Multiwavelength anomalous diffraction (MAD) is the fastest growing method of structure determination in macromolecular crystallography. At least twenty-five new structures solved with MAD were published in the past year. Many factors contribute to the growth of MAD, and its future is extremely bright. The experience gained over the past several years is now being generalized to make MAD more accessible. This paper aims to present a practical overview of MAD. I first review the observational equation for MAD and describe the basis of the phasing signal and how it is estimated for specific problems. This is followed by a discussion of the design of a MAD experiment, schemes for data analysis and phasing, and considerations in solving the anomalous-scatterer partial structure. Finally, there is a discussion of selenomethionine as a phasing vehicle. More comprehensive reviews of MAD have been published by W. A. Hendrickson, who pioneered its development and application in macromolecular crystallography (Hendrickson, 1991; Hendrickson & Ogata, 1997).

Electrons bound in atomic orbitals have specific resonant frequencies corresponding to allowed transitions. Anomalous scattering is the manifestation in X-ray diffraction of these resonance effects. The resonant frequencies of most chemical elements in biological macromolecules are far below the energies used for diffraction experiments, and their anomalous scattering is thus negligible. However, elements of atomic number 24 through 92 have resonant frequencies between 6 keV ( = 2Å) and 40 keV ( = 0.3Å), which give rise to detectable effects in X-ray scattering from macromolecular specimens labeled with these elements. Information about the phase of the scattered X-rays can be derived from the resonance effects, or anomalous scattering. Anomalous scattering is an atomic property and thus enters the equations for X-ray diffraction in the expression for the atomic scattering factor (f), which is the sum of "normal" atomic scattering factor f0 and a complex "anomalous" correction having real (f') and imaginary (f") components:

The formulation of the MAD observational equation used here is based on that of Karle (1980) as modified by Hendrickson et al. (1985).

	|Fobs+/-|2  = |FT|2 + a |FA|2 
			+	b |FT||FA|cos(T-A) 
			+/-	c |FT||FA|sin(T-A),	[1]
where 			a   =  (f"2+f'2)/(f0)2,
			b   =  2f'/f0
and 			c   =  2f"/f0. 

	|FA'|  =  (f'/f0)|FA|
and	|FA"|  =  (f"/f0)|FA|.

Wavelength-dependence and structure-dependence are thus separated into different quantities. All wavelength dependence is in the anomalous scattering factors, f' and f", which do not depend on atomic positions, and all structure dependence is in the normal structure factors F_T and F_A, which do not depend on wavelength. The structure factor F_T represents normal scattering from the total structure, and F_A represents normal scattering from the partial structure of anomalous scatterers. An Argand diagram showing the relationships of these structure factors has been published (Smith, 1991). Eq. 1 describes the case for one type of anomalous scatterer. In general, Eq. 1 will relate experimental observations to unknown quantities whose number equals twice the number of anomalous-scatterer types plus one, here |F_T|, |F_A| and (_T-_A ) for one anomalous-scatterer type.

The MAD observational equation (Eq. 1) involves no approximations, and the accuracy of MAD phases is limited only by the precision of the diffraction data. This is in contrast to isomorphous replacement where phase accuracy is limited most severely by breakdown of the assumption of isomorphism of native and derivative crystals. The new prominence of MAD is due primarily to a significant improvement in the quality of diffraction data in general. This comes from the ability to measure better data faster thanks to widespread adoption of cryocooling techniques and to improvements in synchrotron sources and X-ray detectors.

