. Biosci. Bioeng., 2008, vol. 105, pp. 1–11.PubMedGoogle Scholar
  41. 41.
    Drozdov-Tikhomirov, L.N., Scurida, G.I., and Serganova, V.V., Biotechnologia (Moskow), 1986, vol. 2, pp. 28–37.Google Scholar
  42. 42.
    Drozdov-Tikhomirov, L.N., Scurida, G.I., Davidov, A.V., Alexandrov, A.A., and Zvyagilskaya, R.A., J. Bioinform. Comput. Biol., 2006, vol. 4, pp. 865–885.PubMedGoogle Scholar
  43. 43.
    Vallino, J.J. and Stephanopoulos, G., Biotechnol. Bioeng., 1993, vol. 4, no. 6, pp. 633–646.Google Scholar
  44. 44.
    Papoutsakis, E.T., Biotechnol. Bioeng., 1984, vol. 26, no. 2, pp. 174–187.PubMedGoogle Scholar
  45. 45.
    Desai, R.P., Nielsen, L.K., and Papoutsakis, E.T., J. Biotechnol., 1999, vol. 71, pp. 191–205.PubMedGoogle Scholar
  46. 46.
    Desai, R.P., Harris, L.M., Welker, N.E., and Papoutsakis, E.T., Metab. Eng., 1999, vol. 1, pp. 206–213.PubMedGoogle Scholar
  47. 47.
    Burgard, A.P., Pharkya, P., and Maranas, C.D., Biotechnol. Bioeng., 2003, vol. 84, pp. 647–657.PubMedGoogle Scholar
  48. 48.
    Sanchez, A.M., Bennett, G.N., and San, K.Y., Metab. Eng, 2006, vol. 8, no. 3, pp. 209–226.PubMedGoogle Scholar
  49. 49.
    Pharkya, P., Burgard, A.P., and Maranas, C.D., Biotechnol. Bioeng., 2003, vol. 84, pp. 887–899.PubMedGoogle Scholar
  50. 50.
    Fong, S.S., Burgard, A.P., Herring, C.D., Knight, E.M., Blattner, F.R., Maranas, C.D., and Palsson, B.O., Biotechnol. Bioeng., 2005, vol. 91, pp. 643–648.PubMedGoogle Scholar
  51. 51.
    Hua, Q., Joyce, A.R., Fong, S.S., and Palsson, B.O., Biotechnol. Bioeng., 2006, vol. 95, pp. 992–1002.PubMedGoogle Scholar
  52. 52.
    Edwards, J.S., Ibarra, R.U., and Palsson, B.O., Nat. Biotechnol., 2001, vol. 19, pp. 125–130.PubMedGoogle Scholar
  53. 53.
    Watson, M.R., Comput. Appl. Biosci., 1986, vol. 2, no. 1, pp. 23–27.PubMedGoogle Scholar
  54. 54.
    Ramakrishna, R., Edwards, J.S., McCulloch, A., and Palsson, B.O., Am. J. Physiol. Regul. Integr. Physiol., 2001, vol. 280, no. 3, pp. R695–704.Google Scholar
  55. 55.
    Schiling, C.H., Covert, M.W., Famili, I., Church, G.M., Edwards, J.S., and Palsson, B.O., J. Bacteriol., 2002, vol. 184, no. 16, pp. 4582–4593.Google Scholar
  56. 56.
    Resendis-Antonio, O., Reed, J.L., Encarnación, S., Collado-Vides, J., and Palsson, B.O., PLoS Comput. Biol., 2007, vol. 3, no. 10, pp. 1887–1895.PubMedGoogle Scholar
  57. 57.
    Joyce, R.R. and Palsson, B.O., Method Mol. Biol., 2008, vol. 416, pp. 433–457.Google Scholar
  58. 58.
    Lee, J., Yun, H., Feist, A.M., Palsson, B.O., and Lee, S.Y., Appl. Microbiol. Biotechnol., 2008, vol. 80, no. 5, pp. 849–862.PubMedGoogle Scholar
  59. 59.
    Pharkya, P., Burgard, A.P., and Maranas, C.D., Genome Res., 2004, vol. 14, no. 11, pp. 2367–2376.PubMedGoogle Scholar
  60. 60.
