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Updated: Aug 19, 2026

Hi-C: A Method to Study the Three-dimensional Architecture of Genomes.
Published on: May 6, 2010
Mass fractal dimension and the compactness of proteins
Matthew B Enright1, David M Leitner
1Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557, USA.
Abstract:
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 . Proteins: Struct., Funct. Bioinf. 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 three-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.
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