W. Shepard , M. Ramin , R. Kahn¤, & R. Fourme 

  LURE, B.209D, UniversitŽ Paris Sud, 91405 Orsay, France.

¤ Institut de Biologie Structurale, 41 Avenue des Martyrs, 38027 Grenoble, France.

Contrast variation methods have primarily been applied and developed in low angle scattering studies as a means of extracting information on the shape of a particle dispersed in a solvent medium (for a review see Williams et al., 1994). This method deals with the changes invoked in the scattered intensities of a small angle scattering experiment when the density of the particle is varied relative to its solvent medium. The difference between the particle and solvent densities is defined as the "contrast" (Stuhrmann & Kirste, 1965; Ibel & Stuhrmann, 1975). The term "density" in this context refers to the electronic density in an X-ray scattering experiment, the isotopic substitution ratio (H/D) in a neutron scattering experiment, or any other physical density which scatters the incident beam.

Contrast variation techniques can be extended to macromolecular crystal systems since such crystals typically consist of 30-70% solvent, which is a phase of rapidly interchanging molecules. Bragg & Perutz (1952) applied such methods to a haemoglobin crystal and observed changes in the intensities of low resolution X-ray reflections after altering the electronic density of the mother liquor. In particular, they related these changes to the Fourier transform of the solvent accessible regions of the crystal. In other words, the data from a contrast variation series provides information on the macromolecular envelope.

Others have since applied contrast variation techniques in either X-ray or neutron distraction experiments to glean low resolution structures from macromolecular crystals (Harrison, 1969; Jack, Harrison & Crowther, 1975; Moras et al., 1983; Roth et al., 1984: Bentley et al., 1984; Podjarny et al., 1987). In particular, Carter et al. (1990) used a formalism which separated the diffraction effects of the molecular envelope and the internal fluctuations (Bricogne, unpublished) in the direct phase determination of the molecular envelope of tryptophanyl-tRNA synthetase.

Anomalous dispersion has also been employed in small angle scattering experiments to produce contrast variation. Examples on biological systems are the harnessing of the iron K-edge in ferritin (Stuhrman, 1980) and the phosphorous K-edge in ribosomes (HŸtsch, 1993). In crystallography, the use of anomalous scattering effects from the solvent has been suggested by Wyckoff and others where it could be used as a supplement to a standard contrast variation series (Dumas, 1988; Crumley, 1989; and Carter et al., 1990). However, in these cases, the anomalous scattering was still restricted at a single wavelength. The possibility of exploiting the

full potential of anomalous scattering at several wavelengths was originally put forward by Bricogne (1993).

Here only an outline of the theoretical principles will be given. Readers wishing for a fuller account are referred to Fourme et al. (1995). The starting point of what we call MASC (Multiple- wavelength Anomalous Solvent Contrast) is the basic principles of contrast variation where the macromolecular crystal lattice is assumed to be biphasic: one region of the unit cell is occupied by the macromolecule domain U (Figure 1a), and the other domain V-U (Figure 1b) is occupied by the solvent which is in a liquid-like state of rapid exchange. The domain containing the macromolecule is presumed to be ordered, whereas the solvent regions are presumed to be completely disordered.

We define rs as the electronic density of the solvent volume, which is constant since this region is flat and featureless. GU(h) is the Fourier transform of the indicator function cU(r) defined as equal to 1 inside the volume U and 0 elsewhere (Bricogne, 1974). It should be noted that -GU(h) = GV-U(h) when h ­ 0, such that GV-U(h) is the Fourier transform of the complementary indicator function cV-U(r) which corresponds to the region occupied by the solvent. The total structure factor, F(h), can be written as the sum of two components: one from the ordered regions of the crystal, Fp(h), and the other from the solvent. rsGV-U(h) These two components are related since the volume occupied by either the macromolecule or the solvent are by definition mutually exclusive.

F(h) = Fp(h) - rsGU(h)

Fp(h) is also the Fourier transform of the macromolecule in a vacuum (Figure 1c), and it can be expressed as the sum of the árpñGU(h) and D(h), the latter which is the Fourier transform of the internal density fluctuations from the mean density inside the domain U (i.e. árpñrp(r), see figure 1e).

