Unique Flexibility Patterns of PDB Entries

Abstract

Solid bodies obtain characteristic mass and charge distributions, principle rotational axes as well as internal symmetry axes. Internal symmetry axes are uniquely identified by Normal Mode Analysis (NMA) and are widely used in the fields of engineering and seismology to model the redistribution of modest energy influxes into non-rigid bodies. NMA of protein systems rapidly and reproduceably identify their internal flexibility characteristics. Protein systems typically consist of thousands of atoms and three times as many Cartesian degrees of freedom (dofs). These systems can equally well be characterized by their internal dofs: bond lengths, bond angles and bond rotations. Small energy perturbations like thermal baths primarily activate bond-rotations or dihedrals. Use of dihedral dofs ensures that bond lengths and bond angles remain stereochemically sound. We have shown that use of these dofs combined with distance- and atom-dependent Hookian potentials correctly reproduce theoretical dispersion spectra. Use of linearized potentials permits NMA of PDB coordinates: No initial, structure-distorting energy minimization is required. This feature permits analyses of PDB structures that differ only slightly such as (i) two isoforms of the same X-ray electron density, (ii) the same structure solved in two different crystal forms, or (iii) two evolutionary related proteins that share high structural, not sequence, homology. We examine the modal signatures of several cases and report meaningful differences. In one, glycoside hydrolase family 10 xylanases, the A and B isoforms of the same crystal place three out of 302 residues in alternate conformations. Their modal analyses reveal significant differences in their slowest modes, consistent with predictions that GH-10 members consist of two subgroups with differing mobility. In another, the modal analysis of two closely related tertiary structures with low sequence homology, lactadherin and Factor VIII glycoprotein, reveal significant differences consistent with H/D exchange data.