Anomalous scattering factors in the region of an absorption edge are sensitive to the chemical environment of the absorbing atom, and are significantly enhanced by sharp spectral features in many cases. Therefore, f" and f' for anomalous scatterers in macromolecules cannot be calculated as free-atom anomalous scattering factors (Cromer & Liberman, 1970a,1970b), which are accurate estimates for all chemistries at energies away from absorption edges. Several laboratories have schemes for extracting anomalous scattering factors f' and f" from X-ray spectra, none of which has been published in rigorous detail. However, all exploit the fact that the imaginary component of anomalous scattering f" is proportional to the atomic absorption coefficient ua, which can be obtained easily from raw X-ray fluorescence or transmission data. The scheme of Hendrickson et al. (1988) is described briefly here and illustrated in Fig. 1. The X-ray spectrum of the labeled macromolecule, typically a macromolecule single crystal, is measured as fluorescence through the edge of interest (Fig. 1a). Regions of the experimental spectrum slightly away from the edge are fit to theoretical values using the program XASFIT in order to place the experimental spectrum on an absolute scale (Fig. 1b). Theoretical values are obtained from a program by Don Cromer, modified by Wayne Hendrickson to produce spectra rather than f' and f" at single energies and variously called FPRIME, SPECTRUM or CROMER. Care must be taken to measure enough edge-remote points for reliable fit of the experimental spectrum, which may be quite noisy. A narrow region around the absorption edge is then cut from the scaled experimental spectrum and spliced into the theoretical spectrum. From the hybrid spectrum of f" values thus obtained, f' values are calculated by Kramers-Kronig transformation:

[2]

Figure 1

A. Fluorescence spectrum (I/I₀ on an arbitrary scale) through the Pt LIII absorption edge from a single crystal of -hydroxydecanoyl thiolester dehydrase (Leesong et al., 1996). A single methionine amino acid of the crystalline protein was labeled with Pt by soaking in a solution of K₂PtCl₄.
B. Scaling of fluorescence data to theoretical atomic absorption coefficients (ua). The raw fluorescence spectrum was fit to the theoretical spectrum for the Pt L_III edge using the program XASFIT. The scaled experimental spectrum is shown superimposed on the theoretical free-atom spectrum.

C. Hybrid f" and f' spectra for the Pt LIII edge. Using the program KRAMIG, the edge region has been cut from the experimental spectrum in B and spliced into the theoretical spectrum, ua converted to f", and f' calculated from f" by Kramers-Kronig transformation (Eq. 2).

where E is energy in eV and d is the energy increment of the f" spectrum being transformed. In practice, the point of singularity for each f' (Ei = E) is not included in the summation, and a transformation range of ~500 eV beyond the f' being computed is sufficient to eliminate truncation effects. Splicing and f' calculation (Fig. 1c) are done with the program KRAMIG.

Typical anomalous scattering factors, f"max and f'min, estimated from X-ray spectra of protein crystals taken at MAD experimental stations, are given in Table 1 for several elements. In addition to the electronic environment of the anomalous scatterer, the energy dispersion of the incident X-ray beam also influences the values of anomalous scattering factors in the edge region.

Table 1. Typical anomalous scattering factors

 Element    f0    Edge             f'min            f"max   Reference            
           (e-)             (Å)     (e-)     (Å)      (e-)                           
   Fe       26     K      1.7402     -9     1.7380     5    Hendrickson et al.,1988     
                          1.7425     -8     1.7390     4    Smith et al.,1994      
   Cu       29     K      1.3790     -8     1.3771     4    Guss et al., 1988       
   Zn       30     K      1.2826     -9     1.2818     4    Zhang et al., 1995      
   Se       34     K      0.9793    -11     0.9792     6    Wu et al., 1994         
   Br       35     K      0.9207     -7     0.9196     4    Ogata et al., 1989      
   Sm       62    LII     1.6959    -16     1.6952    17    Tomchick et al., 1996   
   Ho       67    LIII    1.5363    -28     1.5356    20    Weis et al., 1991       
   Yb       70    LIII    1.3857    -33     1.3853    35    Shapiro et al., 1995    
    W       74    LIII    1.2136    -24     1.2123    19    Egloff et al., 1995     
   Os       76    LIII    1.1402    -23     1.1397    20    Cate et al., 1996       
   Pt       78    LIII    1.0720    -21     1.0714    13    Fig. 1c                 
   Hg       80    LIII    1.0094    -18     1.0057    10    Tesmer et al., 1994     
                         1.0095    -25     1.0063    12    Krishna et al., 1994    
    U       92    LIII    0.7213    -21     0.7208    12    Glover et al., 1995     

