International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 18.9, pp. 529-533   | 1 | 2 |
https://doi.org/10.1107/97809553602060000863

Chapter 18.9. Macromolecular applications of SHELX

G. M. Sheldricka*

aLehrstuhl für Strukturchemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany
Correspondence e-mail: gsheldr@shelx.uni-ac.gwdg.de

The SHELX system for small-molecule crystallography dates back to the early 1970s. The current refinement program, SHELXL97, is also useful for high-resolution macromolecular refinement. SHELXC, D and E are more recent additions for experimental phasing using single-wavelength anomalous dispersion (SAD), single isomorphous replacement (SIR), combined SAD and SIR (SIRAS), multi-wavelength anomalous dispersion (MAD) and radiation-damage-induced phasing (RIP) data. They are fast and simple to use, and in favourable cases produce high-quality maps despite very weak initial phase information.

18.9.1. Introduction

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The first version of SHELX was written around 1970 for the solution and refinement of organic and inorganic structures. Since then, most routine structure determinations published in parts B, C and E of Acta Crystallographica have made use of at least one of the SHELX programs. However, this account will be restricted to the experimental phasing and refinement of macromolecular structures; details of other applications may be found in Sheldrick (2008)[link]. The SHELX programs are available as open source and as precompiled executables for common computer systems. They are written in a simple Fortran subset with a strict `zero dependency' philosophy: the stand-alone binaries use no extra programs, libraries, data files or environmental variables etc., which makes them easy to install and use. The programs are designed to be called from a command line and for incorporation into GUIs (graphical user interfaces); for example, experimental phasing with SHELXC, SHELXD and SHELXE may be per­formed inter alia via the HKL2MAP (Pape & Schneider, 2004[link]), CCP4i (Potterton et al., 2003[link]), AUTOSHARP (Vonrhein et al., 2007[link]), HKL-3000 (Minor et al., 2006[link]) and CRANK (Ness et al., 2004[link]) GUIs and the AUTORICKSHAW (Panjikar et al., 2005[link]) and ARCIMBOLDO (Rodriguez et al., 2009[link]) servers. The SHELX programs are general for all space groups in conventional settings or otherwise and make extensive use of default settings to keep user input and confusion to a minimum. Particular care has been taken to test the programs thoroughly on as many computer systems and crystallographic problems as possible before they were released, a process that often required several years!

18.9.2. Experimental phasing with SHELXC/D/E

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Experimental phasing of macromolecules usually requires the presence of a relatively small number of atoms with significantly greater real or anomalous scattering power than the majority of atoms in the structure. These atoms can be e.g. metal or sulfur atoms already present in a native protein, heavy metals or halides introduced by soaking, or selenium incorporated by replacing methionine by selenomethionine using a suitable expression system. It is first necessary to locate the positions of these atoms in the unit cell, often using direct or Patterson methods and programs originally designed to solve small-molecule structures. These atoms (referred to as the substructure) are used to estimate starting phases for the complete macromolecule, which are then refined by modifying the electron density so that it corresponds better to the expected density whilst remaining consistent with the experimental native intensity data. In the SHELX system (Sheldrick, 2008[link], 2010[link]), the program SHELXC is used to analyse and process the reflection data, and write the files that are then read by SHELXD for location of the substructure and SHELXE for derivation of the starting phases and density modification. In these programs, the experimental phasing is reduced to its absolute essentials, with the aim of obtaining an interpretable electron-density map quickly and reliably, rather than finding the most accurate phases. This requires some severe simplifications, for example the assumption that there is only one type of substructure atom present, although in practice a mixture of elements rarely causes problems. The approach has the advantage of producing robust, fast and simple to use programs but is restricted to experimental phasing by MAD (multi­wavelength anomalous dispersion), SAD (single-wavelength anomalous dispersion), SIR (single isomorphous replacement), SIRAS (combined SAD and SIR) and RIP (phasing based on radiation-induced changes in the structure) methods.

