Mathematical Biology: the virtual cell
The course covers the mathematical modelling, analysis and simulation of various biochemical processes that relate to electrica activity in cells, e.g. neurons and pancreatic beta cells. Modelling techniques are highlighted, by using examples. Mathematical concepts from dynamical system theory (e.g. equilibria, periodic solutions, bifurcations, time scale analysis, singular perturbations) are introduced in order to analyse and simulate models using dedicated software. The results are compared to experimental results.
At the end of the course the student is acquainted with the Hodgkin-Huxley, FitzHugh-Nagumo and Morris-Lecar models for electrical activity and the relationships among them and should be capable of exploring further the current research on (biological) neural networks.
Literature:
Computational Cell Biology, C.P. Fall, E.S. Marland, J.M. Wagner and J.J. Tyson (eds.), Interdisciplinary Applied Mathematics, Vol. 20, Springer-Verlag, 2002 (ISBN 0-387-95369-8)
Course material
Slides of lectures:
XPPAUT sample files:
Examination exercises:
- First series (handed out on Monday, 31 March 2008)
Deadline: Monday, 14 April 2008
- Second series (handed out on Monday, 28 April 2008)
Deadline: Wednesday, 21 May 2008, 11.00h
XPPAUT course material (for training purposes):
The XPPAUT simulation software can be obtained from Bard Ermentrout's personal webpage:
http://www.pitt.edu/~phase/
Final presentation programme:
On Friday 20 June 2008, 10.30-15.30h, the final presentations will be held in the Snellius building. The precise room will be announced. Details can be found here.