1. Introduction

De novo crystal structure determination using MAD methods is one of the key steps in both structural genomics projects and conventional structural biology (Smith et al., 1996; Hendrickson, 1999; Ealick, 2000). The ease of the experiment in modern dedicated beamlines (Roth et al., 2002; Pohl et al., 2001) and the use of cryogenic techniques to increase the lifetime of the sample (Garman, 1999) have played a large role in the success of these experiments.

A perusal of publications of structures solved by MAD (see, for example, the compilation by Hendrickson & Ogata, 1997) shows that a very common data-collection strategy consists of collecting data at three wavelengths or sometimes four. Inverse-beam geometry is often used to collect Friedel related reflections. This strategy is devised to obtain highly accurate experimental phases, because the choice of wavelengths is such that both the anomalous and dispersive contributions to the phasing are optimized and a very redundant set of anomalous (measured from acentric pairs, i.e. Friedel or Bijvoet related reflections) and dispersive differences (measured between the same reflections at different wavelengths) are obtained. This data-collection strategy requires six times (eight times with four wavelengths) the amount of data required for a standard complete data set to the same resolution (Dauter, 1997).

Sometimes the acentric pairs are collected in a single angular segment instead of using inverse-beam geometry. Although in general this strategy does not cancel systematic errors between acentric pair measurements,¹ these errors can be corrected to a large extent during scaling (Hendrickson & Teeter, 1981; Friedman et al., 1995; Evans, 1997). In many cases, this strategy can reduce the data needed by as much as half, but for some crystal symmetries and orientations the same amount of data as for the inverse-beam strategy would still be required (Dauter, 1997).

Long experiments can be a problem because the longer the experiment lasts, the higher the radiation dose the crystal will receive, increasing the risk of specific structural changes in the sample caused by radiation damage (Burmeister, 2000; Leiros et al., 2001). Collecting data at all wavelengths simultaneously in small angular wedges, as suggested by Rice et al. (2000), would be the optimal way to minimize the effect of a long data collection on the phases. If the crystal is extremely sensitive to radiation, this strategy could result in three incomplete data sets which cannot be used for phasing unless more data are collected from another crystal or, if the crystal is much larger than the beam in the spindle direction, from an unexposed part of the crystal.

Alternatives to further shorten the time required for the experiment have been suggested. One is to carry out a two-wavelength MAD data collection (Okaya & Pepinsky, 1956). This has been shown to be feasible in several cases provided that one of the two wavelengths has a small and relatively large . This condition is often achieved with a remote wavelength on the high-energy side of the absorption edge (Peterson et al., 1996; González et al., 1999). Another option suggested is SAD data collection. For instance, Dauter et al. (2002) and Rice et al. (2000) studied a large number of cases and proved that single-wavelength phasing (Wang, 1985) can be successful regardless of diffraction resolution, anomalous scatterer and anomalous signal. An advantage of single-wavelength methods over two or more wavelength MAD is versatility: while MAD experiments can only be properly performed at tunable synchrotron beamlines fulfilling certain requirements for wavelength bandpass, stability and reproducibility (Thompson, 1997), SAD data can be collected at any macromolecular crystallography beamline. Even the Cu  K emission at home sources can be used to successfully phase structures (Jaskólski & Wlodawer, 1996; Dauter et al., 1999; Yang & Pflugrath, 2001).

Under current experimental conditions at most beamlines, a case can be made for collecting as much MAD data as possible while the crystal lasts or, if data processing can keep up with data collection, until the user has analyzed the data and produced a clearly interpretable map. This favors the longer three- or four-wavelength data-collection strategies described above. The development of data-collection and processing facilities for high-throughput projects (Kuhn & Soltis, 2001; Abola et al., 2000; Ferrer, 2001) could have an influence on the choice of strategy: an increasing proportion of experiments will be carried out semi- or fully automatically and it is likely that samples belonging to different projects will be stored together for data collection, with the possibility of remounting a sample easily if the data collected previously proved to be insufficient for structure solution without having to reschedule beam time for the project. Under these circumstances, it is important to collect data in the most time-efficient manner, using strategies which minimize the total experiment time without compromising the quality of the data.

In the case of experiments that are being conducted at rapidly tunable beamlines, a careful analysis is required to determine the actual minimal amount of data required to successfully phase a structure. The impact on phasing information from multiple-wavelength data versus completeness and redundancy is directly related to the amount of data and hence the time required for each of the approaches listed above. The purpose of the study presented here is to explore the minimum data amount needed to solve a structure with typical quality data with one-, two- and three-wavelength phasing, and to propose possible strategies for automated data collection.

