Extending the novel |ρ|-based phasing algorithm to the solution of anomalous scattering substructures from SAD data of protein crystals

The novel S M,|ρ| phasing algorithm has been adapted to the determination of anomalous scattering substructures from single-wavelength anomalous diffraction (SAD) data of protein crystals and successfully tested on data sets mostly retrieved from the Protein Data Bank.


Introduction
Important present applications of the single-wavelength anomalous diffraction (SAD) technique are the location of SeMet atoms in crystals of multi-site genetically engineered proteins, the determination of the positions and occupancies of the heavy atoms (or clusters) entering the crystal, e.g. when soaking it in a solution, or also the direct use of chemical species already present in native crystals as anomalous scatterers (S, Cl, P, . . . ). Knowledge of the anomalous scattering (AS) substructure provides starting phase values which can be iteratively improved by density modification. Although the substructure can be solved in favourable cases by the direct interpretation of the anomalous Patterson function (Rossmann, 1961), direct methods (DM) often offer the only alternative in complex cases. The application of DM to SAD data takes advantage of the availability of the experimentally accessible absolute values of the anomalous differences (|D| exp ) between pairs of acentric reflections (Bijvoet pairs) which follows from the atomic scattering factor definition where f n j is the normal scattering factor of atom j, and f 0 j and f 00 j are the corresponding real and imaginary anomalous dispersion corrections (respective symbols for non-vibrating atoms are f 0 , f n 0 , f 0 0 , f 00 0 ). Let us consider a structure composed of N atoms with N A of them scattering anomalously and with r being the atomic position vector. The structure factor of an arbitrary H reflection is then F 00 For two +H and ÀH reflections constituting a Bijvoet pair (from now on, F þH ¼ F þ and F ÀH ¼ F À ), the absolute value of the anomalous difference D is given by which is related to jF 00 j by the simple relationship (30) (see Appendix A) if conditions (7a) and (7b) corresponding to (28) and (29) are met, i.e.
and F j j 2 av ) F 00 2 ð7bÞ Equation (6) constitutes the basis for solving AS substructures by DM. First attempts showing the viability of locating AS in metalloproteins by DM were performed by Mukherjee et al. (1989) with the program MULTAN87 (Debaerdemaeker et al., 1987) following the path previously paved by Wilson (1978) in connection with the isomorphous replacement case and taking advantage of preliminary results on the location of AS using tuneable synchrotron radiation (Einspahr et al., 1985); however, it was the introduction of the dual-space DM that represented a substantial improvement in the determination of AS substructures. This DM strategy refines phases by iteratively alternating structure invariant manipulation (reciprocal space) with Fourier peak optimization (real space). It was first implemented in the Shake-and-Bake program (Miller et al., 1994). This philosophy was also incorporated in SHELX (Sheldrick & Gould, 1995) which evolved to SHELXD by incorporating, among other things, Patterson seeding (Schneider & Sheldrick, 2002). Descriptions of the application of SHELXD to the solution of the AS substructures are given by Usó n & Sheldrick (2018) and Sheldrick (2010). More recently, the capability of SAD phasing in the presence of only weak AS has increased due to the possibility of extending the SAD experiments to longer wavelengths as well as to the availability of faster and more accurate X-ray detectors (e.g. Leonarski et al., 2018), allowing application of lower dose rates and thus increasing data redundancy on a unique crystal (data set scaling from multiple crystals is minimized). A recent promising alternative acquisition mode, especially useful for data collection from small, weakly diffracting and radiationsensitive crystals, is serial crystallography. This technique is based on taking one single image (containing partial Bragg reflection information) from each microcrystal and completing the diffraction data set by combining the individual indexed images from thousands of crystals. A selection of de novo (SAD) phasing serial crystallography studies at synchrotron sources can be found in Nass et al. (2020).
Recently, ||-based DM in the form of the S M,|| phasing algorithm (Rius, 2020) have been extended to large crystal structures through the introduction of the peakness-enhancing ipp (inner-pixel preservation) procedure (Rius & Torrelles, 2021) (hereafter, to simplify its designation, the S M,|| algorithm is specified with the acronym SMAR in which S stands for 'sum function', M for 'modulus function' and AR for 'absolute '). The aim of the present contribution is the adaptation of the ipp-improved SMAR to the solution of AS substructures from SAD data (SAD-SMAR). Its feasibility is shown with SAD data sets either kindly supplied by the respective authors or retrieved from the Protein Data Bank (PDB). All calculations have been carried out with a modified version of XLENS_v1 (Rius, 2011). To help the reader to assess the suitability of the test data, two indicators are given for each data set (extending to all acentric reflections in the corresponding resolution range used in the SAD-SMAR application), namely: (i) The size of the anomalous signal (Bijvoet ratio), hjDji=hjFji (Hendrickson & Teeter, 1981;Wang, 1985) ranging from 0.012 to 0.070 in the selected test examples.
(ii) The precision of jDj given by the hjDj=ðjDjÞi ratio (Schneider & Sheldrick, 2002;Wang, 1985) which should be >1.5 (ideally also for the outermost resolution shell) (Cianci et al., 2008;Giacovazzo, 2014). Logically, the precision of jDj directly depends on the precision of the corresponding jF þ j and jF À j (more strictly of I þ and I À ).
In SAD phasing, redundancy of diffraction data is an important data collection parameter, since it affects the variance of the average intensity estimates. As this work is based on published data sets, the cited redundancy values are those given by the respective authors.

