CHAPTER TWENTY-SIX Linked Analysis of Large Cooperative, Allosteric Systems: The Case of the Giant HBL Hemoglobins Nadja Hellmann,* Roy E. Weber, † and Heinz Decker* Contents 1. Introduction 464 2. Materials 466 2.1. Hb preparation and oxygen-binding curves 466 3. Theory 466 3.1. Fitting function 466 3.2. Models 466 3.3. Influence of allosteric effectors 469 3.4. Constraints on the allosteric equilibrium constants 471 3.5. Statistics 472 4. HBL Hb from L. terrestris 473 5. HBL Hb from M. decora 476 6. What Is the Advantage of Hierarchical Function? 478 7. Concluding Remarks 480 Appendix A 481 References 483 Abstract Homotropic and heterotropic allosteric interactions are important mechanisms that regulate protein function. These mechanisms depend on the ability of oligomeric protein complexes to adopt different conformations and to transmit conformation-linked signals from one subunit of the complex to the neighboring ones. An important step in understanding the regulation of protein function is to identify and characterize the conformations available to the protein complex. This task becomes increasingly challenging with increasing numbers of inter- acting binding sites. However, a large number of interacting binding sites allows for high homotropic interactions (cooperativity) and thus represents the most interesting case. Examples of very large, cooperative protein complexes are the Methods in Enzymology, Volume 436 # 2008 Elsevier Inc. ISSN 0076-6879, DOI: 10.1016/S0076-6879(08)36026-1 All rights reserved. * Institute for Molecular Biophysics, Johannes Gutenberg University, Mainz, Germany { Zoophysiology, Institute of Biological Sciences, University of Aarhus, Denmark 463