Hemoglobin is an efficient oxygen carrier in blood because affinity of hemoglobin for oxygen depends on how much oxygen is already bound to the molecule. Each hemoglobin molecule can bind up to four oxygen molecules. When no oxygen is bound the affinity is low; when four oxygen molecules are bound, the affinity is high. This means that in the lungs hemoglobin is easily loaded with oxygen, and will carry that oxygen until it encounters an area of low oxygen tension, where the oxygen should be delivered. Once the oxygen starts to unload, the process is accelerated by the low affinity of the deoxy form of hemoglobin. This property is vital for human life. Although the structures of both oxy and deoxy forms of hemoglobin are known (and different), Nobody knows specifically how the binding of one oxygen molecule directly affects the affinity of the other three sites for oxygen. We have developed novel methods for describing the change in conformation between structures in terms of shifts of a small number of rigid bodies relative to one another. Our method is based on finding sets of interatomic distances, which are the same before and after the structural change. We have applied this method to hemoglobin and found that such a description provides a simple and plausible framework for analysis of the structural changes related to oxygen binding. We first examined the Alpha-Beta half molecule, composed of two of the four subunits in hemoglobin, and developed a description of the changes on oxygenation. This work was published in July 1997 in the Journal of Molecular Biology. We have now done an analysis of the ways in which the two Alpha-Beta dimers interact with one another, and find unexpected connections between the different binding sites in the molecule. A manuscript on this subject is in preparation. We will continue this project by studying the interaction between properties of oxy and deoxy heme as developed by Dr. Kim Baldridge from quantum mechanical studies, and the rigid bodies surrounding the heme pocket. Experimentally testable predictions of this model will be studied through a collaboration with Prof. Gary Ackers of Washington University in St. Louis. A direct extension of the methods developed for the study of hemoglobin is a method for determining spatial similarity of two proteins, treated as a problem of congruence of two space curves with gaps and insertions. This method has been used to structurally align all known protein kinases with results, which agree with known sequence homology. It appears that spatial congruence may be a powerful tool for detection of unexpected relationships, since it depends only on coordinates and not on sequence. We will explore this technique and develop distributable software for it during the next grant year.