Patterson techniques

As suggested by Patterson in 1934, the complex coefficients in the forward Fourier transformation (Eqs. 2.129 and 2.132) may be substituted by the squares of structure amplitudes, which are real, and therefore, no information about phase angles is required to calculate the distribution of the following density function in the unit cell  

the multiplier 2 appears because only one-half of a reciprocal space is used in the summation, thus the validity of Friedel s law is implicitly assumed. 

The resultant function, unfortunately, does not reveal the distribution of atoms in the unit cell directly but it represents the distribution of interatomic vectors, all of which begin in a common point - the origin of the unit cell. Thus, Puvw is often called the function of interatomic vectors and it is also known as the Patterson function of the F -Fourier series. The corresponding vector density distribution in the unit cell is known as the Patterson map. 

The interpretation of the Patterson function is based on a specific property of Fourier transformation (denoted as 3[...]) when it is applied to convolutions ( 8 ) of functions  

As follows from Eq. 2.137, the multiplication of functions in the reciprocal space (e.g. structure amplitudes) results in a convolution of functions (e.g. electron or nuclear density) in the direct space, and vice versa. Since Eq. 2.136 contains the structure amplitude multiplied by itself, the resultant Patterson function, P yy, represents a self-convolution of the electron (nuclear) density. Hence, it may be described as follows  

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Patterson methods have also been successfiilly used for structure solution from powder diffraction data. By taking advantage of the Patterson function Fi, usefiil information about the crystal structure can be deduced. Compared to Direct methods, Patterson techniques are more suitable for powder diffraction data with lower resolution, and peak overlap causing significant difficulties. The Patterson function can be calculated by using the equation... 

The application of the Patterson technique to locate strongly scattering atoms is often called the heavy atom method (which comes from the fact that heavy atoms scatter x-rays better and the Patterson technique is most often applied to analyze x-ray diffraction data). This allows constructing of a partial structure model ( heavy atoms only), which for the most part define phase angles of all reflections (see Eq. 2.107). The heavy atoms-only model can be relatively easily completed using sequential Fourier syntheses (either or both standard, Eq. 2.133, and difference, Eq. 2.135), sometimes enhanced by a least squares refinement of all found atoms. 

Patterson technique should be an adequate tool to solve this crystal structure. ... 

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. 

As with the isomorphous replacement method, the locations x, y, z in the unit cell of the anomalous scatterers must first be determined by Patterson techniques or by direct methods. Patterson maps are computed in this case using the anomalous differences Fi,u — F-h-k-i-Constructions similar to the Harker diagram can again be utilized, though probability-based mathematical equivalents are generally used in their stead. 

The value of heavy atom derivative is made, so that now FH1, FH2, FHpi, FHp2 and FP are to be determined. This is called multiple isomorphous replacement (MIR) and is generally used rather than the single isomorphous replacement technique. The values for FHi and Fh2 can be determined using Patterson techniques. Two equations similar to equation 6.6 now exist ... 

M. M. Markowit2 and E. W. De2melyk, A. Study of the Application ofEithium Chemicals to Air Regeneration Techniques in Manned Sealed Environments, AMRL-TDR-64-1, Wright-Patterson Air Force Base, Ohio, Feb. 1964. 

Very careful analysis of trace elements can have a major effect on human life. A notable example can be seen in the career of Clair Patterson (1922-1995) (memoir by Flagel 1996), who made it his life s work to assess the origins and concentrations of lead in the atmosphere and in human bodies minute quantities had to be measured and contaminant lead from unexpected sources had to be identified in his analyses, leading to techniques of clean analysis . A direct consequence of Patterson s scrupulous work was a worldwide policy shift banning lead in gasoline and manufactured products. 

The structure was solved by the multiple isomorphous replacement technique using four heavy atom derivatives uranyl acetate, plati-nous chloride, tetramethyllead acetate, and p-chloromercury benzoate. All four derivatives gave interpretable heavy atom Patterson syntheses. The heavy atom sites could be correlated between the de-... 

Over the next 30 years, Patterson used mass spectroscopy and clean laboratory techniques to demonstrate the pervasiveness of lead pollution. He traced the relationships between America s gas pump and its tuna sandwiches, between Roman slaves and silver dimes, and between Native American Indians and polar snows. He forged as close a connection between science and public policy as any physical scientist outside of medical research. He made the study of global pollution a quantitative science. And marrying his stubborn determination to his passionate conviction that science ought to serve society, Patterson never budged an inch. 

In his polar studies, Patterson analyzed such small traces of lead that, for 20 years, no other scientist could replicate his data. As the French glaciologist Claude Boutron noted in 1994, The difficulty of making these measurements was not fully appreciated at the time. With no attempt at diplomacy, Patterson said, It was beyond their ability by factors of thousands, or tens of thousands. Ten years later, Patterson and a graduate student, Amy Ng, used more sophisticated techniques on lead samples 100 times smaller than those he had analyzed in the 1960s and confirmed his earlier data. 

At a 1981 EPA conference called to discuss the issue, Patterson offered to train government scientists in his clean laboratory techniques. Soon afterward, a parade of key scientists visited Pasadena to study with Settle. Within six months, Patterson announced that the FDA had made considerable improvement both in its laboratory and in reducing lead levels in infant formula. 

Today, the scientific community can identify tiny trace amounts of chemicals in the environment. A quarter-century after Wallace Carothers introduced science-based industrial research to the United States, Clair Patterson adapted techniques developed for determining the age of the Earth to identify microtraces of global pollutants. Today scientists can analyze industrial contaminants in the parts per billion in 1991 when a university scientist discovered in the atmosphere a harmful, low-level contaminant produced by the manufacture of nylon, industry volunteered within weeks to change production methods. 

The potential of live cell imaging to address mechanisms of cellular biology is ever expanding. Directed protein-tagging techniques have been used to visualize nascent versus mature protein in vivo (Rodriguez et al., 2006). This technique involves the use of arsenic-based dyes, such as FiAsH or ReAsH, which bind to tetracysteine (TC) tags (Zhang et al, 2002). In addition, photo-activatable variants of GFP have been shown to determine the kinetics of protein movement in live cells (Patterson and Lippincott-Schwarz, 2002). Furthermore, techniques such as FRET and the... 

Perkins JH, Patterson BR (1997) Pest pesticides and the environment A historical perspective on the prospects for pesticide reduction. In Pimentel D (ed) Techniques for reducing pesticide use. Wiley, New York, USA, pp 13-33... 

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