Protein crystal disorder

In addition to the dynamic disorder caused by temperature-dependent vibration of atoms, protein crystals have static disorder due to the fact that molecules, or parts of molecules, do not occupy exactly the same position or do not have exactly the same orientation in the crystal unit cell. However, unless data are collected at different temperatures, one cannot distinguish between dynamic and static disorder. Because of protein crystal disorder, the diffraction pattern fades away at some diffraction angle 0max. The corresponding lattice distance <7mm is determined by Bragg s law as shown in equation 3.7 ... 

Proteins crystallized from very low salt concentrations (examples are carboxypeptidase A and elastase) can often be treated exacdy like proteins crystallized from alcohol-water mixtures. Their low solubility in water allows them to be transferred from their normal mother liquor to a distilled water solution or to a solution of low (10-20%) alcohol concentration without disorder. It is advisable to carry out this transfer at near 0 C to further decrease the protein solubility. From this stage it is trivial to add alcohol while cooling, as described above. Complications arise, however, when the salt employed as a precipitant in the native mother liquor is insoluble in alcohols. The solution to this problem is to replace the salt by ammonium acetate at equivalent or higher ionic strength. Ammonium acetate is soluble up to 1 M in pure methanol, and is very soluble in nearly all alcohol-water mixtures, even at low temperature. It therefore provides a convenient substitute for salts such as sodium sulfate or sodium phosphate. 

Another kind of stadc disorder which can exist in a protein crystal and which is different from a distribution of discrete conformations is lattice... 

Burling, F. T. and Brunger, A. T. (1994) Thermal motion and conformational disorder in protein crystal structures. Isr. J. Chem. 34,165-175. 

The number of additional terms based on Eq. 4 is determined by the solvent fraction of the crystal. If the solvent content is 50% (which is the average for protein crystals), N independent, additional equations of type 4 are introduced. As these equations can be substituted into the Fourier summations of Eq. 1, they effectively reduce the number of unknowns by 2N times the solvent fraction -provided they accurately distinguish disordered solvent from protein. 

An x-ray analysis will measure the diffraction pattern (positions and intensities) and the phases of the waves that formed each spot in the pattern. These parameters combined result in a three-dimensional image of the electron clouds of the molecule, known as an electron density map. A molecular model of the sequence of amino acids, which must be previously identified, is fitted to the electron density map and a series of refinements are performed. A complication arises if disorder or thermal motion exist in areas of the protein crystal this makes it difficult or impossible to discern the three-dimensional structure (Perczel et al. 2003). 

SANS on disordered food systems is quite different from X-ray crystallography of protein crystals. The former studies systems in their native solution state, with information limited by various averaging effects. The latter can obtain very detailed information on single proteins in a highly ordered crystal, which is a non-native state. 

Careful analysis of electron-density maps usually reveals many ordered water molecules on the surface of crystalline proteins (Plate 4). Additional disordered water is presumed to occupy regions of low density between the ordered particles. The quantity of water varies among proteins and even among different crystal forms of the same protein. The number of detectable ordered water molecules averages about one per amino-acid residue in the protein. Both the ordered and disordered water are essential to crystal integrity, and drying destroys the crystal structure. For this reason, protein crystals are subjected to X-ray analysis in a very humid atmosphere or in a solution that will not dissolve them, such as the mother liquor. 

Recall that stable protein crystals contain a large amount of both ordered and disordered water molecules. As a result, the proteins in the crystal are still in the aqueous state, subject to the same solvent effects that stabilize the structure in solution. Viewed in this light, it is less surprising that proteins retain their solution structure in the crystal. 

FIGURE 6.22 Diffraction images frequently reveal problems with particular crystals that are sometimes blatant but occasionally subtle. These include disorder, multiple crystals, or twinned crystals. In (a), the pattern initially appears very ordered and proper, but close inspection of the row of reflections indicated provides evidence that this monoclinic thaumatin crystal is in fact twinned. In (b), the reflections from a Bence-Jones protein crystal fall not on a single reciprocal lattice but multiple, interwoven lattices indicative of twinned or multiple crystals. In (c), a tetragonal crystal of Bence-Jones protein is seriously disordered as evidenced by the smeared, highly mosaic reflections and high background scatter. 

Displacements may arise not only from thermal motion but also from static disorder when corresponding atoms in different unit cells take up slightly different mean positions. Certain side chains, especially those exposed, may take up a few radically different conformations in different molecules so that separate images of them can be seen with reduced occupancy in electron density maps. The mean square displacement will also include contributions from lattice disorders but these are usually small in protein crystals that diffract well to high resolution [191]. In principle, the thermal vibrations can be distinguished from static disorder by varying temperature. Simple harmonic vibrations are expected to decrease linearly with temperature. 

