Abstract

A country that owns high-performance computing facilities and mathematical modeling algorithms is able to provide its competitiveness in all the sectors of economy. The application of mathematical modeling is environmentally safe and cost effective and increases the technical and general culture of production. First of all, this concerns the development of new technologies. That is why the creation of new products in both the pharmaceutical and food industries is already impossible without the use of mathematical modeling. Today this is a necessity, the fulfilment of which has already been specified in relevant technical regulations. The simultaneous use of both mathematical methods and experiment provides not only the reduction of time, energy, and financial expenditures, but also the acquisition of additional information and the establishment of a direction of studies. This considerably reduces the time between the generation of an idea and its implementation in the form of a product. The technologies of the use of L-phenylalanine ammonia-lyase for the achievement of certain objectives in medicine, biotechnology, agriculture, and food industry have been developed by now. The insufficient application of algorithmic and mathematical approaches by researchers for development and analysis can be considered as a factor limiting the active use of biotechnological methods in the production of this enzyme. The description of microbial biosynthesis mechanisms by classical mathematical methods encounter some difficulties due to the combined effect of numerous chemical, physical, biological, engineering, and other factors. Another important thing is the more profound study of the kinetics of microbiological synthesis susceptible to both internal and external effects. The batch cultivation of pigmented yeast has been studied by probabilistic methods. A stochastic model providing the system study of the biosynthesis of L-phenylalanine ammonia-lyase by pigmented yeast has been formulated. The cultivation of microorganisms is described by the birth-and-death process. The mathematical expectation and dispersion of the number of population members are proposed as efficiency characteristics. The dependence between the amount of synthesized enzyme and the birth and death rates of a cultivated population is derived through the concentration of cultivated microorganism biomass and the birth and death rates of its members.

Keywords

cultivation of microorganisms, biosynthesis of enzyme, probability, stochastic model, mathematical expectation, dispersion, differential equations

REFERENCES

1. Varfolomeev, S. D. and Kalyuzhnyi, S.V., Biotekhnologiya: Kineticheskie osnovy mikrobiologicheskikh protsessov (Biotechnology: Kinetic Principles of Microbiological Processes), Moscow: Vysshaya shkola, 1990.
2. Rubin, A.B., Pyr’eva, N.F., and Riznichenko, G.Yu., Kinetika biologicheskikh protsessov (Kinetics of Biological Processes), Moscow: Izd. MGU, 1987.
3. Pirt, S.J., Principles of Microbial and Cell Cultivation, Oxford: Blackwell, 1975.
4. Tsiperovich, A.S., Fermenty. Osnovy khimii i tekhnologii (Enzymes. Principles of Chemistry and Technology), Kiev: Tekhnika, 1971.
5. Nikitin, G.A., Biokhimicheskie osnovy mikrobiologicheskikh proizvodstv (Biochemical Principles of Microbiological Production), Kiev: Vysshaya shkola, 1992.
6. Bisswanger, H., Enzyme Kinetics. Principles and Methods, Weinheim: Wiley-VCH, 2008.
7. Glick, B.R. and Pasternak, J.J., Molecular Biotechnology. Principles and Application of Recombinant DNA, Washington, DC: ASM Press, 2000.
8. Babich, O.O., Soldatova, L.S., and Razumnikova. I.S., Klonirovanie i ekspressiya gena L-fenilalanin-ammonii-liazy v Escherichia Coli i vydelenie rekombinantnogo belka (Cloning and expression of the L-phenylalanine-ammonium-lyase gene in Escherichia Coli and extraction of recombinant protein), Tekhnika i tekhnologiya pishchevykh proizvodstv (Technics and Technology of Food Industry), 2011, no. 1, pp. 8–13.
9. Babich, O.O., Biotekhnologiya L-fenilalanin-ammonii-liazy (Biotechnology of L-Phenylalanine-ammonium-lyase), Novosibirsk: Nauka, 2013.
10. Babich, O.O., Dyshlyuk, L.S., and Milent’eva, I.S., Expression of recombinant L-phenylalanine ammonia-lyase in Escherichia Coli, Food and Raw Materials, 2013, vol. 1, no. 1, pp. 48–53.
11. Feller, W. An Introduction to Probability Theory and Its Applications, New York: Wiley, 1968, vol. 1.
12. Venttsel’, E.S. and Ovcharov, L.A., Teoriya sluchainykh protsessov i ee inzhenernye prilozheniya (Theory of Stochastic Processes and Its Engineering Applications), Moscow: Vysshaya shkola, 2000.
13. Kleinrock, L. Queueing Systems. Theory, New York: Wiley, 1975, vol. 1.
14. Saaty, T.L., Elements of Queueing Theory with Application, New York: McGraw Hill, 1961.
15. Haefner, J.W. Modeling Biological Systems: Principles and Applications, New York: Springer, 2005.
16. Zhu, G.-Y., Zamamiri, A.M., Henson, M.A., and Hjortso, M.A., Model predictive control of continuous yeast bioreactors using cell population models, Chemical Engineering Science, 2000, vol. 55, no. 24, pp. 6155–6167.
17. Zhang, Y., Henson, M.A., and Kevrekidis, Y.G., Nonlinear model reduction for dynamic analysis of cell population models, Chemical Engineering Science, 2003, vol. 58, no. 2, pp. 429–445.
18. Xiong, R., Xie, G., Edmondson, A.E., and Sheard, M.A., A mathematical model for bacterial inactivation, International Journal of Food Microbiology, 1999, vol. 46, no. 1, pp. 45–55.
19. Gordeeva, Yu.L., Ivashkin, Yu.A., and Gordeev, L.S., Modeling the continuous biotechnological process of lactic acid production, Theoretical Foundations of Chemical Engineering, 2012, vol. 46, no. 3, pp. 279–283.
20. Skichko, A.S. and Kol’tsova, E.M., Mathematical model for describing oscillations of bacterial biomass, Theoretical Foundations of Chemical Engineering, 2006, vol. 40, no. 5, pp. 503–513.
21. Khoroshevsky, V.G. and Pavsky, V.A., Calculating the efficiency indices of distributed computer system functioning, Optoelectronics, Instrumentation and Data Processing, 2008, vol. 44, no. 2, pp. 95–104.
22. Yustratov, V.P., Pavskii, V.A., Krasnova, T.A., and Ivanova, S.A., Mathematical modeling of electrodialysis demineralization using a stochastic model, Theoretical Foundations of Chemical Engineering, 2005, vol. 39, no. 3, pp. 259–262.
23. Ivanova, S.A. Stokhasticheskie modeli tekhnologicheskikh protsessov pererebotki dispersnykh system obezzhirennogo moloka (Stochastic Models of the Processing of Dispersed Skim Milk Systems), Kemerovo, KemTIPP, 2010.
24. Pavsky, V.A., Pavsky, K.V., and Khoroshevsky, V.G., Vychisleniye pokazatelei zhivuchesti raspredelennykh vychislitel’nykh sistem i osushchestvimosti resheniya zadachi (Calculating the characteristics of the robustness of distributed computational systems and the feasibility of problem solutions), Iskusstvennyi intellect (Artificial Intelligence), 2006, no. 4, pp. 28–34.
25. Riznichenko, G.Yu., Matematicheskie modeli v biofizike i ekologii (Mathematical Models in Biophysics and Ecology), Moscow–Izhevsk: Institut komp’yuternykh issledovanii, 2003.
26. Bozhkov, A.I., Biotekhnologiya. Fundamental’nye i promyshlennye aspekty (Biotechnology. Fundamental and Industrial Aspects), Kharkiv: Fedorko, 2008.