Section 25.2.1.  PHASES

Heavy-atom-based phasing by the methods of isomorphous replacement (Green et al., 1954) and/or anomalous scattering (Pepinsky & Okaya, 1956) are initiated by reading one or more `scaled' files into the program PHASIT, along with estimates of the heavy-atom or anomalous-scatterer positional, occupancy and thermal parameters. Each input file can contain either isomorphous-replacement, derivative anomalous-scattering or native anomalous-scattering data. MAD (multiple-wavelength anomalous diffraction) data are treated as both isomorphous and anomalous-scattering data, in which case one simply inputs the scattering-factor differences (real part) appropriate for the wavelengths comprising the `isomorphous' data sets and the actual scattering factors (imaginary part) appropriate for the `anomalous' data sets. All possible combinations of isomorphous-replacement data, conventional anomalous-scattering data and MAD data are allowed and can be used simultaneously during phasing.

Solvent flattening and negative-density truncation are carried out following the strategy developed by Wang (1985); however, a reciprocal-space equivalent of the automated solvent-masking procedure is used (Furey & Swaminathan, 1997; Leslie, 1987). In addition, during solvent-mask construction all density near heavy-atom sites is automatically ignored, leading to more accurate masks. The complete process is fully automated and carries out three solvent-mask iterations with at least 16 solvent flattening and phase combination cycles. Optionally, an arbitrary number of additional cycles can be carried out for phase extension. A program is provided to interactively examine or edit the solvent mask or to create the mask by hand if desired.

Noncrystallographic (NC) symmetry averaging cases (Rossmann & Blow, 1963; Bricogne, 1974) are treated in direct space by operating on `submaps', i.e. arbitrary regions in an electron-density map encompassing all of the molecules to be averaged that are unique by true crystal symmetry. Many of the averaging programs were derived from routines originally written by W. Hendrickson & J. Smith and have been described earlier (Bolin et al., 1993), but they were substantially rewritten for incorporation into the PHASES package. Programs are supplied to: generate and examine the required submaps; refine the NC symmetry operators; interactively create averaging envelope masks; average density within the envelopes; convert the submaps to full-cell maps; invert the modified maps; and combine the phases with those from another source. An automated procedure is provided to carry out a specified number of averaging and phase combination cycles in addition to solvent flattening and negative-density truncation. This procedure allows for a gradual phase extension, if desired, extending by one reciprocal-lattice point in each direction for a given number of cycles.

Several programs are included to carry out partial structure phase combination with a variety of weighting options as an aid to structure completion. If density modification (solvent flattening or negative-density truncation and/or NC symmetry averaging) is performed, then phase (and amplitude) extension is also possible by manual or automated procedures.

The current package includes 44 Fortran programs and one C subroutine, with the C subroutine used only to provide an interface between the Fortran programs and standard X-Window graphics-library routines. All programs communicate only through files with a simple common format. For the major programs, memory is allocated from a single large one-dimensional array which gets partitioned as required for each problem at run time. This greatly simplifies redimensioning if needed for very large problems, since at most only two lines of code need to be changed. All source code is provided, along with compilation procedures or shell scripts appropriate for most workstations, including Silicon Graphics, Sun, IBM R6000, ESV and DEC Alpha AXP (both OSF and OpenVMS). A flow chart illustrating the major programs and data flow for common phasing procedures is given in Fig. 25.2.1.1.

Figure 25.2.1.1| top | pdf | Flow chart for the major phasing path encompassing native and derivative scaling, heavy-atom-based phasing, solvent flattening, negative-density truncation, and phase combination. Boxed entries represent programs while lines represent files. Optional paths for noncrystallographic symmetry averaging and phase extension are included by considering the additional programs offset from the main path by dashed lines.

Vital data common to nearly all calculations, such as the cell dimensions, lattice type and space-group symmetry, are entered only once in a single `parameter file'. All interactive programs prompt for the name of this file and for batch programs it is to be supplied on the first input line. The parameter file can also optionally contain the name of a `running' log file. If used, the running log file is opened in `append' mode by each program in the package, and a copy of all screen or printed output is added to the file along with a time and date stamp indicating what program was run and when. This allows the user to maintain a complete history of all calculations and results on a given problem in a single, chronologically accurate file.