The composition of the |D| set
Solving AS substructures by DM requires a previous selection of the experimental |D| values, |D| exp , since not all of them are appropriate. A preliminary check should ensure that the Bijvoet-pair reflections have |F| av values satisfying conditions (7a) and (7b). This is accomplished by preserving in the initial set of |D| differences only those reflections with |F| av values (expressed as |E|'s) larger than a given ECUT cut-off value. In the test calculations, the used ECUT is ffi 0.25 which causes the suppression of approximately 5% of the total of acentric reflections. The selection process continues with two additional rejection criteria which are directly applied to the |D| anomalous differences (to increase their reliability and the absence of outliers). Since |D| is in general much smaller than |F| av , random errors inherent to |F + | and |F À | seriously affect the precision of |D|. Consequently, only those reflections fulfilling the |D| > DFCUT Â (|D|) criterion are preserved in the |D| set (Hendrickson et al., 1988;Grosse-Kunstleve & Brunger, 1999). In the test calculations, DFCUT is in general $0.4 which represents the additional removal of 10-15% of acentric reflections from the |D| set. The selection process ends with the outlier elimination, i.e. all reflections with |D|/ r.m.s.d.(|D|) greater than $4.0 are filtered out (Hendrickson et al., 1988;Grosse-Kunstleve & Brunger, 1999)  The SAD-SMAR algorithm uses, instead of the experimentally inaccessible quasi-normalized |E| values of the substructure (Main, 1976), the normalized X values based on (6) and defined by the quotient with ¼ ' 0 À ' 00 and where s is the resolution shell corresponding to jF 00 j 2 . Since jF 00 j 2 and sin 2 may be assumed uncorrelated, the average term in the denominator can be decomposed into the product of hjF 00 j 2 i s and hsin 2 i s . Furthermore, since ' 0 predominantly depends on the protein atoms and ' 00 only on the anomalous scatterers, both phases can be considered largely uncorrelated and hence hsin 2 i s can be assumed to be 0.5, so that On the other hand, according to the |E| definition, hjF 00 j 2 i s in (10) can be replaced by jF 00 j 2 =jE 00 j 2 , so that the expression relating X 2 and jE 00 j 2 reduces to If X 2 is averaged over all reflections in its corresponding s resolution shell, then hX 2 i s = 1, since hjE 00 j 2 i s is 1 by definition and hsin 2 i s is 0.5.
In addition to X values, SAD-SMAR also uses modified X values called |X m |. These are obtained (i) by calculating the M modulus function with X as Fourier coefficients (extending the sum to the H reflections), (ii) by suppressing the negative regions in M, and (iii) by back Fourier transforming the modified M function (Karle, 1980).

Calculation of X from |D| exp
The relation between X and |D| is easily found by introducing the squared (6) into (10) where k is the scaling constant putting jDj exp on the same scale as jDj. The hjF 00 j 2 i s quantity in the denominator, i.e. the average intensity of the s shell, can be expressed as where B is the overall atomic displacement parameter including vibrational and disorder effects. At this point, for convenience, each f 00 0j will be converted to q j by dividing by f 00 0L (= the largest f 00 0j ). Replacement of f 00 0j by q j f 00 0L in (13) and subsequent introduction of the modified (13) into (12) leads to the final expression which allows the derivation of X 2 from ðjDj exp Þ 2 provided that the AS composition is known. In view of (14), the estimation of the K constant and the B parameter can be obtained from a Wilson plot, since for each reciprocal-space shell, both hX 2 i s and the hðjDj exp Þ 2 i s = P N A j¼1 q 2 j quotient are known.

