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Analogies between chemical and biological processes occurring in autowave mode

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Abstract

On the examples of frontal polymerization, tumor growth, and propagation of the nerve impulse, we examined nonlinear phenomena in chemistry and biology. The results of theoretical and experimental studies on the loss of stability of thermal waves of frontal polymerization were presented. The stationarity loss limits for the reactions of epoxide resin curing, polymerization of metal-containing acrylamide complexes, and copolymerization of methyl methacrylate and styrene in the presence of single-walled nanotubes were experimentally studied and theoretically calculated. It was shown that stability of the frontal process waves depends on the heat balance of the exothermic polymerization reaction. Nonlinear phenomena at variation of the polymerization kinetic parameters were studied. The limits of the transition from stationary to nonstationary mode were determined on the basis of experimental data and theoretical calculations. Theoretical study of a diffusion-kinetic model of tumor growth was discussed; the wave nature of the propagation of tumors was shown. The FitzHugh–Nagumo model was studied in view of the diffusion equation; the possibility of formation of the oscillatory modes during the nerve impulse propagation was demonstrated.

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References

  1. Vavilin, V.A., Priroda (Moscow, Russ. Fed.), 2000, no. 5.

  2. Merzhanov, A.G. and Khaikin, B.I., Teoriya voln goreniya v gomogenykh sredakh (Theory of Combustion Waves in Homogeneous Media), Chernogolovka: Inst. Strukt. Makrokinet., Akad. Nauk SSSR, 1992.

    Google Scholar 

  3. Yu, C. and Wei, J., Chaos, Solitons Fractals, 2009, vol. 41, no. 3, p. 1223. doi doi 10.1016/j.chaos.2008.05.007

    Article  Google Scholar 

  4. Pojman, J.A., Frontal Polymerization: in Nonlinear Dynamics with Polymers: Fundamentals, Methods and Applications, New York: Wiley, 2010.

    Book  Google Scholar 

  5. Davtyan, S.P., Tonoyan, A.O. Teoriya i praktika adiabaticheskoi i frontal’noi polimerizatsii (Theory and Practice of Adiabatic and Frontal Polymerization), Palmarium Academic, 2014.

    Google Scholar 

  6. Epstein, R. and Pojman, J.A., Chaos, 1999, vol. 9, p. 9.

    Article  Google Scholar 

  7. Volpert, A.I., Volpert, Vit.A., and Volpert, Vl.A., Traveling Wave Solution of Parabolic Systems, Translation of Mathematical Monographs, 2003, vol. 140, AMS Books.

  8. Davtyan, S.P., Begishev, V.P., Volpert, V.A., and Malkin, A.Ya., Dokl. Akad. Nauk SSSR, 1973, vol. 208, p. 208.

    Google Scholar 

  9. Babadzhanyan, A.S., Vol’pert, V.A., Vol’pert, Vl.A., Davtyan, S.P., and Megrabova, I.N., Fiz. Goreniya Vzryva, 1989, no. 1, p. 1.

    Google Scholar 

  10. Davtyan, S.P., Shaginyan, A.A., Tonoyan, A.O., and Ghazaryan, L., in Compounds and Materials with Specific Properties, Howell, B.A., Lekishvili, N., and Zaikov, G.E., Eds., New York: Nova Science, 2008, p. 88.

  11. Stewart, F., Meehan, T., and Pojman, J.A., Chaos, 1999, vol. 9, p. 9.

    Google Scholar 

  12. Davtyan, S.P., Berlin, A.A., and Tonoyan, A.O., Rev. J. Chem., 2011, vol. 1, no. 1, p. 56.

    Article  Google Scholar 

  13. Pojman, J.A., Frontal polymerization, in Polymer Science: A Comprehensive Reference, Matyjaszewski, K. and Möller, M., Eds., 2012, vol. 4, p. 4.

    Google Scholar 

  14. Davtyan, S.P., Hambartsumyan, A.F., Davtyan, D.S., Tonoyan, A.O., Hayrapetyan, S.H., Bagyan, S.H., and Manukyan, L.S., Eur. Polym. J., 2002, no. 38, p. 38.

