Section 18.4.5.6. Bulk solvent and the low-resolution reflections

As stated in the preceding section and first reviewed by Matthews (1968) and more recently by Andersson & Hovmöller (1998), macromolecular crystals contain substantial regions of totally disordered, or bulk, aqueous solvent, in addition to those solvent molecules bound to the surface. The average electron density of the crystal volume occupied by protein is 1.35 g cm⁻³ (according to Matthews) or 1.22 g cm⁻³ (according to Andersson & Hovmöller), while that of water is 1.0 g cm⁻³. This is because the atoms are more closely packed within the protein, as they are connected by covalent bonds, while in solvent regions they form sets of hydrogen-bonded networks.

To model both solvent and protein regions of the crystal appropriately, it is necessary to have a satisfactory representation of the bulk solvent. The high R factors generally observed for most proteins for the low-resolution shells are partly symptomatic of the poor modelling of this feature or of systematic errors in the recording of the intensities of the low-angle reflections. For atomic resolution structures, the R factor can fall to values as low as 6–7% around 3–5 Å resolution. However, in lower-resolution shells it then rises steadily, often reaching values in the range of 20–40% below 10 Å. These observations indicate serious deficiencies in our current models or data.

The poorest approach is to ignore bulk solvent and assign zero electron density to those regions where there are no discrete atomic sites, as this leads to a severe discontinuum. An improved approach is to assign a constant value of the electron density to all points of the Fourier transform that are not covered by the discrete, ordered sites. This provides substantial reduction in the R factor for low-resolution shells of the order of 10% and requires the introduction of only one extra parameter to the least-squares minimization. An improvement of this simplistic model is the introduction of a second parameter, , described by where and are the scale factors for the protein, and and are the equivalent parameters for the bulk solvent (Tronrud, 1997). In effect, this provides a resolution-dependent smoothing of the interface contribution, rather than an overall term applied equally to all data. The physical basis of this is discussed by Tronrud and implemented in several programs, for example SHELXL (Sheldrick & Schneider, 1997) and REFMAC (Murshudov et al., 1997) (Fig. 18.4.5.2).

Figure 18.4.5.2| top | pdf | Schematic representation of the bulk-solvent models described in the text. (a) No bulk-solvent correction, i.e. solvent density set to zero. (b) Constant level of solvent outside the macromolecule and ordered water envelope. Here, sharp edge effects remain. (c) The model as in (b), but smoothed at the edge of a macromolecule, equivalent to the application of a B value to the solvent model.

Nevertheless, there remain severe problems in the modelling of the interface. The border between the two regions is not abrupt, as there is a smooth and continuous change from the region with fully occupied, discrete sites to one which is truly fluid, but this passes through a volume with an increasing level of dynamic disorder and associated partial occupancy. Modelling of this region poses major problems, as described above, and the definition of disordered sites with low occupancy remains difficult even at atomic resolution. At which stage the occupancy and associated ADP can be defined with confidence is not yet an objective decision. In addition, refinement and modelling at this level of detail is very time consuming in terms of human intervention.