Cluster 9

Mathematical Modeling in Molecular Biology





In this cluster we will introduce students to the field of DNA topology that combines experimental, mathematical and computational methods to analyze DNA structure and DNA-protein interactions. We will introduce basic biological concepts and the mathematical and computational techniques used to model them. This cluster will have a strong biological laboratory component where students will learn how to experimentally identify different topological forms of DNA. The mathematical methods come from the fields of geometry and topology (especially knot theory) and statistical physics of polymers. The computational methods involve learning about Monte Carlo methods and visualization through the software Knotplot. No prior knowledge in these mathematical and biological topics is necessary, but a strong interest in both is required. Previous knowledge of computer programming is not required but strongly recommended.



Core Courses


Mathematical and computational modeling of DNA

The human genome is 2m (6 feet) long and is packed inside a spherical volume 10μm in diameter.  How this is accomplished remains to be determined. This course will introduce the three dimensional structure of the DNA molecule and some mathematical/computational methods to study it. We will emphasize methods and algorithms to model the behavior of long DNA molecules as polymers. More specifically, students will learn key concepts such as DNA supercoiling and random knotting. They will also learn how to design, implement and analyze Monte-Carlo simulations of DNA molecules and how they are used to study DNA packing in viruses and in cells.

Applications of knot theory to DNA-protein interactions

DNA-protein interactions are at the center of key biological processes such as viral infection, DNA transcription and DNA recombination, and their disruption is associated with a number of diseases. DNA-protein interactions can be captured through studying topological changes of circular DNA molecules. This course will introduce knot theory tools that help describe the mechanism of proteins that change the topology of DNA.