Fp(h) = árpñGU(h) + D(h).

Substituting in this expression for Fp(h) gives

Fp(h) = (árpñ - rs)GU(h) + D(h).

The term (árpñ - rs) is defined as the contrast (Stuhrmann & Kirste, 1965), and when it is equal to zero the system is said to be at the constrast matching point (see figure 1d) whereby only the internal electronic density fluctuations contribute to the overall structure factor. A demonstration of this expression can be found in Carter et al. ( 1990).

Figure 1. The 1-dimensional slices of different components in contrast variation theory: a) Indicator function of the ordered domain, U, containing the protein. b) Indicator function of the disordered domain, V-U, containing the solvent. c) The electronic density of only the ordered domain, U. This corresponds to the macromolecule in a vacuum. d) The electronic density for both the macromolecule and solvent regions. Three different electronic densities of the solvent are represented by the three shades of grey. The contrast is shown for one of these. e) The internal electronic density fluctuations inside the macromolecule. f) The anomalous electronic density for both the MAD and MASC cases.

Figure 2. On the left, anomalous R-factors for MASC data of HEW lysozyme in 0.5M YbCl3. Four wavelengths at the Yb LIII-edge plus the R-factor for true symmetry related reflections (i.e. respecting the differences between I+ and I-). On the right, ordered sites of Yb3+ ions in HEW lysozyme crystals. A phased anomalous Fourier map is superimposed on to a map of the protein envelope. Dark spots show Yb3+ positions in crevices and near the surface of the protein.

P43212 P43212 P43212 P43212 P3221 P3221

Scatterer [A] YbCl3 YbCl3 NaBr (NH4)2SeO4 (NH4)2SeO4 Rb2SO4

Absorption Edge YbLIII-edge YbLIII-edge Br K-edge Se K-edge Se K-edge Rb K-edge

wavelength l (�)

long-l remote Ð 1,39294 0,9222 0,99188 0,99188 0,8222

short-l remote 1.38084� 1,37762 0,9155 Ð 0,97912 0,8139

Table 2. Results obtained from MADLSQ and GFROMF. R-Factors quoted are based upon |Fobs(h)| & |Fcalc(h)|, where |Fobs(h)| is from MADLSQ or GFROMF and |Fcalc(h)| is calculated from the known model.

Protein P64k Xylose isomerase Lysozyme

dmin 20� 20� 20�

Nmeas/Nposs 73 / 73 215 / 233 7 / 12

R-MADLSQ 32.5% 26.3% 32.1%

R-GFROMF 33.6% 29.7% 37.2%

Extension to the case where anomalous scatterers are present in the solvent can be done using the seminal idea of Karle (1980) where the structure factors are separated into wavelength independent (f¡) and dependent parts (lf' + ilf"),

lf = f¡ + lf'+ ilf".

For our discussion here, we assume that there is only one anomalous scatterer which is randomly dispersed in the solvent domain V-U such that it has a uniform distribution and no ordered sites bound to the surface of the macromolecule. For simplicity, we also assume that any scattering factor at low resolution is constant with respect to scattering angle to within a first order approximation. The density of the anomalous scatterers in the solvent can be treated as a complex quantity, lrsA, which is dependent upon wavelength,

lrsA = ¡rsA (1 + lf'/f¡ + ilf"/f¡),

and where ¡rsA is the normal electronic density of the anomalous scatterer. The total electonic density of the solvent, lrs, becomes a function of the wavelength, and can be separated into wavelength independent and dependent parts,

lrsA = ¡rs + lrsA (lf'/f¡ + ilf"/f¡)

Note that the term 0rs includes the normal scattering part of the anomalous scatterer. Thus one obtains,

lF(h) = (árpñ - lrs) GU(h) + D(h)

lF(±h) = { (árpñ - ¡rs) GU(h) + D(h) } - {¡rsA (lf'/f¡ ± ilf"/f¡) GU(h) + D(h) }

The terms in between the first set of brackets represent the wavelength independent part of the overall structure factor, denoted ¡F(h). It includes the envelope, constrast and fluctuation terms. The second set of brackets is wavelength dependent, and incorporates the envelope and the anomalous structure factors of A, lf' and lf". Note that the wavelength dependent contribution is substracted from the normal scattering part indicating that the anomalous and dispersive structure factors of A are applied to the Fourier transform of the indicator function of the solvent accessible domain, - GU(h)