    Kim, J.I., Varner, J.D., and Ramikrishna, D., Biotechnol. Prog., 2008, vol. 24, no. 5, pp. 993–1006.PubMedGoogle Scholar
  61. 61.
    Chassagnole, C., Noisommit-Rizzi, N., Schmid, J.W., Mauch, K., and Reuss, M., Biotechnol. Bioeng., 2002, vol. 79, pp. 53–73.PubMedGoogle Scholar
  62. 62.
    Hoefnagel, M.H., Starrenburg, M.J., Martens, D.E., Hugenholts, J., Kleerebezem, M., Van Swam, I.I., Bongers, R., Westerhoff, H.V., and Shoep, J.L., Micobiology, 2002, vol. 148, pp. 1003–1013.Google Scholar
  63. 63.
    Bruggeman, F.J., Boogerd, F.C., and Westerhoff, H.V., FEBS J., 2005, vol. 272, pp. 1965–1985.PubMedGoogle Scholar
  64. 64.
    Heijnen, J.J., Biotechnol. Bioeng., 2005, vol. 91, pp. 534–545.PubMedGoogle Scholar
  65. 65.
    Heinrich, R., Rapoport, S.M., and Rapoport, T.A., Prog. Biophys. Mol. Biol., 1977, vol. 32, pp. 1–2.PubMedGoogle Scholar
  66. 66.
    Hatzimanikatis, V., Floudas, C.A., and Bailey, J.E., AIChE J., 1996, vol. 42, pp. 1277–1292.Google Scholar
  67. 67.
    Nielsen, J., Biochem. J., 1997, vol. 321, pp. 133–138.PubMedGoogle Scholar
  68. 68.
    Visser, D. and Heijnen, J.J., Metab. Eng., 2003, vol. 5, no. 3, pp. 164–176.PubMedGoogle Scholar
  69. 69.
    Wu, L., Wang, W., van Winden, W.A., van Gulik, W.M., and Heijnen, J.J., Eur. J. Biochem., 2004, vol. 271, non. 16, pp. 3348–3359.PubMedGoogle Scholar
  70. 70.
    Nikerel, I.E., Van Winde, W.A., Verheijen, P.J., and Heijnen, J.J., Metab. Eng., 2009, vol. 11, pp. 20–30.PubMedGoogle Scholar
  71. 71.
    Voit, E.O. and Savageau, M.A., Biochemistry, 1987, vol. 26, no. 21, pp. 6869–6880.PubMedGoogle Scholar
  72. 72.
    Shiraishi, F. and Savageau, M.A., J. Biol. Chem., 1992, vol. 267, pp. 22912–22918.PubMedGoogle Scholar
  73. 73.
    Hernandez-Bermejo, B., Fairen, V., and Sorribas, A., Math. Biosci., 1999, vol. 16, pp. 83–94.Google Scholar
  74. 74.
    Hernandez-Bermejo, X.B., Fairen, V., and Sorribas, A., Math. Biosci., 2000, vol. 167, pp. 87–107.PubMedGoogle Scholar
  75. 75.
    Likhoshvai, V.A., Ignat’eva, E.V., and Podkolodnaya, O.A., Izv. Akad. Nauk, Ser. Biol., 2001, vol. 35, pp. 1072–1079.Google Scholar
  76. 76.
    Likhoshvai, V.A., Ratushnyi, A.V., Bazhan, S.I., Oshchepkova, E.A., Fadeev, S.I., Khlebodarova, T.M., and Kolchanov, N.A., Metody modelirovaniya dinamiki molekulyarno-geneticheskikh sistem. Sistemnaya komp’yuternaya biologiya (Dynamics Simulation Methods for Molecular-Genetic Systems. Systemic Computer Biology), Kolchanov, N.A., Goncharov, S.S., Likhoshvay, V.A., and Ivanisenkov, V.A., Eds., Novosibirsk: Izd. SO RAN, 2008, pp. 333–393.Google Scholar
  77. 77.
