research papers
Oneandahalf wavelength approach
^{a}Synchrotron Radiation Research Section, National Cancer Institute, NSLS, Brookhaven National Laboratory, Building 725AX9, Upton, NY 11973, USA
^{*}Correspondence email: dauter@bnl.gov
In many cases singlewavelength anomalous diffraction (SAD) phasing leads to a successful structure solution, but it is impossible to predict beforehand if singlewavelength data with a certain amount of anomalous signal resulting will be sufficient. It is therefore safer to continue collecting data at different wavelengths according to a MAD protocol, but to simultaneously attempt to phase the first data set by the SAD method. If this is successful, then further data collection can be abandoned. This `1.5wavelength' approach may save a substantial amount of time and effort and diminishes the effects of crystal radiation damage. The principles of SAD phasing are illustrated using vector diagrams in the Argand plane.
Keywords: anomalous scattering; SAD; MAD; macromolecular phasing.
1. Introduction
Currently, the most common way of solving novel macromolecular crystal structures is the ). Instead of collecting diffraction data from the native crystal and a number of derivatives, as in the multiple (MIR) approach, the MAD technique is based on data sets, usually three or four, recorded at various wavelengths from only one kind of crystal containing suitable anomalous scatterers. Whereas in MIR the protein phases are estimated from the additional scattering of the heavy atoms present in the derivative structures, in MAD the protein phases are calculated from the wavelengthdependent quantitative differences in the contribution of certain atoms contained in the crystal. There are two basic approaches to The first, classic, method (Karle, 1980; Hendrickson, 1991) is based on the algebraic solution of the system of equations. The alternative method (Ramakrishnan & Biou, 1997) applies the MIR phasing techniques, treating MAD as a special case of MIR.
method (Smith & Hendrickson, 2001Since the introduction of the MAD method (Karle, 1980; Phillips & Hodgson, 1980; Hendrickson, 1991), the recommended procedures have evolved considerably. The first MAD structures have been solved with diffraction data collected at secondgeneration synchrotrons at ambient temperatures. Under these conditions, crystal diffraction decay has been a very significant factor. The strict procedures leading to good resulting phases involved collecting successively narrow batches of rotation images at several wavelengths in the inversebeam mode. This ensured that the same reflections and their Friedel mates were measured under as similar conditions as possible at all wavelengths. The introduction of cryogenic cooling has changed these requirements, to a large extent alleviating the radiationdamage effects. It became more effective in terms of time and effort to collect a full data set at one wavelength before setting the monochromator to the next wavelength. The introduction of extremely bright thirdgeneration synchrotron beamlines changed the situation again, since at APS, ESRF or SPring8 even frozen crystals undergo significant radiation damage within a few minutes of irradiation.
In parallel to the technological advances of cryocrystallography and synchrotron beamlines and, in addition, in the production of selenomethionine protein variants by genetic engineering, methodological progress in the phasing procedures has led to faster, more automatic and reliable algorithms and programs. Macromolecular crystallography has now evolved to such an extent that structural genomics projects, aiming at rapidly solving a large number of new structures in a short time, are actively and successfully pursued in many laboratories.
The necessity of rapid turnover of new crystal structures has led to efforts directed towards speeding up Xray data collection and phasing procedures. One of the possibilities is to limit the number of data sets necessary to solve a novel ). Wang's simulations (Wang, 1985) suggested that an anomalous signal as small as 0.6% of the total scattering may be sufficient for successful phasing.
It has been shown that only onewavelength data suffice to solve the structure if the anomalous diffraction signal of the scatterers introduced to the crystal or inherently present within the macromolecule is measured accurately. Early examples include the use of the anomalous signal of sulfur for the solution of the structure of crambin (Hendrickson & Teeter, 1981In general, there is no guarantee that a singlewavelength diffraction (SAD) approach will lead to the structure solution, but data collected at the first wavelength should be interpreted and the preliminary phasing performed as rapidly as possible. In favourable cases, collection of data at the second wavelength can be interrupted before completion. This would lead to the `oneandahalf wavelength' (1.5λ) approach, which can be treated as SAD with an additional insurance policy.
2. Examples of the 1.5λ approach
An approach similar to 1.5λ has been implicitly proposed by Rice et al. (2000), who reinterpreted several SeMet MAD structure solutions and concluded that the solutions could have been achieved by SAD using only one, peakwavelength, data set. The authors suggested that in the MAD work the firstwavelength data with maximum anomalous signal should be collected particularly accurately, with high redundancy, before moving to the other wavelength.
