Mathematics of the genetic information

Understanding the origin and the management of the genetic information is currently the main topic under investigation. Professors Fimmel, Gumbel and Strüngmann ask the fascinating question why and how life can exist. Naturally, this question has many facets that involve various scientific disciplines. Historically, the discovery of the double helix of DNA proved an interesting link between genetics, coding theory and mathematics that seemed to reduce the biochemical puzzle of the genetic code to abstract combinatorics of symbols. Tremendous efforts had been made in sequencing genomes of different organisms. finally leading to the sequencing of the whole human genome. However, this did not meet the expectations on the possibility of diagnosing and treating many serious diseases. It turned out that either we do not have enough data yet or it is necessary to investigate more deeply the nature of the genetic information based on first principles from Chemistry, Physics and Mathematics.

We follow this second approach: On the one hand Biology, Chemistry and also Physics tell us how the process of translating the genetic information into life (could) possibly work but we are still very far from a complete understanding of this process. On the other hand, Mathematics and Statistics give us methods to describe such natural processes (or parts of it) in a theoretical framework. Also, they provide us with hints and predictions that can be tested at the experimental level. Furthermore, there are peculiar aspects of the management of genetic information that are closely related to Information theory and Communication theory and Computer Science provides the technical tools to make most of the analyses possible.

Together with a team from the University of Bologna (Italy) we investigate error detecting and error correcting properties of the genetic code. In particular, circular codes and comma-free codes are in the focus of our research. These are codes (subcodes of the genetic code) that allow to detect and possibly correct frame shifts in the reading process of the ribosome. A project supported by the Karl-Völker-Stiftung is dedicated to use these investigations in order to predict the structure of proteins and their folding process.