By defining G(h) = - ¡rsAGU(h) one generates a expression of the overall structure factor similar to the starting point used for the algebraic MAD method (Hendrickson, 1985) where G(h) replaces the normal scattering component of the of the partial structure A, ¡FA(h).

lF(±h) = ¡F(h) + (lf'/f¡ ± ilf"/f¡) ¡FA(h) ÒMADÓ

lF(±h) = ¡F(h) + (lf'/f¡ ± ilf"/f¡) G(h) ÒMASCÓ

The substitution of G(h) for ¡FA(h) has an obvious physical meaning. The anomalous partial structure, A, which is a set of a few punctual and ordered scatterers in a MAD experiment is exchanged for an extended uniform electron density in a MASC experiment (see figure 1f). The separation of the effects of the anomalous partial structure A (and hence the Fourier transform of the solvent accessible volume) from the overall diffraction effects can be applied using a set of equations analogous to the MADLSQ equations, where they are solved for |¡FT(h)|, |G(h)| and phase difference between ¡FT(h) and G(h), Df = (fT - fG), i.e.

|lF(±h)|2 = |¡FT(h)|2 + a(l) |G(h)|2 + b(l) |¡FT(h)| |G(h)| cos(Df ± c(l)|¡FT(h)| |G(h)| sin(Df)

where, a(l) = lf'2 + lf"2)/(f¡2), b(l) = 2lf'/f¡, c(l) = 2lf"/f¡.

A MASC experiment has an advantage over other contrast variation methods, since the contrast variation is generated by inducing a physical change. This eliminates the possibility of changes in the crystal lattice due to varying ionic strength, pH, precipitant concentration, etc... which can arise in a chemical contrast series, and thus enforces strict isomorphism.

The strength of the signal in an anomalous contrast variation series can be quantified in a similar way to those in the MAD method, i.e. by measuring differences between Bijvoet pairs (anomalous or lf" contribution) and wavelengths (dispersive or lf' contribution). Intuitively, the magnitude of the anomalous signal in a MASC experiment is expected to vary considerably with resolution, being very large in the lowest resolution shells and then diminishing rapidly with increasing resolution. One also expects the anomalous signal to be directly proportional to the concentration of the anomalous scatterer in the solvent accessible volume. Furthermore, the signal will be maximised at the point of contrast matching. By making a certain number of approximations, it is possible to derive expressions for and calculate the expected anomalous and dispersive ratios (Fourme et al., 1995), but for the purpose of succintness only the final expressions will be given here. Thus for anomalous and dispersive differences one gets ,

á|lDF(±h)|ñ / á|lF(h)|ñ = 3.44 ´ 10-4 [A] (2lf"/feff) (MW1/12 s)-2 exp(-Bs2/4)

and

á|DlDF(h)|ñ / á|lF(h)|ñ = 3.44 ´ 10-4 [A] (Df'/feff) (MW1/12 s)-2 exp(-Bs2/4).

Clearly, the anomalous signal is dependent on a number of factors, such as the molar concentration of the anomalous scatterers, [A] and the magnitudes of f" and Df'. However, the resolution, s, has the strongest effect on the anomalous signal which drops away as a function of 1/s2 and exp(-Bs2/4). The term exp(-Bs2/4) represents a Gaussian smoothing of the

  Where s = 2sinq/l, |lDF(±h)| = | |lF(+h)| - |lF(-h)| |/álF(h)ñ, á|lF(h)|ñ = | |lF(+h)| + |lF(-h)| 1/2, and

|DlDF(h)| = | |liF(h)| - |ljF(h)| | / { ( á|liF(h)ñ + á|ljF(h)|ñ ) /2 }.

envelope boundary, where B is pseudo-temperature factor which defines the thickness of the interface rather than the temperature factor of the macromolecule or solvent. The signals are also somewhat dependent upon the molecular weight, but a 100kDa protein will still produce 68% of the signal of a 10kDa protein. For a hypothetical case of a 50kDa protein in 3.5M (NH4)2SeO4, where f"=7.0e-, Df'=8.6e- and B=100�2, expected anomalous and dispersive ratios (respectively) are 0.441 and 0.274 at 33� resolution, 0.156 and 0.097 at 20� resolution, and 0.032 and 0.020 at 10� resolution. Hence one expects in the lowest resolution shells very large signals, which will decrease sharply with increasing resolution. If one wishes to obtain a measurable anomalous signal out to 10� resolution, then one requires either multimolar quantities of a K-edge scatterer or molar quantities of a L-edge scatterer.

