The course covers the mathematical modelling, analysis and simulation of various biochemical processes that relate to cell signaling, in particular to electrical activity in e.g. neurons and pancreatic beta cells. Modelling and analysis techniques are highlighted by using examples. It is illustrated how models of subsystems (and understanding of their behaviour individually) may be combined to get ‘whole cell’ models and gain insight in their behaviour. Mathematical concepts from dynamical system theory (e.g. equilibria, periodic solutions, bifurcations, time scale analysis, singular perturbation) are introduced in order to analyse and simulate the models using dedicated software. The results are compared to experimental results. At the end of the course the student is acquainted with the fundamental Hodgkin-Huxley, FitzHugh-Nagumo and Morris-Lecar models for electrical activity of cells and the relationships among them and should be capable of exploring further the current research on (biological) neural networks. Moreover, students have learned how to determine effective transport rates for transporter proteins based on the underlying biochemistry using the King-Altman computational scheme. They then know how to combine models for subsystems, to derive information on the dynamics of the combined system and to interpret the output of simulation tools.
Lectures and computer-supported practice sessions
Exercises and literature research with subsequent presentation(s) of results
The course is part of the Bio-informatics master track of the Technical University Delft and University Leiden. See http://www.delftleiden.nl/BIO/ for more information and details on the schedule.