1.1. Technical reasons for the difficulty in obtaining and modelling protein-ligand complex structures

1.1.2. Ligand binding is always incomplete

A further complication arises from the fact that the occupancy of the ligand site is a direct function of the binding affinity and ligand concentration. This can be simply derived from the definition of the dissociation constant K_d, which has been illustrated in great detail in this journal (Danley, 2006) and is reviewed in basic textbooks (Rupp, 2009). The simple fact, as illustrated in Fig. 1, is that if a ligand does not have a high binding affinity it will not have full occupancy and therefore even less of its scattering mass will contribute to the global refinement residuals. Similarly, any contributions to the corresponding ligand electron density will be reduced in proportion to the ligand occupancy.

Figure 1 The fraction of occupied receptor sites plotted against ligand equilibrium concentration for three different binding constants. While in the millimolar and lower Kd range small concentrations of ligand suffice to achieve reasonable binding-site occupancy (between 70 and 90%), quite impractical concentrations of ligand in the crystallization drop are required for poor binders. On the other hand, given a sufficiently high concentration, even weakly binding (and non-native) ligands can be forced into a binding site. From Rupp (2009), reproduced with the permission of Garland Science.

The increase of occupancy with increasing ligand concentration, on the other hand, means that anything that is present in the crystallization mother liquor at a high enough concentration, whether a native ligand or not, may partly occupy the binding site. Binding sites have, by nature, evolved to attract ligand moieties, and while specifics assure that in vivo the correct substrate is processed, even remotely similar molecular moieties (i.e. anything from expression host cellular contents to purification buffers to crystallization-cocktail components) can be forced by high concentration into a binding site (and even partly replace or entirely compete out the desired ligand). This can be used to advantage in fragment-based drug lead discovery (Burley, 2004; Hajduk & Greer, 2007), but it also can lead to unexpected ligands such as buffers in the binding site (Gokulan et al., 2005) and, somewhat more insidiously, produce some kind of obscure partial density in the binding site that beckons to be filled with a ligand of desire (Bacon, 1620).

1.2. Primary evidence: electron density

The protein structure model, as interpreted by the crystallographer from the electron density and deposited in the PDB, is in principle nothing more than a listing of the Cartesian coordinates of all located atom positions, including a probabilistic measure (the B factor) indicating the amplitude of the variation in atomic position throughout the crystal lattice (which absorbs all types of contributions). This model is the end result of repeated cycles of model building and refinement, and the electron density is the primary crystallographic evidence for the presence and location of the model atoms. The fit of the model to minimally biased electron density is therefore also the primary indicator of local model quality, including ligands. Various statistical measures exist to quantify and visualize the correspondence between model and electron density, primarily the real-space R value (RSR), the real-space correlation coefficient (RSCC) and difference density measures. These were introduced decades ago (Brändén & Jones, 1990), their usefulness has been repeatedly reiterated (Rupp, 2006) and they are publicly available for deposited PDB structures through the Uppsala Electron Density Server (EDS; Kleywegt et al., 2004). Despite their undisputed practicality for real-space model validation, the RSR and the RSCC have the flaw of not distinguishing between model accuracy and model precision. Newly developed statistical measures for real-space validation (Tickle, 2012) can distinguish between local model accuracy and model precision, which ultimately depends on data quality. Real-space validation scores and other quality indicators have been summarized by Weiss & Einspahr (2011).

The electron density is commonly presented in the form of _A-derived maximum-likelihood (ML) maps (Read, 1986; Pannu & Read, 1996) with Fourier coefficients of the form (2mF_o - DF_c)exp(i) suitable for initial building, and difference density maps of (mF_o - DF_c)exp(i) best suited for model correction. Here, m is the figure of merit (directly related to the mean phase angle uncertainty as m = <cos>, D is the Luzzati factor (Luzzati, 1953) and is the phase angle calculated from the model. The derivation and meaning of the ML coefficients have been summarized, for example, in Rupp (2009).

