Size, shape, and flexibility of proteins and DNA

Size, shape, and flexibility are the important topological parameters which characterize the functional specificity and different types of interactions in proteins and DNA. The size of proteins and DNA, often measured by the radius of gyration (R(G)), are determined from the coordinates of their respective structures available in Protein Data Bank and Nucleic Acid Data Bank. The mean square radius of gyration obeys Flory's scaling law given by R(G) (2) approximately N(2nu) where N is the number of amino acid residues/nucleotides. The scaling exponent nu reflects the different characteristic features of nonglobular proteins, natively unstructured proteins, and DNA. The asymmetry in the shapes of proteins and DNA are investigated using the asphericity (Delta) parameter and the shape parameter (S), calculated from the eigenvalues of the moment of inertia tensor. The distributions of Delta and S show that most nonglobular proteins and DNA are aspherical and prolate (S>0). Natively unstructured proteins are comparatively spherically symmetrical having both prolate and oblate shapes. The flexibility of these molecules is characterized by the persistence length (l(p)). Persistence length for natively unstructured proteins is determined by fitting the distance distribution function P(r) to the wormlike chain (WLC) model in the limit of r>>R(G). For nonglobular proteins and DNA, l(p) may be computed from the Benoit-Doty approximation for unperturbed radius of gyration of the WLC. The flexibilities of the proteins and DNA increases with the chain length. This is due to an increase in the nonlocal interactions with the increase in N, needed to minimize the conformational fluctuations in the native state. The persistence length of these proteins has not yet been measured directly. Analysis of the two-body contacts for the proteins reveals that the nonglobular proteins are less densely packed compared to the natively unstructured proteins with least side-chain side chain contacts even though side-chain backbone contacts predominate in the two types of proteins.