A number of examples among the data collected at the X9B beamline at the National Synchrotron Light Source (Brookhaven National Laboratory, Upton, NY, USA) can be classified as the 1.5λ approach. Some of them will be briefly described here. In all examples, the diffraction images were interpreted and data processed with HKL2000 (Otwinowski & Minor, 1997).
2.1. Glucuronyltransferase
This structure has been solved from crystals of the SeMet variant (Pedersen et al., 2000). It contains two molecules of 261 amino acids, each containing three ordered Se atoms per of the P2_{1} crystal. In the text of the publication, the authors stated that the structure has been solved by the SAD technique, whereas in fact the data have been collected at the next wavelength as well. However, the rapidly processed 1.6 Å resolution data from the first, peak, wavelength displayed a very clear anomalous signal and the SAD structure solution with SHELXD (Sheldrick, 1998), MLPHARE (Otwinowski, 1993) and DM (Cowtan & Zhang, 1999) up to the initial electrondensity map display took less than half an hour, when the collection of data at the second wavelength was not yet halfway through. The course of this procedure is summarized in Table 1 and a fragment of the experimental map is shown in Fig. 1(a).

The interpretation of the first diffraction images was performed against the first exposures, so that the image integration proceeded parallel to the exposure of further images. The integration of the firstwavelength data set was finished very shortly after the end of all exposures. Although the structure analysis of glucuronyltransferase was not performed within the framework of highthroughput projects, it illustrates very clearly the possibility of such rapid structure determinations.
2.2. Thioesterase
The human acylprotein thioesterase crystallizes with two molecules of 28 kDa each in the et al., 2000). The crystal was soaked for a short time in cryosolution containing 1 M NaBr and the first diffraction data set was collected at the Br wavelength to a resolution of 1.8 Å. The anomalous signal was very clear and several bromide sites were quickly identified by SnB (Weeks & Miller, 1999). Collection of data at the next wavelength was therefore abandoned. Six initially identified Br sites were expanded in three iterations of SHARP (de La Fortelle & Bricogne, 1997) phasing to 22 sites; after density modification by DM, the figure of merit increased from 0.40 to 0.85 and the resulting map (Fig. 1b) showed clearly most of the protein chain. 347 out of the total 464 amino acids of the protein model were built automatically by wARP (Perrakis et al., 1999).
(Devedjiev2.3. PSCP
The structure of Pseudomonas serinecarboxyl proteinase (PSCP) was previously solved from the anomalous signal of the cryosoaked bromides (Dauter et al., 2001). The crystals of PSCP contain one molecule with 372 amino acids in the In this case, only the 1.8 Å resolution peakwavelength data were used for phasing, but the threewavelength MAD data were collected for the purpose of comparison of different phasing approaches. Nine Br sites identified by SHELXD were input to SHARP (FOM 0.21) and the resulting protein phases were improved by DM (FOM 0.74), leading to a very clear map (Fig. 1c). The warpNtrace procedure automatically built 363 out of 372 residues with most of the correct side chains.
An analogous procedure where the full threewavelength MAD data were used led to a SHARP FOM of 0.43 and DM FOM of 0.63, the latter value being lower than that obtained from the SAD phasing. However, the DM procedure in the threewavelength converged after four cycles, whereas in the SAD case it ran for seven cycles. Nevertheless, the MAD map was slightly superior to the SAD, although the SAD data collection and phasing required more than three times less time for the successful solution of the structure.
3. Background of SAD
is caused by the resonant effects of electrons whose is close to the energy of the incident Xrays. It can be described by the additional corrections, real () and imaginary (), to the atomic scattering factor,
where the normal scattering, f_{j}^{0}(θ), depends on the diffraction angle θ but not on the wavelength, and the anomalous corrections, real (λ) and imaginary (λ), depend on wavelength but not on the diffraction angle. If the crystal contains A atoms diffracting anomalously and N normal atoms then, neglecting the displacement parameters, the total for reflection F_{T}(h) will be
This is illustrated in Fig. 2(a), where contributions from individual atoms of the structure are represented as vectors in the Argand plane. As seen in Fig. 2(b), the Friedelrelated reflection, F(−h), has all contributing vectors directed at the negated phase, except the imaginary contributions of the anomalously scattering atoms, which point in a direction 90° more positive than that of the normal scattering of these atoms. That is strictly true if all anomalous scatterers are of the same kind, since then
Otherwise, the vector corresponding to the total anomalous contribution, , is not perpendicular to that of the normal contribution, F_{A} + . As a result, the total scattering vectors for the two Friedel mates F(h) and F(−h) differ in length and in phase if the crystal contains anomalous scatterers. It is customary to represent the vectors corresponding to the negative Friedel mate F(−h) as reflected to the other side of the diagram, i.e. to draw its complex conjugate *F(−h), since it visualizes more easily the phase relations between the two Friedelrelated reflections (Fig. 2c).
