Mathematical modeling of regular contours of gene networks

G. V. Demidenko   ; N. A. Kolchanov   ; V. A. Likhoshvai   ; Yu. G. Matushkin   ; S. I. Fadeev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 12, pp. 2276-2295

Bibliographie

[1] Kolchanov N. A., Ananko E. A., Kolpakov F. A. i dr., “Gennye seti”, Mol. biologiya, 34:4 (2000), 533–544

[2] Fellenberg K., Hauser N. C., Brors B. et al., “Correspondence analysis applied to microarray data”, Proc. Nat. Acad. Sci. USA, 98 (2001), 10781–10786 | DOI

[3] Sherlock G., Hernandez-Boussard T., Kasarskis A. et al., “The Stanford microarray database”, Nucl. Acids Res., 29 (2001), 152–155 | DOI

[4] Ananko E. A., Podkolodny N. L., Stepanenko I. L. et al., “GeneNet: a database on structure and functional organization of gene networks”, Nucl. Acids Res., 30:1 (2002), 398–401 | DOI

[5] Kolchanov N. A., Ananko E. A., Likhoshvai V. A. et al., “Gene networks description and modeling in the GeneNet system”, Gene Regulation and Metabolism, Ch. 7, MIT Press, Cambridge, 2002, 149–180

[6] Ratner V. A., Geneticheskie upravlyayuschie sistemy, Nauka, Novosibirsk, 1966

[7] Galimzyanov A. V., Tchuraev R. N., “An investigation of the structural stability of drosophila control gene subnetwork in computer experiments”, Bioinformatics of Genome Regulation and Structure, Kluwer Acad. Publs., Boston etc., 2004, 301–310

[8] Kauffman S. A., “Metabolic stability and epigenesist in randomly constructed genetic net”, J. Theor. Biol., 22 (1969), 437–467 | DOI | MR

[9] Thomas R., “Boolean formalization of genetic control circuits”, J. Theor. Biol., 42 (1973), 563–585 | DOI

[10] Thomas R., “Logical analysis of systems comprising feedback loops”, J. Theor. Biol., 73:4 (1978), 631–656 | DOI

[11] Savageau M., “A theory of alternative designs for biochemical control systems”, Biomed. Biochim. Acta, 44 (1985), 875–880

[12] Mjolsness E., Sharp D. H., Reinitz J., “A connectionicst model of development”, J. Theor. Biol., 152:4 (1991), 429–454 | DOI

[13] McAdams H., Arkin A., “Stochastic mechanisms in gene expression”, Proc. Nat. Acad. Sci. USA, 94 (1997), 814–819 | DOI

[14] Marnellos G., Mjolsness E., “A gene network approach to modeling early neurogenesis in Drosophila”, Pacific Symposium on Biocomputing, World Scient., Maui, Hawaii, USA, 1998, 30–41

[15] Savageau M. A., “Design principles for elementary gene circuits: Elements, methods, and examples”, CHAOS, 11:1 (2001), 142–159 | DOI | Zbl

[16] Hofestadt R., Meineke F., “Interactive modeling and simulation of biochemical networks”, Comput. Biol. Med., 25 (1995), 321–334 | DOI

[17] Freier A., Lange M., Hofestaedt R., “Integrative analysis of gene networks using dynamic process pattern modelling”, Bioinformatics of Genome Regulation and Structure, Kluwer Acad. Publs., Boston ets., 2004, 257–264

[18] Likhoshvai V. A., Matushkin Yu. G., Vatolin Yu. N., Bazhan S. I., “A generalized chamical kinetic metod for simulating complex biological systems. A computer model of $\lambda$ phage ontogenesis”, Comput. Technol., 5:2 (2000), 87–99 | MR

[19] Likhoshvai V. A., Matushkin Yu. G., Ratushnyi A. V. i dr., “Obobschennyi khimiko-kineticheskii metod modelirovaniya gennykh setei”, Mol. biologiya, 35:6 (2001), 1972–1980

[20] Vatolin Yu. N., Bazhan S. I., Likhoshvai V. A., “Matematicheskoe modelirovanie vnutrikletochnogo razvitiya fagov”, I Otraslevaya konf. po primeneniyu matem. modelirovaniya i ASU v nauch. uchrezhdeniyakh i na predpriyatiyakh (1–3 marta 1978 g.), Novosibirsk, 1978, 22–32

[21] Kravchenko V. V., Shamin V. V., Gileva I. P. i dr., “Mekhanizm regulyatsii translyatsii politsistronnykh mRNK. Rol vzaimnogo raspolozheniya tsistronov”, Dokl. AN SSSR, 295:3 (1987), 745–748 | MR

[22] Bachinskii A. G., Likhoshvai V. A., Vliyanie defektnykh interferiruyuschikh chastits na reproduktsiyu virusa venesuelskogo entsefalomielita loshadei v kletochnykh kulturakh, VNIIMB, Koltsovo, 1988

[23] Kravchenko V. V., Shamin V. V., Gileva I. P. i dr., “Vliyanie alternativnykh vtorichnykh struktur na effektivnost translyatsii polistronnoi mRNK”, Dokl. AN SSSR, 301:2 (1988), 480–484 | MR