1.2.1. Proper use of difference electron-density maps

An F_o - F_c-type difference map of a ligand structure that actually contains a ligand will show distinct positive difference density for the omitted ligand, while a difference map calculated with a placed ligand where no ligand exists will show equally distinct negative difference density for the ligand. It is therefore imperative to declare in electron-density figures the type of (difference) density that is being displayed, the contour level, and the procedure through which the electron density was generated. As an example, without specifying the electron density in Fig. 9(a) accurately as negative difference density, it could be interpreted, particularly in a greyscale or black-and-white figure, by a non-expert as a 2mF_o - DF_c map actually demonstrating the presence of the last two (in fact absent) saccharide moieties. Care must be taken not to mistake clear negative difference density indicating an absent ligand for normal 2mF_o - DF_c density or positive difference density.

Alternatively, if an already refined isomorphous apo structure (a target protein without bound ligand) and data for the corresponding ligand-bound structure are available, an F_o - F_o(apo) difference map using model phases from the refined apo structure can be generated. Of importance in this case is that a high level of isomorphism is necessary, in general indicated (but not guaranteed) by a change in unit-cell parameters of only a few percent.

Difference density analysis is meaningful only when (i) either the model contributes to the calculated scattering factors F_c and/or (ii) there is an actual experimental contribution of a ligand to the observed structure factors F_o. If the ligand model does not contribute to F_c and the F_o data do not contain any ligand contribution, then a Fourier synthesis based on the F_o - F_c difference becomes a noise-level subtraction and meaningless (Fig. 2). This is the case with either extreme B factors refined for an absent ligand and/or when using very low (partial) ligand occupancies.

Figure 2 Difference density map results with Fourier coefficients (F1 - F2)exp(i) based on the presence or absence of scattering contributions in the data and/or model. If neither an Fo nor an Fc contribution is present, the difference map becomes meaningless. Interpretable positive omit difference density (i.e. a difference density map calculated from the model with the ligand omitted) is therefore the primary evidence providing distinct proof for the presence of a ligand.

1.3. Prior expectations: ligand geometry and contacts

In a Bayesian model of inductive inference (reviewed, for example, in Rupp, 2009, 2010), the likelihood of a model being correct can be expressed as a joint conditional probability of how well it reproduces the data (e.g. its match to the electron density) and how well it complies with independently acquired prior knowledge about its intrinsic properties (e.g. reasonable stereochemistry). Many ligand models suffer from improbable stereochemistry, largely as a result of improper or incomplete stereochemical restraints (Kleywegt & Harris, 2007; http://eds.bmc.uu.se/eds/valligurl.php ). The observation of improbable conformations often coincides with the absence of restraining electron density or experimental scattering contributions. It is imperative that a ligand has reasonable stereochemistry and makes reasonable contacts to its binding partner, thus providing a strong positive and amplifying prior probability term to the likelihood that the ligand may exist, provided that clear primary evidence in the form of positive omit difference density is also present.

Proper ligand stereochemistry practically always requires correct geometry-restraint files for refinement. Several tools exist to generate proper restraint files such as the Grade Server (Smart et al., 2011), PRODRG (Schüttelkopf & van Aalten, 2004), JLigand (Lebedev et al., 2012) or the PDB Ligand Expo (http://ligand-expo.rcsb.org ), which provides a collection of tools to access ligand structures already in PDB files. For the examination of ligand binding, visualization tools such as LigPlot+ (Laskowski & Swindells, 2011) or the validation tools within the model-building program Coot can be used. The macromolecular program package PHENIX (Adams et al., 2010) provides a module eLBOW (electronic Ligand Builder and Optimization Workbench) for proper restraint-file generation (Moriarty et al., 2009).