    Likhoshvai, V. and Ratushny, A., J. Bioinform. Comput. Biol., 2007, vol. 5, pp. 521–531.PubMedGoogle Scholar
  78. 78.
    Likhoshvai, V. and Ratushny, A., Proc. of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure, BGRSX2006, Kolchanov, N. et al., Eds., Novosibirsk: IC&G Press, 2006, vol. 2, pp. 13–18.Google Scholar
  79. 79.
    Ratushny, A.V., Nedosekina, E.A., Lashin, S.A., Turnaev, I.I., Vladimirov, N.V., Podkolodnyi, N.L., and Likhoshvai, V.A., Baza matematicheskikh modelei molekulyarno-geneticheskikh protsessov (ModelER) (Base of Mathematical Models of Molecular-Genetic Processes (ModelER)), RF Inventor’s Certificate no. 2006620196, 2006.Google Scholar
  80. 80.
    Khlebodarova, T.M., Lashin, S.A., and Apasieva, N.V., Proc. of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure, BGRSX2006, Kolchanov, N. et al., Eds., Novosibirsk: IC&G Press, 2006, vol. 2, pp. 55–59.Google Scholar
  81. 81.
    Ratushny, A., Usuda, Y., Matsui, K., and Podkolodnaya, O.A., Proc. of the Fifth International Conference on Bioinformatics of Genome Regulation and Structure, BGRSX2006, Kolchanov, N. et al., Eds., Novosibirsk: IC&G Press, 2006, vol. 2, pp. 25–29.Google Scholar
  82. 82.
    Oshchepkova-Nedosekina, E.A. and Likhoshvai, V.A., Theor. Biol. Med. Model., 2007, vol. 4, p. 11.PubMedGoogle Scholar
  83. 83.
    Cornish-Bowden, A., Biochem. J., 1977, vol. 165, pp. 55–59.PubMedGoogle Scholar
  84. 84.
    Akowski, J.P. and Bauerle, R., Biochemistry, 1997, vol. 36, pp. 15817–15822.PubMedGoogle Scholar
  85. 85.
    Hochstadt-Ozer, J. and Stadtman, E.R., J. Biol. Chem., 1971, vol. 246, pp. 5294–5303.PubMedGoogle Scholar
  86. 86.
    Tarmy, E.M. and Kaplan, N.O., J. Biol. Chem., 1968, vol. 243, pp. 2587–2596.PubMedGoogle Scholar
  87. 87.
    Jiang, G.R., Nikolova, S., and Clark, D.P., Microbiology, 2001, vol. 147, pp. 2437–2446.PubMedGoogle Scholar
  88. 88.
    Wilson, H.R., Archer, C.D., Liu, J.K., Turnbough, C.L., Jr., J. Bacteriol., 1992, vol. 174, pp. 514–524.PubMedGoogle Scholar
  89. 89.
    Hommais, F., Krin, E., Coppee, J.Y., Lacroix, C., Yeramian, E., Danchin, A., and Bertin, P., Microbiology, 2004, vol. 150, pp. 61–72.PubMedGoogle Scholar
  90. 90.
    Spiro, S. and Guest, J.R., Trends Biochem. Sci., 1991, vol. 16, no. 8, pp. 310–314.PubMedGoogle Scholar
  91. 91.
    Cotter, P.A. and Gunsalus, R.P., FEMS Microbiol. Letts., 1992, vol. 70, pp. 31–36.Google Scholar
  92. 92.
    Lynch, A.S. and Lin, E.C., J. Bacteriol., 1996, vol. 178, no. 21, pp. 6238–6249.PubMedGoogle Scholar
  93. 93.
    Salmon, K.A., Hung, S.P., Steffen, N.R., Krupp, R., Baldi, P., Hatfield, G.W., and Gunsalus, R.P., J. Biol. Chem., 2005, vol. 280, no. 15, pp. 15084–15996.PubMedGoogle Scholar
  94. 94.
    Tseng, C.P., Albrecht, J., and Gunsalus, R.P., J. Bacteriol., 1996, vol. 178, pp. 1094–1098.PubMedGoogle Scholar
  95. 95.
    Compan, I. and Touati, D., Mol. Microbiol., 1994, vol. 11, no. 5, pp. 955–964.PubMedGoogle Scholar
  96. 96.