Knowledge of anomalous scattering factors allows estimation of the MAD signal for a specific anomalous scatterer in a specific macromolecule. The orthogonal components of the phasing signal, due to the real and imaginary anomalous scattering factors f' and f", are estimated separately because both are required for phase determination. The maximum MAD Bijvoet signal is due to Bijvoet differences at the energy of peak absorption, or f"max, and is proportional to 2f"max of Table 1. The maximum MAD dispersive signal is due to wavelength differences between structure amplitudes at the energy of the inflection point of the edge (f'_min) and at a remote energy(f'_remote), and is proportional to |f'_min-f'_remote|.

The magnitude of the MAD phasing signal is estimated as the ratio of expected Bijvoet or dispersive difference to expected total scattering of the macromolecule. This is

based on calculation of expected structure amplitudes <|F|>, where <|F|> = and <|F|> = for N atoms of identical f (Crick & Magdoff, 1956). The diffraction ratios of interest to MAD (Hendrickson, 1985) are, for the dispersive signal,

[3]

for N anomalous-scatterer sites with 1 chosen at f'_min and 2 chosen for |f'₁-f'₂|_max, and, for the Bijvoet signal,

[4]

with chosen at f"_max. These diffraction ratios are analogous to the usual calculation of isomorphous signal from experimental data in which

[5]

where f⁰ is for the heavy atom. Values for f⁰, f'_min and f"_max are those in Table 1. The denominator of all diffraction ratios is the expected total scattering of the macromolecule, which can be estimated for 2 = 0 with the expressions in Table 2.

Table 2. Estimates of scattering strength for macromolecules, <|FT|>

  Macromolecule     NA = # atoms     NR = # residues   MW = molecular weight 
                       (e-)              (e-)              (e-)                                     
     Protein        6.70 (NA)1/2       (346 NR)1/2            (3.14 MW)1/2         
       DNA          7.20 (NA)1/2      (1128 NR)1/2            (3.87 MW)1/2    
       RNA          7.26 (NA)1/2      (1183 NR)1/2            (3.89 MW)1/2        

Three important considerations distinguish the design and execution of a MAD experiment from more familiar monochromatic experiments in macromolecular crystallography. These are wavelength selection, data completeness and data quality. A discussion of the design of beamline components for MAD experiments is presented in another paper in this volume by A. W. Thompson.

The largest MAD phasing signal is obtained at energies with the most extreme values of f' and f", which correspond to the sharpest features of the absorption edge. Therefore, it is critical to determine the position of the absorption edge experimentally from the labeled macromolecule at the time of a MAD experiment. Even when the position of the edge is well known, small unanticipated chemical changes in the sample or energy changes in the X-ray beam can reduce the MAD signal very significantly if the sharp edge features are missed in selecting energies for data collection. Energies are selected at the peak of sample absorption just above the edge ("_Epeak" for f"_max) to optimize the Bijvoet signal and at the inflection point of the edge ("E_dip" for f'_min) to optimize the orthogonal dispersive signal. The dispersive signal is further optimized if a third energy remote from the edge ("E_remote") is chosen. The choice of Eremote is experiment dependent, although it is typically above rather than below the edge due to the larger Bijvoet signal. Eremote may also be chosen to avoid complications from other edges or to obtain data at a wavelength optimal for model refinement.

