Anomalous scattering phase problem

Application. Anomalous X-ray diffraction (AXRD), anomalous wide-angle X-ray scattering (AWAXS), and anomalous small-angle X-ray scattering (ASAXS) are scattering methods which are selective to chemical elements. The contrast of the selected element with respect to the other atoms in the material is enhanced. The phase problem of normal X-ray scattering can be resolved, and electron density maps can be computed. 

Alternative methods of solving the phase problem are also used now. When a transition metal such as Fe, Co, or Ni is present in the protein, anomolous scattering of X-rays at several wavelengths (from synchrotron radiation) can be used to obtain phases. Many protein structures have been obtained using this multiple wavelength anomalous diffraction (MAD phasing) method.404 407 408 Selenocysteine is often incorporated into a protein that may be produced in... 

The most demanding element of macromolecular crystallography (except, perhaps, for dealing with macromolecules that resist crystallization) is the so-called phase problem, that of determining the phase angle ahkl for each reflection. In the remainder of this chapter, I will discuss some of the common methods for overcoming this obstacle. These include the heavy-atom method (also called isomorphous replacement), anomalous scattering (also called anomalous dispersion), and molecular replacement. Each of these techniques yield only estimates of phases, which must be improved before an interpretable electron-density map can be obtained. In addition, these techniques usually yield estimates for a limited number of the phases, so phase determination must be extended to include as many reflections as possible. In Chapter 7,1 will discuss methods of phase improvement and phase extension, which ultimately result in accurate phases and an interpretable electron-density map. 

An alternative procedure, called molecular replacement, uses information about known structures that are believed to be similar to that of the species being investigated. The known structure is used to estimate the electron density of the unknown structure, which is then refined and improved. Another method of dealing with the phase problem is to introduce atoms which absorb radiation in the region of the incident X-rays, leading to a process called anomalous scattering . For proteins, a popular method is to replace S by Se by using selenomethionine in place of methionine. For nucleic acids, iodouracil or iodocytosine can be used in place of thymine and cytosine respectively. 

Okaya, Y., and Pepinsky, R. New formulation and solution of the phase problem in X-ray analysis of noncentric crystals containing anomalous scatterers. Phys. Rev. 103, 1645-1647 (1956). 

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. 

Excellent and detailed treatments of the use of anomalous dispersion data in the deduction of phase information can be found elsewhere (Smith et al., 2001), and no attempt will be made to duplicate them here. The methodology and underlying principles are not unlike those for conventional isomorphous replacement based on heavy atom substitution. Here, however, the anomalous scatterers may be an integral part of the macromolecule sulfurs (or selenium atoms incorporated in place of sulfurs), the iron in heme groups, Ca++, Zn++, and so on. Anomalous scatterers can also be incorporated by diffusion into the crystals or by chemical means. With anomalous dispersion techniques, however, all data necessary for phase determination are collected from a single crystal (but at different wavelengths) hence non-isomorphism is less of a problem. 

The phenomenon of anomalous scattering is extensively used in modem macromolecular crystallography to solve the phase problem. To understand how this is done, we need to return to the simple picture of X-rays reflecting from Bragg planes, where it makes no difference which side of the plane is the reflecting surface . This leads to two structure factors Fhki and F h differing only in the sign of their phase. The phase — a complex number - drops out because we measure intensities (/= F2 see above) and I k,i and are equal. 

The first X-ray photographs of a protein crystal were described 50 years ago by Bernal and Crowfoot [1], These remarkable photographs indicated that a wealth of structural information was available for protein molecules once methods for the solution of the patterns had been developed. At that time the determination of atomic positions even in the crystals of small molecules was a difficult task. In 1954, Perutz and his colleagues [2] showed that the technique of heavy atom isomorphous replacement could be used to solve the phase problem. The method was put on a sound systematic basis by Blow and Crick [3] and extended to include the use of anomalous scattering [4,5]. Until recently, these methods provided the basis for all protein structure determinations. They have been remarkably effective (as illustrated below) and new developments have both increased the size of the problem solvable and provided greater insights. 

In the past 10 years, anomalous dispersion (AD) effects have been used more and more frequently to solve the phase problem. All elements display an AD effect in x-ray diffraction. However, the elements in the first and second row of the periodic table, for example, C, N, O, and so on, have negligible AD effects. For heavier elements, especially when the x-ray wavelength approaches an atomic absorption edge of the element, these AD effects can be very large. The scattering power of an atom exhibiting AD effects is... 

For instance, three-beam diffraction (one transmitted and two diffracted beams) is used for determination of triplet phases (see Direct Methods) and provides also a means of resolving the enantiomorphism problem without the need for anomalous scattering. 

The application of molecular replacement relies on similar model proteins. If there are no known proteins that are similar to the proteins we want to study, then in such cases, what we face are the de novo structures, and molecular replacement is not valid any more. Isomorphous replacement or anomalous scattering methods have to apply in order to solve the phase problems. 

To solve protein structures by the isomorphous replacement method is quite difficult (Figure 7.9). The growth of the protein crystals is not easy, and it is necessary to search for the condition of isomorphous replacement or maybe more than two isomorphous replacements. It can be imagined how many trials need to be done during such process. Therefore, the anomalous scattering method is proposed to solve the phase problem of protein structure determination. 

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