18.9.2.1. Substructure location with SHELXD

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The program SHELXD (Usón & Sheldrick, 1999[link]; Schneider & Sheldrick, 2002[link]; Sheldrick, 2008[link]: see also Chapter 16.1[link] in this volume) was originally designed for the ab initio solution of macromolecular structures from atomic resolution native data alone, but has proved very useful for substructure solution at much lower resolution. The dual-space approach of SHELXD was inspired by the Shake and Bake philosophy of Miller et al. (1993[link], 1994[link]) but differs in many details, in particular in the use it makes of the Patterson function, which proves very effective in substructure solution. An advantage of the Patterson function is that it provides a good noise filter for the ΔF or FA data: negative regions of the Patterson function can simply be ignored. On the other hand, the direct-methods approach is efficient at handling a large number of sites, whereas the number of Patterson peaks to analyse increases with the square of the number of atoms. Thus, for reasons of efficiency, the Patterson function is employed at two stages in SHELXD: at the beginning to obtain pseudo-random starting atom positions that are consistent with the Patterson (usually referred to as Patterson seeding) and to cal­culate a triangular table in which the off-diagonal elements are a Patterson minimum function for vectors between one potential atom and a second atom including all its symmetry equivalents (Schneider & Sheldrick, 2002[link]). This table, which also showed the minimum distances between atoms taking symmetry into account, was very useful for recognizing NCS (noncrystallographic symmetry) in substructures obtained from borderline data, but proved difficult to automate and so has remained a `crossword table' for the amusement of experts (it is still written by SHELXD to the listing file). Similarly, a figure of merit PATFOM calculated by SHELXD on the basis of this table has proved less useful than expected in practice, because the values are not on an absolute scale; they tend to be much higher for small substructures.

18.9.2.2. Practical considerations for substructure solution

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The resolution to which the data have to be truncated is usually the most critical decision for substructure solution. When the anomalous signal is weak, using data out to the diffraction limit introduces noise and may well not lead to a solution. On the other hand, truncating the resolution too strongly leads to less precise atomic positions and may result in weaker sites being missed. The mean ratio of the average absolute anomalous difference to its estimated standard deviation can be used as a guide as to where to truncate the data, but this requires good estimates of the standard deviations of the measured intensities. A better guide is the correlation coefficient between the signed anomalous differences for the different wavelengths in a MAD experiment (Schneider & Sheldrick, 2002[link]), or for two different crystals in a SAD experiment. In a sulfur SAD experiment, the two sulfur atoms in a disulfide bridge behave as a single `super-sulfur' atom at resolutions less than about 2.1 Å. Although this is no impediment to finding them with SHELXD, their phasing power is significantly enhanced if they are resolved into their two component sulfur atoms using the DSUL instruction in SHELXD.

To allow for possible variations in occupancy or displacement parameters (B values) and the presence of different types of marker atoms, it has proved useful to refine the occupancies in the last two dual-space cycles. A sharp fall-off in the refined occupancy between the last true site and the first noise peak is also a useful test for a good solution, but cannot be used for halide soaks, for which a continuous range of occupancies is usually found; usually the peak list is truncated at about 0.2 times the occupancy of the highest peak, because experience indicates that weaker peaks may well be noise. The correlation coefficient (CC) between the observed and calculated E values usually enables correct solutions to be identified unambiguously, and the value of CC(weak), the correlation coefficient based on the reflections not used in the dual-space recycling, is also a good check. It is like a free R value, but is not quite independent because all the data are used in the occupancy refinement.

For large substructures, it is important not to terminate the search after too small a number of trials. Often, a much better solution is found if more trials are performed. Several structures have given only one correct solution in 10 000 trials (and in one case only one in 1.6 million trials!). Since the default SHELXD action is to start each job with a different random number seed, one efficient approach is to run several copies in parallel, e.g. one per CPU (Fu et al., 2007[link]). This may conveniently be combined with different values for the resolution cutoff.

