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Lecturer(s)
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Lazár Dušan, prof. RNDr. Ph.D.
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Course content
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- Introduction (mathematics in biology, purpose of modelling, motivating example - AIDS/HIV research) - Basic mathematics (linear, exponential and other functions, differential equations) - Descriptive models and basic data analysis (linear and exponential regressions, ?2 method) - Estimation of model parameters (different methods) - Model validation and verification (Kullback-Liebler divergence, Occam's razor principle, Akike information criterion) - Chemical reaction kinetics and its modelling (types of reactions, reaction order, law of mass action, master equations, Markov chain) - Michaelis-Menten and Hill enzymatic kinetics - Transition state rate theory and rate of electron tunneling - Modelling of oscillating chemical/biological systems (phase space, criteria for oscillations, Lotka-Voltera model, Brusselator, Belousov-Zhabotinsky reaction, Oregonator, glycolysis in yeast, photosynthetic oscillations) - Metabolic control analysis (assumptions, control and response coefficients, elasticity, summation and connectivity theorems, biological examples) - Examples of complex models - modeling of photosynthetic processes (different models)
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Learning activities and teaching methods
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Lecture
- Preparation for the Exam
- 24 hours per semester
- Attendace
- 30 hours per semester
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Learning outcomes
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Obtaining basic general knowledge about in silico biology, i.e., about studying of biological organisms and processes by means of computer modelling and simulations.
The student will be able to define, write and solve mathematical models of basic biological processes.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Mark
Passing the oral examination.
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Recommended literature
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Bisswanger, H. (2008). Enzyme Kinetics, 2nd Edition. Wiley-Vch.
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Britton, N. F. (2003). Essential Mathematical Biology. Springer.
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Edelstein-Keshet, L. (2005). Mathematical Models in Biology. Siam.
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Ellner, S. P., Guckenheimer, J. (2006). Dynamic Models in Biology. Princeton University Press.
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Haefner, J. W. (2005). Modeling Biological Systems, Principles and applications, 2nd Edition. Springer.
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Laisk A., Nedbal L., Govindjee, eds. (2009). Photosynthesis In Silico: Understanding Complexity from Molecules to Ecosystems. Springer.
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Otto, S. P., Day, T. (2007). A Biologist´s Guide to Mathematical Modeling in Ecology and Evolution. Princeton University Press.
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Roussel, M. R. (2012). A Life Scientist´s Guide to Physical Chemistry. Cambridge University Press.
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Rubin, A., Riznichenko, G. (2014). Mathematical Biophysics. Springer.
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