As a MASC experiment utilises the variation of f' and f", data collection should ideally be carried out at X-ray wavelengths near absorption edges of the anomalous scatterer. Thus the requirements are very similar to a MAD experiment - i.e. tuneable X-rays with a narrow band pass (Dl/lÅ10-4), a X-ray fluorescence detector to determine precisely the wavelengths of f"max and |f'|max, the recording of Bijvoet mates or Friedel pairs close in time, etc... - but with the additional requirement that the experimental setup is designed to collect reflections at the lowest possible resolution. This often requires the mounting of a small beamstop just in front of the detector entrance window. Other practical considerations are to use an area detector with a large dynamic range to accommodate the accurate measurement of the most intense low resolution reflections with those weaker reflections at more moderate resolution.

A variety of anomalous scatterers may be used in a MASC experiment, and the most suitable ones will depend on the crystallisation conditions of the macromolecule. Analogues of the precipitating agent are good choices since such compounds are less likely to perturb the crystalline lattice (e.g. selenate for sulphate, bromide for chloride, tribromoacetate for acetate etc...). To date, MASC data have been collected on crystals of three proteins of differing molecular weights and with a variety of different anomalous scatterers (see Table 1). In order to develop the MASC method, all of the cases are known crystal structures, which allows the experimental results to be compared with the correct envelope transform moduli and phases. In each of the experiments described below, the X-ray diffraction data were recorded at the wavelengths corresponding to the |f'|max and the f"max which were determined from the X-ray fluorescence spectra from a solution of the anomalous scatterer, as well as for at least one wavelength remote of the absorption edge. A small beamstop (Å2-3mm) was mounted and aligned just in front of the entrance window of the detector. Where possible, the crystallographic axes were aligned so that Bijvoet pairs could be measured on the same image. Below we describe in detail the experiments and the results for only two anomalous scatterers.

The very first MASC experiment was conducted on single crystals of lysozyme directly crystallised from solutions of 0.3-0.5M YbCl3. This combination was chosen because of the

Figure 3. Fluorescence and absorption effects of the diffraction pattern from a xylose isomerase crystal in 2M (NH4)2SeO4 recorded at four different wavelengths about the Se K-edge and of the same region of reciprocal space.

Figure 4. Whiteline structure of the Se K-edge of 0.1M (NH4)2SeO4 recorded on the TROìKA beamline station, ESRF, France (left), and the extended absorption spectra recorded at LURE, Orsay, France (right).

Figure 5. Anomalous it-factors as a function of resolution for P64k and xylose isomerase in (NH4)2SeO4. Please note that the resolution is broken down as a function of l/d2 for P64k and l/d for xylose isomerase.

ease of obtaining crystals and their robustness, as well as for the white line structure of the Yb LIII-edge. The Yb3+ ion concentration could be increased to 0.8M using vapour diffusion techniques before the crystal quality would deteriorate. X-ray diffraction data were collected at three wavelengths including one remote on the high energy side of' the Yb LIII-edge on the D23 station (Kahn et al., 1986) at LURE-DCI (Orsay, France). Bijvoet ratios are shown in Figure 2. The results confirmed the large anomalous signal at low resolution as expected by theory. At the wavelength corresponding to the maximum of f", the Bijvoet ratio reaches Å50% for the lowest resolution shell and then diminishes sharply with increasing resolution. The internal agreement between true equivalent reflections is within Å1-3%, implying that the anomalous signal is real, reproduceable and not artifact of either the data processing or the beamstop shadow. The anomalous signal however extends well beyond 10� resolution indicating that some Yb3+ ions have bound to the protein. Anomalous difference Patterson maps did not reveal the positions of three bound Yb3+ ions, which were eventually found in a phased anomalous difference Fourier map (Fig. 2). The reason for this might be because the diffraction data is only Å60% complete. This experiment has recently been repeated with 0.5M YbCl3 on the DW2lb station at LURE-DCI to obtain a complete MASC data set and also to investigate the possibility of using the ordered sites of the anomalous scatterer in an overall phasing and phase extension strategy.