2. Methods

A total of six samples were selected for this study. Of those samples, five were selenomethionine proteins. Selenium is the most commonly used anomalous scatterer in macromolecular MAD experiments because of the well developed method of substituting the sulfur in methionine by selenium (Doublié, 1997) and it is the anomalous scatterer of choice for high-throughput projects (Lesley et al., 2002). All the selenium-containing samples were produced by the Joint Center for Structural Genomics (JCSG) project to obtain the structure of the proteins coded by the Thermotoga maritima bacterium genome (Lesley et al., 2002). The other sample was recombinant sperm whale myoglobin (Mb), an iron metalloprotein. Some relevant sample characteristics are listed in Table 1. A wide range of crystal symmetries, solvent content and anomalous signal are represented by the samples. All those factors may play a role in the amount of data needed to solve the structure.

Table 1 Sample characteristics and results of the data analysis using all data collected The merging statistics are given for the remote-wavelength data set.   Mb Tm0423 Tm0665 Tm1083 Tm1102 Tm0667 PDB code 1jw8 1kq3 1j6n 1j5u 1o0w 1j6o No. anomalous scatterers# 1 (1) 7 (7) 48 (46) 1 (0) 10 (8) 1 (0) Fractional anomalous signal+ 0.03 0.06 0.09 0.03* 0.06 0.02* No. of residues§ 150 364 1164 124 480 256 Solvent content## (%) 55 40 40 60 43 29 Space group P6 I422 P21 P4332 P1 P212121 Oscillation++ (°) 270 52.5 × 2 96 × 2 45 × 2 360 120 × 2 Maximum resolution (Å) 2.1 2.0 2.0 2.1 2.0 2.0 Resolution limit of anomalous signal§§ (Å) 2.1 2.0 2.1 3.2 2.7 2.7 I/(I)### 6.5 (2.6) 11.7 (6.5) 11.4 (3.6) 7.6 (1.6) 6.8 (2.5) 5.7 (2.3) Rmeas###+++ 0.11 (0.34) 0.06 (0.12) 0.04 (0.15) 0.11 (0.55) 0.09 (0.38) 0.1 (0.33) Completeness§§§ (%) 100 100 87.5 100 93.7 100 Acentric completeness§§§ (%) 100 100 87 100 92.9 100 Multiplicity 14.8 8.1 4.1 17.9 3.9 9.1 Residues traced (%) 99 97 88 95 95 86 #Values in parentheses are the number of sites with a temperature factor higher than 50  Å3. +Defined as (N/2)1/22/, where N is the number of ordered anomalous scatterer sites in the asymmetric unit and is the total structure-factor amplitude (in the cases labelled *, the single disordered anomalous scatterer was assumed to have an occupancy of 0.5). §Total number of residues in the asymmetric unit. ##Estimated from the contents of the unit cell. ++Total range collected at each wavelength (factored by 2 when an inverse-beam pass was performed). §§Resolution to which the correlation of the anomalous differences is larger than 0.3. ###Values in parentheses are for the highest resolution bin. +++R factor weighted for multiplicity (Diederichs & Karplus, 1997). §§§Unique and acentric data completeness for one wavelength.

3. Results

All the structures in the study could be solved as described above using either three or two wavelengths, with fewer data than the total collected. Half of the structures could also be traced after SAD phasing. In the other cases this was not possible even using all data collected at the peak wavelength. The models obtained after tracing had the same or a similar number of residues to those traced using all data. Table 2 summarizes the results of phasing with the minimal data. The discussion below will focus mainly on the results obtained with the minimal data sets, unless stated otherwise.

Table 2 Minimal data sets required to solve the structure automatically by SAD and two- and three-wavelength MAD For MAD phasing, the unique data, acentric completeness and multiplicity refer to the inflection-wavelength data set. The correlation coefficient to the refined model is given both for the map calculated after density modification (DM) and the experimental map (Exp).     Completeness (%)   Correlation (%)   Sample # (°) Unique Acentric Multiplicity DM Exp Relative dose+ Three-wavelength MAD   Mb 135 92 44 2.7 66 36 0.05   Tm0423 72 88 60 2.0 65 44 0.04   Tm1083 30 91 70 2.7 66 35 0.03   Tm0665 288 86 66 2.1 62 45 0.11   Tm1102 750 93 77 2.0 50 35 0.80   Tm0667 540 100 100 7.9 50 36 0.32 Two-wavelength MAD   Mb 110 96 64 3.3 67 37 0.04   Tm0423 51 91 64 2.0 66 43 0.02   Tm1083 20 91 70 2.7 65 35 0.02   Tm0665§ 326 86 74 3.5 67 45 0.09   Tm1102 700 94 93 3.7 51 35 0.60   Tm0667 360 100 100 7.9 51 35 0.18 SAD   Mb 170 100 100 9.4 61 32 0.05   Tm0423 52.5 100 97 4.1 60 37 0.04   Tm1083 20 99 97 4.7 62 27 0.03 # is the total angular range of data necessary to solve the structure, i.e. the oscillation range collected at each wavelength multiplied by the number of wavelengths used. +Estimate of the dose absorbed by the crystal for the minimal data set, in fractions of the Henderson limit (2 × 107  Gy; Henderson, 1990). §The figures given for this case correspond to the instance where all the automatically found Se sites were included in the phasing. When no incorrect sites were used (this could be achieved by rejecting the ten sites with lowest occupancy), the structure could be solved with a total rotation range of 222°.