With this method, the derivative scattering, on average, is made equal to the native scattering by plotting with the averages taken in corresponding resolution shells. A least-squares fit of a straight line to the plot yields a slope equal to (twice the difference between overall isotropic temperature parameters for derivative and native data sets) and an intercept of ln . From these values, the derivative data are put on the scale of the native by multiplying each derivative amplitude by

With this option, applied after relative Wilson scaling, the unique parameters of a symmetric 3 × 3 scaling tensor S are determined by two cycles of least-squares minimization of with respect to S, where is a weighting factor, and , , are direction cosines of the reciprocal-lattice vector expressed in an orthogonal system. The derivative data are then placed on the scale of the native by multiplying each derivative amplitude by the appropriate S.

With this option, again applied after relative Wilson scaling, a scale factor for each reflection is also determined by minimizing equation (25.2.1.3) with respect to S, but here S is a scalar and the summation is taken only over neighbouring reflections within a sphere centred on the reflection being scaled. The sphere radius is initially set to include roughly 125 neighbours, and the scale factor is accepted if at least 80 are actually present. If insufficient neighbours are available, then the sphere size is increased incrementally and the process repeated until a preset maximum radius is encountered. If the maximum is reached, the process terminates with the message that the data set is too sparse for local scaling. Scaling is achieved by multiplying each derivative amplitude by the appropriate S.

Rejection of outliers is often desirable, as erroneously large isomorphous or anomalous differences can lead to streaks in difference-Patterson maps and complicate identification of heavy-atom or anomalous-scatterer sites. The interactive program TOPDEL facilitates identification and rejection of such outliers while selecting reflections for use in difference-Patterson calculations. An input `scaled' file is read in, and user-supplied resolution and cutoffs are applied. The data are then sorted in descending order of magnitude of ΔF (either isomorphous or anomalous differences) and the largest differences are listed for examination. The user is then prompted to determine which, if any, of the large differences are to be rejected as outliers and to determine what percentage of the remaining largest differences are to be used in the Patterson-map synthesis. The appropriate Fourier-coefficient file is then created.

Selected regions of an electron-density map that are useful for NC symmetry applications can be extracted from the full-cell maps produced by FSFOUR with the programs EXTRMAP (batch) or MAPVIEW (interactive). The `submap' regions can cover any arbitrary volume and cross multiple cell edges if desired.

Programs MAPORTH and SKEW (both run in batch mode) are provided to modify submaps, as modification is sometimes useful or required with NC symmetry applications. MAPORTH simply converts the map to correspond to an orthogonal grid, which simplifies refinement of NC symmetry operators. SKEW also converts the map to an orthogonal grid, but changes the axis directions such that the new b axis can be arbitrarily oriented. This is useful in NC symmetry applications where one may want to examine maps looking directly down the NC symmetry rotation axis. Both programs compute density values at the new grid points by using a 64-point cubic spline interpolation and can also orthogonalize or skew masks to maintain correspondence with the modified submaps.

Program GMAP (interactive) is used to extract any region from a FSFOUR map, possibly crossing multiple cell edges, and convert it to a form directly readable by the external interactive graphics programs TOM [SGI version of FRODO (Jones, 1978)], O (Jones et al., 1991) or CHAIN (Sack, 1988). In addition to the output map file, one may also output a corresponding skeleton (Greer, 1974) file (for TOM) or skeleton data block (for O) to facilitate chain tracing.

Program PSRCH (batch) lists the largest peaks in a Fourier map and is useful in identifying additional heavy-atom or anomalous-scatterer sites from a map phased by a tentative model. Either positive or negative peaks can be listed, with the latter sometimes useful in MAD phasing applications, depending on the assignment of `native' and `derivative' data sets. Only unique peaks are listed, and the peak positions are interpolated from the map.

