Status: List C for Mathematics.

Prerequisites: Previous experience with Markov chains and hidden Markov models is highly desirable, eg from suitable Statistics courses or the Systems Biology module BS915 Advanced Bioinformatics. Familiarity with basic probability is assumed, (ST112 Probability B). ST217 Mathematical Statistics B and/or ST202 Stochastic Processes would be helpful.

Content: Systems biology is an emerging area in the Mathematical Sciences, bringing together mathematics and statistics to applications in Biology and Medicine, where the emphasis is on attaining an understanding at a systems level, ie the dynamics and behaviour as a consequence of all the interacting components. The ideas of Mathematical Biology are thus coupled with statistics to obtain a full circle from experimental data, mathematical model through to model testing against the data. However the emphasis is much more on noise and stochasticity than traditional Mathematical Biology. Thus this module is an ideal complement to MA390 Topics in Mathematical Biology.

This module will use a wide variety of ideas from Mathematics and Statistics, both in the form that models can take and in their inference from data. The module includes:

Part I: Networks.

• Models of gene networks, eg Bayesian networks, logic models, state space models.
• Bayesian inference methodologies, such as Markov chain Monte Carlo (MCMC), theory and algorithms.
• Inference of selected network models, eg Gaussian regression models.
• Network modelling and inference using hidden variables.
• Integration of different data types into models, eg Factor models.
• Model selection methods, eg AIC, BIC.

Part II: Small circuit dynamics.

• Stochastic models of transcription and translation.
• Dynamics of small networks, including steady state analysis with bifurcation theory.
• Stochastic effects on bifurcation behaviour.

It is unlikely that you will be familiar with all the techniques used and handouts on basic material will be available. Previous experience with Biology is not required.

Assessment: 3 hour examination.

Lecturer: Nigel Burroughs (Rm 331 Coventry House).