Abstract
Structural motions along a reaction pathway hold the secret about how a biological macromolecule functions. If each static structure were considered as a snapshot of the protein molecule in action, a large collection of structures would constitute a multidimensional conformational space of an enormous size. Here I present a joint analysis of hundreds of known structures of human hemoglobin in the Protein Data Bank. By applying singular value decomposition to distance matrices of these structures, I demonstrate that this large collection of structural snapshots, derived under a wide range of experimental conditions, arrange orderly along a reaction pathway. The structural motions along this extensive trajectory, including several helical transformations, arrive at a reverse engineered mechanism of the cooperative machinery (Ren, companion article), and shed light on pathological properties of the abnormal homotetrameric hemoglobins from α-thalassemia. This method of meta-analysis provides a general approach to structural dynamics based on static protein structures in this post genomics era.
Highlights
Protein crystallography, a powerful yet largely static technique, has greatly advanced our knowledge of protein structures by providing observation of atomic details, but at a cost of crystallization
Rapid progresses in structural genomics and broad applications of protein crystallography are contributing to the mounting entries of data in the Protein Data Bank (PDB) at a current growth rate greater than 10% annually [2]
Singular value decomposition (SVD; see Ref. [6] for a brief summary), a linear algebraic procedure, ranks the significance of information according to their consistency among multiple sources, thereby achieving a big picture via information concentration
Summary
A powerful yet largely static technique, has greatly advanced our knowledge of protein structures by providing observation of atomic details, but at a cost of crystallization. A small handful of n decomposed lower triangles of distance matrices (MM; Figure S2) are sufficient to reconstruct hundreds of N experimental structures using linear combination coefficient sets obtained from SVD.
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