Contouring electron density maps

FIGURE 9.6 (cont d). The fully contoured electron-density map. Carbon atoms represented by filled circles, nitrogen and oxygen atoms by open circles. Contour interval 1 electron/A, zero contour dotted. 

Figure 6. The 3-d contour electron density map of 5,10,15,20-tetramethyl porphyrin.

The relief and contour electron density maps for diborane in the plane of the bridging H atoms are shown in Figures 13.15(a) and (b), respectively. One notable feature here Is that the atomic surface boundaries for the two bridging H atoms actually touch one another. Although there is no direct bond path between the two bridging H atoms, the larger value of the electron density in this plane can be used to explain the fact that DFT calculations indicate that the H H interaction... 

Fig. 3 The electron density map (0.002 au contour) for diiodine, colored by the electrostatic potential. Red is the most negative potential and blue is the most positive...

Figure 1. Electron-density maps (5 A x 5 A) in the plane (110). Horizontal axes [001], vertical axes [110]. (a) Monopoles omitted and (b) monopoles included. Contours at 0.05 eA 3, negative - broken, positive - full lines. 

Fig. 13. Stereo drawing of one contour level in the electron density map at 2 A resolution for the residue 54-68 helix in staphylococcal nuclease. Carbonyl groups point up, in the C-terminal direction of the chain the asterisk denotes a solvent peak bound to a carbonyl oxygen in the last turn. Side chains on the left (including a phenylalanine and a methionine) are in the hydrophobic interior, while those on the right (including an ordered lysine) are exposed to solvent.

Figure 8.IB shows an experimental contour map of electron density for the H2O molecule in plane y-z, after Bader and Jones (1963). The electron density is higher around the nuclei and along the bond directrix. The experimental electron density map conforms quite well to the hybrid orbital model of Duncan and Pople (1953) with the LCAO approximation.

It is also possible to determine accurate electron density maps for the ionic crystal structures using X-ray crystallography. Such a map is shown for NaCl and LiF in Figure 1.45. The electron density contours fall to a minimum—although not to zero—in between the nuclei and it is suggested that this minimum position should be taken as the radius position for each ion. These experimentally determined ionic radii are often called crystal radii the values are somewhat different from the older sets and tend to make the anions smaller and the cations bigger than previously. The most comprehensive set of radii has been compiled by... 

A portion of the structure model and the 2F0-FC electron density map contoured at 1.0 standard deviation. The region containing the inhibitor, magnesium, parts of AdoMet, and the residue Glul99 is shown. The sphere marked with W represents a water molecule. 

Fig. 6.32 Differential electron density map of crystalline sodium cyanide. NaCN. Solid contours indicate increased electron density upon compound formation from the atoms, dashed contours represent decreased electron density. [From Coppens. P. Ange v. Chent. Int. Ed. Engl. 1977, 16, 32. ...

In the fifth step of an X-ray structure determination the electron density map is calculated using the intensities and phase information. This map can be thought of as a true three-dimensional image of the molecule revealed by the X-ray microscope. It is usually displayed as a stereoscopic view on a computer graphics system (Fig. 3-22). It is also often prepared in the form of a series of transparencies mounted on plastic sheets. Each sheet represents a layer, perhaps 0.1 ran thick, with contour lines representing different levels of electron density. 

Figure 3-23 (A) Stereoscopic a-carbon plot of the cystolic aspartate aminotransferase dimer viewed down its dyad symmetry axis. Bold lines are used for one subunit (subunit 1) and dashed lines for subunit 2. The coenzyme pyridoxal 5 -phosphate (Fig. 3-24) is seen most clearly in subunit 2 (center left). (B) Thirteen sections, spaced 0.1 nm apart, of the 2-methylaspartate difference electron density map superimposed on the a-carbon plot shown in (A). The map is contoured in increments of 2a (the zero level omitted), where a = root mean square density of the entire difference map. Positive difference density is shown as solid contours and negative difference density as dashed contours. The alternating series of negative and positive difference density features in the small domain of subunit 1 (lower right) show that the binding of L-2-methylaspartate between the two domains of this subunit induces a right-to-left movement of the small domain. (Continues)...

