Macromolecules electron density maps

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. 

Isomorphous replacement is now employed in the determination of the structures of biological macromolecules. These molecules crystallize with 50% or more of the crystal volume filled with solvent molecules. Murray Vernon King, working with David Harker, conceived the idea of soaking protein crystals in solutions of compounds containing a heavy atom. These heavy-atom compounds are diffused into the crystals through the solvent channels and settle on preferred sites on protein molecules. The diffraction patterns of the unperturbed crystal (described as "native ) and the heavy-atom derivative are then compared in such a way that an electron-density map for the protein results. The method of isomorphous replacement, and the manner by which it is used to derive relative phases, are described in detail in Chapter 8. 

Such maps are primarily used to refine a trial structure, to find a part of the structure that may not yet have been identified or located, to identify errors in a postulated structure, or to refine the positional and displacement parameters of a model structure. A difference map is very useful for analyses of the crystal structures of small molecules. It is also very useful in studies of the structures of crystalline macromolecules, since it can be used to find the location of substrate or inhibitor molecules that have been soaked into a crystal once the macromolecular structure is known. A formula like that in Equation 9.1.5 is then used. When a structure determination is complete, it is usual to compute a difference electron-density map to check that the map is flat, and approximately zero at all points. 

For macromolecules it may be difficult to determine the overall conformation of the protein from the electron-density map, but some interesting methods are in use for aiding in the interpretation of this map. 

Ten Eyck, L. F. Fast Fourier transform calculation in electron density maps. Methods in Enzymology. Diffraction Methods for Biological Macromolecules. Part B. (Eds., Wyckoff, H. W., Hirs, C. H. W., and Timasheff, S. N.) 115 324-337 (1985). 

The high solvent content of macromolecular crystals leads to another way to modify the electron density. The electron density map is the space average of all the unit cells in the crystal, so atoms that are in random positions (as in liquid water) in different unit cells will not show up as peaks. Why They do not obey the periodicity of the crystal (remember that the FTs concerned periodic functions) and so are called disordered. The crystal then consists of ordered molecules, where the electron density is the same in each unit cell, and so visible, and disordered solvent, where the electron density averages to zero. In order to make physical sense, the electron density also has to be positive a property not imposed by the FT. Consequently, electron density peaks outside the macromolecule are noise and can be got rid of, as can negative electron density inside the macromolecule. We can therefore apply these conditions modify the initial electron density so that it is zero outside the molecules and positive within them. This, as for noncrystallographic averaging, alters the electron density map to conform to what must be true, and the map is thus a better representation than the initial map. 

A difference map with F0t,s - Fcaic as amplitudes helps to identify discrepancies between the observed and calculated data. A negative peak (a hole) in the difference electron density map indicates something in the model that is not supported by the experimental data (Figure 30), while a positive peak indicates some feature in the data that is not in the model (Figure 30). As difference maps by definition subtract out all the real features currently accounted in our model, they are noisy, with many peaks and holes at the level of one to two standard deviations (a). We thus interpret only peaks that are above 3covalently bound to the macromolecule, such as a bound ligand. 

After a first complete set of a (hkl) phase angles has been determined with data obtained from the MIR method, or equivalent, an electron density map may then be calculated. If sufficient X-ray diffraction data has been acquired then this map will fit the known primary sequence of the biological macromolecule reasonably well, giving a preliminary model... 

Figure 6.16 Electron Density Map Example of an electron density map generated computationally from electron density data that has been derived by the application of the equations and principles described in the main text from X-ray crystallographic scattering data. The electron density map corresponds with part of the active site of an enzyme LysU (see next Fig. 6.19 Chapters 7 and 8) from the organism Escherichia coli. This electron density map has been "fitted" with the primary sequence polypeptide chain of LysU (colour code - carbon yellow oxygen red nitrogen blue). Once an electron density map has been determined, fitting of the known primary sequence of the biological macromolecule to the electron density map is the final stage that leads to a defined three-dimensional structure (from Onesti et al., 1995, Fig. 9).

At 6 A resolution, the macromolecule usually appears as a blob of electron density and the chain backbone is generally unrecognizable. At 3.0 A resolution, it is possible to trace the path of the macromolecular chain backbone. The double helices of nucleic acids are traced readily. At 2.0 A resolution, almost all protein side chains, nucleic acid nucleotides and polysaccharide glycoses are visible. A model of the protein, nucleic acid or glycan can be constructed if the amino acid, nucleotide or monosaccharide sequence is known. At higher resolution, individual atoms begin to be seen. It is possible to identify amino acid side chains, nucleotides and glycose units directly from the electron density map. 

A structure at atomic resolution gives a much more detailed picture of a macromolecule than for example a structure at medium resolution. On one hand the higher resolution leads to smaller details becoming visible in electron density maps. On the other hand the much more elaborate parameterization of the model allows answering qualitatively new questions, like whether the anisotropic ellipsoids of two atoms in an active site are pointing towards each other. 

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