2.7 MODEL REBUILDING AND FINAL REFINEMENT
2.7.4 BULK SOLVENT CORRECTION
In contrast to the ordered water structure, most solvent is disordered in the solvent regions between the protein molecules in the crystal lattice. The effective scattering from the disordered solvent regions (known as bulk solvent), particularly at low resolution, causes large discrepancies between the observed and calculated structure factors, leading to calculated structure factor amplitudes which are systematically much larger than the observed structure factor amplitudes at a resolution below -5
A
(Vij ayan, 1 980). This systematic deviation leads to severe problems in scaling, in least-squares refinement, and in difference Fourier map calculations. It was common practice i n theChapter 2 MATERIALS AND METHODS
past to avoid these problems by omitting the low resolution data during refinement. However, doing so causes series termination errors in Fourier syntheses (Tronrud,
1 996b).
Two bulk solvent models are currently available to solve this problem. One of them is the exponential scaling model based on the application of Babinet's principle (Moews and Kretsinger, 1 975). This simple model can be expressed in a computationally convenient fashion, and thus it is implemented in most of the crystallographic refinement programs, including TNT (Tronrud, 1 992; Tronrud et al., 1987). Therefore this approach was first adopted in the refinement of the FPGS structure. By application of B abinet's principle, it is assumed that the structure factors of the bulk solvent electron density are directly proportional to the structure factors of the protein electron den sity with strictly opposite phases. From this approximation, the total calculated structure factor amplitude can be derived as follows (Moews and Kretsinger, 1 975):
Eq. 2.7- 1
where Fe is the calculated structure factor amplitude of the protein model including bulk solvent model, and F m is the calculated structure factor amplitude of the protein model.
The scale factor Ksol reflects the ratio of the solvent electron density to the protein electron density with typical values 0.75-0.95 and Bsol restricts the down-scaling of F m to resolutions below -5
A
with typical values 1 50-250A2.
Thus the bulk solvent modelling has been reduced to a scaling problem. With an absolute scale factor K, and an overall B factor, Fo can be scaled to F m by the formula:Eq. 2.7-2
All four scaling parameters (K, B, Ksol, Bsol) were used in program TNT for the refinement of the FPGS model. The estimates of the scale factor K and overall B factor are based on Wilson statistics (Wilson, 1 942). Ksol was determined by the program and B sol was set as 1 50
N
in earlier stages of refinement without including low resolution data. Both scale factors were calculated by the program in the later stages of refinement, with all data (40.0-2.4A).
Chapter 2 MATERIALS AND METHODS
Due to the assumption of strictly opposite phases, this exponential scaling model underestimates the contrast between protein and bulk solvent electron density. Another more realistic mask model has also been developed and is implemented in X-Plor version 3 .85 1 (Jiang and Brunger, 1 994). In this mask bulk solvent model, the protein molecules are placed on a grid in the unit cell, and all grid points outside the protein region are filled with bulk solvent. The calculated structure factors of the bulk solvent electron density, scaled with a factor Ksol and smoothed with an artificial temperature factor Bsol, are then vectorially added to the calculated structure factors of the protein model to give the total calculated structure factors as follows (Kostrewa, 1 997):
Pc
=Pm
+ Ksol�I
exp(-Bsol Sin2S/,,}) Eq. 2 .7-3The two scaling parameters Ksol and Bsol are determined by a least squares refinement. Typical refined values for these two parameters are Ksol =0.3-0.4, reflecting the electron density of the crystallization buffer, and Bsol = 1 5-40
A2,
which produces a rather steep fall-off of the bulk solvent electron density with minimum overlap with the protein electron density. No assumption is made about the phase relationship between the protein structure factors and the bulk solvent structure factors.As an alternative approach to correct the effects of bulk solvent, this mask model was also adopted late in the refinement of MgATP-FPGS structure by using X-Plor 3 .85 1 (Jiang and Brunger, 1 994). The mask bulk solvent correction gave a better approximation to the observed structure factor amplitudes than the exponential scaling bulk solvent correction.
The crystallographic R-factor and free R-factor for the final model of MgATP-FPGS are 1 8.6% and 25.7% with the mask bulk solvent model, compared to 1 9.4% and 27.7% with the exponential scaling bulk solvent model, differing largely in the low resolution range. The difference Fourier maps calculated with the mask bulk solvent correction were also employed in late stages of model rebuilding. Some new density in the regions of missing structure were clearly seen in difference maps with the mask model correction in contrast to that with the exponential scaling model correction (see Fig. 2.7.4-1), although it was still difficult to locate all of missing residues, probably because of inherent disorder.
Chapter 2 MATERIALS AND METHODS
�o
(a)
�O
(b)
Fig. 2.7.4-1 The 2Fo-Fc maps (at 1 .0 0') calculated with clifferent bulk solvent correction
models: (a) the exponential scaling model and (b) the mask model correction. A clisordered
loop region, residues ( 1 5 -20) which were omitted in the maps, is shown.