Abstract and keywords
Abstract (English):
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.

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


Microbiological synthesis products (enzymes) find wide application in various branches of petrochemical, food, and processing industries, medicine, pharmacology, etc. The principal stages of fermentation are the selection of a producing strain and the determination of conditions for its cultivation, during which the microbiosynthesis of a certain enzyme proceeds. Fermentation is most often implemented as a continuous process (maintaining the cultivation conditions throughout the entire period of its duration), but many metabolites can be obtained only via batch synthesis with the withdrawal of a product at the end of the process. The regularities governing the formation of an enzyme complex strongly depend on many process parameters (physicochemical, engineering, biological, and other factors [1–7]), the adjustment of which provides the efficient organization of this process. The technology of such a process usually ensures the simultaneous attainment of a maximum of both productivity and quality at minimum expenditures.

Since the synthesized enzyme is extracted from a cultivated biomass or a cultural liquid, it is necessary to perform a series of studies on the effect of the birth and death rates of cultivated population members on the amount of formed biomass. The consumption of time in this project will be reduced by constructing a mathematical model, which adequately describes the process of fermentation.

The objective of this work is to construct mathematical models providing the system description of the microbial cultivation and biosynthesis of the target enzyme and to study the kinetic regularities governing the duration of batch cultivation.


Biokinetic regularities were studied using the cultivation of the Escherichia coli strain, a recombinant Rhoodesporidium foruloides L-phenylalanine ammonia-lyase producer, grown at the Research Institute of Bioengineering of the Kemerovo Institute of Food Science and Technology [8–10]. The submerged batch cultivation of yeast in a fermenter was performed following the existing producer recommendations (in a culture medium containing (g/l): glucose, 20.0; peptone, 10.0; yeast extract, 5.0), at a temperature of 26°C for 24 h in the regime of non-controlled pH. Control measurements were performed every half hour beginning from the moment of pitching. The biomass and protein concentrations were determined from the absorbance in compliance with the manufacturer’s manuals for an UV-1800 spectrophotometer (Shimadzu, Japan) [9].


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