P64k is a 64kDa outer membrane protein from Neisseria meningitidis currently under study in our lab (Li de la Sierra et al., 1994; Li de la Sierra et al., 1997), and it crystallises from ammonium sulphate solutions. Xylose isomerase also crystallises from ammonium sulphate solutions but as a tetramer (173.2kDa) in the asymmetric unit (Rey et al., 1988). Both of these proteins represent large macromolecular structures on the scale of those typically solved by the MAD method. Ammonium sulphate in the mother liquor of the crystals could be substituted with multimolar concentrations of ammonium selenate via simple soaking techniques. Crystals of both proteins could withstand 3.5M (NH4)2SeO4, which brings the solvent electronic density equal to the average protein electronic density, i.e. the contrast matching point. This allowed us to collect MASC data at the Se K-edge of selenate which features a white-line structure at a wavelength near Å1�. In the first series of these experiments done on the TROIKA station at the ESRF (Grenoble, France), the diffracting power of the P64k crystals deteriorated rapidly under the intense radiation of the undulator beam despite cooling the sample at 4¡C. In order to collect a complete MASC data set off of one crystal, the experiments were later repeated using flash cooling and cryogenic techniques. Images recorded at the Se K-edge showed a marked decrease in the diffraction intensities as well as a substantial increase in the overall background. Although such absorption and fluorescence effects have been previously noted, they were never so severe (see Figure 3). This could be understood once it was realised that selenate has an exceptionally large whiteline resonance (see Figure 4) which could only be revealed when using the finer energy resolution of the monochromated X-rays from the Si(333) crystal instead of the diamond C(lll) crystal used in the previous run. To circumvent and

Figure 6. Ordered sites of selenate ions in P64k (left) and XI (right). In each case a phased anomalous Fourier map is superimposed on to a map of the protein envelope. Dark spots on each map show selenate positions in crevices and near the surface of the protein.

Figure 7. Agreement as a function of resolution of |GU(h)| values of xylose isomerase in 2.0M (NH4)2SeO4 calculated from MADLSQ, GFROMF and its model.

minimise the absorption and fluorescence effects, a number of precautions were taken: i) Crystals were rapidly rinsed or washed in an analogous sulphate solution just prior to freezing, thus removing mother liquor containing any excess selenate surrounding the crystal, ii) smaller crystals were used to reduce the amount of absorption relative to the crystal volume, and iii) finer oscillation angles were recorded for the wavelength corresponding to the maximum of f" to improve the signal to background ratio. There are other tactics which could be employed to minimise fluorescence effects. For X-ray energies used in typical crystallography experiments (0.5� - 2.0�), the fluorescence yield after absorbing an incident photon is 2-3 times higher for the K-edges than for the L-edges (Kortright, 1986). For example, the fluorescence yield is Å60%, for Se at its K-edge, whereas the fluorescence yield is only Å20% for Yb at one of its L-edges. Another method to reduce fluorescence effects is simply to increase the sample-to-detector (D) distance since fluorescence which is radiated isotropically will fall off as l/D2, while the diffracted beams being quasi-parallel will remain essentially constant with D.

The anomalous signal for both proteins follows the expected trend, being very large for the Bijvoet pairs at lowest resolution and decreasing rapidly with increasing resolution (see Figure 5 ). At higher resolution, the Bijvoet ratios for both proteins are of the order of the internal agreement, but despite this low anomalous signal, up to 12 possible selenate ion sites have been located from phased anomalous difference Fourier maps in the P64k crystals (see Figure 6). Similarly, several selenate ion sites have been found in the crystals of xylose isomerase. All sites are at or near the macromolecular boundary, often in crevices, and their relative occupancies vary considerably. The existence of ordered anomalous sites appears to be more general than expected, but it opens up a potential of phasing to higher resolution once a model for envelope is determined.

