We study the dynamic propensity of the backbone hydrogen bonds of the protein MDM2 (the natural regulator of the tumor suppressor p53) in order to determine its binding properties. This approach is fostered by the observation that certain backbone hydrogen bonds at the p53-binding site exhibit a dynamical propensity in simulations that differs markedly form their state-value (that is, formed/not formed) in the PDB structure of the apo protein. To this end, we conduct a series of hydrogen bond propensity calculations in different contexts: 1) computational alanine-scanning studies of the MDM2-p53 interface; 2) the formation of the complex of MDM2 with the disruptive small molecule Nutlin-3a (dissecting the contribution of the different molecular fragments) and 3) the binding of a series of small molecules (drugs) with different affinities for MDM2. Thus, the relevance of the hydrogen bond propensity analysis for protein binding studies and as a useful tool to complement existing methods for drug design and optimization will be made evident.