Phasing by heavy-atom-based methods (isomorphous replacement and/or anomalous scattering) begins when one or more `scaled' data sets are input to the program PHASIT (batch). User-specified rejection criteria are first applied to each data set, and structure factors corresponding to the heavy-atom or anomalous-scatterer substructure are computed from where is the occupancy, is the (possibly complex) scattering factor, is the isotropic temperature parameter and , , are the fractional coordinates of the jth atom. Sc is a scale factor relating the calculated structure factor (absolute scale) to the scale of the observed data. The summation is taken over all heavy atoms or anomalous scatterers in the unit cell. Alternatively, anisotropic temperature parameters can be used for each atom if desired. A subset of reflections comprising all centric data (plus the largest 25% of the isomorphous or anomalous differences if there are insufficient centric data) is selected and used to estimate Sc by a least-squares fit to the observed differences. Initial estimates of the `standard error' E (expected lack of closure) are determined from this subset as a function of F magnitude, treating centric and acentric data separately. SIR (single isomorphous replacement) or SAS (single-wavelength anomalous scattering) phase probability distributions are given by where the lack of closure is defined by for isomorphous-replacement data and for anomalous-scattering data, with the and − superscripts denoting members of a Bijvoet pair, and with φ denoting the protein phase, and and denoting the heavy-atom structure-factor amplitude and phase, respectively. The distributions, however, are cast in the A, B, C, D form (Hendrickson & Lattman, 1970). After all input data sets are processed in this manner, the individual phase probability distributions for common reflections are combined via with k as a normalization constant and the sums taken over all contributing data sets. The resulting combined distributions are then integrated to yield a centroid phase and figure of merit for each reflection. The standard error estimates, E, as a function of structure-factor magnitude are then updated for each data set, this time using all reflections and a probability-weighted average over all possible phase values for the contribution from each reflection (Terwilliger & Eisenberg, 1987a,b). With these updated standard error estimates, the individual SIR and/or SAS phase probability distributions are recomputed for all reflections and combined again to yield an improved centroid phase and figure of merit for each reflection. The resulting phases, figures of merit and probability distribution information are then available for use in map calculations or for further parameter or phase refinement. This method is used to produce MIR (multiple isomorphous replacement), SIRAS (single isomorphous replacement with anomalous scattering) MIRAS (multiple isomorphous replacement with anomalous scattering) and MAD phases as well as other possible phase combinations.

Structure-factor amplitudes and phases for a macromolecular structure can be computed directly from atomic coordinates corresponding to a tentative model with the programs PHASIT and GREF (both run as batch processes). This allows one to obtain structure-factor information from an input model typically derived from a partial chain trace or from a molecular-replacement solution. Equation (25.2.1.5) is used, but this time the sum is taken over all known atoms in the cell, and the scale factor is refined by least squares against the native amplitudes rather than against the magnitudes of isomorphous or anomalous differences. The computed structure factors may be used directly for map calculations, including `omit' maps, or for combination with other sources of phase information. One can output probability distribution information for the calculated phases, if desired, as well as coefficients for various Fourier syntheses, including those using sigma_A weighting (Read, 1986) for the generation of reduced-bias native or difference maps.

For the purpose of improving phases by density-modification methods, such as solvent flattening, negative-density truncation and/or NC symmetry averaging, one must compute structure factors by Fourier inversion of an electron-density map rather than from atomic coordinates. The program MAPINV (batch) is a companion program to FSFOUR and carries out this inverse Fourier transform. It accepts a full-cell map in FSFOUR format and inverts it to produce amplitudes and phases for a selected set of reflections when given the target range of Miller indices. A variable-radix 3D fast Fourier transform algorithm is used. Optionally, the program can modify the density prior to inversion by truncation below a cutoff and/or by squaring the density values. Other types of density modification are handled by different programs in the package and are carried out prior to running MAPINV. The indices, calculated amplitude and phase are written to a file for each target reflection.