There has been much debate about the optimal number of data-collection energies for successful phase determination by MAD. In the commonest MAD experiment |F⁺| and |F^-| are measured at each of E_dip, E_peak and E_remote. If the difference in f' is large enough to produce a detectable signal, then one could in principle obtain phases from three measurements: |F⁺| and |F^-| at E_peak and either |F⁺| or |F^-| at E_dip (Peterson et al., 1996). However, redundancy is one of the best ways to minimize the effects of measurement error in macromolecular crystallography. In the full three-energy experiment, the Bijvoet signal is redundant because the remote energy is above the edge. The orthogonal dispersive signal is redundant because two measurements are taken at each of Edip and Eremote. There are several examples of even more redundant four- or five-wavelength MAD experiments. While greater redundancy is desirable, it should not be gained at the cost of good counting statistics. Unfortunately, considerations of available beam time frequently preclude MAD experiments with more than three energies.

The MAD phasing signal is derived from intensity differences that may be similar in magnitude to measurement errors. Thus a general philosophy in the design of a MAD experiment is to equalize systematic errors among the measurements whose differences will contribute to each phase determination. This is achieved for each single reflection by recording Bijvoet measurements at all wavelengths from the same asymmetric unit of the same crystal at nearly the same time. Bijvoet mates can be recorded simultaneously by alignment of the crystal with a mirror plane perpendicular to the rotation axis, or Friedel images can be recorded in an "inverse beam" experiment. (Friedel images are related by 180^o. rotation of the crystal about any axis perpendicular to the incident beam, usually the data-collection axis). If crystal decay is a problem, small blocks of Bijvoet data can be recorded at each of the selected wavelengths before moving to another block of reciprocal space. When such a data collection strategy is followed, the resulting MAD data set will be complete with respect to recording all multiwavelength, Bijvoet measurements for all regions of the reciprocal lattice that are covered in the experiment. Coverage of reciprocal space can be monitored during the experiment by a strategy program, if available, or by reduction of diffraction images to integrated intensities for data from at least one wavelength. Completeness of the MAD data set is at least as important as for any diffraction experiment that will be used for phasing. If data, and hence phase information, are incomplete, it may be difficult to reproduce the same beam and sample conditions during a subsequent experiment, which is likely to occur only after some weeks or months.

Measurement errors are of major importance in all areas of macromolecular crystallography, but are the limiting factor in phase determination by MAD. MAD data should be of high quality by the usual measures (R_sym, redundancy, completeness), especially in experiments where the phasing signal is weak. In the hypothetical 500-residue protein with 10 Se anomalous scatterers, a 5% MAD signal will become undetectable as it is exceeded by R_sym "noise". Thus data with good counting statistics are of paramount importance. In a carefully designed experiment, the effect of increasing Rsym with increasing is mitigated somewhat by equalizing systematic errors. Nevertheless, if R_sym (I) is 30% for the outer shells of data, there will be virtually no detectable MAD phasing signal for these reflections in the hypothetical example. Disappearance of the phasing signal into R_sym noise is the major reason that useful MAD phases generally are not obtained to the diffraction limit of crystals even though anomalous scattering does not fall off with increasing .

Data processing and scaling

Concerns about signal size dominate special schemes for handling MAD data. Scaling strategies for MAD are discussed in detail elsewhere in this volume by P. R. Evans. Special computer programs for scaling MAD data have been developed (Hendrickson et al., 1988; Friedman et al., 1994). Two general approaches to data handling for MAD have been employed.

The approach originally proposed by Hendrickson, known as "phase first, merge later," represents the extreme interpretation of the scheme for equalizing systematic errors - the individual observations constituting a multiwavelength Bijvoet set, as determined by the data-collection strategy, are grouped together and scaled as usual, but are merged with redundant measurements only after phases are determined. Error estimates from the phasing or the agreement of redundant phase determinations can be incorporated into weights for averaging, or can be used to reject outliers. This approach involves complicated, experiment-dependent bookkeeping to assemble exactly the correct observations for each unmerged set.

