Difference maps

Figure 1. Difference map after high order refinement - data cutoff at sin 0/k = 0.9A1 for reflections with F2 > (a) this work (b) SC. Model map after multipole refinement - data cutoff at... 

Fig. 3. Different MAPs based on lysine units. The open bars represent antigens [11]...

Typical examples of density- and density difference maps for ion-molecule complexes are shown in Chapter V. For our purpose we do not need the detailed spatial information which is rather confusing for a discussion of charge transfer. We proposed therefore 113> to choose an axis of the complex (2-axis), which is characteristic for the type of interaction that we are interested in. In Li+... OH2 or Li+... OCH2 this is evidently the twofold symmetry axis C2. In other cases like e.g. F-... HOH or (H20)2, the connection line of the three atoms forming the hydrogen bond will be appropriate ). After defining a 2-axis in this way we can calculate a density difference curve Aq(z) by simple integration (35) ... 

The second approach is to use Fourier methods to calculate the electron density based on the model (using calculated Fs and phases, the vector Fc) and compare this with the electron density based on the observations (with calculated phases, the vector Fo). An electron-density map is calculated based on I To I — I. Pc I- This so-called difference map will give an accurate representation of where the errors are in the model compared with the experimental data. If an atom is located in the model where there is no experimental observation for it, then the difference map will show a negative density peak. Conversely, when there is no atom in the model where there should be, then a positive peak will be present. This map can be used to manually move, remove, or add atoms into the model. 

Fig. 18. The active site region of the electron density difference map between N-carbobenzoxy-L-alanine-elastase at —SS C and native elastase at the same temperature. The resolution is 3.5 A. The bilobed feature is consistent with the binding of the alanyi portion of the substrate to the oxygen of the catalytic serine, with weak interaction of the carbobenzoxy group to the surface of the enzyme.

Different maps were calculated by inverse Fourier transformation of the amplitudes and phases of all reflections at different stages of image processing. Lattice averaged maps were obtained from the amplitudes and phases directly as extracted from the images, before the CTF correction and imposing the S5mimetry. 

A linear descriptor naturally contains an ordering of its elements, which makes it very easy to compare them. In a tree structure however, it is not clear which parts should be mapped onto each other. Different mappings will result in different similarity values ... 

Experimental X-Ray Values are in Brackets. 24 is a rotomer of 103 with the Me trans to hydride. X-ray data in parentheses for comparison, in 103 and 104 the hydride atoms were located from the difference map and refined. 

Recently, the RMAP algorithm was published by Smith etal. [28]. It efficiently uses two different mapping criteria, both based on approximate matching of the read and the reference genome. 

The final R values were 0.051 and 0.035, corresponding in both cases to final difference maps exhibiting peaks lower than 0.4 eA . ... 

Such effects will contribute to the discrepancies between X-ray (X) and neutron (N) temperature parameters, which have been found to exist even room-temperature studies, for which temperature ambiguities are minimal (Craven and McMullan 1979). The effect of TDS can be especially pronounced in room-temperature studies of often soft molecular crystals, and, if not recognized, can lead to an artificial enhancement of features in difference maps based on a combination of the two techniques (Scheringer et al. 1978) (see chapter 5). 

FIG. 11.11 Electron-density difference maps on Li2BeF4 calculated with all reflections < sin 6/1 = 0.9 A"1 (81 K). (a) Based on the neutral atom procrystal model, (b) based on the ionic model. Contour levels are drawn at intervals of 0.045 eA"3.1 Full lines for positive density, dashed lines for negative and zero density. The standard deviation, estimated from [2Lff2(F0)]1/2N, is 0.015 eA-3. Source Seiler and Dunitz (1986). 

Electron delocalization, 13 190, 191 Electron densities, 38 436 difference map, four-iron clusters, 38 458... 

Using time-resolved crystallographic experiments, molecular structure is eventually linked to kinetics in an elegant fashion. The experiments are of the pump-probe type. Preferentially, the reaction is initiated by an intense laser flash impinging on the crystal and the structure is probed a time delay. At, later by the x-ray pulse. Time-dependent data sets need to be measured at increasing time delays to probe the entire reaction. A time series of structure factor amplitudes, IF, , is obtained, where the measured amplitudes correspond to a vectorial sum of structure factors of all intermediate states, with time-dependent fractional occupancies of these states as coefficients in the summation. Difference electron densities are typically obtained from the time series of structure factor amplitudes using the difference Fourier approximation (Henderson and Moffatt 1971). Difference maps are correct representations of the electron density distribution. The linear relation to concentration of states is restored in these maps. To calculate difference maps, a data set is also collected in the dark as a reference. Structure factor amplitudes from the dark data set, IFqI, are subtracted from those of the time-dependent data sets, IF,I, to get difference structure factor amplitudes, AF,. Using phases from the known, precise reference model (i.e., the structure in the absence of the photoreaction, which may be determined from... 

Notes Relaxation times are available for the wild-type and L29W mutant. For the L29F and YQR Mb mutants, approximate relaxation times were derived by visual inspection of the difference maps and by inspecting the time course of integrated difference electron densities, respectively. 

After the crystal structure of the compound has been solved, or deduced, from the X-ray data, the initial parameters (atomic positions, bond lengths, and bond angles) are only approximate and have to be improved. The usual method employed is that of least-squares refinement, although electron-density difference-maps and trial-and-error procedures are also used. Electron-density difference-maps give the approximate difference between the actual structure and the trial structure. 

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