18.9.2.3. SHELXE: density modification

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The density modification in SHELXE does not make use of solvent flattening or histogram matching. Instead, the sphere of influence algorithm (Sheldrick, 2002[link]) is used to provide an indication as to how likely it is that each individual voxel (volume element) in the map corresponds to a true atomic site. The variance V of the density on a spherical surface of radius 2.42 Å is calculated for each voxel in the map. The use of a spherical surface rather than a spherical volume was intended to save time and add a little chemical information (2.42 Å is a typical 1,3 distance in proteins and DNA). V gives an indication of the probability that a voxel corresponds to a true atomic position. Voxels with low V are flipped (ρ′ = −ργ where γ is usually set to 1.0). For voxels with high V, ρ is replaced either by {ρ4/[υ2σ2(ρ) + ρ2]}1/2 [where ν is usually 0.5 and σ2(ρ) is the variance of the density ρ over the whole cell] if positive or by zero if negative. An empirical weighting scheme for phase recombination is used to combat model bias. The variance over all voxels in the asymmetric unit of the individual variances V, output by the program as the `contrast', is a good indication of which marker atom enantiomorph is correct; it is almost invariably higher for the correct choice, especially after 5–10 density-modification cycles.

A further simple and effective algorithm to improve the phases of the experimentally measured reflections is to extrapolate the data and phases to a higher resolution than was actually accessible: the free lunch algorithm (Caliandro et al., 2005[link]; Yao et al., 2006[link]). This has also been implemented in SHELXE (Usón et al., 2007[link]). This algorithm is effective when data have been measured to a resolution of 2.0 Å or better, and can lead to improvements in the mean phase error of the measured reflections of between 5 and 30°.

18.9.2.4. Integrated density modification and autotracing

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A relatively fast iterative autotracing algorithm has been incorporated into the density modification in SHELXE (Sheldrick, 2010[link]). It is primarily designed to get a toehold in maps with very poor starting phases, e.g. with a mean phase error greater than 60°. The tracing proceeds as follows:

  • (i) Find potential α-helices in the density and try to extend them at both ends. Then find other potential tripeptides and try to extend them at both ends in the same way.

  • (ii) Add traces obtained by applying NCS operations derived from the heavy-atom positions, provided that they fit the density well.

  • (iii) Tidy up and splice the traces as required.

  • (iv) Use the traced residues to estimate phases and combine these with the initial phase information using σA weights (Read, 1986[link]), then restart the density modification. The refinement of one B value per residue provides a further opportunity to suppress wrongly traced residues.

Crystallographic symmetry is taken into account at all stages, and the backbone traces are selected with the help of the following criteria:

  • (i) The modified density ρ′ should be high at the atomic sites and low at the dummy-atom positions (generated at sites where no atom should be found).

  • (ii) The chains must be long enough (in general at least seven amino acids); longer chains are given a higher weight.

  • (iii) A few Ramachandran outliers can be tolerated, e.g. for glycines, but in general the ϕ and ψ angle pairs should lie in the well populated regions of the Ramachandran diagram.

  • (iv) There should be a well defined secondary structure (i.e. ϕ/ψ pairs should tend to be similar for consecutive residues).

  • (v) On average, there should be significant positive density 2.9 Å from N in the N→H direction (to a hydrogen-bond acceptor). This takes into account that the large majority of main-chain NH groups in proteins take part in hydrogen bonds with oxygen or other electronegative atoms.

At the time of writing, the autotracing version of SHELXE is still at the β-test stage, but the results are encouraging. The ability to trace the structure in a way that is consistent with the above criteria is a very good indicator as to whether the structure has been solved. Two internet servers for experimental phasing that use this version effectively are AUTORICKSHAW (Panjikar et al., 2005[link]) and ARCIMBOLDO (Rodríguez et al., 2009[link]). In the latter, Usón and co-workers use this ability to trace maps with large initial phase errors, and so to find a few correct solutions in a large number of trials generated by molecular-replacement searches for short α-helices, as part of a procedure for the ab initio solution of protein structures with data down to 2.0 Å resolution (see Chapter 16.1[link] ).

