The structural model. Reliability of the structural model
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A model which has been "validated," according to the criteria described in another chapter, and which therefore shows:
is a reliable model. However, the concept of reliability is not a quantitative magnitude which can be written in terms of a single number. Therefore, to interpret a structural model up to its logical consequences one has to bear in mind that it is just a simplified representation, extracted from an electron density function:
Electron density in a point of coordinates x,y,z
in which the atoms have been located and which is being affected by several conditions (see below)...

Regardless of the subjects 
included below, the experienced reader should also consult the contents of the comments included in the following articles:
The advanced reader, with interest in macromolecular crystallography, should also have a look to the results published in Nature (2016) 530, 202-206. This article shows that, in addition to the coherent diffraction (Bragg peaks), the diffraction patterns can display additional information in the form of continuous diffraction, very useful, among others, to increase the degree of resolution of the model. A brief summary of the article can be found through this link.

The effect of resolution

For instance, we must take into account the effect of the resolution level of the electron density function. The value that 
ρ(xyz) displays in each point in the unit cell is dependent on the sum of all structure factors (the waves diffracted by the atoms contained in the unit cell). Therefore, the amount of structure factors used in the sum, and their degree of observability, is an important aspect in obtaining a realistic value of the electron density at each point. The degree of precision (resolution level) of an electron density map is defined as the inverse of the distance that we would be able to "see" in the map, which is dependent on the radiation wavelength (λ) and on the maximum detection angle (θ). The minimum value of the "visible" distance (known as the resolution level, although actually is the inverse of the resolution level) can deduced from Bragg's Law:

λ / 2.sen θmax
Minimum "visible" distance in an electron density map (also known as resolution)

It seems obvious, therefore, that to obtain a high resolution map (to see fine details of the structure), we will need to use a small wavelength (small numerator) and to get diffraction data (structure factors) up to high diffraction angles (large denominator).

For crystals of low structural complexity, the number of structure factors available through a diffraction experiment is usually sufficient to obtain realistic values of 
ρ(xyz), and thus the map permits us to see structural details at high resolution (0.5 Angstroms or less), but this is not the usual case for macromolecules. For this reason, in all cases (but especially in protein crystals) the amount of experimental data is a crucial aspect.

Left: Low resolution: 5.0 Angström
Right: Medium resolution: 3.0 Angström

High resolution: 1.7 Angström
Pictures of the electron density map at different data set resolutions of the same region of a protein. The two maps at resolutions of 5.0 and 3.0 A show the protein backbone as a yellow line. It seems obvious that from the map at 5.0 A it would be almost impossible to recognize the peptidic chain. In the map at 3.0 A resolution the chains appear clearly, but the map at 1.7 A shows even the amino acid side chains. 

Constructing a peptide segment
Constructing a peptide segment on the electron density function obtained using amplitudes and phases from a diffraction pattern with a resolution of 1.7 Angstrom. 

Effect of resolution (amount of experimental data)

The movie  shows how the electron density map, in a region of a protein, changes as the resolution limit is adjusted from 0.5 to 6.0 Å, that is as the contribution of reflexions with the highest Bragg angles is being omitted. For this calculation the phases are perfect and so are the amplitudes (R = 0,0%). Note that, even for a perfect map (in terms of phases and amplitudes) one expects side chains to poke out of density at 3.5 Å resolution. Movie taken from EMBO Bioinformatics Course.

The effect of amplitudes (intensities)

Similarly, to assess the reliability of a model one has take into account the effect of the precision attained for the diffraction amplitudes (intensity measurements):

The importance of amplitudes (precision attained by measuring intensities)

The movie above displays the effect of calculating an electron density map with "wrong" amplitudes. The images in the movie represent the slow changing of all the amplitudes to a different set of randomly selected values while phases are kept constant. The gradual change goes from R=10% (reasonable disagreement) up to R=75% (random amplitudes). It is interesting to note that the map hardly changes at all until the R factor gets higher than 50%. The resolution is 1.5 Å and the phases are always perfect. Movie taken from EMBO Bioinformatics Course.

The importance of phases

Finally, it should be noted that the parameter which most affects the reliability of a structural model is the correctness of the phases assigned to the diffraction amplitudes, as shown by the following movie.

The effect of phases (errors in the phases)

The movie displays the effect of calculating a map with "wrong" phases. The "figure of merit" (the cosine of the phases error) is displayed as "m". The images are calculated by merging a perfectly calculated map with another map, calculated with the same amplitudes, but using phases obtained from a model with randomly positioned atoms. By merging these two maps amplitudes are always preserved but the phases change slowly. The resolution is 1.5 Å and the R-factor is always 0.0%. It is important to note the strong dependence between the correctness of the phases and the accuracy of the map in order to recognize the atomic positions.  Movie taken from EMBO Bioinformatics Course.

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