1.4. Human factors: the ligands of desire

Basic scientific epistemology requires that a strong claim must be supported by equally convincing specific evidence and that the claim should not violate independently acquired and established prior knowledge (while at the same time, in exceptional cases of extraordinarily powerful evidence, even prior expectations or beliefs are subject to revision). This guiding principle of empirical inductive reasoning, which originally evolved during the Enlightenment in the 15th century (Bacon, 1620), was put into a framework of formal logic about a century later by Bayes (1763). Probabilistic Bayesian models were adopted early on in protein crystallography, ranging from first applications to intensity statistics (French, 1978), to overarching acceptance of a comprehensive probabilistic approach towards protein crystallography (Read, 1986; Bricogne, 1988, 1997; Rupp, 2009) and to many specific applications such as density modification (Terwilliger, 2003) and geometric restraint implementation (Roversi et al., 2000).

A recent educational paper describes the use of a simplified qualitative Bayesian reasoning model allowing practitioners of crystallography to assess their beliefs and expectations against the (sometimes painful) necessity of balancing experimental evidence against desired outcomes (Rupp, 2010). The type of cognitive bias creating the tendency to find what one seeks and to ignore contradictory evidence (or the absence of evidence) is well documented in psychology literature as confirmation bias (see, for example, Koehler, 1993). An additional deep-rooted problem seems to be the resistance to correction of errors, as documented by the persistence of false positives in the scientific literature (Simmons et al., 2011). Once a finding has passed review and is in print (or is in the PDB), it becomes very hard to correct.

The point to reiterate here is very simple: publications of protein-ligand complexes usually carry exciting fundamental information such as elucidating the mechanism of an enzymatic reaction, or they provide high-impact, also commercially valuable, information about drug-target interactions. This potential of significant intellectual and pecuniary rewards carries with it a responsibility to ensure that the asserted claim is sound by providing a valid protein-ligand structure model that is supported by crystallographic evidence; that is, (positive omit) electron density for the ligand.

In the following, we examine how well a small subset of ligand structures fare in view of the necessity for strong experimental evidence.

2.1. The Twilight script

The Twilight script used to identify, extract and rank ligand structures from the PDB is described in detail in an accompanying publication (Weichenberger et al., 2013). Twilight allows the inspection of a sorted list of ligands ranked by real-space correlation (Brändén & Jones, 1990), the addition of comments for each single case analysed, and viewing of the three-dimensional protein-ligand complex and its associated electron-density maps with Coot or through direct links to the EDS (Kleywegt et al., 2004). In addition, journal links, PMID codes and links to the PDBe are provided.

We analysed ligands including covalently bound sugars from glycosylations, but omitted any common buffer or solvent molecules (Weichenberger et al., 2013). The program is freely available for download from http://www.ruppweb.org/twilight/ . We encourage readers to install the tool and examine the evidence themselves in the form of electron density and provide annotations as to their personal preferences. 93 false positives were identified in 1259 ligands distributed in roughly 528 PDB entries. Given the possibility that some of the problematic PDB entries may result from the deposition of incorrect experimental data sets, authors of annotated entries are invited to examine the evidence and to use the opportunity to provide correct experimental data files that reproduce the appropriate ligand density.

2.2. Electron-density map calculations and density figures

If not stated otherwise, in the figures the model obtained directly from the PDB is shown with a 2mF_o - DF_c maximum-likelihood omit map contoured at 1 (blue) plus the corresponding mF_o - DF_c map contoured at +3 (green) and -3 (red). Omit maps were calculated by removing the ligands in question followed by refinement in REFMAC (Murshudov et al., 2011). For the initial ligand inspection, electron-density maps were in most cases downloaded from the EDS (http://eds.bmc.uu.se/eds/ ; Kleywegt et al., 2004). If unavailable via EDS, the map coefficients were calculated from the deposited model and structure factors without refinement but after the inclusion of bulk-solvent correction using REFMAC and were rendered in PyMOL (http://www.pymol.org ). For electron-density inspection 2mF_o - DF_c map levels of 0.8 were used and additional contouring down to noise level was used to detect (or exclude) minor contributions that might justify the proposed ligand poses. In all specific cases discussed below, electron-density maps were calculated using model phases calculated directly from the deposited models. Ligands were omitted from calculations as indicated in the captions.