18.9.3. Macromolecular refinement using SHELXL

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SHELXL is a very general refinement program and is equally suitable for the refinement of minerals, organometallic structures, oligonucleotides or proteins (or any mixture thereof) against X-ray or neutron single- (or twinned!) crystal data. It has even been used with diffraction data from powders, fibres and two-dimensional crystals. The price of this generality is that it is somewhat slower than programs specifically written only for protein structure refinement. Structure factors are calculated by summation rather than by a fast Fourier transform; this is more precise but slower. Any protein- (or DNA-)specific information must be input to SHELXL by the user in the form of refinement restraints etc. Refinement of macromolecules using SHELXL has been discussed by Sheldrick & Schneider (1997)[link].

Least-squares (LS) refinement has the advantage that it provides proper estimates of the standard deviations in all refined and derived parameters. However, at low data-to-parameter ratios, maximum likelihood (ML) refinement is better at avoiding overfitting and is less sensitive to reflection outliers. For this reason, ML refinement, as implemented in, for example, REFMAC (Murshudov et al., 1997[link]), PHENIX_REFINE (Adams et al., 2002[link]) or BUSTER-TNT (Blanc et al., 2004[link]), is recommended when the data-to-parameter ratio falls below about 5. ML refinement also enables experimental phase information to be incorporated (Pannu et al., 1998[link]).

18.9.3.1. Constraints and restraints

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In refining macromolecular structures, it is almost always necessary to supplement the diffraction data with chemical information in the form of restraints. A typical restraint is the condition that a bond length should approximate to a target value with a given estimated standard deviation; restraints are treated as extra experimental data items. Even if the crystal diffracts to 1.0 Å, there may well be poorly defined disordered regions for which restraints are essential to obtain a chemically sensible model (the same can be true of small molecules too!). SHELXL is generally not suitable for refinements at resolutions lower than about 2.0 Å because it cannot currently handle general potential-energy functions, e.g. for torsion angles or hydrogen bonds; if noncrystallographic symmetry restraints can be employed, this limit can be relaxed a little. Unimodal restraints, such as target distances, are less likely to result in local minima than are multimodal restraints, such as torsion angles; multimodal functions are better used as validation criteria. It is fortunate that validation programs, such as MolProbity (Davis et al., 2007[link]), make good use of multimodal functions such as torsion angles and hydrogen-bonding patterns that are not employed as restraints in SHELXL refinements.

For some purposes (e.g. riding hydrogen atoms, rigid-group refinement, or occupancies of atoms in disordered side chains), constraints, exact conditions that lead to a reduction in the number of variable parameters, may be more appropriate than restraints; SHELXL allows such constraints and restraints to be mixed freely. Riding hydrogen atoms are defined such that the C—H vector remains constant in magnitude and direction, but the carbon atom is free to move; the same shifts are applied to both atoms, and both atoms contribute to the least-squares derivative sums. This model may be combined with anti-bumping restraints that involve hydrogen atoms, which helps to avoid unfavourable side-chain conformations. SHELXL also provides, e.g., methyl groups that can rotate about their local threefold axes; the initial torsion angle may be found using a difference-electron-density synthesis calculated around the circle of possible hydrogen-atom positions.

