Date hub proteins are a type of proteins that show multispecificity in a time-dependent manner. To understand dynamic aspects of such multispecificity we studied Ubiquitin as a typical example of a date hub protein. Here we analyzed 9 biologically relevant Ubiquitin-protein (ligand) heterodimer structures by using normal mode analysis based on an elastic network model. Our result showed that the self-coupled motion of Ubiquitin in the complex, rather than its ligand-coupled motion, is similar to the motion of Ubiquitin in the unbound condition. The ligand-coupled motions are correlated to the conformational change between the unbound and bound conditions of Ubiquitin. Moreover, ligand-coupled motions favor the formation of the bound states, due to its in-phase movements of the contacting atoms at the interface. The self-coupled motions at the interface indicated loss of conformational entropy due to binding. Therefore, such motions disfavor the formation of the bound state. We observed that the ligand-coupled motions are embedded in the motions of unbound Ubiquitin. In conclusion, multispecificity of Ubiquitin can be characterized by an intricate balance of the ligand- and self-coupled motions, both of which are embedded in the motions of the unbound form.