Two major choices have to be made in a DM run. They are the real-space density-modification modes and reciprocal-space phase-combination modes. Moreover, the phase-extension schemes can be selected if needed. This can also be left to the program, which uses its default automatic mode for phase extension. The choices of various modes are described in the following sections.
The following density-modification modes (specified by the MODE keyword) are provided by DM:
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(1) Solvent flattening: This is the most common density-modification technique and is powerful for improving phases at fixed resolution, but weaker at extending phases to higher resolution. Its phasing power is highly dependent on the solvent content. Solvent flattening can be applied at comparatively low resolutions, down to around 5.0 Å.
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(2) Histogram matching: This method is applied only to the density in the protein region. This method is weaker than solvent flattening for improving phases, but is much more powerful at extending phases to higher resolutions. This is due to a unique feature of histogram matching which uses a resolution-dependent target for phase improvement. The phasing power of histogram matching is inversely related to the solvent content. Therefore, histogram matching plays a more important role in phase improvement when the solvent content is low. Histogram matching works to as low as 4.0 Å, but does no harm below that. Histogram matching should probably be applied as a matter of course in any case where the structure is not dominated by a large proportion of heavy-metal atoms. Even in this case, histogram matching may be applied by defining a solvent mask with solvent, protein and excluded regions.
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(3) Multi-resolution modification: This method controls the level of detail in the map as a function of resolution by applying histogram matching and solvent flattening at multiple resolutions. This strengthens phase improvement at fixed resolution, although it generally improves phase-extension calculations too.
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(4) Noncrystallographic symmetry averaging: Averaging is one of the most powerful techniques available for improving phases and is applicable even at very low resolutions. In extreme cases, averaging may be used to achieve an ab initio structure solution (Chapman et al., 1992![[link]](/graphics/greenarr.gif) ; Tsao et al., 1992). It should therefore be applied whenever it is present and the operators can be determined.
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(5) Skeletonization: Iterative skeletonization is the process of tracing a `skeleton' of connected densities through the map and then building a new map by filling density around this skeleton. The implementation in DM is adapted for use on poor maps, where it is sometimes but not always of use. To bring out side chains and missing loops, the ARP program (Lamzin & Wilson, 1997) is more suitable.
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(6) Sayre's equation: This method is more widely used in small-molecule calculations, and is very powerful at better than 2.0 Å resolution and when there are no heavy atoms in the structure. However, its phasing power is lost quickly as resolution decreases beyond 2.0 Å. The calculation takes significantly longer than other density-modification modes.
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The most commonly used modes are solvent flattening and histogram matching – these give a good first map in most cases. Recently, multi-resolution modification has been added to this list. Averaging is applied whenever possible. Skeletonization and Sayre's equation are generally only applied in special situations.
Density-modification calculations are somewhat prone to producing grossly overestimated figures of merit (Cowtan & Main, 1996). Users should be aware of this. In general the phases and figures of merit produced by density-modification calculations should only be used for the calculation of weighted ![[F_{o}]](/teximages/dach2o1/dach2o1fi149.svg)
maps. They should not be used for the calculation of difference maps or used in refinement or other calculations (the REFMAC program is an exception, containing a mechanism to deal with this form of bias). The use of ![[2F_{o} - F_{c}]](/teximages/fach19o1/fach19o1fi1.svg)
-type maps should be avoided when the calculated phases are from density modification, since they are dependent on two assumptions, neither of which hold for density modification: that the current phases are very close to being correct and that the calculated amplitudes may only approach the observed values as the phase error approaches zero.
To limit the problems of overestimation, three phase-combination modes are provided (controlled by the COMBINE keyword):
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(1) Free-Sim weighting: This is the simplest mode to use. Although convergence is weaker than the reflection-omit mode, the calculation never overshoots the best map. If there is averaging information, then convergence is much stronger and the phase-combination scheme is much less important. In addition, phase relationships in reciprocal space limit the effectiveness of the reflection-omit scheme. Therefore, the free-Sim weighting scheme should usually be used when there is averaging.
