An unreasonable man in a quasi-equivalent world.

On January 10 and 11, 1997, a two-day symposium titled Quasi-Equivalence: Motion and Adaptability in Living Molecules was held at Florida State University on the occasion of the 70th birthday of Dr. Donald L. D. Caspar. This issue of the Biophysical Journal contains articles presented at that symposium in recognition of the contributions that Dr. Caspar has made to our understanding of the structures of viruses, proteins, and macromolecular assemblies. Dr. Caspar, a former president of the Biophysical Society and a member of the National Academy of Sciences, is a pioneer in the study of macromolecular assemblies, and one of the first to use the term “structural biology.” The students that he has trained, and the scientists with whom he has shared his unique perspectives and insights into molecular structure, today constitute a major force in the advancement of structural biology. The articles presented here provide a glance at a few of the many directions of thought that have grown from his work, his collaborations, and his endless conversations over the past forty years. It has been over twenty years since I first asked Don Caspar what “quasi-equivalence” means. I didn’t like the answer he gave me then, and I still don’t like it. He said that it was unwise to define a word too precisely, because once you did it became very much less useful. With that, he just turned around and walked away, leaving me to wonder just what quasi-equivalence did mean. It may have been the shortest conversation I ever had with him. Over the past thirty years, our view of proteins has moved progressively from that of rigid blocks to relatively flexible, almost fluid structures; from single-function gene products, to multipurpose molecular machines. The concept of quasiequivalence started us down the intellectual path that has led to the view of protein structure, dynamics, and function that we hold today. The term “quasi-equivalence” was introduced by Caspar and Klug in their 1962 paper on the structure of viruses. The paper was written to address a fundamental problem of virus architecture. Don Caspar had recently shown that tomato bushy stunt virus (TBSV) had icosahedral symmetry (Caspar, 1956), and it seemed likely that all “spherical” viruses had cubic symmetry and probably icosahedral symmetry (Crick and Watson, 1956). However, icosahedral symmetry specifies exactly 60 identical positions about a point (or, in this case, 60 identical units making up a virus capsid), and it was entirely clear that many viruses use more than 60 copies of a single coat protein to construct the protein shell that protects their genome. Caspar and Klug, benefiting from the work of Buckminster Fuller on geodesic domes, laid out what appeared at the time to be an exhaustive compilation of the possible ways that proteins could be arranged with icosahedral symmetry, such that the proteins