The simplest procedure is to refine against the magnitudes of isomorphous or anomalous structure-factor amplitude differences, which can be carried out with the program GREF (batch mode). In this case, one minimizes for isomorphous-replacement data or for anomalous-scattering data with respect to the desired parameters contributing to , where is a weighting factor. For anomalous-scattering data, only the imaginary component of the scattering factors is used during the structure-factor calculation. For isomorphous-replacement data, the summation is taken only over centric reflections, plus the strongest 25% of differences for acentric reflections if insufficient centric data are present. For anomalous-scattering data, the summation is taken only over the strongest 25% of Bijvoet differences. An advantage of these methods is that only data from the derivative being refined are used (plus the native with isomorphous data), hence there is no possibility of feedback between other derivatives which may not be truly independent. A disadvantage is that, apart for the centric reflections, the target value in the minimization is only an approximation to the true . The accuracy of this approximation is improved by restricting the summations to the strongest differences.

An alternative procedure available in the program PHASIT (batch) is to refine against the observed derivative amplitudes. In this case, one minimizes the `lack of closure' (now based on amplitudes instead of intensities) with respect to the desired parameters contributing to , including the derivative-to-native scaling parameters. In all cases, the calculated derivative amplitudes are obtained from equation (25.2.1.9). To use this procedure, one must have an estimate of the protein phase φ. Several variations of this method, all available in PHASIT, are described below and are generally referred to as `phase refinement'.

The files produced by PHASIT for isomorphous data sets contain the information needed to produce the Fourier coefficients where and are the calculated heavy-atom structure-factor amplitude and phase, respectively, and is computed from where and are the current derivative and native phases, respectively. These coefficients are more accurate than using simple isomorphous difference magnitudes to approximate and can be computed once phasing has begun, since estimates of the required phase differences are then available. Alternatively, the program MRGDF (interactive) can be used to produce Fourier coefficients of the form where m is the current figure of merit. This method suffers somewhat as phase differences are ignored, but it has the advantage that the amplitude difference does not necessarily involve any derivative previously used in the computation of . If amplitudes from a new derivative and from the native are used, then peaks in the resulting `cross-difference' Fourier synthesis for the new derivative will automatically correspond to the same origin and hand as prior sites used in the phasing process, although the hand may still be incorrect. Finally, GREF can be used to generate the Fourier coefficients with the second set producing a map similar to that obtained using equation (25.2.1.16). Both coefficient sets in equation (25.2.1.19) are lacking in that the phase difference is ignored, but the second set [and also those in equation (25.2.1.16)] has the advantage that heavy-atom sites already in the model are subtracted away, allowing any remaining minor sites to stand out in the resulting map.

The files produced by PHASIT for anomalous-scattering data sets contain the information needed to produce the Fourier coefficients or where is the protein phase used when computing . The coefficients in equation (25.2.1.20) correspond to a conventional Bijvoet difference Fourier map, which should show large positive peaks at the locations of anomalous-scattering sites when the hand is correct. The coefficients in equation (25.2.1.21) correspond to the case in which contributions from known anomalous scatterers are subtracted out. As in the isomorphous-replacement case, a program MRGBDF (interactive) is also provided to generate the Fourier coefficients where the Bijvoet difference does not necessarily have to come from a derivative used in the phasing. If the difference doesn't come from a derivative used in phasing, then a `cross-Bijvoet difference' Fourier map is obtained, which should produce large positive peaks at anomalous-scatterer locations in the new derivative when the original hand is correct. Additionally, GREF can be used to generate the Fourier coefficients where and are the heavy-atom structure-factor amplitude and phase, used when computing . These coefficients can also be used to identify additional anomalous-scatterer sites, but they are insensitive to the hand. As in equation (25.2.1.21), if the second set in equation (25.2.1.23) is used, then contributions from anomalous scatterers already included in the phasing will be subtracted out.

Finally, the program HNDCHK (interactive) is provided to determine the enantiomorph by examination of a Bijvoet difference Fourier map. One inputs the map along with the anomalous-scatterer positions used in the phasing. The program then uses a 64-point cubic spline interpolation algorithm to obtain the density precisely at the input coordinates and also at coordinates related to them by a centre of symmetry. If the input heavy-atom configuration had the correct hand, large positive peaks should occur exactly at the input locations. If the hand is incorrect, even larger negative peaks occur at the true positions, i.e. those related to the input positions by a centre of symmetry.