A second approach, "merge first, phase later," is to scale and merge data at each wavelength, keeping Bijvoet pairs separate, and then to scale data at all wavelengths to one another. This is most easily and reliably done by scaling all data against a common standard data set, which can be the unique data from one wavelength with Bijvoet mates averaged. If the data collection followed one of the strategies outlined above, then measurements for each unique reflection are identically redundant, which itself minimizes systematic errors in the amplitude differences used for phasing. The second approach is computationally simpler than the first because it is experiment independent. However, unanticipated, minor experimental disasters may be more difficult to overcome in the "merge first, phase later" approach to data handling.

There are two general approaches to MAD phasing. One is to treat the problem explicitly and solve the MAD observational equation (Eq. 1). This explicit approach is embodied in the MADSYS package from the Hendrickson laboratory (Wu & Hendrickson, 1996), in particular in the phasing program MADLSQ. The other approach is to treat MAD phasing as a special case of multiple isomorphous replacement (MIR). The pseudo-MIR approach is discussed elsewhere in this volume by V. Biou and in two recent publications (Ramakrishnan & Biou, 1997; Terwilliger, 1997). Both approaches have been quite successful, and there are no hard-and-fast rules for which sorts of problems are more amenable to which approach, rumors in the community notwithstanding. There are advantages and disadvantages to both approaches.

The explicit approach provides the quantities |F_T|, |F_A| and (_T-_A). Estimates of the anomalous scattering factors at the wavelengths of data collection are required to fit the observations to the MAD phase equation. These estimates can be refined within MADLSQ, so they need not be highly accurate. A second calculation is required to obtain _T from the phase differences (_T-_A). There are two advantages to the explicit approach. First, it is amenable to the "phase first, merge later" scheme of data handling because refinement of the anomalous-scatterer partial structure is entirely separate from phase calculation. In this case redundancies are merged to produce a unique data set at the level of the derived quantities |F_T|, |F_A|, (_T-_A) and their error estimates. These error estimates or the agreement of redundant phase determinations can be used to weight terms in a Fourier synthesis from |F_T| and _T. Phase probability coefficients (ABCDs) have been derived from the MAD phase equation (Pähler et al., 1990). The second principle advantage of the explicit approach is calculation of an experimentally derived estimate of the normal structure amplitude |F_A| for the anomalous scatterer. This is the quantity with which the partial structure of anomalous scatterers is most directly solved and refined, and therefore should be highly sought. However, while MADLSQ is quite successful in the least-squares fit of the MAD phase equation to |F_obs| for high-quality data, it is poorly conditioned to extracting |F_A| from noisy data and requires careful pruning of outliers from the |F_A| values produced. A Bayesian method of |F_A| estimation (Terwilliger, 1994) should be more robust than the least-squares procedure.

In the pseudo-MIR approach data at one wavelength are designated as "native" data, which include anomalous scattering, and data at the other wavelengths as "derivative" data. This approach has the advantage that nothing need be known about the anomalous scattering factors prior to phasing. These quantities are incorporated into heavy-atom atomic "occupancies" and refined along with other parameters. Of course, the partial structure of anomalous scatterers must be known, and refinement of the partial structure is concurrent with phasing. In refinement of the "heavy atom" parameters, greater weight is given to the data set selected as "native." This bias should be removed by the new maximum-likelihood refinement of de La Fortelle and Bricogne (1997), which treats data at all wavelengths as statistically equivalent. The amplitudes |F_A| are not determined in the pseudo-MIR approach, and the partial structure is solved from Bijvoet differences between |F⁺| and |F^-| or dispersive differences between |F₁| and |F₂|, with wavelengths selected to optimize the signal. The pseudo-MIR approach is used more frequently than the explicit approach due to the greater familiarity of crystallographers with software for isomorphous replacement.

