Protein patterns, functional cell units

The molecular replacement method used for protein structure determination (50,51) involves determining the orientation and the position in the unit cell of a known structure such as that of a homologous protein that has previously been determined or the same protein in a different unit cell (a polymorph). For the rotation function the Patterson map is systematically laid down upon itself in all possible orientations (Fig. 23). Six parameters that define the position and orientation of the protein in the unit cell are found from maxima in a function that describes the extent of overlap between the two placements of the Patterson function. This function will reveal the relative orientations of protein molecules in the unit cell. The rotation function is thus a computational tool used to assess the agreement or degree of coincidence of two Patterson functions, one from a model and the other from the diffraction pattern. 

The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are attached to the protein, and the coordinates of these heavy atoms in the unit cell are determined. The X-ray diffraction pattern of both the native protein and its heavy atom derivative(s) are determined. Application of the so-called Patterson function determines the heavy atom coordinates. Following the refinement of heavy atom parameters, the calculation of protein phase angles proceeds. In the final step the electron density of the protein is calculated. 

Equation (5.15) describes one structure factor in terms of diffractive contributions from all atoms in the unit cell. Equation (5.16) describes one structure factor in terms of diffractive contributions from all volume elements of electron density in the unit cell. These equations suggest that we can calculate all of the structure factors either from an atomic model of the protein or from an electron density function. In short, if we know the structure, we can calculate the diffraction pattern, including the phases of all reflections. This computation, of course, appears to go in just the opposite direction that the crystallographer desires. It turns out, however, that computing structure factors from a model of the unit cell (back-transforming the model) is an essential part of crystallography, for several reasons. 

As I described earlier, this entails extracting the relatively simple diffraction signature of the heavy atom from the far more complicated diffraction pattern of the heavy-atom derivative, and then solving a simpler "structure," that of one heavy atom (or a few) in the unit cell of the protein. The most powerful tool in determining the heavy-atom coordinates is a Fourier series called the Pattersonfunction P(u,v,w), a variation on the Fourier series used to compute p(x,y,z) from structure factors. The coordinates (u,v,w) locate a point in a Patterson map, in the same way that coordinates (x,y,z) locate a point in an electron-density map. The Patterson function or Patterson synthesis is a Fourier series without phases. The amplitude of each term is the square of one structure factor, which is proportional to the measured reflection intensity. Thus we can construct this series from intensity measurements, even though we have no phase information. Here is the Patterson function in general form... 

Proteins are the functional units of a cell. They have constantly changing expression levels, locations, and PTMs that may be associated with the onset, progression, and remission of disease. Proteomic technologies (as described in Section 2) are used to detect patterns of differentially expressed proteins that have numerous potential clinical applications. Techniques such as 2D-PAGE and HPLC combined with MS can be used to identify proteins for early detection, diagnosis, prognosis, and response to treatment. 

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