SAD-SMAR recycling
Phasing with the SMAR algorithm was first shown by Rius (2020). Later on, the ipp procedure, a simple way of enhancing peakness in Fourier maps, was added (Rius & Torrelles, 2021). To show how the SAD-SMAR modification works, one phase refinement cycle is described in detail in Fig. 1. It has been divided into four stages, each one including one Fourier transform operation. These are: (i) Calculation of the 00 density function. The phase refinement cycle begins with the introduction of È h , the subset of ' 00 phases of the h reflections to be refined (either initial or updated estimates). Unlike in non-anomalous SMAR applications where È h contains the phases of all large reflections (i.e. those H reflections with |E| ! 1.00), in the case of SAD-SMAR, È h only includes the ' 00 h phases of those H reflections with X larger than a given XCUT cut-off (here XCUT = 1.00). Since X=2 1=2 is equal to |E 00 | |sin |, the largest possible value of |E 00 | for a given X is X=2 1=2 (which is reached for |sin | = 1). The recursive SAD-SMAR phase refinement algorithm with enhanced peakness (ipp). Compared with the unmodified SMAR, the principal differences are the composition of È h as well as the replacement of |E| values either by X = |E 00 sin | or by |X m |.
In general, |sin | will be lower than 1 and therefore X=2 1=2 is a lower estimate of |E 00 | (Grosse- Kunstleve & Adams, 2003). How the composition of È h depends on the X values is illustrated in Table 1 for XCUT = 1.00. It can be seen that most phases of reflections with |E 00 |'s > 1.00 are present in È h ; however, this number decreases significantly for |E 00 |'s between 1.00 and 0.70 and, finally, for |E 00 |'s < 0.70, it becomes zero. In this work the initial estimates of ' 00 h are the phase values corresponding to the Fourier coefficients of M 0 , i.e. the randomly shifted modulus function (Rius & Torrelles, 2021). As can be seen in Fig. 1, the Fourier synthesis with jX m;h j expði' 00 h Þ as Fourier coefficients gives the 00 density function from which the m 00 mask is derived (and stored). According to Rius (2020), m 00 is 1 (for 00 > 0), 0 (for 00 between 0 and Àt) and À1 (for 00 < Àt) with 2 being the variance of 00 (È h ) and t $2.65.
(ii) Calculation of the Fourier transform of | 00 |. It gives the jC 00 H j expði 00 H Þ Fourier coefficients and provides the updated 00 H .
(iii) Calculation of 00 M . The 00 M density function is the inverse Fourier transform of the ½ðX H À hXiÞ expði 00 H Þ coefficients formed by the experimental X H À hXi values and the updated 00 H phases. The calculated 00 M is then multiplied with the previously stored m 00 mask to give the product function.
(iv) Calculation of the Fourier transform of . Peakness in is enhanced by applying the ipp density modification procedure. Once completed, the modified is Fourier-transformed to provide the new ' 00 h and jE 00 h j values, the latter being used in the calculation of the CC h figure-of-merit to follow the phase refinement convergence, If convergence is not achieved, the next cycle begins until the preset maximum number of cycles is reached.

Fourier refinement and figure-of-merit
After applying SAD-SMAR, the phases are further refined by Fourier recycling (five to ten cycles). In order not to have to modify the Fourier refinement module of already existing DM programs, e.g. of XLENS_v1 (Rius, 2011), the F 00 n structure factor corresponding to a hypothetical structure with scatterers of f 0L q j strengths is introduced (with f 0L being the normal scattering factor corresponding to the largest f 00 0L ). For this purpose, (11) and (14) are equated and both sides of the expression multiplied by f 2 0L . After rearranging the resulting expression, we obtain E 00  Table 2 Relevant data collection parameters and indicators.
1 Detailed author references in Section 5; 2 main anomalous scatterers; 3 redundancy of diffraction data taken from the published/deposited data (and later normalized to the point group order); 4 highest resolution (in Å ) of SAD data used in the structure refinement with R free values 5 from the respective authors; 6 highest resolution for SAD-SMAR application; Bijvoet ratio 7 estimation; and hjDj=ðjDjÞi 8 calculations (in the whole range and in the outermost reciprocal-space shell   Notice that the first three factors of the left-hand side of (17) correspond to jF 00 n j 2 . Replacement of these by jF 00 n j 2 gives, after taking the square root, the best approximation À to the modulus of the structure factor À ¼ F 00 which is used as observational data in the ð2À À jF 00 n j calc Þ expði' 00 calc Þ Fourier coefficients during recycling. At the end of the last Fourier refinement cycle, the (correlation coefficient based) residual is calculated wherein the sums only include the H reflections with X ! 0.7.

