Multiscale Mathematical Biology (BM)
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Biological systems are so complex, that biologists often need collaborate with mathematicians and computational scientists to unravel them. For mathematicians, these questions constitute a rich source of applied mathematical problems, for which often a range of mathematical and computational techniques need to be combined with one another. For biologists, this mathematical viewpoint often leads to surprising new insights: basic knowledge of the main regulatory mechanisms and organizing principles will help them recognize these in their own experimental systems. Mathematical insight into dynamical systems, pattern formation, complex networks, multiscale dynamics and parallel processing turn out to be a tremendous help while trying to ‘make sense of life’.
Biological systems are so complex, that biologists often need to call in the help from mathematicians and computational scientists. These questions constitute a rich source of applied mathematical problems, for which often a range of mathematical and computational techniques need to be combined with one another. Mathematical insight into dynamical systems, pattern formation, complex networks, multiscale dynamics and parallel processing turn out to be a tremendous help while trying to ‘make sense of life'.
This course will in particular introduce you to the mathematical modeling of healthy and diseased multicellular organisms, like ourselves. A key question is how cells cooperate to create biological structure, and how this biological structure feeds back on gene expression. The focus will be on how to sharpen one’s intuition on the emergence of biological systems and patterns by using and further developing a variety of continuous and discrete mathematical models of biological systems. Mathematical techniques include ordinary-differential equations, partial-differential equations, cellular automata, Hamiltonian systems, and in many cases combinations of those. This course will cover a range of multicellular phenomena, including development of animals and plants, blood vessel networks, bacterial pattern formation and diversification, tumor growth and evolution.
At the end of course students will have an overview of and some hands-on experience with a range of mathematical and computational techniques that computational biologist use in the study of collective cell behavior and biological pattern formation. They are familiar with recent literature on multiscale biological modeling and they have some experience with constructing basic computational models and hypotheses of phenomena described in the biological literature.
The course consists of a series of lectures, practical assignments using biological modeling environments, and a final project.
1) Practicum assignments, 20%
2) Final product, 30%
3) Written exam, 50%
The ‘final product’ contains a small research project and a short presentation.
Basic knowledge of programming and differential equations is useful for some lectures, but not necessary overall.
Handouts of slides, partial lecture notes and research papers will be provided during the course.
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