Electron-density difference map

Two helices are packed antiparallel in the orthorhombic unit cell. Association of the helices occurs through a series of periodic carboxylate potassium water - carboxylate interactions. An axial projection of the unit-cell contents (Fig. 23b) shows that the helices and guest molecules are closely packed. This is the first crystal structure of a polysaccharide in which all the guest molecules in the unit cell, consistent with the measured fiber density, have been experimentally located from difference electron-density maps. The final / -value is 0.26 for 54 reflections, of which 43 are observed, and it is based on normal scattering factors.15... 

The structure was refined by block-diagonal least squares in which carbon and oxygen atoms were modeled with isotropic and then anisotropic thermal parameters. Although many of the hydrogen atom positions were available from difference electron density maps, they were all placed in ideal locations. Final refinement with all hydrogen atoms fixed converged at crystallographic residuals of R=0.061 and R =0.075. 

The difference electron density map following the last cycle of least squares refinement did not show evidence for a simple disorder model to explain the anomalously high B for the hydroxyl oxygen. Attempts to refine residual peaks with partial oxygen occupancies did not significantly improve the agreement index. 

A search for intermolecular bonds resulted in one possible hydrogen bond between hydroxyl 013 and lactone carbonyl Ol. The distance between 01 and 013 is 2.85 A, a value well within the range expected for OH-O hydrogen bonds (25). The hydrogen atom position for hydroxyl 013 was chosen to be along the 013-01 vector. The hydrogen position was not evident in the difference electron density map, presumably due to problems modeling the 013 position. 

PbTX-1 also cx)ntains the intermolecular hydrogen bond between hydroxyl 013 and carbonyl 01 already discussed. Only for dihydro PbTX-1 was it possible to locate an 012 hydroxyl hydrogen atom position from difference electron density maps. In that structure a peak appeared at 1.1 A from 012 and 2.1 A from symmetry related 05. 

The intrazeolite cations necessary to balance the negative charge on the framework aluminum atoms are poorly shielded and as a result high electric (electrostatic) fields on the order of 1-10 V/nm are found in their vicinity. The magnitudes of the electric fields can be calculated from measured effects on the vibrational frequencies or intensities of IR bands of small diatomics such as CO or N2.24 They can also be determined from difference electron density maps determined by X-ray diffraction methods.25 These high electric fields can dramatically influence the stabilities of transition states with significant charge separations. 

The crystal structures of two ferulic acid complexes of HRP C have been solved, one with resting state enzyme (to 2.0 A resolution) and the other with the cyanide-ligated enzyme (to 1.45 A resolution) 195). These represent a major achievement for the crystallography of peroxidase complexes. The binary complex is heterogenous, according to the 2Fo-Fc omit difference electron density map of the active site. The disordered density observed has been interpreted in terms of three... 

Deoxvhemerythrin. Henrerythrin appears to retain its triply bridged crae structure in the deoxy form. A low (3.9 A) resoluticm difference electron density map of deoxyHr vs. metHr fi- n X-ray diffraction suggests that the iron atoms move slightly further apart in deoxyHr, but remain five and six coordinate, respectively (29). Confirmation of the iron coordination comes from near-IR absorption and circular dichroism spectra (40,46,47). Based on model high-spin ferrous complexes, the six coordinate iron is expected to give two of the three observed transitions near 10000 cm- while the five-coordinate iron accounts for the d-d transition at ca. 5000 cm-. ... 

As discussed in the following chapter, difference electron density maps, representing Ap = pobs — pcak, are based on the Fourier transform of the complex difference structure factors AF, defined as... 

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)...

Difference electron density map 136 Differential scanning calorimetric curves 395 Differentiation... 

Ban et al 7 Courtesy of T. A. Steitz. The peptidyltransferase center is marked by the green image of the transition state inhibitor shown in Fig. 29-13. (F) Model of three tRNAs bound to a ribosome from Thermus thermophilus in the A (a mi noacyl), P (pepti-dyl), and E (exit) sites. These are based on 0.75-nm X-ray data and a number of difference electron density maps. The 3-CCA end of the A-site tRNA is not modeled hut is... 

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... 

FIGURE 1. X X difference electron density map of cyclopropa[a]cyclobuta[d] benzene (34) in the molecular plane. Reproduced with permission from Advances in Strain in Organic Chemistry (Ed. B. Halton), Vol. 2, JAI Press London, 1992, p 290... 

In the Li,Tl-C difference electron-density maps there are large peaks at four positions. These positions we assume to be partially... 

There are two ways for including the contribution from bulk water. One was first introduced in fiber diffraction analysis of polynucleotides. It subtracts the X-ray scattering contribution of bulk water from the individual atomic scattering factors used in the structure analysis [700,836], The other incorporates the continuous electron density of liquid water, 0.34 e/A3, in the electron density calculations. As a result the more localized solvent atoms are I more clearly defined in difference electron density maps [837]. 

Fig. 23.11a, b. Difference electron density maps showing the hydration of the active site region of S. griseus protease A. a The native enzyme, b The enzyme in complex with the product tetrapep-tide Ac-Pro-Ala-Pro-iyr. Also shown are two internal water molecules 0326,0244. Note similarity in electron densities due to bound solvent and to product [843]... 

There remain concerns about the actual amount of trapped L in the studies, based in part on the published visible spectra of the crystals (Balashov and Ebrey, 2001). In particular, the contamination by the M intermediate (deprotonated Schiff base, Amax near 410 nm, at least 12% of sample) would tend to dominate the changes in diffraction intensities due to the relatively larger structural changes of the M and later photocycle intermediates. In this case difference electron density maps... 

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.

Refinement of intensity data for Cl02GeF5 led to convergence with a weighted R factor of 0.068 (unweighted R = 0.059) and a standard deviation in an observation of unit weight of 3.938. The largest peak on a final difference electron density map was 0.285 e/A ... 

F hkl), may be either the observed, F(/ifc/) <, or calculated, F hkl) structure factor in a difference electron-density map, the coefficient is the difference between these two quantities,... 

Difference electron-density maps these maps are calculated... 

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. 

Extensive use of three-dimensional electron-density or difference electron-density maps in crystallography became possible only with the advent of high-speed computers. The magnitude of the problem can be illustrated" for a compound crystallizing in an orthorhombic unit cell with dimensions a = 11.98, 6 = 15.82, c = 11.49 A, Z = 4, for which 4397 (independent) Bragg reflections were measured at a resolution of... 

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