    Robin, J.P., Penverne, B., and Herve, G., Eur. J. Biochem., 1989, vol. 183, pp. 519–528.PubMedGoogle Scholar
  97. 97.
    De Staercke, C., Van Vliet, F., Xi, X.G., Rani, C.S., Ladjimi, M., Jacobs, A., Triniolles, F., Herve, G., and Cunin, R., J. Mol. Biol., 1995, vol. 246, pp. 132–143.PubMedGoogle Scholar
  98. 98.
    Wild, J.R., Loughrey-Chen, S.J., and Corder, T.S., Proc. Natl. Acad. Sci. USA, 1989, vol. 86, pp. 46–50.PubMedGoogle Scholar
  99. 99.
    Daniel, R., Kokel, B., Caminade, E., Martel, A., and Le Goffic, F., Anal. Biochem., 1996, vol. 239, pp. 130–135.PubMedGoogle Scholar
  100. 100.
    Bjornberg, O., Gruner, A.C., Roepstorff, P., and Jensen, K.F., Biochemistry, 1999, vol. 39, pp. 2899–2908.Google Scholar
  101. 101.
    Shimosaka, M., Fukuda, Y., Murata, K., and Kimura, A., J. Bacteriol., 1984, vol. 160, pp. 1101–1104.PubMedGoogle Scholar
  102. 102.
    Donovan, W.P. and Kushner, S.R., J. Bacteriol., 1983, vol. 156, pp. 620–624.PubMedGoogle Scholar
  103. 103.
    Bucurenci, N., Serina, L., Zaharia, C., Landais, S., Danchin, A., and Barzu, O., J. Bacteriol., 1998, vol. 180, pp. 473–477.PubMedGoogle Scholar
  104. 104.
    Ginther, C.L. and Ingraham, J.L., J. Biol. Chem., 1974, vol. 249, pp. 3406–3411.PubMedGoogle Scholar
  105. 105.
    MacDonnell, J.E., Lunn, F.A., and Bearne, S.L., Biochim. Biophys. Acta, 2004, vol. 1699, pp. 213–220.PubMedGoogle Scholar
  106. 106.
    Villadsen, I.S. and Michelsen, O., J. Bacteriol., 1977, vol. 301, pp. 136–143.Google Scholar
  107. 107.
    Teusink, B., Larsson, C., Diderich, J., Richard, P., van Dam, K., Gustafsson, L., and Westerhoff, H.V., J. Biol. Chem., 1996, vol. 27, pp. 24442–24448.Google Scholar
  108. 108.
    Higgins, J., Proc. Natl. Acad. Sci. USA, 1964, vol. 51, pp. 989–994.PubMedGoogle Scholar
  109. 109.
    Carre, I.A. and Edmunds, L.N., Jr., J. Cell. Sci., 1993, vol. 104, pp. 1163–1173.PubMedGoogle Scholar
  110. 110.
    Likhoshvai, V.A., Kazantsev, F.V., Akberdin, I.R., Bezmaternykh, K.D., Lashin, S.A., Podkolodnaya, N.N., and Ratushny, A.V., Computer System for Constructing, Computation, and Analysis of Molecular-Genetic System Models (MGSmodeller), RF Inventor’s Certificate no. 2008612820, 2008.Google Scholar
  111. 111.
    Likhoshvai, V.A., Khlebodarova, T.M., and Kolchanov, N.A., Ekologicheskaya, biotekhnologicheskaya, meditsinskaya i teoreticheskaya mikrobiologiya (Ecological, Biogtechnological, Medicinal, and Theoretical Microbiology), Vlasov, V.V., Degermendzhi, A.G., Kolchanov, N.A., Parmon, V.N., and Repin, V.E., Eds., Novosibirsk: Izd. SO RAN, 2009, pp. 277–290 (in press).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • V. A. Likhoshvai
    • 1
    • 2
  • T. M. Khlebodarova
    • 1
  • M. T. Ree
    • 1
  • N. A. Kolchanov
    • 1
    • 2
  1. 1.Institute of Cytology and Genetics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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