Protein crystals density

Traditionally, least-squares methods have been used to refine protein crystal structures. In this method, a set of simultaneous equations is set up whose solutions correspond to a minimum of the R factor with respect to each of the atomic coordinates. Least-squares refinement requires an N x N matrix to be inverted, where N is the number of parameters. It is usually necessary to examine an evolving model visually every few cycles of the refinement to check that the structure looks reasonable. During visual examination it may be necessary to alter a model to give a better fit to the electron density and prevent the refinement falling into an incorrect local minimum. X-ray refinement is time consuming, requires substantial human involvement and is a skill which usually takes several years to acquire. 

The amplitudes and the phases of the diffraction data from the protein crystals are used to calculate an electron-density map of the repeating unit of the crystal. This map then has to be interpreted as a polypeptide chain with a particular amino acid sequence. The interpretation of the electron-density map is complicated by several limitations of the data. First of all, the map itself contains errors, mainly due to errors in the phase angles. In addition, the quality of the map depends on the resolution of the diffraction data, which in turn depends on how well-ordered the crystals are. This directly influences the image that can be produced. The resolution is measured in A... 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

The result is the electron density map of the protein crystal. The final task for the crystallographer is to build the appropriate protein model, i. e., putting amino acid for amino acid into the electron density. Routinely the theoretical amplitudes and phases are calculated from the model and compared to the experimental data in order to check the correctness of model building. The positions of the protein backbone and the amino acid side chains are well defined by X-ray structures at a... 

Jensen [3.11] as well as Teeter [3.12] studied by X-ray diffraction the structure of water molecules in the vicinity, at the surface and inside of protein crystals. Jensen used rubredoxin (CEB) crystals to deduce the structure of water from the density distribution of electrons, calculated from diffraction pictures. Jensen found that water molecules which are placed within approx. 60 nm of the protein surface form a net, which is most dense in the distance of a hydrogen bond at the donor- or acceptor- molecules of a protein. In distances larger than 60 nm, the structure of water becomes increasingly blurred, ending in a structureless phase. Water molecules are also in the inside of proteins, but are more strongly bound than... 

Often the initial phases from one of the above techniques (particularly MIR and MAD) are not sufficiently accurate to build in all the atoms and further improvement of the phases must be carried out. The standard approach for this is called density modification, or solvent-flattening. The idea is that if a unit cell contains a sufficient amount of solvent in it (usually around 50%, which is reasonable for most protein crystals), you will be able to use this information to improve the phases for the protein. The region of the unit cell that contains the solvent is set to an average value and new structure factors and phases are then calculated for... 

Solvent flatness. On average, protein crystals contain about 50% solvent, which on an atomic scale usually adopts a random, non-periodic structure within the crystal and hence is featureless within the averaged unit cell. Therefore, if we know the location of the solvent regions within a macro-molecular crystal, we already know a considerable part of the electron density (i.e. the part that is flat and featureless), and flattening the electron density of the solvent region can improve the density of our macromolecule of interest. 

Non-crystallographic symmetry. Many protein crystals contain multiple copies of one or more molecules within the asymmetric unit. Often the conformations of such chemically indistinguishable but crystallographically non-equivalent molecules are sufficiently alike to treat them as identical. In this case, we can improve the signal to noise ratio of the electron density of our molecule of interest by averaging the density of the multiple copies in the asymmetric unit. 

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). 

In Fig. 20, B, R, B2, and R2 are the positions of the base and ribose components of the dinucleotide or independent pyrimidine and purine nucleotides, respectively. The phosphate position pi can be occupied by the 3, 5"-diester (5" refers to the 5 position of R2 in a diester) or the 3 - and 5 -nucleotides, respectively. In the protein crystal a sulfate ion occupied this position in variable degree depending on the pH. Histidine 119 can be in any one of four or more positions depending on various factors. The second base might be in position B2 when it is a pyrimidine. The phosphate of a cyclic substrate or pentacovalent intermediate may be at p,. The position labeled H20 is the position of an isolated peak on the electron density map which is interpreted to be a water molecule, Wi, present in the protein and in the complexes. 

The interpretation of density at pi is based on crystallographic titration of the sulfate in the protein crystal, the absence of a phosphate peak in difference maps for the mono- and dinucleotide, on arsenate and pyrophosphate binding, and by analogy with RNase-A where phosphate and arsenate peaks have been reported near His 119. 

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. 

Another useful physical property of the crystal is its density, which can be used to determine several useful microscopic properties, including the protein molecular weight, the proteinlwater ratio in the crystal, and the number of protein molecules in each asymmetric unit (defined later). Molecular weights from crystal density are more accurate than those from electrophoresis or most other methods (except mass spectrometry) and are not affected by dissociation or aggregation of protein molecules. The proteinlwater ratio is used to clarify electron-density maps prior to interpretation (Chapter 7). If the unit cell is symmetric (Chapter 4), it can be subdivided into two or more equivalent parts called asymmetric units (the simplest unit cell contains, or in fact is, one asymmetric unit). For interpreting electron-density maps, it is helpful to know the number of protein molecules per asymmetric unit. 

The product of the crystal density and the unit-cell volume (determined from crystallographic analysis, Chapter 4) gives the total mass within the unit cell. This quantity, expressed in daltons, is the sum of all atomic masses in one unit cell. If the protein molecular mass and the number of protein molecules per unit cell are known, then the remainder of the cell can be assumed to be water, thus establishing the proteinlwater ratio. 

In the X-ray analysis of a protein crystal structure, solvent molecules appear as spheres of electron density in difference Fourier maps calculated at the end of a refinement. In a strict sense, the electron density map exhibits preferred.s/tes of hydration which are occupied by freely interchanging solvent molecules. This electron density is well defined for the tightly bound solvent molecules and can be as spurious as just above background for ill-defined molecules which exhibit large temperature factors and/or only partly occupied atomic positions. Since these two parameters are correlated in least-squares refinement, this gives rise to methodological problems. 

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