Solvent-mask construction follows the procedure suggested by Wang (1985), with the exception that electron density in the vicinity of heavy-atom sites is temporarily ignored during the mask-building process. This allows one to use a tight solvent mask, which maximizes the phasing power of the method while preventing artificial extension of the protein envelope into the solvent region in the vicinity of surface-bound heavy-atom sites. Failure to do this has occasionally been found to deplete the protein region elsewhere to compensate for the incorrectly extended region.

Once a solvent mask is constructed, solvent flattening and negative-density truncation is carried out using the program BNDRY. An electron-density map and corresponding mask are input along with an empirical constant S, which is used to estimate the value of on the scale of the input map. The estimation follows the procedure of Wang (1985) and is based on the assumption that for typical solvent conditions and proteins not containing heavy metals, the ratio of mean solvent electron density to maximum protein electron density is constant, although for phasing purposes the optimum values are resolution-dependent. Typical values of S are supplied in the package. One simply couples the value of S taken from known structures with density values obtained from the experimental maps to estimate on the appropriate (but unknown) map scale by solving the equation for . Once the estimate of is obtained, solvent flattening and negative-density truncation are carried out simultaneously by resetting all map values according to the relationships

The scaled data are sorted into bins according to d spacing, and a three-term polynomial is fitted to the mean values of as a function of resolution. For each reflection, a unimodal phase probability distribution is constructed using a modification (Bricogne, 1976) of the Sim (1959) weighting scheme via where the average in the appropriate resolution range is determined from the polynomial. This distribution is cast in the A, B, C, D form with Phase combination with the anchor set then proceeds according to equation (25.2.1.10), and the combined distributions are integrated to give a new phase and figure of merit for each reflection.

As an alternative to the procedure above, in the BNDRY program the weights, W, used when constructing the unimodal probability distributions in equations (25.2.1.30) can be computed according to where and are normalized structure-factor amplitudes for the observed and calculated structure factors, respectively, and is determined by the procedure described by Read (1986). For acentric reflections, equation (25.2.1.31) is used whereas for centric reflections, W is one half the value given by equation (25.2.1.31).

Normally, the distributions constructed for the calculated phases are combined with those for the anchor set with full weight in equation (25.2.1.10). However, in BNDRY, one can supply a damping factor in the range 0–1 to down-weight the contributions of the anchor set. The damping factor simply multiplies the distribution coefficients such that a factor of 1 (default) indicates no damping, and values less than one place more emphasis on the map-inverted or partial structure phases. If set to zero, the calculated phases are accepted as they are, since there is effectively no phase combination with the anchor set.

If phase extension is requested during the phase combination step, an additional file (prepared by the interactive program MISSNG) is also supplied to the BNDRY program. This file contains unique reflections absent from the anchor set but for which observed amplitudes (and possibly phase probability distribution coefficients) are available. Phase combination then proceeds exactly as above, except that for any extended reflections lacking phase probability information, the calculated phases are accepted as they are. Phase extension is required when phasing purely by SAS methods as it is the only way to phase centric reflections. As a final option, phase and amplitude extension is possible, in which case both the calculated amplitude and phase are accepted as they are for reflections having only indices provided on the extension file. This is sometimes desirable to include low-resolution reflections that may have been obscured by the beam stop.

NC symmetry operators are specified in terms of the parameters φ, ψ, χ, , , and t, which refer to a Cartesian coordinate system in Å, obtained by orthogonalization of the unit cell as in the Protein Data Bank (Bernstein et al., 1977). The angles φ and ψ determine the direction of the NC rotation axis, while χ determines the amount of rotation about it. , and are coordinates of a point through which the rotation axis passes, and t is a post-rotation translation parallel to the rotation axis. The relationships between the angles, orthogonal reference axes X, Y, Z and the unit cell are given in Fig. 25.2.1.2. Coordinates for a pair of points related by NC symmetry are then expressed in the orthogonal system by where and are three-element column vectors containing coordinates for the related points, is a 3 × 3 rotation matrix derived from the angles, O is a three-element column vector containing coordinates for a point through which the rotation axis passes, t is the post-rotation translation scalar in Å and is a three-element column vector containing direction cosines of the rotation axis. This type of parameterization simplifies transfer of information from self-rotation functions, which are usually calculated in spherical polar angles anyway, and also makes obvious pseudo-space-group symmetry type operations such as pseudo-screw axes. For convenience, a program O_TO_SP is provided to convert from a 3 × 3 rotation matrix and 1 × 3 column vector representation of the NC symmetry operation, as used in some programs, to the parameters described here.

