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 plants and animals, including 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, and tumor growth and evolution.
The final grade consists of homework (20%), a final product (a small research project and a short presentation performed in a team of two, 40%) and a written (retake) exam (40%). To pass the course, the grade for the (retake) exam should be at least 5, the grade for the final product at least 5.5, and the (unrounded) weighted average of the three partial grades at least 5.5. No minimum grade is required for the homework in order to take the exam or to pass the course. The deadline for the project report is December 31st, followed by a retake opportunity January 31st. The homework counts as a practical and there is no retake for it; the homework consists of 5 assignments, of which the lowest grade is dropped.
Some basic experience of programming is helpful, but the required skills can be picked up during the course. Basic knowledge of differential equations is required.
Handouts of slides, partial lecture notes and research papers will be provided during the course.
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.
Mode of instruction
The course consists of a series of lectures, practical assignments using biological modeling environments, and a final project.