Results of the test calculations
Relevant experimental information about the data sets used in the test calculations is given in Table 2. To improve the readability of the text, the test compounds are simply referenced with the appropriate PDB code. The verification of the SAD-SMAR tests was greatly facilitated by the availability of the refined model coordinates either kindly provided by the authors or deposited by them in the PDB. In this way, the r.m.s.d.'s between our substructure models and the deposited ones could be calculated. The most relevant results of the test calculations are summarized in Table 3. Table 4 complements this information by giving, for most test examples, the peak heights at the end of the Fourier recycling stage. Peak heights are always given in peak / units, where peak is the density at the peak centre and 2 is the variance of .
To get a rough idea of the quality of the deposited/supplied SAD refinements, the deposited R free values (listed in  (Read et al., 2011). It is found that the R free values are less than or equal to the corresponding median R free values in all cases, except for 2g4s and 4tno, for which R free is significantly higher.
A preliminary test was the substructure solution of the proenzyme of proabylysin (PDB code 4jiu; a = 34.679, b = 44.896, c = 72.233 Å , P2 1 2 1 2 1 ). The data set was measured at ID29 (ESRF) at the Zn absorption edge ( = 1.282 Å ) (Ló pez-Pelegrin et al., 2013). The structure refinement (deposited by the same authors) contains one Zn ion, one macromolecule and 148 water molecules in the asymmetric unit (a.u.), amounting to 1055 atoms. The successful run of this simple case (separation between found and deposited Zn ion positions is $0.15 Å ) confirmed the capability of SAD-SMAR to solve AS substructures at 2.5 Å resolution (B ffi 25.1 Å 2 ).
Next, it was tested with more challenging cases. To simplify the discussion, the test compounds are divided into three groups.

SeMet derivatives
Compared with other SAD situations, Se-SAD is particularly favourable due to the large AS strength of Se (f 00 0Se $3.9 and $3.3 e À for = 0.979 and 0.919 Å , respectively) and because the substitution of S by Se in the methionine amino acids is normally complete. The data sets of the three tested SeMet derivatives correspond to: 5cx8: a = 56.64, b = 184.74, c = 144.31 Å , P2 1 2 1 2. A major immunodominant outer-membrane surface receptor antigen of Porphyromonas gingivalis measured at beamline (BL) XALOC (ALBA, Barcelona) ; Se derivative refinement deposited in PDB entry 5cx8; SAD data supplied by one of them). There are 12 Se positions, two macromolecules and 509 water molecules in the a.u., amounting to 8119 atoms. Application of SAD-SMAR yields the positions of the 12 Se atoms (B ffi 2.3 Å 2 ) with r.m.s.d. = 0.24 Å compared with the deposited refined model (Table 3) Table 3 Comparison of the SAD-SMAR phase refinement results for DFCUT = $0.4 and 0.0. 1 Completeness as c D = N D /N asy in % (N D = number of reflections in |D| set; N asy = number of unique reflections); 2 n.c.t. = number of converging (correct) trials out of 25; 3 (average) number of cycles to reach convergence; 4,5 final CC h and R CC values for correct solutions; 6 number of sites found in the a.u. compared with published refined values; 7 sep. = root-mean-square deviation in Å between found and published refined site positions.  (Kanitz et al., 2019; SAD and refinement data deposited in PDB entry 5lac). There are 12 Se positions (one of them split in the refinement), one macromolecule and 303 water molecules in the a.u., amounting to 4875 atoms. Application of SAD-SMAR yields the positions of the 12 Se atoms (B ffi 4.9 Å 2 ) with r.m.s.d. = 0.18 Å compared with the deposited model.