3.4. Map quality

The experimental MAD maps calculated with the minimal data sets are clearly better than the SAD maps (see Fig. 1). This is expected because SAD phasing results in bimodal phase distributions for all the reflections. After density modification, the SAD maps show a proportionally larger improvement than the MAD maps. This has also been observed by Rice et al. (2000). The SAD maps always had a slightly lower correlation and tended to lack connectivity compared with the MAD maps obtained with the same amount of data. The two- and three-wavelength maps are of similar quality and are equally improved by density modification.

Figure 1 Tm0423 maps calculated from SAD and MAD phases using the same total amount of data (52.5°). (a) SAD experimental map. (b) SAD map after density modification. (c) Two-wavelength MAD experimental map. (d) Two-wavelength MAD after density modification. The part of the structure shown is an -helix near the surface of the protein (the helix backbone is displayed). The arrows near the top of the view labeled A and B point to zones where the density-modified SAD map (b) has breaks in the electron density. The experimental SAD map (a) shows density for the A zone, but this density disappears after density modification. The two-wavelength MAD maps (c) and (d) exhibit continuous density over these areas.

Before autotracing, the map correlation is somewhat lower when phasing with the minimal amount of data than when the complete data sets with higher reflection multiplicity are used. As shown in Table 2, when phasing with the minimal data sets the map correlation coefficients are between 0.3 and 0.4 for the experimental maps and are 0.5-0.7 for the density-modified maps in most cases. When phasing with the data sets containing all the data, the typical experimental correlation coefficients rise to between 0.4 and 0.6 and, after density modification, are between 0.5 and 0.8. After autotracing, a very similar model was always arrived at independently of the number of wavelengths and the completeness of the data employed for phasing. More autotracing cycles were needed to obtain a complete model as the data completeness decreased.

4. Discussion

A critical factor determining the minimum amount of data necessary to solve the structure is the number of reflections with a sufficiently well determined phase to serve as an adequate starting point for solvent-flattening and phase-extension schemes to work successfully. With `perfect' phases calculated from a model, structure solution has sometimes been found to succeed with about only 60% of the unique reflections. When the phases must be calculated from the small anomalous and dispersive differences derived from the experimental data, the total number of measurements needed to achieve the critical number of phased reflections is obviously much larger.

A comparison of the results of single- and multiple-wavelength phasing for the same structure indicates that multiple-wavelength phasing consistently requires less data completeness and redundancy than the single-wavelength counterpart. A likely explanation is that both the dispersive and anomalous differences contribute to the phasing in the former case. In a standard MAD experiment, with the same zone of the crystal sampled at each wavelength, the number of dispersive difference measurements will be roughly equal to the number of unique reflections, regardless of space group and crystal orientation. In contrast, a reasonably complete set of anomalous difference measurements, which are the only source of experimental phase information in SAD phasing, is not in general achieved with a complete set of unique reflections (Dauter, 1997).

Another contribution to the number of phased reflections in MAD experiments, which may be of some importance in some space groups, is made by centric reflections. These do not contribute to experimental SAD phases but, because the dispersive term always causes a change in the amplitude of the scattering factor at different wavelengths, are phased in MAD experiments.

Two-wavelength MAD can in some cases require more data at each wavelength than three-wavelength MAD because the value of is relatively small at the inflection and remote wavelengths used for the two-wavelength phasing analysis, which can result in somewhat fewer accurate phases than when both anomalous and dispersive differences are optimized.² Other sample-dependent factors, such as good diffraction quality and high anomalous signal, are likely to downweight the contribution of a third wavelength.

5. Data-collection strategy

The comparison of the two- and three-wavelength MAD phasing shows that two-wavelength MAD is a more time-effective experiment, at no significant cost in the model quality. The results obtained for SAD phasing with Mb, Tm1843 and Tm0423 appear to indicate that a two-wavelength MAD experiment would not as a rule require more data than SAD experiments and can even be shorter in some cases. Therefore, two-wavelength MAD appears to be as suitable as SAD to increase the productivity of dedicated macromolecular crystallography beamlines.

