Macromolecular crystals Patterson maps

The Patterson synthesis (Patterson, 1935), or Patterson map as it is more commonly known, will be discussed in detail in the next chapter. It is important in conjunction with all of the methods above, except perhaps direct methods, but in theory it also offers a means of deducing a molecular structure directly from the intensity data alone. In practice, however, Patterson techniques can be used to solve an entire structure only if the structure contains very few atoms, three or four at most, though sometimes more, up to a dozen or so if the atoms are arranged in a unique motif such as a planar ring structure. Direct deconvolution of the Patterson map to solve even a very small macromolecule is impossible, and it provides no useful approach. Substructures within macromolecular crystals, such as heavy atom constellations (in isomorphous replacement) or constellations of anomalous scattered, however, are amenable to direct Patterson interpretation. These substructures may then be used to solve the phase problem by one of the other techniques described below. 

It may not be obvious how we would locate the x, y, z coordinates of the heavy atom in the unit cell. Indeed it is sometimes not a simple matter to find those coordinates, but as for the heavy atom method described above, it can be achieved using Patterson methods (described in Chapter 9). As we will see later, Patterson maps were used for many years to deduce the positions of heavy atoms in small molecule crystals, and with only some modest modification they can be used to locate heavy atoms substituted into macromolecular crystals as well. Another point. It is not necessary to have only a single heavy atom in the unit cell. In fact, because of symmetry, there will almost always be several. This, however, is not a major concern. Because of the structure factor equation, even if there are many heavy atoms, we can still calculate Juki, the amplitude and phase of the ensemble. This provides just as good a reference wave as a single atom. The only complication may lie in finding the positions of multiple heavy atoms, as this becomes increasingly difficult as their number increases. 

The Patterson function has been employed since its formulation in 1935 for determining the locations of heavy atoms in crystals of conventional compounds. This alone made possible application of the heavy atom technique (see Chapter 8) for structure determination. For conventional molecules the information for the heavy atom positions is contained entirely within the native diffraction data, unlike macromolecules, where the information is embedded in differences between two independent data sets, or differences between Friedel mates. Aside from the coefficients employed, use of the function is virtually identical in all cases. Perhaps the major difference arises from the fact that diffraction data from macromolecular crystals, and therefore corresponding difference Patterson maps, contain more noise than... 

A Patterson map, different for each space group, is a unique puzzle that must be solved to gain a foothold on the phase problem. It is by finding the absolute atomic coordinates of a heavy atom, for both small molecule and macromolecular crystals, that initial estimates (later to be improved upon) can be obtained for the phases of the structure factors needed to calculate an electron density map. 

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