Native crystals soaked in heavy metal/metal cluster solutions
The first four cases of this subsection are native crystals soaked in a solution containing iodide ions and with their diffraction data being collected in-house on rotating anodes (Cu K radiation) where the anomalous signal for I is large (f 00 0I $6.9 e À ). The fifth case corresponds to crystals soaked in a Cd 2+ -containing solution.
5iqy: a = 40.89, b = 132.08, c = 97.57 Å , C222 1 . An apodehydroascorbate reductase from Pennisetum glaucum (Krishna Das et al., 2016; SAD and refinement data deposited in PDB entry 5iqy). According to the deposited data, there are 26 sites occupied by a total of 13.3 I 1À , one macromolecule and 95 water molecules in the a.u. (1719 atoms). Application of SAD-SMAR yields 15 sites (B ffi 45.5 Å 2 ) containing 9.74 I 1À which show a good agreement with the deposited data (r.m.s.d. = 0.43 Å ) as shown in Fig. 2. Table 5 compares the resulting  site occupancies with the deposited ones. 3k9g: a = 55.81, c = 200.90 Å , P4 3 12. A plasmid partition protein (Abendroth et al., 2011; SAD and refinement data deposited in PDB entry 3k9g). According to the structure refinement deposited in the PDB, there are 12 I 1À sites, one macromolecule and 91 water molecules in the a.u. (1858 atoms) with 6.6 I 1À in the 12 sites. Application of SAD-SMAR yields nine coincident I 1À sites (B ffi 19.8 Å 2 ) (r.m.s.d. = 0.35 Å ) which justify a total of 5.3 I 1À , i.e. 81% of the refined I 1À content. By normalizing the sum of the heights of the nine strongest Fourier peaks to 5.3, the respective found and deposited site occupancies ( Table 5). Table 4 Heights of peaks in the final map of Fourier recycling for most test examples expressed in peak / units ( peak = maximum peak density; 2 = variance of ).
The peaks in the a.u., ordered in decreasing height, are divided into two sets: A containing all correct signal peaks down to the first uninterpreted peak (only the heights of the first and last peaks are given, followed by the corresponding number of AS in brackets); B with mixed correct and uninterpreted peaks (with the heights of the latter in italics). According to these results, cut-off values of peak /() for considering Fourier peaks as part of the substructure model can be set at around 5.0-7.0 (for soaked native crystals, they are slightly higher).  -Dieckmann et al., 2007; SAD and refinement data deposited in PDB entry 2g4h). Anomalous signal for Cd 2+ at = 2.00 Å is large (f 00 0Cd $7.2 e À ). According to the deposited refinement, the a.u. contains five Cd 2+ sites (with occupancies > 0.10), two Cl 1À sites, 101 water molecules and one apoferritin subunit (a macromolecule with 1374 atoms). Apoferritin is made up of 24 such protein subunits which assemble to form a roughly spherical hollow shell, with an external diameter of $120 Å and an internal diameter of $80 Å (Chrichton, 2019). The shell is placed at the nodes of the F lattice complex. Application of SAD-SMAR yields the five Cd 2+ sites (B ffi 33.7 Å 2 ) with the found positions and occupancies close to the deposited values (r.m.s.d. between corresponding sites is 0.32 Å ). The respective found and deposited occupancies (using the original site labelling) are Cd1: 0.50,0.50;Cd2: 0.25,0.25;Cd3: 0.14,0.20;Cd4: 0.20,0.18;Cd5: 0.14,0.16). The Cd1 sites are located pairwise ($8 Å separation) at the 12 vertices of a cubo-octahedron centred at (0, 0, 0) (with opposite vertices separated by $129 Å ), i.e. close to the external diameter of the hollow shell. The same applies for Cd2 but with a somewhat longer intra-pair distance ($13 Å ) and a separation between opposite vertices of $75 Å which roughly corresponds to the internal diameter of the hollow shell.

S-SAD phasing
The data sets of Pf1117 and Pf0907, two hypothetical proteins from Pyrococcus furiosus, were collected at BL X06DA at the Swiss Light Source (Weinert et al., 2015; the corresponding SAD and refinement information deposited with respective PDB codes 4tno and 4pgo).
4tno: a = 47.21, c = 82.28 Å ; P4 1 2 1 2. According to the deposited data, its a.u. contains one macromolecule, three methionine S atoms and two Cl 1À (709 atoms; f 00 0Cl $ 1.20 and f 00 0S $ 0.95 e À ). Application of SAD-SMAR yields the two Cl 1À and two S atoms (B ffi 47.9 Å 2 ). The third (more disordered) S atom could not be located.  -Dieckmann et al., 2007; SAD and refinement data deposited in PDB entry 2g4s). According to the deposited refinement, the a.u. contains, besides the macromolecule and the refined water molecules, four methionine S atoms (one of them with a higher B value) (689 atoms; f 00 0Cl $1.11 and f 00 0S $0.91 e À ). Application of SAD-SMAR shows the four expected S atoms (B ffi 42.6 Å 2 ), three of them as the three strongest Fourier peaks with a r.m.s.d. of only 0.18 Å compared with the deposited model. The fifth-ranked Fourier peak corresponds to the fourth S atom (the one with the higher B value in the refinement) and is shifted by 1.1 Å from the deposited position. The fourth-ranked Fourier peak could not be assigned (perhaps corresponding to some missing Cl 1À ).