3.1. Glycosylation sites

Covalently attached sugar moieties are the most common form of post-translational modification of protein molecules. Anecdotal evidence suggests that these decorations impede protein crystallization, thus making structures of glycosylated proteins more difficult to obtain. Positive results with (conformationally homogenous) glycosylations confirm that, on the other hand, they can play a role in the formation of crystal contacts (Garcia et al., 1996; Fusetti et al., 2002). With respect to the refinement of such models, it should be expected that in most cases the sugar moieties will be disordered since they do not generally form extended specific interactions with the protein (except for the covalent linkage) or specific crystal contacts to symmetry mates in the crystal. Hence, there is a great potential that the corresponding electron density will become progressively featureless, decreasing in level and clarity with increasing distance from the linkage site and consequently making the exact placement of an extended single conformation problematic. In addition to such occurrences, where the glycosylation site appears to be disordered to some extent yet present, in a significant number of cases the extended modelled carbohydrate chains were obviously not present and are characterized by an absence of positive omit difference density in the difference density map (Fig. 3).

Figure 3 Missing density: extended glycosylations. The specific conformation of the last three -D-mannose moieties (A5-A7) of the extended branched glycosylation in PDB entry 3ib0 (Mir et al., 2009) is unsupported by electron density in the structure of bovine lactotransferrin, while the first two sugar moieties (A3-A4) are clearly present. The 1.4 Å resolution mFo - DFc map contoured at +3 (green) was calculated after refining a model omitting the sugar moieties of the glycosylation site.

3.2. Lipid and detergent molecules

Given the hydrophobic nature of the transmembrane surface of membrane proteins, lipid/detergent molecules are routinely added to the crystallization medium to make them soluble and to promote crystallization. It is expected that these additives will be present in the crystal structure. Yet, given the lack of specific interactions with the protein, these moieties rarely show completely interpretable electron density. Often only a part of the lipid/detergent molecule reveals any density, yet it is added to the model in its entirety in a random orientation that can be misleading when inspected outside the context of displayed electron density (Fig. 4).

Figure 4 Missing density: detergents. Two examples of detergent molecules placed into models of membrane proteins. (a) The plant SLAC1 anion channel structure, PDB entry 3m73 (Chen et al., 2010), shows two molecules (BOG A317/A318) that have clear density for the hydrophobic acyl chain but not for the head groups. (b) The presence of detergent molecules (BOG A700/A801 is shown) in the crystal structure of the Escherichia coli membrane enzyme glycerol-3-phosphate dehydrogenase, PDB entry 2qcu (Yeh et al., 2008), appears to be entirely unsupported by the electron density. The 1.15 Å (a) and 1.75 Å (b) resolution mFo - DFc maps contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit maps contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

3.3. Partially disordered ligands

A significant fraction of the identified problematic ligand molecules in crystal structures deposited in the PDB appear to have at least some part of the ligand placed in density that is in fact consistent with the chemical structure of the ligand molecule, yet the remainder of the ligand is not supported by electron density (Fig. 5). In some cases there is strong evidence that the problem arises from partial disorder, similar to the cases in which side chains of protein molecules or extended glycosylations appear to be missing in electron density. Ligand molecules may also break into fragments owing to chemical degradation, but crystallographic evidence alone is insufficient to distinguish such cases from partial disorder. Irrespective of the actual cause of the absence of ligand density, presenting the entire ligand molecule in one specific conformation is misleading unless the consumer of the structure has the knowledge and skill to interpret the likely elevated B factors or to directly inspect the electron-density maps. In practice, none of this seems to be routinely performed, thus making it highly desirable that a publicly available database is created that contains a list of ligands in protein structures that require further inspection.