The difference between amplitudes of two Friedel mates depends on the mutual disposition of the phases of the total scattering vector F_{T} and those of the normal scattering of the anomalous scatterers F_{A}. Fig. 3 shows two extreme possibilities, where these two vectors are either parallel or perpendicular. In the former case, no Bijvoet difference is observed since both mates, F_{T}^{+} and F_{T}^{}, have equal length. This is always true for centrosymmetric reflections, since all normal scattering vectors are purely real, mutually parallel or antiparallel (Fig. 4). For those reflections, the real contribution (usually negative) diminishes or increases the measured reflection amplitude if F_{T} and F_{A} have equal (both 0 or 180°) or opposite (one 0 and another 180°) phases, respectively. The significant imaginary contribution always increases the measured centrosymmetric amplitudes, irrespective of the phase difference.
If the scattering vectors of the normal and anomalous atoms are perpendicular, φ_{T} − φ_{A} = ± 90°, the magnitude of the Bijvoet difference, F_{T}^{+} − F_{T}^{}, is the largest possible. Theoretically, the Bijvoet differences should depend sinusoidally on the difference between the two phases (Hendrickson, 1979),
Fig. 5 shows this dependence for experimental diffraction data and phases calculated from the refined atomic model. The sinusoidal relationship is apparent in general, although both the measurement and model errors are significant.
To identify the positions of anomalous scatterers within the crystal, it is, in principle, necessary to extract their diffraction vectors F_{A}. This is not possible from onewavelength data, where only two measurements, F_{T}^{+} and F_{T}^{}, are available for each reflection. It becomes possible when additional data are collected at different wavelengths with different and/or anomalous contributions. In a MAD experiment, several data sets collected with wavelengths around the of the anomalous scatterer provide different magnitudes of and (Fig. 6) and the relations between various contributing vectors and their phases can be solved analytically, as proposed by Karle (1980).
However, if only SAD data are available, it is possible to locate the anomalous scatterers using the largest Bijvoet differences instead of F_{A} values. For reflections with the largest anomalous differences where the φ_{T} − φ_{A} phase difference is close to ± 90° (one of the cases in Fig. 3), the measured Bijvoet difference is proportional to F_{A},
so that the large Bijvoet differences can be used in ).
or Patterson searches to find positions of the anomalous scatterers. The use of Bijvoet differences to locate anomalous scatterers was first proposed by Rossmann (1961When positions of the anomalous scatterers are known, it is possible to calculate their contribution to the total diffraction. However, even in the ideal case of errorfree measurements, this does not provide a unique solution to the φ_{T} symmetrically placed around the φ_{A} − 90°, direction (Fig. 7a), also illustrated in Fig. 5. The possible values of φ_{T} are (Ramachandran & Raman, 1956)
since in general there are two possible arrangements satisfying the vector relations. They lead to two possible total protein phase valueswhere
Only for the largest Bijvoet differences does this SAD ambiguity degenerate to a single solution with φ_{T} − φ_{A} = ± 90°.
The reflection intensities measured in a diffraction experiment inevitably contain errors. The (b), shows that instead of two sharp solutions there are two regions where the total protein phase φ_{T} may lie. The probability that the protein phase has a particular value, given the known Bijvoet difference ΔF^{±}, calculated anomalous scatterers phase φ_{A} and imaginary contribution , is (Hendrickson & Teeter, 1981)
signal is usually small, at the level of a few percent of the total crystal diffraction. The anomalous diffraction data should therefore be collected very carefully with proper estimation of the errors (standard uncertainties) associated with the measured intensities. If measurement errors are taken into account, the modified SAD vector diagram, Fig. 7where E is the standard error and N the normalizing factor. This can also be expressed using the Hendrickson–Lattman (Hendrickson & Lattman, 1970) coefficients,
or, since this function is symmetric around φ_{A} − 90°,
The above analysis of the phasing information based on the singlewavelength anomalous signal is analogous to the single F_{PH} − F_{P} and SIR also leads to an ambiguity, with two possible protein phases symmetrically placed around the heavyatom phase φ_{H} (Fig. 8a). The SIR error treatment, originally derived by Blow & Crick (1959), leads to a similar equation for the protein phase probability, P_{heavy}(φ_{P}), which can be expressed similarly in terms of Hendrickson–Lattman coefficients (Fig. 8b).
