Mathematical Modelling of Microbiological Processes

Major: Biotechnology and Bioengineering
Code of subject: 6.162.00.O.032
Credits: 3.00
Department: Technology of Biologically Active Substances, Pharmacy and Biotechnology
Lecturer: Doctor of Economical Sciences, Professor Sofiya Vasylyuk
Semester: 6 семестр
Mode of study: денна
Мета вивчення дисципліни: The acquisition of knowledge and skills by students in the field of mathematical modeling and analysis of population growth and development processes under conditions of periodic and continuous cultivation, as well as the synthesis of target products
Завдання: The ability to apply knowledge in practical situations. The ability to use professional-profile knowledge and practical skills to address specific tasks in the field of biotechnology and bioengineering. The ability to apply knowledge of mathematics and physics to the extent necessary to achieve other educational program outcomes. The ability to understand and apply mathematical modeling to study the modes, conditions, and regularities of microbiological processes.
Learning outcomes: Being able to apply modern mathematical methods to solve practical problems related to the research and design of biotechnological processes. Utilizing knowledge of physics for the analysis of biotechnological processes. Being able to calculate key criteria for assessing the efficiency of a biotechnological process (parameters of biological agent growth, rate of synthesis of the target product, synthetic capacity of biological agents, economic coefficient, output of the target product from the substrate, productivity, cost of nutrient medium, etc.). Conducting calculations of parameters for biotechnological equipment based on the analysis of heat and mass exchange processes. Having an awareness of the need for lifelong learning to deepen existing knowledge and acquire new professional expertise. Being capable of utilizing various methods, including modern information technologies, for effective communication at both professional and social levels.
Required prior and related subjects: Prerequisites: General Microbiology and Virology; General Biotechnology; Biophysics; Informatics Co-requisites: Processes and Equipment of Biotechnology Industry; Design and Equipmentof Biotechnical
Summary of the subject: This discipline allows future biotechnological engineers to study the laws underlying biotechnological processes - the kinetics of growth and development of microbial populations, the synthesis of metabolic products of microorganisms, as well as hydrodynamic, mass exchange and heat exchange processes in bioreactors. The subject of the discipline is the study of mathematical models of the processes of periodic and continuous cultivation of microorganisms, taking into account the influence of various physical and chemical factors and their analysis. The methods of determining the quantitative characteristics of the growth and development of microbial cultures, the synthesis of target products, and the calculation of optimal conditions for the synthesis of metabolic products are considered.
Опис: Tasks and content of the course. Theoretical foundations of modeling. Specifics of mathematical modeling of living systems. Mathematical modeling of biotechnological (microbiological) processes. Population growth process of microorganisms. Kinetic curves of biomass growth. Malthus and Mono postulates. Mathematical description of biomass growth. Inhibition of microorganism growth. Integral form of the equation for microbial population growth. Model RLC. Determination of the capacity of a periodically operated fermenter. Known kinetic models of biomass growth. Michaelis–Menten kinetics of enzymatic reactions. Calculation of the capacity of continuously operated apparatus. Single-stage homogeneous continuous cultivation. Multistage homogeneous continuous cultivation. Negative-feed batch cultivation method for biomass. Single-stage homogeneous cultivation with biomass recirculation. Physico-chemical justification of the Monod equation. The simplest scheme of cell-substrate interaction. Scheme with equilibrium "saturation" of microorganism cells with substrate. Scheme with irreversible transformation of substrate in cells. "Microscopic" approach to the kinetics of biomass growth. Mathematical modeling of the biosynthesis of metabolic products.
Assessment methods and criteria: The main methods of knowledge diagnosis are: current (PC) and semester control (SC), which is carried out from educational material, the scope of which is determined by the work program of the discipline for the semester. Current control is carried out during lectures and laboratory classes in order to check the level of assimilation of theoretical and practical knowledge and skills of the student. PC is conducted in the form of: performance and defense of control work and express survey in laboratory classes. Semester control is carried out in the form of differentiated assessment
Критерії оцінювання результатів навчання: Semester assessment is conducted in the form of differentiated grading. Performance in laboratory work - 20; Written-oral express control - 65; Control work - 15.
Recommended books: 1. О.В. Болотін, І.М. Мага, В.В. Нечипорук, В.І. Ткач. Математичне моделювання в мікробіології та хімічній технології харчових добавок: Навч. посібник.-Ужгород: Вид-во В.Падяка, 2014. – 361, [4] с. 2. Біотехнології та біоінженерія. Частина 1. Основи біотехнології. Рекомендації до виконання практичних робіт [Електронний ресурс] : навчальний посібник для здобувачів ступеня бакалавра, які навчаються за освітньо-професійною програмою «Регенеративна та біофармацевтична інженерія» спеціальності 163 Біомедична інженерія / КПІ ім. Ігоря Сікорського ; уклад.: В. В. Мотроненко, Т. М. Луценко, Л. М. Дронько. – Електронні текстові данні (1 файл: 1,13 Мбайт). – Київ : КПІ ім. Ігоря Сікорського, 2022. – 96 с. 3. Варфоломеев С.Д., Калюжный СВ. Биотехнология: Кинетические основы микробиологических процессов: Учеб. пособие для биол. и хим. спец. вузов. - М.: Высш. шк, 1990.-296 с. 4. Сидоров ЮЛ., Влязло Р.Й., Новіков В.П. Процеси і апарати мікробілогічної промисловості. Технологічні розрахунки. Приклади і задачі. Частина І. Ферментація. - Львів: Видво НУ "Львівська політехніка", 2004.- 240 с. 5. Васильев Н.А., Амбросов В.А., Складнев А.А. Моделирование процессов микробиологического синтеза. – М., Изд. «Лесная промышленность», 1975, 344 6. Succurro A, Ebenhoh O. Review and perspective on mathematical modeling of microbial ecosystems. Biochem Soc Trans. 2018 Apr 17;46(2):403-412. doi: 10.1042/BST20170265. Epub 2018 Mar 14. PMID: 29540507; PMCID: PMC5906705.

