Multifractal analysis of solvent accessibilities in proteins

The solvent accessibilities of amino acid side chains in a protein can be determined computationally from x-ray crystallographic data. The sequential profile of these accessibilities shows a seemingly random variation. A generalized box-counting analysis of such profiles shows multifractal behavior. Multifractal spectra obtained for a variety of proteins are broader than a corresponding random array, indicating an underlying hierarchical structure to the proteins. The multifractal parameters are used to extract an underlying binary multiplicative process with one-step memory. Similar binary processes occur in the generation of helix-coil sequences in biopolymers. Computer simulations were performed that generated misfolded proteins. The misfolded proteins have narrower multifractal spectra than the properly folded ones. Thus, this multifractal analysis can be used as a diagnostic tool in assessing proper folding in structure prediction algorithms.