Tuesday, June 18

8:30 AM

Mudd Hall Auditorium

Chair: Lenore Cowen, The Johns Hopkins University

## IP3

Mathematical Challenges in Protein Folding

Biologists are interested in determining how proteins assemble into their geometric structures, and how to predict protein structure given sequence data or other constraints. Biologists have been able to obtain some information experimentally. Our challenge is to help fill in the picture and speed up the process. Three examples of mathematical problems that arise in this fashion occur in the areas of secondary structure prediction, virus shell assembly, and distance geometry.
Biologists have sequenced the one-dimensional amino acid code of many proteins, but this information does not give a protein's three-dimensional structure.
Pattern recognition and probabilistic methods may help to find regions in a sequence that will fold into a known secondary structure, or motif.

Virologists have long been able to observe, albeit mostly only at low resolution, the structure of virus shells, but it has long been a mystery how hundreds of similar protein subunits can self-assemble into such intricate and symmetric structures. New mathematical modeling of the geometry of a scaffolding structure that is believed to guide assembly may shed some light on this process.

Finally, biologists and chemists have obtained data on inter-atomic distances using current technologies such as NMR. Techniques based on random sampling, rigidity theory, and some basic extremal graph theory seem like they may be helpful, even in the presence of incomplete data or errors, in the reconstruction of three-dimensional structure.

As time allows, the speaker will describe recent advances in these topic areas.

**Bonnie A. Berger**

Department of Mathematics

Massachusetts Institute of Technology

*MEM, 3/21/96*