FRACTAL ASPECTS OF PROTEIN STRUCTURE AND DYNAMICS

Abstract

Proteins have well-defined three dimensional structures which are dictated by their amino acid sequence. Despite this great specificity, general structural and dynamic properties exist. Scaling relationships for the radius of gyration and surface area of a large data set of proteins are demonstrated in this work. These results show that proteins scale as collapsed polymers. Thermal fluctuations are examined for two different proteins by an analysis of the Debye-Waller factors derived from X-ray crystallographic data. Long-range correlations exist between fluctuations along the backbone. A disordered Ising model is presented which gives similar correlations. To further examine the role of multiple connectivity in protein structures, the vibrational spectrum for an alpha helix (linear chain with H-bonds) is analyzed from recursive relationships derived using a decimation technique.