R factors are commonly 20-30% for proteins, whereas for small molecules they are 2-5%. A rule of thumb is that the R factor (in %) should be around 10 times the resolution (in A). One of the contributors to the R factor is thermal motion (even at 100 K) this motion is reported as a 5 factor (sphere in which the atom can be found) some structures may be accurate enough to determine separately anisotropic B factors, describing thermal motion in three orthogonal directions. Since protein crystals are up to 70% water, assumptions have to be made about the distribution of these waters. Certain regions of the protein may be disordered, with some crystals having one protein conformation and others another. The occupancy of various sites is then an important consideration. 

The chemical preparation step in which the protein is isolated, purified, and crystallized is critical in that the protein preparation must be chemically homogeneous otherwise, the resulting disorder will muddle the electron-density map. The preparation of isomorphous derivatives by soaking native protein crystals in various mercury, platinum, lead, uranium, etc., solutions also is critical since several crystals of each derivative are required for x-ray data collection (because of irradiation damage) and all the crystals should have the same heavy-atom distribution and concentration. The protein structure documentation should provide evidence that the preparative protein chemistry is sound. 

The great potential of the X-ray data for obtaining motional information has recently led to a molecular dynamics test197 of the standard refinement techniques that assume isotropic and harmonic motion. Since simulations have shown that the atomic fluctuations are highly anisotropic and, in some cases, anharmonic (see Chapt. VI.A.1), it is important to determine the errors introduced in the refinement process by their neglect. A direct experimental estimate of the errors resulting from the assumption of isotropic, harmonic temperature factors is difficult because sufficient data are not yet available for protein crystals. Moreover, any data set includes other errors that would obscure the analysis, and the specific correlation of temperature factors and motion is complicated by the need to account for static disorder in the crystal. As an alternative to an experimental analysis of the errors in the refinement of proteins, a purely theoretical approach has been used.197 The basic idea is to generate X-ray data from a molecular dynamics simulation... 

The first protein structures were derived using a technique called isomorphous replacement (IR), developed in the late 1950 s. The materials used are heavy metal derivatives of protein crystals. To obtain a heavy metal derivative of a protein, the protein crystal is soaked in a solution of a heavy metal salt. The metals most used are Pt, Hg, U, lanthanides, Au, Pb, Ag and Ir. The heavy metal or a small molecule containing the heavy metal, depending upon the conditions used, diffuses into the crystal via channels created by the disordered solvent present. The aim is for the heavy metal to interact with some surface atoms on the protein, without altering the protein structure. This is never exactly achieved, but in suitable cases, the changes in structure are slight. 

Because the structures of the active sites of enzymes are extremely responsive to the binding of substrates and substrate analogues, conformational changes may take place which give rise to cracking or disorder of the crystal. It is important, however, that the crystals of protein plus inhibitor be closely isomorphous with the native protein crystals, at least with respect to the cell dimensions so that the molecular transform is sampled at the same reciprocal lattice points. In those instances where large conformational changes occur, de novo structure determination has to be attempted. 

At absolute zero the Bj are close to zero (equation (9.20)) and so are the thermal uj (equation 9.21)). However, for a protein crystal each unit cell is not exactly identical to the next, i.e. there is a statistical population of atomic coordinates causing an effective random disorder for all temperatures. Since the disorder is random equations (9.18) and (9.22) still apply and there are corresponding uj (equation (9.21)) due to the disorder. 

Unfortunately, no protein crystal exists with such a very small molecular disorder for the anomalously scattering atom and which is coolable to absolute zero if it did then the effective electron density for an anomalous/ or/" of only a few electrons would have an electron density considerably higher than the normal scattering electron density (by 50-100 times). In a practical case for metallo-proteins with a natural metal cofactor buried in the protein core, the disorder 5-factor will be considerably less than the overall disorder factor for the whole protein where the surface residues will have particularly large temperature factors. On the other hand, a heavy atom derivative bound to the surface of the protein will have a large disorder factor. 

Since leucine will not bind Fe directly, the effect of the pro/leu substitution must be on the higher order protein structure of ferritin. X-ray crystallography analysis of protein crystals showed that the pro/leu substitution disrupted the C/D helices near the turn. The effect of the single amino acid change was amplified by proximity to the junction of three-subunits [49]. The pro/leu protein assembled normally, but there were eight regions of localized disorder distributed around the molecule, at the... 

Especially in protein crystals, but also in other structures that show relatively large voids or cavities, one can find solvent molecules that do not show any order at all. Such solvent regions can be interpreted as a liquid that is amorphously frozen during data collection (assuming that you collect the data at low temperature as you always should). Following the Babinet Principle, this extreme case of disorder is described as bulk solvent and can be refined using a two-parameter approximation (Moews and Kretsinger, 1975). See Example 5.3.5. 

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