FIGURE 23. Difference electron-density maps of 201. (a) Section in the plane through the midpoint of and perpendicular to the bridging Cl—C3 bond of the bicyclobutane part, (b) Section in the plane of the three-membered ring C1, C2, C3. Contour lines are at 0.05 e A-3 intervals. Full lines indicate positive, dashed lines negative regions. Reproduced by permission of the International Union of Crystallography from Reference 309... 

Because the Patterson function contains no phases, it can be computed from any raw set of crystallographic data, but what does it tell us A contour map of p(x,y,z) displays areas of high density (peaks) at the locations of atoms. In contrast, a Patterson map, which is a contour map of P(u,v,w), displays peaks at locations corresponding to vectors between atoms. (This is a strange idea at first, but the following example will make it clearer.) Of course, there are more vectors between atoms than there are atoms, so a Patterson map is more complicated than an electron-density map. But if the structure is simple, like that of one or a few heavy atoms in the unit cell, the Patterson map may be simple enough to allow us to locate the atom(s). You can see now that the... 

Plate 21 Model and portion of electron-density map of bovine Rieske iron-sulfur protein (PDB lrie). The map is contoured around selected residues only. (For discussion, see Chapter 11.) Image SPV/POV-Ray. 

Fig. 5. Deformation electron density map in the N(l), 0(1), 0(2) plane for HMX. Solid contours are positive, dotted contours are negative, and dashed contours are zero. Contour interval is 0.05 eA°.

Theoretically, the radius of an ion extends from the nucleus to the outermost orbital occupied by electrons. The very nature of the angular wave function of an electron, which approaches zero asymptotically with increasing distance from the nucleus, indicates that an atom or ion has no definite size. Electron density maps compiled in X-ray determinations of crystal structures rarely show zero contours along a metal-anion bond. 

A model of the structure must be fit to the map. This used to be done with the "Richards box", a device containing a half-silvered mirror to give the illusion of superposition of a physical model and the electron density map (conventionally contoured in serial sections, traced onto transparent film, and stacked (17).) Recently, some protein structures have been determined using interactive computer graphics to fit a stick model of a structure to an electron density map (18, 19). 

Fig. 9. Sections from a three-dimensional electron-density map for the O-p-bromobenzoate derivative of batrachotoxinin A (2). The contours are spaced by 2e/A3.

Fig. 10.3 Automatic analysis of ligand electron density. The electron density was interpreted and models of compounds automatically fitted using AutoSolve . Although the binding affinity is weak (AT000037 IC5o=46 pM AT000056 ICso=l mM) the fragments bound into the pocket of Trypsin adopt a clearly ordered conformation. Electron density maps are contoured at 3o- and density due to protein and solvent has been removed for clarity.

Figure 3 The electron density map of the Mn4Ca cluster, calculated after omission of each metal of the WOC. The maps are contoured at 8cr for Mnl, Mn2, and Mn3 and la for Mn4 and Ca. (Reprinted with permission fromK. Ferreira, T. Iverson, K. Maghlaoui, J. Barber and S. Iwata, Science Express, DOI 1093087 (2004). 2004 AAAS)...

Fig. 10. Averaged FOx2d-FC p2d difference electron density map plus atomic model around the trinuclear copper site. Contour levels -18.0, solid line 18.0, dashed line. Magnitudes of the hole are less than -35.0.

Fig.6. 22 The three-membered C—H—M nng in a diazinne molecule (a) Electron density through the plane of the diazinne ring. Coniouis arc at S x I0 e pm-. (b) Diffierenial electron density map through the plane of the diazinne ring showing increases (solid lines) and decreases (broken lines) of electron density upon bond formation. Contours are at 4 X lO e pm ). Note the fauldmp of electron density oauide the C——N Iriar. ...

Figure 2. Stereoview of the electron density map in the vicinity of Asn30, the mutation site. Contour level is 0.8o.

Electron-density map A contour representation of electron density in a crystal structure. Peaks appear at atomic positions. The map is computed by a Fourier synthesis, that is, the summation of waves of known amplitude, periodicity, and relative phase. The electron density is expressed in electrons per cubic A. 

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