    Article  Google Scholar 

  15. Illescas, J., Sanna, R., Alzari, V., Nuvoli, D., Casu, M., Rivera, E., and Mariani, A., J. Polym. Sci., Part A: Polym. Chem., 2013, vol. 51, p. 51.

    Google Scholar 

  16. Scognamillo, S., Bounds, C., Thakuri, S., Mariani, A., Wu, Q., and Pojman, J.A., J. Appl. Polym. Sci., 2014, vol. 131, p. 131.

    Article  Google Scholar 

  17. Ilyashenko, V.M. and Pojman, J.A., Chaos, 1998, no. 8, p. 8.

    Article  Google Scholar 

  18. Pojman, J.A., Ilyashenko, V.M., and Khan, A.M., Phys. D (Amsterdam, Neth.), 1995, no. 84, p. 84.

    Google Scholar 

  19. Davtyan, S.P., Zakaryan, H.H., and Tonoyan, A.O., Chem. Eng. J., 2009, vol. 155, p. 155.

    Article  Google Scholar 

  20. Carranza, A., Gewin, M., and Pojman, J.A., Chaos, 2014, vol. 24, p. 248. doi doi 10.1063/1.4876438

    Article  Google Scholar 

  21. Ruiu, A., Sanna, D., Alzari, V., Nuvoli, D., and Mariani, A., J. Polym. Sci., Part A: Polym. Chem., 2014, vol. 52, p. 52.

    Article  Google Scholar 

  22. Corcione, C.E., Freuli, F., and Frigione, M., Materials, 2014, vol. 7, p. 7.

    Article  Google Scholar 

  23. Nuvoli, D., Alzari, V., Pojman, J.A., Sanna, V., Ruiu, A., Sanna, D., Malucelli, G., and Mariani, A., ACS Appl. Mater. Interfaces, 2015, vol. 7, p. 7.

    Google Scholar 

  24. Illescas, J., Ramí rez-Fuentes, Y.S., Zaragoza-Galán, G., Porcu, P., Mariani, A., and Rivera, E., J. Polym. Sci., Part A: Polym. Chem., 2015, vol. 53, p. 53.

    Article  Google Scholar 

  25. Tonoyan, A.O., Davtyan, D.S., Varderesyan, A.Z., Hamamchyan, M.G., and Davtyan, S.P., Synthesis of bentonite and diatomite-containing polymer nanocomposites and their characteristics, in High-Performance Polymers for Engineering-Based Composites, Mukbaniani, O.V., Abadie, M.J.M., and Tatrishvili, T., Eds., Apple Academic, 2016, ch. 19.

  26. Tonoyan, A.O., Davtyan, S.P., and Müller, S.C., Influence of nanoparticles on the mechanism and properties of nanocomposites obtained in frontal regime, in Bottom-Up Self-Organization in Supramolecular Soft Matter, Müller S.C. and Parisi, J., Eds., Springer, 2015, ch. 5, p. 101.

    Google Scholar 

  27. Davtyan, S.P., Tonoyan, A.O., Varderesyan, A.Z., and Müller, S.C., Eur. Polym. J., 2014, vol. 57, p. 57.

    Article  Google Scholar 

  28. Laroussi, M., Mohades, S., and Barekzi, N., Biointerphases, 2015, vol. 10, p. 101. doi doi 10.1116/1.4905666

    Article  Google Scholar 

  29. Davtyan, S.P. and Müller, S.C., Macromol. React. Eng., 2014, vol. 8, no. 5, p. 442.

    Article  Google Scholar 

  30. Tonoyan, A.O., Davtyan, D.S., Ketyan, A.G., and Davtyan, S.P., Khim. Zh. Armenii, 2015, vol. 68, no. 2, p. 285.

    Google Scholar 

  31. Davtyan, D.S., Pirumyan, P.A., Bagyan, S.E., Zakaryan, A.O., Tonoyan, A.O., Mair, T., and Davtyan S.P, Khim. Zh. Armenii, 2006, vol. 59, no. 4, p. 22.