Two methods have been utilised to extract the moduli of GU(h) from multiple-wavelength diffraction data. One uses the algebraic equations in the MAD method as implemented in the program MADLSQ (Hendrickson, 1985), and the other uses the program GFROMF (Carter & Bricogne, 1987), which is designed to extract the |GU(h)| from the |iFobs(h)| of a chemical contrast variation series. Both methods give satisfactory results up to at least 20� resolution.

Prior to using either method of extracting the |GU(h)|, the X-ray data were set on a common scale using the program SCALA (Evans, 1993). The data were scaled in two steps: i) an internal scaling for each wavelength to correct for incident beam fluctuations and sample decay, and ii) a pseudo-local scaling between a reference wavelength (low f") and the other wavelengths to minimise absorption effects.

As mentioned above, the program MADLSQ, which was originally designed for multiple- wavelength diffraction data, solves the set of equations by non-lineal least-squares for |¡FT|, |¡FA| and the phase difference DfT-A. For MASC data, |G(h)| (or rsA|GU(h)|) replaces |¡FA(h)|, and the phase difference becomes DfT-G. The program also has the ability to refine or fix the

values of f' and f" of the different wavelengths. Results are shown in Figure 7 for the data collected on xylose isomerase crystals soaked in (NH4)2SeO4 and as compared to the |GU(h)| calculated from the coordinates of the 3D structure deposited in the Protein Data Bank (Rey et al. l988). Note the sharp asymptotic decrease in |GU(h)| with increasing resolution. The agreement between model and experiment deteriorates beyond 10-20 � resolution for several reasons: i) the relative magnitudes of |GU(h)| are small, ii) the absorption effects are more pronounced at higher diffracting angles, and iii) the possibility of ordered anomalous scattering sites contributes to the partial structure extracted from the MADLSQ equations (i.e. |G(h)| is more precisely defined as |G(h)+¡FA(h)).

In chemical contrast variation studies, the program GFROMF (Carter & Bricogne, 1987) extracts the |GU(h)| from the diffraction data |iFobs(h)| for i=l,...,N where i corresponds to a different solvent density, irs. To extend this to multiple wavelength cases, we simply substitute in for the contrast series |liFobs(h)| where li = l1,..., lN and the solvent density becomes lirs. The same formalism is used to describe the overall structure factor in terms of the Fourier transforms of the envelope (GU(h)) and the internal density fluctuations (D(h)). If X(h) and Y(h) are the real and imaginary components of D(h) relative to GU(h), one has

|iFcalc(h)| = iK { [X(h) + (árpñ - irs) |GU(h)| }2 + Y(h)2 }1/2

The GFROMF scheme carries out the non-linear least-squares refinement of |GU(h)|, X(h) and Y(h) from scaled data summed over all contrasts, and minimises the function,

SiShklsobs(h)-2 (|iFobs(h)| - |iFcalc(h)|)2,

where sobs(h) is standard deviation of |iFobs(h)|. Note that X(h) and Y(h) represent both the magnitude and the phase difference between GU(h) and D(h). In practice, iK, a scale factor between the different data sets should be refined for all but one contrast or wavelength.

The original program was modified to incorporate anomalous scattering contributions such that,

|liFcalc(±h)|=liK { [X(h)+(árpñ-rs-(lif'/f¡)¡rsA) |GU(h)| ]2+[Y(h)±(-(lif"/f¡)¡rsA) |GU(h)| ]2 }1/2

Tests executed on simulated MASC data of kallikreen (52kDa), at three different contrasts of selenate and three wavelengths per contrast, returned exact values of |GU(h)|, X(h) and Y(h) of the simulated observed data. With experimental data, the results gave R-factors of Å30-35% for P64k and xylose isomerase crystals (see Table 2). This level of agreement is satisfactory considering that many of the parameters are unrefined. In particular. the values of lif' and lif" employed were derived from previous runs of MADLSQ, and theoretical values of the contrast were used rather than allowing them to refine. The scale factors between different wavelengths

(liK) were set to unity since the data were already set on a common scale. In principle, all of these parameters should be refineable in the GFROMF scheme, even though the number of observations in the lower resolution shells is not overly large. What is certain is that prior precise knowledge of the values of the contrasts, lif' and lif" is important to extract |GU(h)| values of satisfactory quality.