A prerequisite for MAD-phased electron density, regardless of the phasing technique, is determination of the partial structure of anomalous scatterers. As described above, the optimal quantities for solving and refining the partial structure of anomalous scatterers are the normal scattering amplitudes |F_A|. Frequently |F_A| values are not extracted from the MAD measurements, and the largest Bijvoet or dispersive differences are used instead. This involves the usual approximation of representing structure amplitudes (|F_A|) as the subset of larger differences (||F⁺|-|F^-|| or ||F₁|-|F₂||). The approximation is accurate for only a small fraction of reflections because there is no correlation between the phase of F_P and the phase of F_A. However, it suffices for a suitably strong signal and a suitably small number of sites. For virtually all structures determined by MAD, the anomalous-scatterer sites have been located by Patterson methods. However, the problem quickly becomes intractable by Patterson methods when there are more than a handful of sites. This is a current challenge for MAD, where the aim is to solve the macromolecule structure from one MAD data set using any number of anomalous scatterer sites. Statistical direct methods clearly hold the answer to this problem. Recent results are promising in this regard. Bertrand et al. (1997) have solved a 12-atom Se partial structure in a 437-residue protein by direct methods using |F_A|s, and S. Doublié (personal communication) has solved a 15-atom Se partial structure in an asymmetric unit of 108kDa using dispersive differences, also by direct methods. These results open the door for routine MAD determination of quite large structures with many anomalous scatterer sites. New direct methods techniques, such as described in this volume in papers by G. M. Sheldrick, by C. M. Weeks and by G. Bricogne, hold great promise for a major expansion in the complexity of anomalous-scatterer partial structure that can be solved.

The correct enantiomorph for the anomalous-scatterer partial structure must be determined (_A vs. -_A) in order to obtain an electron-density image of the macromolecule. However, it cannot be determined directly from MAD data. The correct hand is chosen by comparison of electron density maps based on both enantiomorphs of the partial structure. Unlike the situation for MIR, the density based on the incorrect hand of the anomalous-scatterer partial structure is not the mirror image of that based on the correct hand and contains no image of the macromolecule. The correct map is distinguished by features such as a clear solvent boundary, positive correlation of redundant densities, and a macromolecule-like density histogram. If the anomalous scattering centers form a centric array, then the two enantiomorphs are identical and both maps are correct.

The most successful MAD phasing vehicle to date has been selenium in the form of selenomethionine (SeMet). This particularly clever experiment was devised by Wayne Hendrickson (1985), who also pioneered its use (Yang et al., 1990; Hendrickson et al., 1990). Briefly, proteins are labeled with Se by biological substitution of SeMet for methionine amino acids. This is achieved by blocking methionine biosynthesis in the cells in which the protein is produced and substitution of SeMet for Met in the growth medium. The generality of the labeling scheme for proteins is the root of its success. SeMet labeling technology is discussed in a recent review by Doublié (1997).

SeMet incorporation has been done most frequently for proteins expressed in E. coli strains that are auxotrophic for Met (strain DL41, Hendrickson et al., 1990; strain B834, Leahy et al., 1994 and Doherty et al., 1995; strain LE392, Ceska et al., 1996; strain MIC88, Shamoo et al., 1995). Nearly complete incorporation has also been reported in nonauxotrophic bacterial strains (E. coli strain BL21, Harrison et al., 1994; E. coli strain XA90, Van Duyne et al., 1994, Labahn et al., 1996), in a mammalian cell line (Lustbader et al., 1995) and in baculovirus-infected insect cells (Chen & Bahl, 1991). Special precautions must be taken to prevent oxidation of SeMet proteins. In almost all cases, somewhat higher-than-normal concentrations of disulfide reducing agents, such as dithiothreitol or -mercaptoethanol, are sufficient to protect SeMet from air oxidation to the selenoxide (Brot et al., 1984). In a few cases, crystallization in an inert atmosphere has been necessary (Dyda et al., 1994; Wu et al., 1994). Because Se is a light element, the position of the K absorption edge moves to slightly higher energy upon oxidation, and a mixture of oxidation states in a sample crystal is predicted to obliterate the MAD signal.

