Journal article Open Access

Mass fractal dimension and the compactness of proteins

Enright, Matthew B.; Leitner, David M.


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    <subfield code="a">Vibrational dynamics and energy flow in a protein are related by Alexander-Orbach
theory to the protein's mass fractal dimension, D, and spectral dimension, d . Burioni et
al. [Proteins: Struct., Funct. and Bioinformatics 55, 529 (2004)] recently proposed a
relation between d and protein size based on their computational analysis of a set of
proteins ranging from about 100 to several thousand amino acids. We report here values
for D computed for 200 proteins from the Protein Data Bank (PDB) ranging from about
100 to over 10,000 amino acids and examine variation of D with protein size. The
average D is found to be 2.5, significantly smaller than a completely compact 3-
dimensional collapsed polymer. Indeed, we find that on average a protein in its PDB
configuration fills about three-quarters of the volume within the protein surface. Protein
mass is also found to scale with radius of gyration with an exponent of 2.5 for this set of
proteins.</subfield>
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