Figure 25.2.1.2| top | pdf | Relationships between noncrystallographic symmetry rotation axis direction, orthogonal reference system axes X, Y, Z and crystallographic axes. The X axis is aligned with the crystal a. The Y axis is parallel to . The Z axis is parallel to , i.e. . ψ is the angle between the NC rotation and +Y axes. φ is the angle between the projection of the NC rotation axis in the XZ plane and the +X axis, with +φ counterclockwise when viewed from +Y toward the origin. χ is the amount of rotation about the directed axis, with +χ clockwise when viewed from the axis toward the origin.

Refinement of the NC symmetry operator parameters is achieved by least-squares minimization of the squared difference in electron density for all NC-symmetry-related points. Thus, one minimizes with respect to the operator parameters, where the sum is taken over all points within the appropriate averaging envelope(s). One starts refinement with low-resolution data (∼6 Å) on a coarse (∼2 Å) grid and monitors progress by following the correlation coefficient between the related electron-density values. Once convergence is obtained, the calculation is resumed with higher-resolution data on a finer grid. Typically, a correlation coefficient of around 0.4 or higher (for a 3 Å MIR map, 1 Å grid) indicates that the operator has been correctly located. The operator refinement is confined to submaps and is facilitated by use of an orthogonal grid. A submap containing the molecules to be averaged is obtained from the programs MAPVIEW or EXTRMAP and can be converted to an orthogonal grid, if needed, by the program MAPORTH, as described earlier.

Masks encompassing the region(s) to be averaged are usually created by hand in the interactive program MAPVIEW. Here, one reads in a submap comprising the desired region of whatever type of map is available, usually an MIR map. An appropriate contour level and initial section are selected and the contoured electron density for that section appears on the screen. One then selects the `add next section' menu item two or three times to create a projection over several sections of the map, since in the projection the molecular boundary is usually more obvious. Selecting the `trace mask' menu item then allows the user to hand-contour the molecular envelope by directing the cursor tied to a mouse or other pointing device. One then moves to an adjacent section and repeats the process until the complete 3D mask is obtained. To simplify matters and speed up the process, there are `copy next mask' and `copy previous mask' menu items allowing one to take advantage of the fact that the mask is a slowly changing function, particularly when near the centre of the molecule. One can use this feature to copy a mask from the previous or following section and apply it to the current section. Up to twelve distinct 3D masks can be selected. Each mask is colour-coded and can be simultaneously displayed superimposed on the contoured electron-density section. Once the mask is completed, the `make asu' menu item is selected to apply crystallographic symmetry operations to all points within the generated envelope masks. If these operations generate a point also within the envelope masks, the point is flagged in red to indicate that it is redundant, indicating that when tracing the mask, one inadvertently strayed into a symmetry-related molecule. After this check for redundancy, all points within the submap distinct from but related to points within the molecular envelopes by crystal symmetry are flagged in green. This enables one to detect packing contacts and also to ensure that all significant electron density has been assigned to some envelope. Upon completion, the mask is written to a file suitable for use either in averaging, solvent flattening (after expansion by BLDCEL), or operator refinement. In cases of `proper' NC symmetry, it is often desirable to trace the averaging envelope mask in a `skewed' map, such that one is looking directly down the NC rotation axis. In this case, it is usually very obvious where the NC symmetry breaks down, simplifying identification of the averaging envelope. If the averaging mask is created in a skewed submap, then the batch program TRNMSK can be used to transform it so as to correspond to the original, unskewed submap for use in averaging calculations (which do not require skewing).

