In the past decade, some new methods have been developed to improve phases.
They all apply real space constraints based on known features of a protein electron density map in order to improve the approximate phase information obtained from experimental sources. These new methods have also been incorporated into many density-modification techniques. A recent review on density modification has been given (Kleywegt and Read, 1 997).
The initial MIR phases (to 3 .0
A
resolution) for MgATP-FPGS were improved and extended (to 2.4A
resolution) using real space density modification procedures (solvent flattening, histogram matching, phase extension). In the early stages of model building, phases from the partial model and the M IR phases were combined to 3.0A
resolution, and the same density modification procedures then were applied to improve and extend the phases. Some of the density modification procedures used for the MgATP-FPGS complex are described below.Chapter 2 MATERIALS AND METHODS
2.5. 1 Solvent flattening (Wang, 1 985)
Protein crystals contain between about 20% and 80% solvent with a typical solvent content of 50%. Most solvent is disordered in time and space and therefore does not contribute to the measured diffraction intensities. This means that the solvent regions should appear relatively flat and empty. Also the protein regions should have no negative density. Given that, it can be assumed that significant deviations of a real electron density map from these criteria are due to errors. Thus, some of the errors can be eliminated by levelling the density in the solvent regions and truncating negative intensities in the protein regions. The modified map is then back transformed and the resulting phases, appropriately weighted, are combined with the original phases. In solvent flattening, the density in the solvent regions is typically replaced by its average value at each cycle of density modification.
The solvent flattening procedure for MgATP-FPGS was implemented in the DM program suite (Cowtan, 1 994). The program used the automatic Wang molecular envelope mask calculation based on input solvent content value.
2.5.2 Histogram matching
In the histogram matching technique (Lunin, 1 993; Zhang and Main, 1 990), it is assumed that the distribution of density values for a protein is known and depends only on resolution and a temperature factor (B). In this way, a match can be found which transforms the histogram of density values from the current electron density into a known one. Prior information concerning protein density distribution is therefore incorporated during phase refinement. Since the histogram matching procedure is applied to points in the protein region, solvent flattening together with the histogram matching provide real space constraints on the electron density over the entire volume of the protein crystal.
Histogram matching for MgATP-FPGS was implemented together with solvent flattening using DM (Cowtan, 1 994). The calculation of scale factors and B-factors for the data are automatic. This is performed by comparison with an empirically derived
Chapter 2 MATERIALS AND M ETHODS
database of map variance at different resolutions, and IS more reliable than the conventional Wilson plot.
2.5.3 Phase extension
Phase extension was first used in the structure determination of tobacco mosaic virus (TMV) (Bloomer et al., 1 978). This technique has also been incorporated into various density modification programs to propagate phase information from low resolution to a higher resolution that is typically near the diffraction limit. A concise formulation of the theory of phase extension has been given (Lawrence, 1 99 1 ).
The phase extension technique in the program DM (Cowtan, 1 994) was used for phase extension of the data. A specific "COMBINE OMIT" mode, in which a reflection omit calculation is used to reduce dependency between initial and modified structure factors, was chosen for the phase extension and combination of modified structure factors. All unphased data were introduced during phase extension by taking thin isotropic resolution shells of data and adding them to the current set of phased data. The shell width at different resolutions was adjusted so that approximately equal numbers of reflections were added at each step. For the MgA TP-FPGS data, there were 845 1 of 1 5725 reflections initially phased by MIR. Phase extension was from 2.99 to 2.40
A,
and the shells were of width 0.04-0.02A
over the extension range. This resulted in the introduction of between 300 and 400 reflections at each extension step.2.5.4 Phase combination with MIR phases
Another frequently used phase improvement procedure is phase combination. The phases calculated from the partial structure in early modelling stages were combined with the MIR phases at 3.0
A
resolution, using the program SIGMAA (Read, 1 986).It was proposed (Rossmann and B low, 1 96 1 ) that the combination of different sources of phase information could be realized by simple multiplication of the corresponding phase probability distributions using the following formula:
Chapter 2 MATERIALS AND M ETHODS
where pea) is the combined phase probability distribution, and PiS/a) and Pc(a) are the isomorphous and partial structure phase probability distributions, respectively. In SIGMAA, a computationally convenient phase combination method is used, depending on the Hendrickson and Lattman (Hendrickson and Lattman, 1 970) formulation of the phase probability profile for a phase a:
pea) = exp(Acosa+Bsina+Ccos2a+Dsin2a) Eq. 2.2
where A, B, C, D are the phase coefficients. In this way, the phase information from different sources can be combined by a simple addition of the phase coefficients from each determination.
The phase probability distributions from MIR were calculated by the method of B low and Crick (Blow and Crick, 1 959), and the phase probability distributions for the partial model structure were based on a weighting scheme proposed by Sim (Sim, 1 959; Sim, 1 960). As reported in other structure determinations (Rice, 198 1 ; Rice et al., 1 988), this phase combination technique proved very useful in the density modification of the MgA TP-FPGS structure.
2.5.5 Overview of approach taken
The density modification techniques described above were used in a cyclic manner. The initial map with MIR experimental phases was first modified by solvent flattening, histogram matching and phase extension in DM. After the first partial structural model was obtained, phase combination of the MIR phases with the phases calculated from the partial model was carried out to produce much better maps upon which the DM density modifications were again applied. The same procedures were iterated until a virtually complete structural model had been obtained. The striking improvements of density maps by the DM and phase combination techniques for the MgATP-FPGS structure can be clearly seen in Fig. 2.5-1.
Chapter 2 MATE RIALS AND METHODS
(a)
(b)
Fig. 2.5-1 The improvement of electron density map by the OM and phase combination
techniques for the MgA TP-FPGS structure. The density maps for part of helix AS are
calculated from, (a) the i nitial MIR phases at 3.0 A. resolution; (b) the combined phases
after density modification and extension to 2.4 A.. This region contains the four consecutive
aromatic residues YWYF ( 1 29- 1 32) identified firstly in the sequence asSignment (see
Chapter 2 MATERIALS AND METHODS