Previous methods of phasing |GU(h)| from either X-ray contrast variation series (e.g. Carter, et al ) or H/D substitution contrast variation series (Moras et al., 1983; Roth et al., 1984; Bentley et al., 1984; Podjarny et al., 1987; Roth, 1991) employed the assumptions that the set of |GU(h)| behave much in the same way as the structure factors of small molecule crystal structures. Hence such attempts have used the programs of traditional direct methods of small molecule crystallography. As a starting point, we have also examined this strategy in preliminary trials for phasing a set of |GU(h)| from MASC data, but it is clear that the limited success with these methods necessitates a re-examination of the phasing methods used up to now.

Using 1664 calculated |GU(h)| up to 10� resolution from a model of xylose isomerase, phase sets for the |GU(h)| were generated using the program MITHRIL (Gilmore, 1984). Normalisation was carried out empirically, by dividing the entire set of |GU(h)| by a constant which set the 397 largest |GU(h)| to greater than 1.3. Of the phase sets generated, using triplets, magic integers and statistically weighted tangent refinement, the best solutions gave correlation coefficients of Å0.74 for 20� resolution maps. However, none of the conventional figure-of-merits were capable of distinguishing a correct phase set.

The limited success obtained from the use of traditional direct methods is not surprising considering that such methods are based on a variety of assumptions which are not valid for a set of |GU(h)|. For example, envelopes are not point scatterers, as can be assumed for atoms. Also an envelope also does not represent a random distribution of scatterers; quite the contrary, by definition of the biphasic model, the scatterers are confined inside the volume of the solvent. Consequently, a set of |G(h)| does not follow Wilson statistics. In addition, normalisation of' |G(h)| can not be accomplished as in traditional methods because of the relatively few reflections at low resolution and their very large dynamic range. Despite these differences with small molecules, a set of |G(h)| has the advantage in being complete with relatively few reflections (i.e. there are only a total of 73 unique reflections to 20� resolution for P64k).

The problem of phasing a set of |GU(h)| clearly needs to be readdressed. We are currently considering other methods towards phasing |GU(h)|, and the use of Maximum Entropy and Likelihood ranking to test envelope hypotheses. The literature shows an increasing interest in the field of low resolution phasing. Some of these methods approximate globular proteins as spheres or a few large Gaussian spheres (Andersson & Hovmšller, 1996); Harris, 1995; Lunin et al., 1995; Urzhumtsev et al., 1996), or as a gas of hard sphere point scatterers (Subbiah, 1991); Subbiah, 1993).

It has been demonstrated that contrast variation in macromolecular crystallography can be generated using anomalous dispersion techniques in a MAD-like experiment. The method benefits from the strict isomorphism imposed by the external physical chance of the wavelength of the X- rays applied to a single sample. This is clearly advantageous over a chemical contrast series experiment which typically requires several samples soaked in different media. and which risks destroying any isomorphism.

From the studies presented here, large anomalous signals are observed in the lowest resolution shells. In all of the cases studied to date, the anomalous signal extends to higher resolution indicating the presence of ordered anomalous scattering sites. Such sites have little effect at low resolution, and they are a bonus in a MASC experiment because they may provide a path for phasing the 3D structure to higher resolution once the envelope is known. Extracting the set of |GU(h)| from MASC data can be accomplished using two different procedures; one based on the algebraic equations of multiple-wavelength diffraction data (MADLSQ) and the other based on the equations derived from a chemical contrast variation series (GFROMF).

The process of phasing a set of |GU(h)| needs further attention. Traditional direct methods. which are intended for small molecule structures, are not suitable for this type of phase problem. If the phasing step of a set of |GU(h)| can be dealt with, then the combination of anomalous dispersion and contrast variation techniques can lead to a general method for low resolution phasing of very large macromolecules including those beyond the scope of MIR and MAD methods. Finally, knowledge of the macromolecular envelope will help phase the structure to higher resolution.

We thank A. Thompson, A. Gonzalez, G. GrŸbel, D. Abernathy & M. Lehmann for support during the experiments on the TROìKA beamline at the ESRF, Grenoble, France. We are also grateful to D. Ragonnet. D. Chandesris and the SEXAFS group at LURE for assistance with the DW21 beamline.

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