The objective of the proposed research is to discover the principles that govern the three-dimensional structure of protein molecules. Previous work has shown that most of the intramolecular interactions in a protein involve the close packing of its component alpha-helices and/or beta-pleated sheets (secondary structures). Our approach has been to develop simple models that accurately describe these packings. The models are tested and extended by a detailed geometrical analysis of the residue to residue contacts that occur in known protein structures. We do this analysis using interactive computer graphics and numerical calculations. Our preliminary results show that this approach will be very successful. We will use the results of this work to examine two related problems. First, we will analyze the structure of the hemoglobin molecule to discover how the intramolecular packing facilitates the allosteric changes in tertiary structure that occur when a ligand is bound or released. Second, we will analyze the residue packing that occurs at protein-protein interfaces of oligomeric proteins. The results of this, together with our previous work, will provide a detailed theory for protein recognition.