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Long-range contacts in protein structures were demonstrated to be predictive of different physiological properties of hemoglobin and albumin proteins. Complex networks based approach was demonstrated to highlight basic principles of protein folding and activity. The presence of a natural scaling region ending at an approximate threshold of 120-150 residues shared by proteins of different size and quaternary structure was highlighted. This threshold is reminiscent of the typical size for a macromolecule to have a binding site sensible to environmental regulation.