Regarding the decrease of the total radiation dose absorbed by the crystal, a two-wavelength MAD data collection at the inflection and remote wavelengths would actually be better than SAD, since the maximum wavelength optimal for SAD experiments is that where most radiation is absorbed. This hypothesis is based on the rough estimation of the dose absorbed by the crystal during the exposure time required to collect the minimal data set (Table 2); this has yet to be confirmed experimentally. In addition, the MAD maps also tend to be slightly better and, as suggested by the Tm0665 example, using more than one wavelength can be useful to determine the anomalous scatterer substructure in difficult cases.

Taking these points into account, the optimal strategy for MAD data collection in a dedicated beamline with automatic sample mounting would be to collect data at the inflection of the absorption edge and a remote wavelength far away from the edge. A continuous oscillation range providing close to 95% unique completeness would work well for the majority of cases. Because Friedel pair completeness does not appear to be critical, collecting data in a continuous oscillation segment rather than using the inverse-beam geometry is preferable. Even in the worst-case scenario that the crystal was damaged before the data collection is complete, this strategy would minimize the number of crystals needed to solve the structure.

If the MAD data were also to be used for structure refinement, it would be convenient to aim for close to 100% completeness at least at one wavelength. This can be achieved with very little extra exposure by collecting a non-contiguous rotation segment, particularly if the crystal is mis-set for this purpose.

With automated sample mounting, the sample could be retrieved easily in cases when an unfavorable anomalous-to-total scattering ratio or poor-quality diffraction made it necessary to collect more data (assuming that the data analysis cannot keep pace with the data collection). Alternatively, if the data-collection software was able to access information about initial screening results and sample characteristics from a database, as is the case for some structural genomics projects, an inverse-beam or a similar data-collection strategy aimed at collecting redundant data could be programmed right at the start for potentially difficult experiments such as Tm0667. In cases such as this, a priori knowledge of the very small anomalous signal, low solvent content and moderate diffraction quality makes it easy to predict that more than the minimum standard rotation for the space group is likely to be needed to solve the structure. Extra redundancy can also be useful in experiments aiming towards obtaining an undistorted view of the solvent area or fine structural detail. For these experiments, more accurate experimental MAD phases can be helpful in interpreting the ordered solvent structure (Burling et al., 1996; Schmidt et al., 2002) or guiding the structure refinement (Coste et al., 2002). Using direct methods in combination with MAD (Gu et al., 2001) might help shorten the experiment in these cases.

Because in the general case is not optimized at the wavelengths suggested for two-wavelength experiments, collecting data simultaneously at both wavelengths in small wedges would be preferred to collecting one wavelength at a time. The former strategy would be better at preserving the dispersive differences in case of damage to the sample and to facilitate data analysis on the fly, deriving the heavy-atom substructure from the dispersive differences alone or combined with the anomalous differences. If automatic data analysis is not implemented and it is possible to evaluate the data as they are being collected, as is the case with less intense X-ray sources, it may be more practical to collect one entire wavelength at a time, rather than in wedges, to simplify data processing. In this case, collecting the wavelength with the highest first would allow the fastest determination of the heavy-atom substructure and give the best chance of solving the structure by SAD in case the data collection could not be finished.

Redundant SAD data collection would be a better option than MAD when instrumentation constraints make it difficult or impossible to collect a remote wavelength sufficiently far away from the absorption edge, when the beamline stability, bandpass or reproducibility are not appropriate for MAD and, of course, if the absorption edge of interest is not available.

6. Summary

The examples presented in this paper, representing typical data quality and resolution and processed by conventional methods, show that both two-wavelength MAD at the inflection and remote wavelength, and SAD at the peak wavelength can result in interpretable maps using significantly fewer data than three-wavelength MAD. It was also found that for the samples used in the study, SAD phasing did not require fewer data than two-wavelength MAD phasing. Therefore, both single or two-wavelength experiments may be equally suitable for maximizing beamline throughput and decreasing the exposure of the crystal to radiation. When fulfillment of these requisites is crucial for the experiment, as is the case for high-throughput projects, in experiments with radiation-sensitive samples, when the available beam time is limited etc., the choice of strategy should be made based on the capabilities of the X-ray source and the characteristics of the sample.

In addition to the obvious case where the relevant absorption edge is not accessible at a dedicated beamline, collection at a single wavelength may be advantageous when the beamline wavelength range is limited and a suitable remote wavelength far away from the absorption edge cannot be reached. On the other hand, when the beamline is suitable for MAD and tunable over a large range about the absorption edge of interest so that a large value can be achieved, two-wavelength MAD would be the more advantageous strategy, both because of the somewhat higher accuracy of the phases, which provides an advantage at the model refinement stage (Murshudov et al., 1997), and the possibility of decreasing the radiation damage to the crystal by avoiding collection at the maximum wavelength. A controlled experiment to assess the damage suffered by the crystal under different data-collection strategies would be worthwhile.