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.
- Biosynthesis of enzyme
- Cultivation of microorganisms
- Differential equations
- Mathematical expectation
- Stochastic model