Mathematical and computer-assisted modelling of biological systems are now indispensable. Models enable e.g. to understand complex processes, to test hypotheses, to predict time courses and experiments. Applications range from basic research to from industrial applications to clinical practice. This lecture will provide an introduction to basic concepts and modern methods of systems biology. In particular, we will deal with biochemical reaction networks and deal with the following topics:

• Modelling of biochemical reaction networks (e.g. in signal transductions)
• Analysis of model properties
• Implementation and simulation of models in the computer
• Adaptation of model parameters to experimental data

The lectures are complemented by hands-on exercises. The course is part of the Bachelor’s program in Molecular Biomedicine.

Mathematical models are widely used to achieve a mechanistic understanding of complex biological processes. To develop this models, a broad spectrum of mathematical and computational tools are required, including statistics, numerics, optimization and programming. In this course, will provide an introduction to state-of-the-art approaches for computational modelling:

• Deterministic and stochastic modelling in systems biology
• Statistical modelling of experimental data
• Parameter optimization (e.g. gradient calculation and trust-region methods
• Parameter uncertainty analysis (e.g. MCMC methods)
• Model selection (e.g. AIC, BIC and Bayes factor)

In addition to the established methods, we will point out open problems and challenges. The lectures are complemented by hands-on exercises. Students will learn to implement the different tools in Python, as well as to use established tools. The course is part of the Master’s program in Mathematics and open for PhD students in the Bonn International Graduate School in Mathematics (BIGS).

Students should learn the role and the principle approaches applied in systems immunology, bioinformatics and big data science in generaland particular in respect to the immune system including the relevant methodology applied in the field.

Content:

• Basic principles of the methods applied in systems immunology
• Biological interpretation of high throughput data and the visualization of large dataset
• Application of learned skills to existing datasets addressing immunological questions

The course will provide a deep understanding and detailed overview of a current research focus from the area
of applied probability. Ability to verify the validity of propositions from original literature independently and to question research results critically. Competence to engage in independent study of current research topics

The topics to be covered will be announced at the end of the semester prior to commencement of the course. Possible topics include:

• Stochastic finance (Option pricing, econometrics, optimal stopping)
• Monte Carlo methods (Numerical methods for SDE, MCMC, filtering)
• Branching processes and models from population biology
• Probability on graphs and networks (Random graphs, models of statistical mechanics, stochastic algorithms)