The dynamics of a folded globular protein (bovine pancreatic trypsin inhibitor) have been studied by solving the equations of motion for the atoms with an empirical potential energy function. The results provide the magnitude, correlations and decay of fluctuations about the average structure. These suggest that the protein interior is fluid-like in that the local atom motions have a diffusional character.

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Side-chain torsional potentials in the bovine pancreatic trypsin inhibitor are calculated from empirical energy functions by use of the known X-ray structure of the protein and the rigid-geometry mapping technique. The potentials are analyzed to determine the roles and relative importance of contributions from the dipeptide backbone, the protein, and the crystalline environment of solvent and other protein molecules. The structural characteristics of the side chains determine two major patterns of energy surfaces, E(X1,X2): a gamma-branched pattern and a pattern for longer, straight side chains (Arg, Lys, Glu, and Met). Most of the dipeptide potential curves and surfaces have a local minimum corresponding to the side-chain torsional angles in the X-ray structure. Addition of the protein forces sharpens and/or selects from these minima, providing very good agreement with the experimental conformation for most side chains at the surface or in the core of the protein. Inclusion of the crystalline environment produces still better results, especially for the side chains extending away from the protein. The results are discussed in terms of the details of the interactions due to the surrounding, calculated solvent-accessibility figures and the temperature factors derived from the crystallographic refinement of the pancreatic trypsin inhibitor.

A reaction path is presented by which the effects of oxygen binding in hemoglobin are transmitted from a heme group to the surface of its subunit. Starting from the known deoxy geometry, it is shown by calculations with emirical energy functions and comparisons with available data Iow the change in heme geometry on ligation introduces a perturbation that leads to the tertiary structural alterations essential for cooperativity. It is found that there is little strain on the unliganded heme; instead, the reduced oxygen affinity of hemoglobin results from the strain on the liganded subunit in a tetramer with the deoxy quaternary structure. The cooperative nature of the binding of oxygen by hemoglobin is one of the most intensively studied phenomena in protein chemistry (1). From the classic x-ray work of Perutz and his collaborators (2, 3), supplemented by the physical and chemical studies of others (4, 5), the outlines of the cooperative mechanism have been determined. The essential elements are two quaternary structures (oxy and deoxy) for the hemoglobin tetramer (6), two tertiary structures (liganded and unliganded) for each subunit, and the presence of ionic, van der Waals, and hydrophobic interactions that couple the tertiary structural change of the subunits to the relative stabilities of the quaternary structures. These elements have been incorporated into a statistical mechanical model that describes ligand binding as a-function of solution conditions and accounts for the effects of mutations and chemical modifications (7,8).To complete the description of the cooperative mechanism, the statistical-mechanical model must be supplemented by an understanding of the origin of the important structural changes and their associated energies. It is necessary to know at the atomic level how ligand binding alters the tertiary structure of an individual subunit and how these alterations in subunit geometry affect and can be affected by the quaternary structure of the hemoglobin tetramer. In this paper, we focus on the first of these two problems. From calculations based on empirical energy functions (9) and comparisons with the available data, we are able to determine the properties of the heme group and of the surrounding globin chain that lead to the essential tertiary structural changes. A localized reaction path that involves directly only a relatively small number of globin atoms is found to transmit information concerning ligand binding from the heme group to the surface of the subunit. It is shown that there is little strain on the heme in unliganded hemoglobin, but that the flattening of the heme and shortening of the iron-histidine bond induced by oxygen binding produce steric repulsions between the heme and the globin that alter the subunit geometry. Nonbonded contacts between the asymmetrically positioned His F8(87) and the heme appear to initiate a rotation of the latter. This in turn produces a large displacement of Val FG5(93), which is the key residue in transmitting structural changes to the al...

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