[24] Bazhan S. I., Likhoshvai V. A., “Matematicheskaya model regulyatsii vnutrikletochnogo ontogeneza virusa grippa”, Matem modelirovanie sistemy immuniteta i infektsionnogo protsessa, Tezisy dokl. Vses. konf. (Koltsovo, 26–28 iyulya 1989), Novosibirsk, 1989, 9–10

[25] Likhoshvai V. A., “Rare codons: fortunity or regularity?”, Modeling and Comput. Meth. in Molecular Biol. and Genetics, Nova Sci. Publs., New York, 1992, 463–469

[26] Bazhan S. I., Likhoshvay V. A., Belova O. E., “Theoretical analysis of the regulation of interferon expression during priming and blocking”, J. Theor. biol., 175 (1995), 149–160 | DOI

[27] Bazhan S. I., Likhoshvay V. A., Belova O. E., “Theoretical analysis of the regulation of interferon expression during priming and blocking”, J. Theor. Biol., 175 (1995), 149–160 | DOI

[28] Nikolenko G. N., Kravchenko V. V., Svarovskaya E. S. i dr., “Regulyatsiya translyatsii distalnogo gena $\mathrm{LacZ}$ politsistronnoi mRNK potokom ribosom s proksimalnogo gena”, Bioorgan. khimiya, 23:3 (1997), 200–204

[29] Likhoshvai V. A., Matushkin Yu. G., “Computer model for analysis of evolutionary drift of synonymous codons alogn mRNA”, Comput. Technol., 5:2 (2000), 57–63 | MR

[30] Ratusny A. V., Podkolodnaya O. A., Ananko E. A., Likhoshvai V. A., “Mathematical model of erythoroid cell differentiation regulation”, Proc. I Internat. Conf. on Bioinformatics or Genome Regulation and Structure, v. I, Novosibirsk, 2000, 203–206

[31] Nedosekina E. A., Ananko E. A., Likhoshvai V. A., “Construction of mathematical model of the gene network on macrophage activation under the action of IFN-$\gamma$ and LPS”, BGRS' 2002, Proc. III Internat. Conf. on Bioinformatics of Genome Regulation and Structure, v. 2, Novosibirsk, 2002, 74–76

[32] Ratushnyi A. V., Likhoshvai V. A., Ignateva E. B. i dr., “Kompyuternaya model gennoi seti regulyatsii biosinteza kholesterina v kletke: analiz vliyaniya mutatsii”, Dokl. RAN, 389:2 (2003), 90–93

[33] Latypov A. F., Nikulichev Yu. V., Likhoshvai V. A. et al., “Problems of control of gene networks in a space of stable states”, Modelling and Analys. of Logic Controlled Dynamic Systems, Proc. IFAC Workshop, Irkutsk, 2003, 251–266

[34] Fadeev S. I., Ermakova A., Gudkov A. V., Primenenie metoda prodolzheniya po parametru dlya rascheta ravnovesnykh sostoyanii, opredelyaemykh minimizatsiei svobodnoi energiei Gibbsa, Preprint No 7, In-t matem. SO RAN, Novosibirsk, 1995, 33 pp. | MR | Zbl

[35] Likhoshvai V. A., Fadeev S. I., Demidenko G. V., Matushkin Yu. G., “Modelirovanie mnogostadiinogo sinteza veschestva bez vetvleniya uravneniem s zapazdyvayuschim argumentom”, Sibirskii zh. industr. matem., 7:1(17) (2004), 73–94 | MR | Zbl

[36] Thomas R., Thieffry D., Kaufman M., “Dynamycal behavior of biological regulatory networks. I: Biological role of feedback loops and practical use of the concept of the loop-characteristic state”, Bull. Math. Biology, 57 (1995), 247–276 | Zbl

[37] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “O svyazi grafa gennoi seti s kachestvennymi rezhimami ee funktsionirovaniya”, Mol. biologiya, 35:6 (2001), 1080–1087

[38] Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Zadachi teorii funktsionirovaniya gennykh setei”, Sibirskii zh. industr. matem., 6:2(14) (2003), 64–80 | MR

[39] Likhoshvai V. A., Fadeev S. I., “O gipoteticheskikh gennykh setyakh”, Sibirskii zh. industr. matem., 6:3(15) (2003), 134–153 | MR

[40] Johnson A. D., Poteete A. R., Lauer G. et al., “Lambda repressor and cro-components of an efficient molecular switch”, Nature, 294:5838 (1981), 217–223 | DOI

[41] Van Gemen B., Twisk J., Van Knippenberg P. H., “Autogenous regulation of the escherichia coli ksgA gene at the level of translation”, J. Bacteriology, 171:7 (1989), 4002–4008

[42] Ptashne M., A genetic switch: Phage lambda and higher organisms, Blackwell Sci., Oxford, 1992

[43] Gardner T. S., Cantor C. R., Collins J. J., “Construction of a genetic toggle switch in Escherichia coli”, Nature, 403 (2000), 339–342 | DOI

[44] Kharari F., Teoriya grafov, Mir, M., 1973 | MR

[45] Elowitz M. B., Leibler S., “A synthetic oscillatory network of transcriptional regulators”, Nature, 403 (2000), 335–338 | DOI

[46] Edwards R., Glass L., “Combinatorial explosion in model gene networks”, CHAOS, 10 (2000), 691–704 | DOI | MR | Zbl