Pattern construction tools

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... 

In systems that are constructed from discrete components under well defined rules, geometric or arithmetic patterns usually develop. These may involve various symmetries or repetitive structures, with or without scaling, or regular sequences of numbers describing quantities of the components. In addition to being aesthetically pleasing, these patterns serve both as memory aids and predictive tools for the understanding of ordered systems. 

The technique of low energy electron diffraction (LEED) has been the most widely used tool in the study of surface structure. LEED experiments involve the scattering of monoenergetic and collimated electrons from a crystal surface and detection of elastically diffracted electrons in a backscattering geometry (Figure 2). The characteristic diffraction pattern in LEED arises from constructive interference of electrons when scattered from ordered atomic positions. The diffraction pattern represents a reciprocal map of surface periodicities and allows access to surface unit cell size and orientation. Changes in the diffraction pattern from that of a clean surface can be indicative of surface reconstruction or adsorbed overlayers. 

An alternative vector-driven RNAi tool is patterned after the endogenously expressed miRNAs. Engineered miRNA transcripts can be driven by pol II promoters and therefore have the potential to be expressed in a tissue- or temporal-specific manner. As with shRNAs, miRNA-based constructs can be delivered to cells via viral vectors. The miRNAs are designed to perfectly match their targets so that the mechanism of gene... 

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