Dynamic signature of ligand binding over a protein surface

We study the motion of Zn^{2+} in the presence of ubiquitin by all-atom molecular-dynamics simulations. We observe that unlike normal diffusive liquid, metal ions show an exponential tail in the self-van Hove function (self-vHf). Moreover, the metal ions are trapped strongly by acidic residues which form a binding pocket over the protein surface. The exponential tail disappears by mutation of trapping residues, suggesting that the tail appears due to trapped motion of the ions. The mean-squared displacements, however, in all the cases show linear dependence on time. Our model establishes that ligand binding generically results in an exponential tail of self-vHf. The self-vHf may give an approach to find binding pockets over a protein surface.