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(2) Reflection-omit: The combination of a reciprocal-space omit procedure with SIGMAA phase combination (Read, 1986) leads to much better maps when applying solvent flattening and histogram matching. However, the omit calculation is computationally costly and introduces a small amount of noise into the maps, thus the phases can get worse if the calculation is run for too many cycles. A real-space free-R indicator (Abrahams & Leslie, 1996) is therefore used to stop the calculation at an appropriate point.
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(3) Perturbation-γ correction: This new approach is an extension of the γ correction of Abrahams (1997) to arbitrary density-modification methods. The results are a good approximation to a perfect reflection-omit scheme and required considerably less computation. This is therefore the preferred mode for all calculations.
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In the case of a molecular-replacement calculation or high noncrystallographic symmetry, it may be desirable only to weight the modified phases and not to recombine them back with the initial phases so that any initial bias may be overcome. In the case of high noncrystallographic symmetry, it may also be possible to restore missing reflections in both amplitude and phase. Options are available for both these situations.
When performing phase extension, the order in which the structure factors are included will affect the final accuracy of the extended phases. The phases obtained from previous cycles of phase extension will be included in the calculation of new phases for the unphased structure factors in the next cycle. A reflection with more accurately determined phases might enhance the phase-extension power of the original set of reflections, whereas a reflection with less accurately determined phases might corrupt the phase-extension power of the original set of reflections and make the phase extension deteriorate quickly. The factors that might affect phase extension are the structure-factor amplitudes, the resolution shell and the figure of merit. Based on the above considerations, the following phase-extension schemes are provided in DM:
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(1) Extension by resolution shell: This performs phase extension in resolution steps, starting from the low-resolution data, and extends the phase to the high-resolution limit of the data or that specified by the user. Structure factors are related by the reciprocal-space density-modification function that is dominated by low-resolution terms, as shown by equation (15.1.3.2
) and Fig. 15.1.3.1
in Chapter 15.1. This means that only structure factors in a small region of reciprocal space are related. Thus, when initial phases are only available at low resolution, phase extension is performed by inclusion of successive resolution shells. In the case of fourfold or higher NCS, this can allow extension to 2 Å starting from initial phasing at 6 Å or worse.
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(2) Extension in structure-factor amplitude steps: In this mode, those reflections with larger amplitudes are added first, gradually extending to those reflections with smaller amplitudes in many steps. The contribution of a reflection to the electron density is proportional to the square of its structure-factor amplitude according to Parseval's theorem, as shown in equation (25.2.2.2). This favours the protocol of extending the stronger reflections first so that they can be more reliably estimated. These stronger reflections will be used to phase relatively weaker subsequent reflections.
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(3) Extension in figure-of-merit step: To extend phases for those structure factors with experimentally measured, albeit less accurate, phases and figures of merit, the reflections can be added in order of their figure of merit, starting from the highest to the lowest. It is advantageous to use the more reliably estimated phases with higher figure of merit to phase those reflections with lower figure of merit. This can be useful when working with initial phasing from MAD or MR sources.
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(4) Automatic mode: This combines the previous three extension schemes. The program automatically works out the optimum combination of the above three schemes according to the density-modification mode, the phase-combination mode and the nature of the input reflection data. The automatic mode is the default and is the recommended mode of choice unless specific circumstances warrant a different choice.
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(5) All reflection mode: One advantage of the reflection-omit and perturbation-γ methods is that the strength of extrapolation of a structure-factor amplitude is a good indicator of the reliability of its corresponding phase. As a result, a phase-extension scheme is unnecessary in reflection-omit calculations; all reflections may be included from the first cycle.
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Abrahams, J. P. (1997). Bias reduction in phase refinement by modified interference functions: introducing the γ correction. Acta Cryst. D53, 371–376.Google Scholar