All averaging calculations are carried out by the program MAPAVG (batch), which requires the submap to be averaged along with the envelope masks and NC symmetry operators. A copy of the input submap is made and each grid point in the mask is examined in turn. If the grid point lies within any averaging envelope, then all points related to it by NC symmetry are generated from the operators and examined. If the generated points also lie within the appropriate envelope mask, the electron density there is interpolated, as described earlier, and the density values for all related points are summed. The average value of the electron density is then inserted at the original point in the submap copy. Upon completion, the averaged version of the submap is written to a file and correlation coefficients for regions related by the various NC symmetry operations are output. The averaged submap is then passed to the program BLDCEL along with the averaging mask and the original unaveraged FSFOUR map from which the submap was created. For all points within the averaging envelope(s), their electron-density values and those at points related by crystallographic symmetry are inserted into the full-cell map, and it is written to a file. This file then contains the NC symmetry averaged electron density expanded to a full-cell map that obeys space-group symmetry. As an option, the averaging mask can also be expanded in BLDCEL to a full-cell mask, which could then be used for solvent flattening.

During NC symmetry averaging, phase combination and extension is carried out precisely as described during solvent flattening and negative-density truncation. The only difference is that after generation of each electron-density map, the NC symmetry averaging is carried out on the appropriate submap region, which is then expanded back to a full-cell map prior to each solvent-flattening calculation.

A script to carry out a standard solvent-flattening run is provided along with a description of the expected input files, output files and examples. Not surprisingly, this DOALL procedure does it all. Execution of the script will create a map from an input `anchor' set of phases, typically obtained by MIR, SIR, or MAD methods, and will then create a solvent mask from the map after zeroing out density near heavy-atom sites. This solvent mask is used in four cycles of solvent flattening, combining the map-inverted phase information with the anchor phases. A new solvent mask is then generated, starting from a map produced with the phases after the first four cycles. Four cycles of solvent flattening using the second solvent mask are then carried out, restarting from the original map and combining with the anchor phases. These phases are then used to compute a new map from which a third solvent mask is built. The third mask is then used for eight cycles of solvent flattening, again restarting with the original map and combining with the anchor phases. Supplied in the script, but commented out, are instructions to carry out an arbitrary number of additional phase extension cycles, and then an arbitrary number of phase and amplitude extension cycles, all using the third solvent mask. The combined phases and distribution coefficients are written to a file after all cycles with a given mask are completed.

Additional scripts are provided to carry out phase extension and/or NC symmetry averaging iterations. These scripts are executed after completion of a normal solvent-flattening run with the DOALL procedure. With the EXTNDAVG script, an input number of additional solvent flattening and/or phase combination cycles are carried out, and phase (and possibly amplitude) extension may be requested. Initial and final d spacings are input to the program SLOEXT (batch) along with the number of map modification or phase combination iterations per step, where each step represents the extension by one reciprocal-lattice point in each direction if phase extension is to be carried out. The calculations proceed where the DOALL script leaves off, starting with a map made from the final phases and using the third solvent mask. If NC symmetry averaging is to be carried out, after each map calculation the appropriate submap is extracted from it and is passed to MAPAVG along with the averaging mask. The averaged submap is passed to BLDCEL, where it is expanded to a full-cell map, which then is passed to BNDRY for solvent flattening. Map inversion and phase combination then proceed normally (although possibly with phase extension). Note that, in general, separate masks are used for solvent flattening and averaging.

The EXTNDAVG_MC script carries out the same procedures and options as the EXTNDAVG script, except that it is used when carrying out NC symmetry averaging with multiple crystal forms. Starting phase files, anchor phases, solvent masks, averaging masks and control files are provided for each crystal form. For each form, the solvent flattening and phase combination steps are carried out independently with the appropriate data; however, during the averaging step, maps from all crystal forms are involved.

