Crystal space, mapping

The model protein is used to search the crystal space until an approximate location is found. This is, in a simplistic way, analogous to the child s game of blocks of differing shapes and matching holes. Classical molecular replacement does this in two steps. The first step is a rotation search. Simplistically, the orientation of a molecule can be described by the vectors between the points in the molecule this is known as a Patterson function or map. The vector lengths and directions will be unique to a given orientation, and will be independent of physical location. The rotation search tries to match the vectors of the search model to the vectors of the unknown protein. Once the proper orientation is determined, the second step, the translational search, can be carried out. The translation search moves the properly oriented model through all the 3-D space until it finds the proper hole to fit in. 

Figure 7.10 (a) Double-axis rocking curve of a microgravity-grown GaAs crystal after heater failure, (b) Equivalent triple-axis reciprocal space map CuK 004... 

We will first describe the methods for accurately determining the orientation of the crystals and then, in a second step, we will ejq)lain in detail how reciprocal space mapping can be used to quantitatively analyze the microstracture of epitaxial films. 

The variety of phenomena related to polymorphism (hydration, solvation, amor-phicity and interconversions) demonstrates the importance of acquiring a thorough mapping of the crystal space of a substance that is ultimately intended for some specific application. 

The crystal planes hkl in the real crystal lattice define the coordinates of points of the reciprocal lattice space, also called fe-space. A plane in the real-space maps to a point in the reciprocal space and on the contrary, so there is one-to-one correspondence between planes in the real space and points in the reciprocal space. 

Wark, Whitlock, and co-workers [72]-[75] extend these ideas in shock compression of < 111 >-oriented silicon single crystals. The method of producing the shock wave differs from previous X-ray diffraction studies, but the basic concepts are the same. Higher X-ray fluences result in a time resolution of 0.05-0.1 ns. This permits a sequence of exposures at various irradiances and delay times, thus mapping the interatomic spacing of the shock-compressed surface as a function of time. 

Molecular replacement is where the phases of a known structure are used to determine the structure of a protein that may be identical but crystallized in a different space group or may adopt essentially the same structure (e.g., a homologous protein). Essentially, the calculations find the rotation and translation of the molecule that work with the phases to produce an interpretable electron density map. 

The exact amount of error introduced cannot immediately be inferred from the strength of the amplitudes of the neglected Fourier coefficients, because errors will pile up in different points in the crystal depending on the structure factors phases as well to investigate the errors, a direct comparison can be made in real space between the MaxEnt map, and a map computed from exponentiation of a resolution-truncated perfect m -map, whose Fourier coefficients are known up to any order by analysing log(<7 (x) tm (x)). 

More than half of the volume of the crystals is taken up by liquid of crystallization, which mainly fills the spaces between molecules and shows up as flat, featureless regions in the electron density map. The rest of the map contains regions of high electron density. The boundaries between these two types of regions mark the outlines of the molecules. There are relatively few contacts between neighbouring molecules. 

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