Density modification

After phase determination, the initial electron density map is often still noisy and difficult to interpret due to phase errors. Only in rare cases the initial phases are of such quality that the resulting map is interpretable, allowing a complete model to be built. Therefore, methods have been developed to improve the quality of the electron density by imposing restraints based on common features of electron density maps.

One example of such a feature is non-negativity, which demands that no regions with negative density may exist in electron density maps. Another common feature of high-quality electron density maps is that both the mean value and the variance of the electron density in regions belonging to protein are high, while both values should be low in the solvent region as this is disordered. Imposing such restraints on the electron density in real space will lead to improved phases in reciprocal space upon back-transformation of the map (Wang, 1985). This procedure can be repeated iteratively and also used to extend phases to the full resolution of the dataset.

Two principally different approaches to density modification presently exist. In the conventional density modification protocol, the electron density is modified in real space as described above, and new phases are obtained from back-transformation.

These phases are combined with the original experimental phases, resulting in an improved set of phase estimates that can in turn be used to calculate a map. Yet, this method has two major problems. When combining the two phase sets, they must be

weighted, but the choice of an appropriate weighting scheme is difficult. The second problem is the lack of a robust criterion for ending the cyclic density modification procedure, as conventional phase quality indicators such as the FOM will continue rising (and be overestimated) if enough density modification cycles are calculated. A more recent approach is the use of statistical density modification procedures that treat density modification as an optimisation procedure in reciprocal space involving all available sources of phase information to obtain new structure factors (Terwilliger, 1999).

In this work, the following density modification methods were used as implemented in SHARP/autoSHARP and CCP4:

Solvent flattening and solvent flipping

Protein crystals contain a large amount of loosely bound or disordered solvent (bulk solvent). Both the mean value and the variance of the electron density should be low in solvent regions, while the opposite is true for regions belonging to protein.

Imposing these general features on maps will lead to phase improvement in reciprocal space. The process consists of two steps. The first step is the determination of an appropriate mask to separate protein from solvent regions. This can be done automatically in real or reciprocal space (Leslie, 1987; Terwilliger and Berendzen, 1999;

Wang, 1985). After defining a mask, the electron density in unmasked regions is either set to a constant value (solvent flattening) or inverted (solvent flipping). In statistical density modification, the variance of electron density around a given point is also taken into consideration. Solvent flattening procedures generally become more powerful when the solvent content of the crystal is high.

NCS averaging

If several copies of a molecule are present in the asymmetric unit, the NCS relationships between them can be used to improve the electron density map.

Improved phases from both, solvent flattening and NCS averaging are combined with the original amplitudes, which result in an improved electron density map. As in solvent flattening, a mask must first be defined for each copy. Then, the NCS operators are used to map equivalent regions of electron density in the other copies onto the first one

and average them. The averaged electron density is then mapped back onto the original positions, which now all contain the same averaged density at equivalent positions.

These equivalencies in real space impose restraints on the range of possible phase values after back-transformation of the map. Especially in the case of high-order NCS, averaging can lead to substantial phase improvement. NCS averaging only works well as long as the regions inside the NCS masks are very similar. If the individual copies show significant changes in structure and therefore electron density features, averaging over them will lead to phase deterioration. Therefore, it is important to monitor the correlation coefficients between equivalent densities inside the NCS masks during averaging. If necessary, weights can be applied during averaging that depend on the similarity among the NCS copies (Abrahams and Leslie, 1996). In statistical density modification, deviations from the average density are accounted for by analysing the values of the electron density probability distribution for each grid point (Terwilliger, 2003).

B-factor sharpening

B-factor sharpening is a useful tool for the enhancement of low-resolution electron density maps (Bass et al., 2002; Brunger et al., 2009a; DeLaBarre and Brunger, 2003; DeLaBarre and Brunger, 2006). It entails the use of a negative Bsharp value in a resolution-dependent weighting scheme applied to a particular electron density map (Equation 26).

Equation 26

!

F_{sharpened_map} =exp("B_sharpsin²#/$²)%F_map

with Fmap structure factor of the particular electron density map Fsharpened_map structure factor of the sharpened map

* reflecting angle

& wavelength of the X-ray radiation

A good choice for Bsharp is the negative Wilson B value of the diffraction data. Still, one should always check the resulting Fsharpened_map electron density map. Applying a negative Bsharp value effectively up-weights higher resolution terms. This weighting scheme results in increased detail for higher resolution features such as side-chain conformations. The cost of the increased detail is increased noise throughout the

electron density map. Thus, negative Bsharp sharpening is a density modification technique that is only as good as the diffraction data and the phases available. In this work, negative Bsharp values between -90Ų to -130Ų were applied to the data using the program CAD (CCP4, 1994) (script see 10.4). It should be noted that the up-scaled noise in the phases, resulting in a noisy electron density map, can be reduced if the negative Bsharp is applied to the data prior to density modification.