Methionine is a particularly attractive target for anomalous scatterer labeling. The hydrophobic side chain of methionine, which carries the sulfur atom to be substituted by selenium, is usually buried in the hydrophobic core of globular proteins and is therefore relatively better ordered than are surface side chains. Evidence for isostructuralism of Met and SeMet proteins comes from the labeling experiment itself. All proteins in the biological expression system have SeMet substituted for Met at levels approaching 100%. The cells are viable, therefore the proteins are functional and isostructural with their unlabelled counterparts to the extent required by function.

The natural abundance of methionine in soluble proteins is approximately one in fifty amino acid residues. The N-terminal Met is not included in this estimate because, if present, it is usually disordered. Using Eqs. 3 and 4, this provides a maximal MAD phasing signal of 4-6% of |F|, easily detectable in strongly diffracting protein crystals and detectable with careful data collection from crystals of moderate quality. To improve the phasing signal, in a few cases Met has been substituted for other amino acids by site-directed mutagenesis (Leahy et al., 1994, 1996; Skinner et al., 1994; Tong et al., 1996).

SeMet labeling is now part of the repertoire of protein crystallography, and has broader applicability than for MAD phasing alone. This comes from the relative ease of incorporation of the SeMet label, from the remarkable structural similarity of SeMet and wild type proteins, and from the uniformity and completeness of labeling. Crystals of SeMet proteins are usually isomorphous with those of the wild type, and consequently can be used as isomorphous derivatives. The isomorphous signal comes from the excess of 18 electrons in Se relative to S, making the SeMet isomorphous phasing signal (~10% of |F|, Eq. 5) about twice as strong as the SeMet MAD phasing signal (4-6% of |F|). In most cases SeMet derivatives are more isomorphous, and certainly more rationally produced, than are heavy-atom derivatives produced by the usual soaking procedures. Prior knowledge of exactly how Se labels the protein is itself a powerful tool. For example, the SeMet mutation is an extremely useful amino acid label for fitting a protein sequence to electron density. Also, noncrystallographic symmetry operators usually can be defined more reliably from Se positions in SeMet protein than by heavy-atom positions in conventional derivatives due to the uniformity and completeness of labeling (Tesmer et al., 1996).

An analogous label is available for nucleic acids in the form of brominated bases, particularly 5-bromouridine, which is isostructural with thymidine. Iodinated bases are commonly used as isomorphous derivatives (f⁰ = 53 e^-) for nucleic acids, but the X-ray edges of I ( = 0.38Å for K, = 2.56-2.72Å for L) occur at energies less favorable for accurate macromolecular data collection than does the K edge of Br ( = 0.92Å).

Why is the enthusiasm for MAD so high today? There are three primary reasons. First, cryocrystallography has improved data quality to the point that the precision required for MAD is usual rather than exceptional. Second, new synchrotron sources and new beamlines provide intense, reliably tunable X-ray beams and the instruments to exploit them. Third, MAD works extremely well and very quickly. For many problems, the experimentally phased electron density is of stellar quality. Crystallographers are only beginning to appreciate the value of nearly error-free, model-independent phases (Burling et al., 1996). The remaining challenges are in two areas. The greatest impediment to growth of MAD today is access to suitable experimental facilities. This non-technical problem may be solved only be a concerted effort of the community. The greatest technical challenge is to develop methods for solving large partial structures of anomalous scatterers. Here recent results with statistical direct methods are very promising, and MAD applied to large macromolecules no longer seems such a heroic undertaking. MAD has at last taken its place as a standard tool of macromolecular crystallography.

Work in the author's laboratory has been supported by grants from the U.S. National Institutes of Health (DK42303), and from the Lucille P. Markey Foundation to the Structural Studies Group at Purdue University. Collaboration with the scientific staffs at synchrotron facilities is gratefully acknowledged, especially A. W. Thompson of the European Synchrotron Radiation Facility, and S. E. Ealick of the Cornell High Energy Synchrotron Source.

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