The present application relates to methods for growing crystals of both the uncomplexed and complexed forms of .beta.-secretase (BACE) polypeptide. Polypeptides used herein are derived from human BACE which is also known by the synonyms "mamapsin 2", "human .beta.-site APP-cleaving enzyme, and Asp2". The present application also relates to crystalline forms of uncomplexed BACE and the three-dimensional structure of BACE, as determined from the crystals. In addition, the present application relates to the use of crystalline forms of BACE to identify ligands, preferably inhibitors (antagonists), which bind to, and preferably inhibit the enzymatic activity of, BACE. Furthermore, the present application relates to nucleic acid sequences encoding BACE polypeptide, and methods for making BACE in greater quantity than prior methods, resulting in more effective crystallization.