636-0706-00L Spatio-Temporal Modelling in Biology
Semester | Herbstsemester 2016 |
Dozierende | D. Iber |
Periodizität | jährlich wiederkehrende Veranstaltung |
Lehrsprache | Englisch |
Kurzbeschreibung | This course focuses on modeling spatio-temporal problems in biology, in particular on the cell and tissue level. A wide range of mathematical techniques will be presented as part of the course, including concepts from non-linear dynamics (ODE and PDE models), stochastic techniques (SDE, Master equations, Monte Carlo simulations), and thermodynamic descriptions. |
Lernziel | The aim of the course is to introduce students to state-of-the-art mathematical modelling of spatio-temporal problems in biology. Students will learn how to chose from a wide range of modelling techniques and how to apply these to further our understanding of biological mechanisms. The course aims at equipping students with the tools and concepts to conduct successful research in this area; both classical as well as recent research work will be discussed. |
Inhalt | 1. Introduction to Modelling in Biology 2. Morphogen Gradients 3. Turing Pattern 4. Travelling Waves & Wave Pinning 5. Application Example 1: Dorso-ventral axis formation 6. Chemotaxis, Cell Adhesion & Migration 7. Introduction to Numerical Methods 8. Simulations on Growing Domains 9. Image-Based Modelling 10. Branching Processes 11. Cell-based Simulation Frameworks 12. Application Example 2: Limb Development 13. Summary |
Skript | All lecture material will be made available online Link |
Literatur | 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 |
Voraussetzungen / Besonderes | The course builds on introductory courses in Computational Biology. The course assumes no background in biology but a good foundation regarding mathematical and computational techniques. |