Mathematical Modelling of Microbiological Processes (курсова робота)

Major: Biotechnology and Bioengineering
Code of subject: 6.162.00.O.035
Credits: 2.00
Department: Technology of Biologically Active Substances, Pharmacy and Biotechnology
Lecturer: Doctor of Economical Sciences, Professor Sofiya Vasylyuk
Semester: 6 семестр
Mode of study: денна
Мета вивчення дисципліни: The acquisition of knowledge and skills by students in the field of mathematical modeling and analysis of population growth and development processes under conditions of periodic and continuous cultivation, as well as the synthesis of target products
Завдання: The ability to apply knowledge in practical situations. The ability to use professional-profile knowledge and practical skills to address specific tasks in the field of biotechnology and bioengineering. The ability to apply knowledge of mathematics and physics to the extent necessary to achieve other educational program outcomes. The ability to understand and apply mathematical modeling to study the modes, conditions, and regularities of microbiological processes.
Learning outcomes: Being able to apply modern mathematical methods to solve practical problems related to the research and design of biotechnological processes. Utilizing knowledge of physics for the analysis of biotechnological processes. Being able to calculate key criteria for assessing the efficiency of a biotechnological process (parameters of biological agent growth, rate of synthesis of the target product, synthetic capacity of biological agents, economic coefficient, output of the target product from the substrate, productivity, cost of nutrient medium, etc.). Conducting calculations of parameters for biotechnological equipment based on the analysis of heat and mass exchange processes. Having an awareness of the need for lifelong learning to deepen existing knowledge and acquire new professional expertise. Being capable of utilizing various methods, including modern information technologies, for effective communication at both professional and social levels.
Required prior and related subjects: Prerequisites: General Microbiology and Virology; General Biotechnology; Biophysics; Informatics Co-requisites: Processes and Equipment of Biotechnology Industry; Design and Equipmentof Biotechnical
Summary of the subject: Studying the discipline will allow students to consolidate knowledge about the general theoretical regularities of the growth processes of biomass of microorganisms. Knowledge of these regularities will allow to calculate the volume of fermentation equipment, consciously apply technological options in this or that specific process of biomass cultivation and, ultimately, competently approach the practical design of microbiological productions.
Опис: Execution of an individual research task. Preparation for the presentation and defense of the coursework.
Assessment methods and criteria: Current control over the student's performance of each stage of the course work is carried out by the teacher during consultations. Semester control during course work is carried out in the form of differentiated credit during the presentation and defense of the course work.
Критерії оцінювання результатів навчання: A term paper completed in accordance with the assigned task is evaluated on a scale of 100 points. The points are distributed as follows: 65 points - the maximum score for assessing the content and formatting of the term paper, 25 points - the maximum score for evaluating the oral presentation of the term paper with an oral report, 10 points - the maximum score for answering questions on the topic of the individual work.
Recommended books: 1. О.В. Болотін, І.М. Мага, В.В. Нечипорук, В.І. Ткач. Математичне моделювання в мікробіології та хімічній технології харчових добавок: Навч. посібник.-Ужгород: Вид-во В.Падяка, 2014. – 361, [4] с. 2. Біотехнології та біоінженерія. Частина 1. Основи біотехнології. Рекомендації до виконання практичних робіт [Електронний ресурс] : навчальний посібник для здобувачів ступеня бакалавра, які навчаються за освітньо-професійною програмою «Регенеративна та біофармацевтична інженерія» спеціальності 163 Біомедична інженерія / КПІ ім. Ігоря Сікорського ; уклад.: В. В. Мотроненко, Т. М. Луценко, Л. М. Дронько. – Електронні текстові данні (1 файл: 1,13 Мбайт). – Київ : КПІ ім. Ігоря Сікорського, 2022. – 96 с. 3. Варфоломеев С.Д., Калюжный СВ. Биотехнология: Кинетические основы микробиологических процессов: Учеб. пособие для биол. и хим. спец. вузов. - М.: Высш. шк, 1990.-296 с. 4. Сидоров ЮЛ., Влязло Р.Й., Новіков В.П. Процеси і апарати мікробілогічної промисловості. Технологічні розрахунки. Приклади і задачі. Частина І. Ферментація. - Львів: Видво НУ "Львівська політехніка", 2004.- 240 с. 5. Васильев Н.А., Амбросов В.А., Складнев А.А. Моделирование процессов микробиологического синтеза. – М., Изд. «Лесная промышленность», 1975, 344 6. Succurro A, Ebenhoh O. Review and perspective on mathematical modeling of microbial ecosystems. Biochem Soc Trans. 2018 Apr 17;46(2):403-412. doi: 10.1042/BST20170265. Epub 2018 Mar 14. PMID: 29540507; PMCID: PMC5906705.