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Properly carried out, high-resolution X-ray diffraction data collection followed by careful least-squares refinement can give the spatial distribution of the high-frequency mean-square displacements in a protein. These displacements reflect both individual atomic fluctuations in hard variables (bond lengths and bond angles) and collective motions involving soft variables (torsion angles, nonbonded interactions). Lower frequency, large amplitude motions and rapid but improbable motions are not quantifiable, but they may lead to such complete disorder that their existence can at least be inferred from the absence of interpretable electron density for some sections of the structure. Interior residues are more rigid than groups on the surface, and structural constraints are reflected in restricted motion even for surface residues. Amplitudes of motion of 0.5 Å or greater are not uncommon. The temperature dependence of these fast motions varies considerably over the structure. In general, large 〈x2〉 values have large temperature dependence, while small displacements are less affected by temperature; however, exceptions are common. Significant reduction in 〈x2〉 on cooling establishes that proteins are mobile even in the crystalline state, and that static disorder is not the dominant contributor to the individual mean square displacements. Disordered regions in electron density maps are no longer automatically taken as signs of errors in structure determination. It is now recognized that the absence of strong electron density is often an indicator of conformational flexibility. Some of the functional roles for protein dynamics are beginning to be understood. Missing from these results are the physicochemical details that can be extracted from thermal motion analysis of small molecule crystal structures. Application of these methods to protein data is very difficult, but it is well to remember that just over 10 years ago it was commonly felt that protein structures could not even be refined. Certainly some small, well-diffracting proteins should be amenable to many of the sophisticated small-molecule analyses, as they yield X-ray data to resolutions comparable to simple organic structures. The most important type of analysis that awaits is anisotropic B factor refinement, which would give the principal directions of motion added to the amplitude information now obtained. Unfortunately, refinement of unrestrained anisotropic thermal elipsoids requires six parameters for each atom instead of a single isotropic
B parameter, and even 1.5 Å resolution data do not provide enough overdeterminacy. An alternative approach is to refine selected residues anisotropically while holding the rest of the structure fixed. The only published procedure for restrained anisotropic protein refinement implements restraints based on bond directions29; this approach is invalidated by the result from molecular dynamics that collective motions destroy such a correlation. Optimally, very high-resolution data should be coupled with unrestrained anisotropic refinement for at least a few proteins. These studies would provide the information to develop restrained or group-atom methods in the light of unbiased information. Blundell and associates have undertaken precisely this study on avian pancreatic polypeptide, measuring data beyond 1 Å resolution and refining the structure by small-molecule procedures, including full anisotropic thermal elipsoids in the model. 89 X-Ray diffraction can provide atomic-resolution information about the initial and final states of a process such as ligand binding or triggered conformational change, but the pathway is much more difficult to unravel. Ringe has shown that a bulky ligand can be used to prevent the return of a channel to its resting state after binding, allowing the residues that move to form the channel to be identified.
14 Ligands with chemical “tails” might be used to investigate other channels in proteins. Intermediate states in triggered conformational changes may be trapped at low temperatures90,91 or by careful choice of inhibitors, or by examination of abortive complexes in multisubstrate reactions.
The structure determined by X-ray diffraction studies on a crystalline protein is that of a nonexistent average molecule. It is this structure that will best fit the measured X-ray scattering amplitudes. The average structure contains contributions from all of the different conformational substates that are generated by the thermally driven fluctuations and collective motions of the molecule during the time of data collection,
92 each being weighted according to its probability and lifetime. Any static structure with ideal bond lengths and angles is at best merely one representative from this ensemble of conformations. Most spectroscopic and chemical probes of structure and activity will also reflect the properties of the average molecule, but they may not be sensitive to all members of the conformational distribution and so may see a slightly different average. In certain cases, only one or a few conformations may be seen by a particular technique, or may react with a particular substance. This is the picture of protein structure that has emerged from crystallographicand other studies of protein dynamics