Location of heavy atoms

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... 

All methods of deduction of the relative phases for Bragg reflections from a protein crystal depend, at least to some extent, on a Patterson map, commonly designated P(uvw) (46, 47). This map can be used to determine the location of heavy atoms and to compare orientations of structural domains in proteins if there are more than one per asymmetric unit. The Patterson map indicates all the possible relationships (vectors) between atoms in a crystal structure. It is a Fourier synthesis that uses the indices, l, and the square of the structure factor amplitude f(hkl) of each diffracted beam. This map exists in vector space and is described with respect to axes u, v, and w, rather than x,y,z as for electron-density maps. 

Determination of structure factors, location of heavy atoms for isomorpous crystals. The electron density distribution of the heavy-atom isomorphous crystal is the sum of the electron densities of the parent crystal and of the heavy-atom substituents, i.e. ... 

Polychlorinated biphenyls (PCBs) are colorless toxic organic substances that cause cancer and birth defects. There are more than 200 different types of PCBs, ranging in consistency from heavy, oily liquids to waxy solids, and each type further varying in the number and location of chlorine atoms attached to its molecular carbon rings. They are fire resistant and do not conduct heat or electricity well. Accordingly they have numerous commercial applications as insulation in electrical systems, for example, for transformers. 

Accurate localization of hydrogen atoms is particularly important when small hydrogen atoms are located near heavy atoms for example, transition metals. Generally, it is now well established that x-ray crystallography usually underestimates H- H and Me- H distances by 0.2 to 0.3 A [5], In this sense, even H NMR relaxation experiments performed in solution can lead to more plausible... 

By far, the most common procedure for the determination of heavy-atom positions is the difference Patterson method it is often used in combination with the difference Fourier technique to locate sites in second and third derivatives. 

The only difference between these two models is the first descriptor. Given the location and disparity between the descriptors, both can be considered false bringing attention to a region that is not important to the model. In Model 2 the descriptor adds to the model, yet in Model 4 the descriptor subtracts from the model. Most striking is that the descriptors are separated by 2.24 A as illustrated in Fig. 10 and more than 6 A from either of the other descriptors at the substitution locations of interest. The two descriptors at positions (0, 2, 4, any) and (0, 4, 1, any) at the me la and para substituent locations of the benzene ring are the most important of those displayed. The descriptors represent steric properties because they will accept any type of heavy atom at those two locations the addition of a heavy atom at either of these two locations will improve the bioactivity of a compound from the series. 

It is very difficult to locate hydrogen atoms in large molecules by crystallographic methods. Nevertheless, proximity observations of heavy atoms strongly suggest the existence of bifurcated hydrogen bonds of the type shown below ... 

X-ray diffraction Scattering, mainly by electrons, followed by interference (A = 0.01-1 nm) Electron density map of crystal 10- sbut averaged over vibrational motion crystal —10 cm1 Location of light atoms or distinction between atoms of similar scattering factor difficult in presence of heavy atoms... 

In comparison to the protein structure, this "structure"—a sphere (or very few spheres) in a lattice—is very simple. It is usually easy to "determine" this structure, that is, to find the location of the heavy atom in the unit cell. Before considering how to locate the heavy atom (Section III.C.), I will show how finding it helps us to solve the phase problem. 

Suppose we are able to locate a heavy atom in the unit cell of derivative crystals. Recall that Eq. (5.15) gives us the means to calculate the structure factors Fhkl for a known structure. This calculation gives us not just the amplitudes but the complete structure factors, including each of their phases. So we can compute the amplitudes and phases of our simple structure, the heavy atom in the protein unit cell. Now consider a single reflection hkl as it appears in the native and derivative data. Let the structure factor of the native reflection be Fp. Let the structure factor of the corresponding derivative reflection be FHp. Finally, let FH be the structure factor for the heavy atom itself, which we can compute if we can locate the heavy atom. 

We know IFHpl and IFpl from measuring reflection intensities /HP and /p. So we know the length of the vectors Fhp and Fp, but not their directions or phase angles. We know FH, including its phase angle, from locating the heavy atom and calculating all its structure factors. To solve Eq. (6.9) for Fp and... 

In order to resolve the phase ambiguity from the first heavy-atom derivative, the second heavy atom must bind at a different site from the first. If two heavy atoms bind at the same site, the phases of will be the same in both cases, and both phase determinations will provide the same information. This is true because the phase of an atomic structure factor depends only on the location of the atom in the unit cell, and not on its identity (Chapter 5, Section III.A). In practice, it sometimes takes three or more heavy-atom derivatives to produce enough phase estimates to make the needed initial dent in the phase problem. Obtaining phases with two or more derivatives is called the method of multiple isomorphous replacement (MIR). This is the method by which most protein structures have been determined. 

Before we can obtain phase estimates by the method described in the previous section, we must locate the heavy atoms in the unit cell of derivative crystals. 

Having located the heavy atom(s) in the unit cell, the crystallographer can compute the structure factors FH for the heavy atoms alone, using Eq. (5.15). This calculation yields both the amplitudes and the phases of structure factors Fh, giving the vector quantities needed to solve Eq. (6.9) for the phases ahkl of protein structure factors Fp. This completes the information needed to compute a first electron-density map, using Eq. (6.7). This map requires improvement because these first phase estimates contain substantial errors. I will discuss improvement of phases and maps in Chapter 7. 

So the disparity between intensities of Friedel pairs in the anomalous scattering data set establishes their phases in the nonanomalous scattering data set. The reflection whose phase has been established here corresponds to the vector Fhp in Eq. (6.9). Thus the amplitudes and phases of two of the three vectors in the Eq. (6.9) are known (l)FHp is known from the anomalous scattering computation just shown, and (2) FH is known from calculating the heavy-atom structure factors after locating the heavy atom by Patterson methods. The vector Fp, then, is simply the vector difference establish-... 

As well as neutral molecular carbonyls M (CO), , carbonyl anions are found. Hetero-atoms such as H, C, N and S appear in many cases. Hydrogen atoms - which may be present in both neutral and anionic species - are often difficult to locate with precision because they tend to be invisible to X-ray crystallographers in the presence of heavy atoms. They are sometimes terminal, for example in Mn(CO)5H, an octahedral... 

DISCO considers three-dimensional conformations of compounds not as coordinates but as sets of interpoint distances, an approach similar to a distance geometry conformational search. Points are calculated between the coordinates of heavy atoms labeled with interaction functions such as HBD, HBA or hydrophobes. One atom can carry more than one label. The atom types are considered as far as they determine which interaction type the respective atom would be engaged in. The points of the hypothetical locations of the interaction counterparts in the receptor macromolecule also participate in the distance matrix. These are calculated from the idealized projections of the lone pairs of participating heavy atoms or H-bond forming hydrogens. The hydrophobic points are handled in a way that the hydrophobic matches are limited to, e.g., only one atom in a hydrophobic chain and there is a differentiation between aliphatic and aromatic hydrophobes. A minimum constraint on pharmacophore point of a certain type can be set, e.g. if a certain feature is known to be required for activity [53, 54]. 

Location of light atoms or distinction between atoms of similar scatteriiig factCM difficult in presence of heavy atoms... 

Soak complexes of heavy atoms of various kinds into a crystal. Screen diffraction data from heavy-atom derivatives of the protein for differences in intensities from those in the native data set. Calculate difference Patterson maps and locate the positions of the heavy atoms in the unit cell. 

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