Figure 5 Partially disordered ligand. The fluorescein moiety of the ligand molecule (F6Z A1356) is missing in the electron density of the thyroxine-binding globulin, PDB entry 2xn7 (Qi et al., 2011), even in 0.4 noise-level 2mFo - DFc density. The 1.43 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

3.4. Ligands placed in uninterpretable density likely to originate from mother-liquor components

The vast majority of proteins only crystallize in the presence of a highly concentrated precipitant cocktail. A high concentration of the cryoprotecting agent can be another source of unintended ligands. Consequently, components of the crystallization cocktail are often the source of some electron density that is visible in a known binding site or elsewhere. Occasionally, specific interactions are formed in these sites and the identity of the unexpected ligand is easily revealed (Gokulan et al., 2005). In the case of unexpected ligands that are disordered and appear in or near the predicted target binding sites, it may be rather tempting to place the ligand of interest in an arbitrary or even a plausible pose into such uninterpretable density (Fig. 6). The poor fit may then be explained by invoking the possibility that the ligand binds in multiple conformations, as detailed in §3.3. For instance, in PDB entry 3qd1 (Pyburn et al., 2011) a disaccharide was positioned into difference density that can be readily identified as originating from a HEPES molecule (Yves Muller, personal communication). The resulting misinterpretations and the conclusions drawn from them may make significant portions of the corresponding publications invalid.

Figure 6 Ligands placed into mother-liquor density. In the structure of Bacillus cereus chitinase, PDB entry 3n1a (Hsieh et al., 2010), the cyclo-(L-His-L-Pro) molecule (CHQ A1514) is placed into low-level electron density that is difficult to interpret (a) and which may be plausibly interpreted as an acetate molecule present in the crystallization cocktail at 200 mM supported by a newly formed hydrogen bond between Asp143 and the suggested acetate (b). In the structure of penicillin-binding protein 4 from Staphylococcus aureus, PDB entry 3hun (Navratna et al., 2010), the phenyl moiety of the ampicillin (ZZ7 B501) is placed in a region of the electron density that based on difference density analysis could be better interpreted as a sulfate ion (c). The re-refined model that includes sulfate ion is shown in (d). The 2.0 Å resolution mFo - DFc maps contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit maps contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

In our analysis, we found that a significant fraction of the problematic ligands belonged to the class of misinterpreted crystallization-cocktail components. Naturally, such a classification is somewhat subjective and we used our best judgment to recognize the familiar patterns of common cocktail components in electron density, examples of which include glycerol molecules, sulfate ions, short polyethylene glycol chains etc. (Fig. 6).

3.5. Incorrectly modelled ligands

In a minority of cases, we identified problematic structures in which the correct ligand was inaccurately placed. These cases are easy to correct using modern model-building software (Fig. 7).

Figure 7 Misplaced but correct ligand. In the structure of Streptomyces coelicolor cytochrome P450 158A2, PDB entry 1se6 (Zhao et al., 2005), the MES A632 molecule is correctly identified but is placed in the electron density in an incorrect pose (a), as clearly confirmed by manual rebuilding and real-space refinement in Coot after rotating the buffer molecule by 180° (b). The 1.75 Å resolution mFo - DFc maps contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit maps contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

3.6. Incorrectly identified ligands

Occasionally, the electron density surrounding the ligand was well defined but obviously represented a different ligand. In most cases, this appears to be owing to incorrectly identified components of the crystallization cocktail. Many of these cases constitute incorrect interpretation of the nonspecific interactions with the off-target solute at an off-target site and are thus generally inconsequential to the conclusions derived from the corresponding structures. For the sake of brevity, we do not provide any specific examples here. Readers can readily annotate such entries in the ligand table distributed with Twilight.