18.9.3.2. Least-squares refinement algebra

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The original SHELX refinement algorithms were modelled closely on those described by Cruickshank (1970)[link]. For macromolecular refinement, an alternative to (blocked) full-matrix refinement is provided by the conjugate-gradient solution of the least-squares normal equations as described by Hendrickson & Konnert (1980)[link], including preconditioning of the normal matrix that enables positional and displacement parameters to be refined in the same cycle. The structure-factor derivatives con­tribute only to the diagonal elements of the normal matrix, but all restraints contribute fully to both the diagonal and non-diagonal elements, although neither the Jacobian nor the normal matrix itself are ever generated by SHELXL. The parameter shifts are modified by comparison with those in the previous cycle to accelerate convergence whilst reducing oscillations. Thus, a larger shift is applied to a parameter when the current shift is similar to the previous shift, and a smaller shift is applied when the current and previous shifts have opposite signs. The STIR instruction enables the resolution to be extended stepwise during the refinement, thereby increasing the radius of convergence, and is recommended for the first refinement job starting from an unrefined model. It can also be used to reduce memory effects if the Rfree reflection set has been modified.

SHELXL refines against F2 rather than F, which enables all data to be used in the refinement with weights that include con­tributions from the experimental uncertainties, rather than having to reject F values below a preset threshold; there is a choice of appropriate weighting schemes. Provided that reasonable estimates of σ(F2) are available, this enables more experimental information to be employed in the refinement; it also allows refinement against data from twinned crystals.

18.9.3.3. Full-matrix estimates of standard uncertainties

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Inversion of the full normal matrix (or of large matrix blocks, e.g. for all positional parameters) enables the precision of individual parameters to be estimated (Rollett, 1970[link]), either with or without the inclusion of the restraints in the matrix. The standard uncertainties in dependent quantities (e.g. torsion angles or distances from mean planes) are calculated in SHELXL using the full least-squares correlation matrix. These standard uncertainties reflect the data-to-parameter ratio, i.e. the resolution and completeness of the data and the percentage of solvent, and the quality of the agreement between the observed and calculated F2 values (and the agreement of restrained quantities with their target values when restraints are included).

Full-matrix refinement is also useful (together with the stepwise increase of resolution STIR) when domains are refined as rigid groups in the early stages of refinement (e.g. after structure solution by molecular replacement), since the total number of parameters is small and the correlation between parameters may be large.

18.9.3.4. Refinement of anisotropic displacement parameters

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The motion of macromolecules is clearly anisotropic, but the data-to-parameter ratio rarely permits the refinement of the six independent anisotropic displacement parameters (ADPs) per atom; even for small molecules and data to atomic resolution, the anisotropic refinement of disordered regions requires the use of restraints. SHELXL employs three types of ADP restraint (Sheldrick 1993[link]; Sheldrick & Schneider, 1997[link]). The rigid bond restraint, first suggested by Rollett (1970)[link], assumes that the com­ponents of the ADPs of two atoms connected via one (or two) chemical bonds are equal within a specified standard deviation. This has been shown to hold accurately (Hirshfeld, 1976[link]; Trueblood & Dunitz, 1983[link]) for precise structures of small molecules, so it can be applied as a hard restraint with small estimated standard deviation. The similar ADP restraint assumes that atoms that are spatially close (but not necessarily bonded, because they may be different components of a disordered group) have similar Uij components. An approximately isotropic restraint is useful for isolated solvent molecules. These two restraints are only approximate and so should be applied with low weights, i.e. high estimated standard deviations.

The transition from isotropic to anisotropic roughly doubles the number of parameters and almost always results in an appreciable reduction in the R factor. However, this represents an improvement in the model only when it is accompanied by a significant reduction in the free R factor (Brünger, 1992[link]). Since the free R factor is itself subject to uncertainty because of the small sample used, a drop of at least 1% is needed to justify anisotropic refinement. The resulting displacement ellipsoids should make chemical sense and not be `non-positive-definite'!

