|
MSc in Mathematical Modelling & Scientific Computing |
Special Topic |
12 lectures TT Prof K Burrage |
- This course will address some of the important issues associated with the mod elling and simulation of processes taking place on or inside a biological cell. The following topics will be covered:
- A brief introduction to important aspects of Molecular Cellular Biology.
- How noise arises in cellular processes.
- Intrinsic and Extrinsic noise.
- Discrete stochastic modelling and simulation through Markov processes.
- Continuous stochastic modelling and simulation through stochastic differential equations.
- Trajectorial simulations versus probability density calculations.
- The role of delays in genetic regulation.
- Spatial modelling: granular transport versus reaction diffusion equations.
- Towards multiscale simulation.
- Many of these issues will be discussed in the light of a number of case studies.
- The Hes1 gene as a molecular clock.
- Cascading reactions: Michaelis-Menten and MAPK.
- Stochastic switches.
- Insulin/glucose dynamics.
- All simulations to be done in MATLAB.
- Additional reading:
- Computational Cell Biology (Eds. Fall et al.)
- An introduction to Stochastic Processes with applications to Biology (Linda J.S. Allen)
- Stochastic Modelling for Systems Biology (D.J. Wilkinson)
- Final report to be handed in by Tuesday 13 June 2008.