Biomedical Mathematics

Course Objective

This course consists of two parts, each with its own goals.

Learning goals part 1:

a. The student is able to write down a statistical model for cellular evolution;
b. The student can analyse the properties of such models;
c. The student is able to make inferences using these models and perform generalisations;
d. The student understands the stochastic description of a gene-gene interaction network and knows how to reconstruct such a network data.

Learning goals part 2:

a. The student is able to model biological processes that involve time-dependent dynamics (both in discrete and continuous time);
b. The student can perform an analysis of such a model, consisting of finding steady states and their stability properties using linear stability analysis, and can describe the effects on solutions of parameter perturbations;
c. The student is able to interpret the mathematical results back into the biomedical context;
d. The student is able to study the long-time behaviour of solutions using the concept of dominant eigenvalues.

Course Content

This course consists of two parts.

The first parts has two sections. In both sections processes in the cell are modelled. An event in a cell does not occur in isolation, but occurs in relation to the rest of the cell. In the entire course these dependencies are modelled. Wherever possible examples from the VUmc medical hospotical are used to illustrate statistical techniques. In the first section of this part we focus on modelling DNA sequences. The resulting models are used to describe the evolution of cancer cells. Using hidden Markov chain models the exon-intron structure of a gene is studied. We also describe the evolution of DNA to reconstruct phylogenetic trees (trees of descent). In the second section, we try to unravel the topological structure of gene regulatory networks on the basis of gene expression data. Can we uncover which genes works together?

In the second part of the course, we will cover deterministic models of biological processes, using both discrete and continuous time models. We will treat how to set up equations, analyse the resulting model and how to interpret the results back into the biological context. We will cover various biological and biomedical applications, such as ecology, epidemiology and chemical reactions.

Additional Information Teaching Methods

Lectures and written assignments

Method of Assessment

For the first part, there is only a written exam. For the second part there are hand-in assignments (10%) and a written exam (90%). Both parts need to be passed with a grade of 5.5 or higher.