Statistical descriptors for the size and shape of globular proteins

The atomic structures of proteins epitomize the ideas of complexity and irregularity in three-dimensional objects. For such objects, size and shape are difficult to quantify, and therefore the development of unbiased parameters for these properties could facilitate their description. Statistical analysis of the frequency distribution of interatomic distances in protein structures of different classes has revealed two numerical descriptors that correlate with physicochemical properties of these macromolecules. The median (mu) of the distribution correlates (r greater than .98, n = 45) with variables indicative of size (e.g., molecular weight and radius of gyration). The exponent of the Box-Cox transformation lambda, used for converting this distribution into a symmetrical one, correlated (r = .75, n = 43) with a general dimensionless shape parameter defined as the combination of the shape-related accessible surface (A0s), molecular volume (V), and radius of gyration (Rg) in the form s = (A0sRg/V). It is suggested that for globular proteins lambda is a function of both the shape parameter s and the fractal dimension D of the protein surface. These objective descriptors of size and shape could be useful to describe other complex objects.