    CAS  Google Scholar 

  32. Davtyan, D.S., Pirumyan, P.A., Bagyan, S.E., Zakaryan, A.O., Tonoyan, A.O., Mair, T., and Davtyan S.P, Khim. Zh. Armenii, 2007, vol. 60, no. 1, p. 12.

    CAS  Google Scholar 

  33. Avetisyan, A.S., Tonoyan, A.O., Sukiasyan, Z.K., and Davtyan, S.P., Proc. State Eng. Univ. Armenia, Ser. Chem. Environ. Technol., 2013, vol. 16, p. 16.

    Google Scholar 

  34. Davtyan, S.P., Tonoyan, A.O., Berlin, A.A., and Gevorkyan, L.A., Polym. Sci., Ser. B, 2012, vol. 54, p. 54.

    Article  Google Scholar 

  35. Davtyan, S.P., Berlin, A.A., and Tonoyan, A.O., Russ. Chem. Rev., 2010, vol. 79, no. 3, p. 205.

    Article  CAS  Google Scholar 

  36. Davtyan, D.S., Tonoyan, A.O., Varderesyan, AZ., and Davtyan, S.P., Influence of single-wall nanotubes on the stability of frontal modes and properties of obtained polymer nanocomposites, in High-Performance Polymers for Engineering-Based Composites, Mukbaniani, O.V., Abadie, M.J.M., and Tatrishvili, T., Eds., Apple Academic, 2016, ch. 20, p. 219.

    Google Scholar 

  37. Aleksandryan, A., Tonoyan, A., and Davtyan, S., SETAC Europe 26th Annual Meeting, 2015-11-25.

    Google Scholar 

  38. Spravochnik po spetsial’nym funktsiyam (Manual on Special Functions) Abramovich, M. and Stigan, I., Eds., Moscow: Nauka, 1979.

    Google Scholar 

  39. Kolobov, A.V., Anashkina, A.A., Gubernov, V.V., and Polezhaev, A.A., Komp’yut. Issled. Model., 2009, vol. 1, no. 4, p. 415.

    Google Scholar 

  40. Ping Bi, Shigui Ruan, and Xinan Zhang, Chaos, 2014, vol. 24, no. 2, p. 023101. doi doi 10.1063/1.4870363

    Article  Google Scholar 

  41. Liu, D., Ruan, S., and Zhu, D., Math. Biosci. Eng., 2012, vol. 9, p. 9. doi doi 10.3934/mbe.2012.9.347

    Article  CAS  Google Scholar 

  42. Frieboes, H.B., et al., NueroImage, 2007, vol. 37, p. 37.

    Article  Google Scholar 

  43. Stein, A.M., et al., Biophys. J., 2007, vol. 92, p. 92.

    Article  Google Scholar 

  44. Stephanie, S., Guo, W.-H., Kim, Y., and Wang, Y.-L., Biophys. J., 2013, vol. 104, p. 104.

    Google Scholar 

  45. Huang, Y.L., Tung, C.-K., Zheng, A., Kim, B.J., and Wu, M., Integr. Biol., 2015, vol. 7, p. 7.

    Article  Google Scholar 

  46. Taddei, M., Giannoni, E., Morandi, A., Ippolito, L., Ramazzotti, M., Callari, M., Gandellini, P., and Chiarugi, P., Cell Commun. Signaling, 2014, vol. 12, p. 12.

    Article  Google Scholar 

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Authors and Affiliations

  1. National Polytechnic University of Armenia, ul. Teryana, 105, Erevan, Armenia

    A. O. Tonoyan, S. Yu. Kotikyan & S. P. Davtyan

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  1. A. O. Tonoyan
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  2. S. Yu. Kotikyan
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  3. S. P. Davtyan
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Correspondence to A. O. Tonoyan.

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Tonoyan, A.O., Kotikyan, S.Y. & Davtyan, S.P. Analogies between chemical and biological processes occurring in autowave mode. Ref. J. Chem. 6, 218–251 (2016). https://doi.org/10.1134/S2079978016030031

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  • DOI: https://doi.org/10.1134/S2079978016030031

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