Proteins: Coexistence of Stability and Flexibility

We introduce an equation for protein native topology based on recent analysis of data from the Protein Data Bank and on a generalization of the Landau-Peierls instability criterion for fractals. The equation relates the protein fractal dimension d_f, the spectral dimension d_s, and the number of amino acids N. Deviations from the equation may render a protein unfolded. The fractal nature of proteins is shown to bridge their seemingly conflicting properties of stability and flexibility. Over 500 proteins have been analyzed (d_f, d_s, and N) and found to obey this equation of state.