636-0706-00L Spatio-Temporal Modelling in Biology
Semester | Autumn Semester 2017 |
Lecturers | D. Iber |
Periodicity | yearly recurring course |
Language of instruction | English |
Abstract | This course focuses on modeling spatio-temporal problems in biology, in particular on the cell and tissue level. The main focus is on mechanisms and concepts, but mathematical and numerical techniques are introduced as required. Biological examples discussed in the course provide an introduction to key concepts in developmental biology. |
Objective | Students will learn state-of-the-art approaches to modelling spatial effects in dynamical biological systems. The course provides an introduction to dynamical system, and covers the mathematical analysis of pattern formation in growing, developing systems, as well as the description of mechanical effects at the cell and tissue level. The course also provides an introduction to image-based modelling, i.e. the use of microscopy data for model development and testing. The course covers classic as well as current approaches and exposes students to open problems in the field. In this way, the course seeks to prepare students to conduct research in the field. The course prepares students for research in developmental biology, as well as for applications in tissue engineering, and for biomedical research. |
Content | LECTURES 1. Introduction to Modelling in Biology (Sep 22) Sep 29th: NO LECTURE & NO TUTORIAL 2. Dynamical Systems (Oct 6) 3. Morphogen Gradients (Oct 13) 4. Mathematical Description of Growing Biological Systems (Oct 20) 5. Travelling Waves & Wave Pinning (Oct 27th) 6 Turing Patterns (Nov 3) Nov 10th: NO LECTURE & NO TUTORIAL (ETH FACULTY RETREAT) 7. Chemotaxis & Branching Processes (Nov 17th) 8. Image-Based Modelling (Nov 24th ) 9. Tissue Mechanics (Dec 1st) 10. Growth Control (Dec 8th) 11. Cell-cell Signalling (Dec 15th - Dr Boareto) 12. Summary (Dec 22nd) TUTORIALS Sep 29: Mathematical Methods required for the course Oct 6: Case Study: I: Dorso-ventral axis formation Oct 13: Dynamical Systems Oct 20: Morphogen Gradients Oct 27: Growing Domains Nov 3: Travelling Waves Nov 17: Turing Patterns Nov 24: Chemotaxis & Branching Processes Dec 1: Case Study II: Organogenesis & Image-based Modelling Dec 8: Tissue Mechanics Dec 15: Cell-cell Signalling Dec 22: Summary, Open Questions & Mock Exam |
Lecture notes | All lecture material will be made available online Link |
Literature | The lecture course is not based on any textbook. The following textbooks are related to some of its content. The textbooks may be of interest for further reading, but are not necessary to follow the course: Murray, Mathematical Biology, Springer Forgacs and Newman, Biological Physics of the Developing Embryo, CUP Keener and Sneyd, Mathematical Physiology, Springer Fall et al, Computational Cell Biology, Springer Szallasi et al, System Modeling in Cellular Biology, MIT Press Wolkenhauer, Systems Biology Kreyszig, Engineering Mathematics, Wiley |
Prerequisites / Notice | The course is self-contained. The course assumes no background in biology but a good foundation regarding mathematical and computational techniques. |