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Three Universal Distribution Functions for Native Proteins with Harmonic Interactions

We used statistical thermodynamics of conformational fluctuations and the elements of algebraic graph theory together with data from 2000 protein crystal structures, and showed that folded native proteins with harmonic interactions exhibit distribution functions each of which appear to be universal across all proteins. The three universal distributions are: (i) the eigenvalue spectrum of the protein graph Laplacian, (ii) the B-factor distribution of residues, and (iii) the vibrational entropy difference per residue between the unfolded and the folded states. The three distributions, which look independent of each other at first sight, are strongly associated with the Rouse chain model of a polymer as the unfolded protein. We treat the folded protein as the strongly perturbed state of the Rouse chain. We explain the underlying factors controlling the three distributions and discuss the differences from those of randomly folded structures.