Conclusions
Based on the experimental conditions covered by the test examples, it may be concluded that SAD-SMAR can solve efficiently AS substructures from SAD data (i) with upper resolution limits (RES SMAR ) between 2.50 and 3.3 Å ; (ii) with average Bijvoet ratios of 0.065 (for SeMet derivatives), 0.014 (for S-SAD phasing) and 0.041 (for soaked native crystals); (iii) with hjDj=ðjDjÞi values greater than 1.5; and (iv) with hjDj=ðjDjÞi values for the outermost resolution shell ranging from 0.90 to 1.69 (the average being 1.25). The cut-off values of the various rejection criteria used in the tests have been ECUT ffi 0.25, r.s.m.d.(|D|) = 4 and DFCUT = $0.4. The introduction of DFCUT ensures the suppression of the less reliable |D|'s while keeping enough observations for a satisfactory DM run. It can be clearly seen that the corresponding CC h values are close to 0.88 for converging trials (with the corresponding R CC values lying between 51 and 69). Since for non-converging trials CC h values are normally smaller by 0.02-0.03 (and R CC values are in general 1.3-1.4 times larger), identification of the correct trials should not be a problem. Notable is how quickly convergence is reached, especially for SeMet derivatives and for soaked native crystals. For native crystals with only S and/or Cl as AS, the test results clearly indicate that SAD-SMAR can be successfully applied to them. In the three test structures, the S atoms belong to methionine amino acids and no disulfide bridges are present. Since SAD-SMAR only considers the lattice symmetry operations, it processes the initial phase estimates derived from the research papers Acta Cryst. (2022). A78, 473-481 Rius and Torrelles Extending the novel ||-based phasing algorithm 479 Table 5 5iqy: list of top-ranked iodide site occupancies (!0.40) obtained by applying the SAD-SMAR algorithm compared with those in the deposited refinement (Krishna Das et al., 2016) (see Fig. 2 randomly shifted M 0 modulus function quite efficiently (Rius & Torrelles, 2021). As shown in Table 4, the peak / limit for considering the peaks at the end of Fourier recycling as part of the structure model can usually be set between 5.0 and 7.0.
To evaluate the influence of the DFCUT value in the phase refinement results, the test calculations were repeated with DFCUT = 0.0 and the results included in Table 3 for comparison. It can be seen that, for converging trials, the CC h values are similar ($0.88) and the R CC values are 2 or 3 units larger (an increase which is otherwise logical since the less reliable |D| values enter in the calculation). The comparison of the number of converging trials (n.c.t.) for both series of calculations indicates that DFCUT = $0.4 gives significantly higher n.c.t. values only for 2g4s and 4tno (by factors 1.89 and 1.10, respectively). This is surely related to their higher R free values (0.323 and 0.305, respectively) when compared with the median R free value of the PDB (0.265).
One characteristic of SAD-SMAR is the delivery of almost complete models when it converges. Most probable causes of non-convergence are, besides the poor quality of the experimental data, some functional limitations of the model description, e.g. when the resolution of the data is not enough to resolve the AS peaks in the Fourier map. Fortunately, due to the large separation among anomalous scatterers, this limitation is generally not a problem. However, at intermediate resolutions (>2.0 Å ), the presence of disulfide bridges in proteins, e.g. between cysteine residues, represents a limitation of the otherwise highly effective ipp procedure (the approximate spherical symmetry of individual S Fourier peaks is lost in the overlapped S-S peak). This problem has already been addressed in SHELXD (Usó n & Sheldrick, 2018;Sheldrick, 2010). It is clear that adapting the ipp philosophy to the treatment of disulfide bridges would considerably expand the scope of SAD-SMAR in S-SAD phasing.