Deformation density dynamic maps

Figure 2. L-alanine. Dynamic deformation density in the COO plane, (a) Model dynamic deformation density A Modei. (b) MaxEnt dynamic deformation density (Agj, (x)) map obtained with a non-uniform prior of spherical-valence shells. Map size 6.0A x 6.0A Contour levels from -1.0 to 1.0 eA 3, step 0.075 e A-f...

The MaxEnt deformation density in the COO- plane is shown in Figure 6(a). The deformation map shows correct qualitative features differences between the single C-C bond and the C-0 bonds are clearly visible, and so are the lone-pair maxima on the oxygen atoms. If compared to the conventional dynamic deformation density... 

Figure 6. l-Alanine. Fit to noisy data. Calculation A. MaxEnt deformation density and error map in the COO- plane Map size, orientation and contouring levels as in Figure 2. (a) MaxEnt dynamic deformation density A uP. (b) Error map qME - Model. 

When observed structure factors are used, the thermally averaged deformation density, often labeled the dynamic deformation density, is obtained. An attractive alternative is to replace the observed structure factors in Eq. (5.8) by those calculated with the multipole model. The resulting dynamic model deformation map is model dependent, but any noise not fitted by the muitipole functions will be eliminated. It is also possible to plot the model density directly using the model functions and the experimental charge density parameters. In that case, thermal motion can be eliminated (subject to the approximations of the thermal motion formalism ), and an image of the static model deformation density is obtained, as discussed further in section 5.2.4. 

Figure 5.12 shows both the dynamic and the static model deformation densities in the plane of the oxalic acid molecule, based on the data set also used for Fig. 5.2. The increase in peak height, due to higher resolution, and reduction in background noise relative to the earlier maps is evident. The model acts as a noise filter because the noise is generally not fitted by the model functions during the minimalization procedure.

However, these density maps which give a dynamic deformation density do not readily lead to numbers describing charges and electrostatic properties on the other... 

Once the multipole analysis of the X-ray data is done, it provides an analytical description of the electron density that can be used to calculate electrostatic properties (static model density, topology of the density, dipole moments, electrostatic potential, net charges, d orbital populations, etc.). It also allows the calculation of accurate structure factors phases which enables the calculation of experimental dynamic deformation density maps [16] ... 

For dynamic deformation maps, < >m differs from s when the crystal is acentric. Neglecting this phase difference can underestimate the deformation density of a covalent bond by 0.21 A-3 which represents something like one-third to one-half of the deformation density [76]. 

FIGURE 9.17 (cont d). Examples of deformation density maps, (b) Dynamic deformation-density map in which motion of the atoms has not been corrected for. ... 

Tama et al. developed in the past years a protocol called molecular dynamics-flexible fitting In this proeedure, the normal modes of a protein of known structure are eomputed using simple elastic network model approaches (as described in Seetion 3.2). Then, the protein scaffold is deformed along the computed normal modes in order to fit the electron density map coming from an EM experiment. Once the structure of the protein that best fit the experimental data is found, the atomistic-detailed structure is mapped back starting from the original high-resolution data. In this way, the different conformations of a protein present in a Cryo-EM data set can be resolved at atomistic resolution. 

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