We present a new algorithm for characterization of protein spatial structure basing on the molecular hydrophobicity potential approach. The method is illustrated by the analysis of three-dimensional structure of barnase and barnase-barstar complex. Current approach enables identification of amino acid residues situated in unfavorable environment (these residues may be "active" for binding), and to map quantitatively hydrophobic, hydrophilic and unfavorable hydrophobic-hydrophilic intra- and inter-molecular contacts involving backbone and side-chain segments of amino acid residues. Calculation of individual contributions of amino acid residues to such contacts permits identification of structurally-important residues. The contact plots obtained with molecular hydrophobicity potential calculations, provide easy rules to choose sites for mutations, which can increase a strength of intra- or inter-molecular hydrophobic interactions. The unfavorable hydrophobic-hydrophilic contact can be mutated to favorable hydrophobic, and already existing weak hydrophobic contact can be strengthen by increasing hydrophobicity of residues in contact. Basing on the analysis of the contact plots, we suggest several mutations of barnase which are supposed to increase intramolecular hydrophobic interactions, and thus might lead to increased stability of the protein. Part of these mutations was studied previously experimentally, and indeed stabilized barnase. The other of predicted mutations were not studied experimentally yet. Several new mutations of barnase and barstar are also proposed to enhance the hydrophobic interactions on their binding interface.