Different molecular size scaling regimes for inner and outer regions of proteins

We study the rough statistical features of size scaling in protein backbones by using molecular descriptors associated with their central and external regions. By using a diverse set of experimental structures, we show that the mean radius of gyration and die span of backbones scale differently, leading to a ratio of ''inner'' and ''outer'' scaling size exponents of v(i)/v(o) approximate to 0.8. The span of average proteins is found to scale with the number of amino acids as R similar to n(vo), with 1/2<v(o)<3/5, thus providing a measure of the ''locally'' swollen character of the backbone near the exterior. The result holds for all classes of proteins, including those with the most compact cores.