Shape, flexibility and packing of proteins and nucleic acids in complexes.

Determining the change in topological properties like shape, flexibility and packing of proteins and nucleic acids on complexation is important in characterizing the role of induced structural changes and various interactions which control the functional specificity of proteins and nucleic acids. To this end, we have analyzed and compared the three dimensional structures of several protein-protein, protein-DNA and protein-RNA complexes available in the Protein Data Bank (PDB) and the Nucleic Acid Data Bank (NDB). The size of complexed proteins and nucleic acids, as measured by the radius of gyration, follows Flory's scaling law. The change in the scaling exponents for proteins, RNA and DNA reflects the changes in their respective sizes due to complexation. The anisotropy in the shape of proteins, DNA and RNA in complexes is measured by considering the asphericity and shape parameter, which are calculated from the eigenvalues of the moment of inertia tensor. The distribution of asphericity and shape shows that complexed proteins are mostly spherically symmetrical, while DNA and RNA in complexed states are largely prolate and considerably more aspherical compared to the proteins. Persistence length characterizes the intrinsic flexibility/rigidity of proteins and nucleic acids. The flexibility of all biomolecules decreases with the chain length. For small DNA molecules (6-147 base pairs), persistence length is larger compared to RNA and proteins in protein-protein and protein-RNA complexes. The flexibility of DNA increases, while RNA decreases, in their respective complexed states as compared to that of proteins which remain almost unchanged. The two body contact analysis confirms that the side-chain-backbone contacts are predominant compared to sidechain-sidechain and backbone-backbone contacts in the complexed proteins. The average packing density of proteins decreases in their complexed states, which is measured by the mean value of the contact density of their alpha carbon atoms. The average number of hydrogen bonds are found to be less in the interface region of protein-protein complexes compared to that in protein-DNA and protein-RNA complexes.