The interactive program PRECESS is provided to display diffraction data in the form of pseudo-precession photographs. One can display any zone or step through all zones, with the corresponding intensities mapped to a colour scheme. If a grey scale is selected, the image looks very much like a properly exposed precession photograph taken with Polaroid film. When the cursor is placed near a reciprocal-lattice point, the Miller indices, intensity, standard deviation and d spacing are displayed, allowing one to quickly confirm or identify space groups and Laue symmetry. If a scaled file is input containing isomorphous-replacement or anomalous-scattering data, one can display the corresponding intensity differences instead of the native intensities and quickly visualize the distribution of differences to help assess isomorphism.

The interactive program MAPVIEW can be used to examine contoured electron-density or Patterson maps, as well as to examine, create or edit solvent or averaging masks. Either full-cell FSFOUR maps or submaps (including skewed submaps) can be used, although only from the former can any arbitrary region be obtained and reordered interactively. The mask creation and editing functions have been described earlier. The program is very useful for Patterson analysis, evaluation of phasing results and to help decide which region is appropriate for isolating a molecule for use in model building. It is usually crucial for construction of averaging masks, but is also useful for examining or editing other masks.

While MAPVIEW is extremely useful, there are times when it is desirable to have individual plots available either for comparison, stereo viewing of electron density, or incorporation into documents. The program CTOUR (batch) handles these functions and accepts an input FSFOUR map or submap. The CTOUR program can create any number of plot files in a single run, with each consisting of either an individual section, a mono projection, or a stereo projection, with each projection over different multiple sections. If full-cell FSFOUR maps are input, any desired region may be selected, whereas if submaps (including skewed maps) are input, the accessible regions are limited by those present in the input map.

The plot files created by CTOUR are generic in nature and are not directly displayable. One needs a driver program to convert the generic files to the format appropriate for the desired display device. The appropriate drivers for several popular display devices are provided within the package and are described below.

Within the package, fractional atomic coordinates are used extensively, and the program is provided to convert from PDB (Protein Data Bank) to PHASES coordinate files and vice versa. The program prompts for input and output file names, the direction of the conversion, chain or residue ranges, and whether to reset occupancies and/or thermal factors to specified values. The coordinate ranges (both fractional and in PDB coordinates) spanned by the model are also listed.

The program O_TO_SP is provided to convert NC symmetry operators expressed in terms of a 3 × 3 rotation matrix and 1 × 3 translation vector to the PHASES-style spherical polar system described earlier. Although originally written to convert the transformation operator as defined in the O program (Jones et al., 1991), the procedure works for any rotation or translation operator expressed in this form, provided that the operator is applicable to Cartesian coordinates in Å orthogonalized as in the Protein Data Bank (Bernstein et al., 1977).

For efficiency, structure-factor files used within the package are binary; however, the program RD31 is provided to read these binary files and convert them to formatted files that can be examined and possibly edited by the user. The indices, amplitudes, phases, figures of merit, phase probability distribution coefficients, and markers indicating which reflections are centric along with the allowed phase values are thus made readily accessible. A corresponding program, MK31B, is also provided to reverse the process; it reads the formatted (and possibly edited) versions of the structure-factor files and generates the appropriate binary-file equivalents. Additionally, the program XPL_PHI is supplied to convert the binary structure-factor files to a form readable by the X-PLOR program (Brünger et al., 1987) in order to facilitate complete model refinement. Phase and figure-of-merit information are also passed to the output file, allowing refinement with phase restraints if desired.

The program IMPORT allows users to `import' phase information obtained from programs external to the package so it can be used for subsequent calculations within the package. For example, one can use phase and probability distribution information obtained elsewhere to initiate solvent flattening, negative-density truncation and/or NC symmetry averaging within PHASES, or simply to generate and display maps with MAPVIEW or the other graphics programs. Reflection indices, the observed structure-factor amplitude, figure of merit, phase and phase probability distribution coefficients must be supplied, although free format can be used.

The program PSTATS compares phases in two different structure-factor files. It lists mean phase differences as a function of d spacing for common reflections. The program is very useful for comparing results from different phasing strategies and for testing new procedures against error-free phases. It can also be used to check for convergence in iterative procedures or to assess the relative contributions of phase sets during phase combination.