(SIR) case, where only the native and a single derivative data are available. Again, the heavy atoms can be located using the isomorphous differencesThe SIR ambiguity can be broken by the use of the second derivative, when only one solution for each derivative should coincide, indicating the proper protein phase (Fig. 9a). In the case of anomalous data, this can be achieved by the use of data collected at different wavelengths, where the contributions are different (Fig. 9b). This is the concept of the multiwavelength (MAD) approach. However, the changes in the real, , and imaginary, , contributions play different roles in (in relation to ΔF^{±}) indicates the positions of the two alternative phase solutions, which differ for the second wavelength only if the value is different; otherwise, the possible solutions coincide for both wavelengths, even if the values are different. Therefore, only the differences in indicate which alternative is correct.
The analogy between SAD and SIR is not complete. Comparison of Figs. 7(a) and 8(a) shows that whereas all vectors in the SIR case, F_{P}, F_{H} and F_{PH}, are of equal length in both alternative solutions, in the SAD case the F_{T} and F_{A} vectors have the same length, but the scattering of the normal atoms F_{N} is different. This is more clearly seen in Fig. 10, where in one solution the F_{N} vector is required to be much longer than in the other and significantly longer than the total scattering vector F_{T}; the latter situation is less probable. The anomalous scatterers can be treated as the known partial structure. The theory of protein phase probability with known partial structure has been worked out by Sim (1959, 1964),
where F_{U} is the scattering of the unknown part of the structure and N is the normalizing factor.
The probability resulting from the known partial structure depends on the cosine function of the phase difference φ_{T} − φ_{A} and as a result the combined probability is different for the two alternative solutions for φ_{T} (Fig. 11). Ramachandran & Raman (1956) first postulated that the total phase closer to the anomalous phase should be chosen for map calculation, which agrees with the Sim probability indication based on the partial structure.
4. SAD phasing
The first practical use of the above relations was realised in the solution of the structure of crambin (Hendrickson & Teeter, 1981) by the application of partial structureresolved The positions of six S atoms were located from the anomalous The reflections with largest ΔF^{±} and unimodal probability distributions gave phases φ_{A} ± 90° and other reflections according to the partial structure probability discrimination. Figures of merit were used for weighting in the map calculations. The correct was chosen on the basis of the reasonableness of the Fourier map.
In his classic work, Wang (1985) proposed the iterative singlewavelength (ISAS) approach. This takes advantage of the additive property of the Fourier transform. If the Fourier synthesis is calculated with structure factors corresponding to the sum of two alternative SAD vectors, the map should contain the proper features superimposed on more or less uniform noise, since such vectors represent the sum of the correct structure factors leading to the protein map and of the wrong factors producing only the featureless noise (Fig. 12). In the first approximation, it should be possible to identify in such a map regions corresponding to the protein in contrast to flatter solvent regions. The protein features can then be enhanced by iterative noise filtering, a procedure which evolved into the well known solvent flattening. Moreover, this procedure effectively discriminates between two enantiomeric solutions.
The SHARP (de La Fortelle & Bricogne, 1997). This allows the biasfree of anomalous scatterers and other parameters, and simultaneous estimation of protein phases and their weights. Several other programs, e.g. MLPHARE (Otwinowski, 1993), SOLVE (Terwilliger & Berendzen, 1999) and CNS (Brünger et al., 1998), treat SAD phasing as a special case of MIR or MAD and have been successfully used for this purpose.
approach based on the twodimensional integration of phase and amplitude probabilities and rigorous error treatment is realised inA different approach is based on the application of e.g. Hauptman, 1997; Langs et al., 1999; Liu et al., 1999). One such method is implemented in the program OASIS (Hao et al., 2000).
relying on the statistical relations between phases and Bijvoet differences of selected reflections (5. Conclusions
Numerous examples obtained in last couple of years show that SAD phasing is more powerful than had been anticipated. Various anomalous scatterers have been used (Hendrickson & Ogata, 1997; Dauter et al., 2002), ranging from phosphorus and sulfur to selenium, halides, heavy metals and lanthanides. Clearly, the success of this approach critically depends on the accuracy of the anomalous signal contained in the diffraction data. The dataresolution limit seems to play a less important role, although it is obviously best to have accurate data at high resolution. As in the other approaches, the success of SAD cannot be guaranteed a priori; it therefore seems reasonable to continue collecting diffraction data at further wavelengths with in mind, but in parallel to attempt to solve the structure against the first data set using the SAD approach. With the currently available programs, one can perform this rapidly and, if successful, it may allow one to abandon the collection of further data. If the solution cannot be achieved by SAD, one can continue to perform the full multiwavelength experiment. Such a 1.5wavelength approach may lead to less radiation damage to the crystal and to a substantial saving in time and effort, which is important for the currently pursued highthroughput structural projects.
Acknowledgements
Lars Pedersen is thanked for his kind permission to use glucuronyltransferase as an example of 1.5λ phasing.
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