18.9.3.5. Similar geometry and NCS restraints

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When there are several identical chemical moieties in the asymmetric unit, a very effective restraint is to assume that the chemically equivalent 1,2 and 1,3 distances are the same, but unknown. This technique is easy to apply using SHELXL and is often employed for small-molecule structures and, in particular, for oligosaccharides. Similarly, the P—O bond lengths and six O...O distances in all phosphate anions can be assumed to be the same (but without a target value), i.e. it is assumed that the whole crystal is at the same pH. Local noncrystallographic symmetry (NCS) restraints (Usón et al., 1999[link]) may be applied to restrain corresponding 1,4 distances and isotropic displacement parameters to be the same when there are several identical macromolecular domains in the asymmetric unit; usually, the 1,2 and 1,3 distances are restrained to standard values in such cases and so do not require NCS restraints. Such local NCS restraints are more flexible than global NCS constraints and – unlike the latter – do not require the specification of a transformation matrix and mask.

18.9.3.6. Modelling disorder and solvent

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There are many ways of modelling disorder using SHELXL, but for macromolecules the most convenient is to retain the same atom and residue names for the two or more components and assign a different `part number' (analogous to the PDB alternative site flag) to each component. With this technique, no change is required to the input restraints etc. Atoms in the same component will normally have a common occupancy that is assigned to a `free variable'. If there are only two components, the sum of their occupancies can be constrained to be unity; if there are more than two components, the sum of their free variables may be restrained to be unity. Since any linear restraint may be applied to the free variables, they are very flexible, e.g. for modelling complicated disorder. By restraining distances to be equal to a free variable, a standard deviation of the mean distance may be calculated rigorously using full-matrix least-squares algebra.

Babinet's principle is used to define a bulk solvent model with two refinable parameters (Moews & Kretsinger, 1975[link]), and global anisotropic scaling (Usón et al., 1999[link]) may be applied using a parameterization proposed by Parkin et al. (1995)[link]. An auxiliary program, SHELXWAT, allows automatic water divining by iterative least-squares refinement, rejection of waters with high displacement parameters, difference-electron-density calculation, and a peak search for potential water molecules that make at least one good hydrogen bond and no bad contacts; this is a simplified version of the ARP procedure of Lamzin & Wilson (1993)[link].

18.9.3.7. Twinned crystals

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SHELXL provides facilities for refining against data from merohedral, pseudo-merohedral and non-merohedral twins (Herbst-Irmer & Sheldrick, 1998[link]). Refinement against data from merohedrally twinned crystals is particularly straightforward, requiring only the twin law (a 3 × 3 matrix) and starting values for the volume fractions of the twin components. Failure to recognize such twinning not only results in high R factors and poor quality maps, it can also lead to incorrect biochemical conclusions (Luecke et al., 1998[link]). Twinning can often be detected by statistical tests (Yeates & Fam, 1999[link]), and it is probably much more widespread in macromolecular crystals than is generally appreciated!

18.9.4. SHELXPRO – protein interface to SHELX

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The SHELX system includes several auxiliary programs, the most important of which for macromolecular users is SHELXPRO. SHELXPRO provides an interface between SHELXL and other programs commonly used by protein crystallographers. Often, SHELXL will be used only for the final stages of refinement, in which case SHELXPRO is used to generate the name.ins file from a PDB format file, inserting the necessary restraints and other instructions. A corresponding .hkl file may be generated using the programs XPREP (Bruker AXS, Madison, Wisconsin) or MTZ2HKL (Grune, 2008[link]). SHELXPRO is also used to prepare the name.ins file for a new refinement job based on the results of the previous refinement and to prepare data for PDB deposition. In addition, the refinement results can be summarized graphically in the form of PostScript plots.

18.9.5. Distribution and support of SHELX

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The SHELX system is available free to academics and, for a small licence fee, to commercial users. The programs are supplied as Fortran sources and as precompiled versions for widely used operating systems. The programs, examples and extensive documentation may be downloaded from the Internet or (if necessary) supplied on CD ROM. Details of new developments, answers to frequently asked questions, and information about obtaining and installing the programs are available from the SHELX home page, http://shelx.uni-ac.gwdg.de/SHELX/ . The author is always interested to receive reports of problems and suggestions for improving the programs and their documentation by e-mail (gsheldr@shelx.uni-ac.gwdg.de ).

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