3.7. Entirely unjustified ligands

With alarmingly high frequency, ligands appeared to have been placed into the deposited structural models without any justification through evidence in the form of electron density (Fig. 8). Technically, all of the scenarios discussed above in which the ligands are (incorrectly) placed into the electron density may be considered in the same category of unjustified ligands. We separate the cases discussed here because with the possible exception of the deposition of wrong structure factors or incorrect model coordinates (which could and should be easily corrected) one can hardly find any explanation whereby some common and understandable error in electron-density interpretation might have led to these structures. While it is expected that the electron density for some ligand molecules that are either partially occupied, disordered or degraded either chemically or by radiation will be weak and/or imperfect, we find it nearly impossible to justify a model that produces neither 2mF_o - DF_c electron density nor positive omit difference density above the noise level. Disturbingly, in several cases that we present in the next section it is claimed in the corresponding publications that clear electron density was visible in difference maps, often accompanied by a figure presentation.

Figure 8 Absent ligand density in the omit map. In the structure of the Nudix hydrolase DR1025 from Deinococcus radiodurans, PDB entry 1sz3 (Ranatunga et al., 2004), the nonhydrolyzable GDP analogue (GNP 3030A) is placed in a conformation and position entirely unsubstantiated by 2mFo - DFc electron density. The 1.6 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

4.1. Hyaluronate lyases from Streptococcus pneumoniae and S. agalactiae

A series of four articles report the crystal structures of two enzymes in complex with modelled substrates, including disaccharides, tetrasaccharides and hexasaccharides. The first paper describes the structure determination of the complex of the Y408F mutant of S. pneumoniae hyaluronate lyase with tetrasaccharide and hexasaccharide substrates (Jedrzejas et al., 2002). One of the structure models included in this study, namely that of the hexasaccharide complex, shows positive omit difference electron density that largely corresponds to the tetrasaccharide. The authors label the consecutive disaccharides HA1, HA2 and HA3, and there is no electron density supporting the positioning and/or presence of the HA3 unit. Upon subsequent refinement of the model containing the full hexasaccharide, the B factors of the atoms corresponding to the HA3 unit increase to values of higher than 100 Å², while those for HA1/HA2 remain around 30 Å². Combined with the negative difference electron density observed for the HA3 unit (Fig. 9), this leaves no doubt that the hexasaccharide model is erroneous. Nevertheless, a 2F_o - F_c electron-density figure contoured at the 1 level without specification of Fourier coefficients is provided in the publication (Jedrzejas et al., 2002). The hexasaccharide in the deposited model has low B factors, indicating that it has not been properly refined because the absence of electron density for the saccharide moieties 5-6 is not reflected in the expected increase in B factors for these absent parts. The expected significantly higher B factors (100 Å²) are in fact observed upon proper refinement of the complex structure. Saccharide unit 4 shows weak density but is misplaced, while units 5 and 6 show no distinct density (Fig. 9).

Figure 9 Negative difference density. The difference density map from the EDS (a) shows negative density at the -3 level (indicating absence of the model) for saccharide units 5-6 (HA3) in PDB entry 1loh (Jedrzejas et al., 2002). Saccharide unit 4 of HA2 is present but is partly displaced from density owing to the incorrect placement of the subsequent units 5 and 6. Omit maps (b) provide no electron density consistent with placement of the two HA3 units. The 2.0 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

In subsequent work, Nukui and coworkers studied a set of mutations that affect the `hydrophobic patch' which is presumed to be responsible for the positioning of the HA1 unit of the full substrate (Nukui et al., 2003). The mutant enzyme structures (PDB entries 1n7n , 1n7o and 1n7p ) were presented and, apart from some modelling errors affecting remote parts of the molecule, they are correct. In addition, two further structures (PDB entries 1n7q and 1n7r ) are presented of the hexasaccharide complexes with the W291A/W292A and W291A/W292A/F343V mutants. While the similar complex structure described above was only missing the HA3 unit of the substrate molecule, there is no electron density at all in the complex structures 1n7q and 1n7r that would support the presence of any ligand in the active site of the enzyme. Several very basic crystallographic tests consistently lead to this unequivocal conclusion. Specifically, no significant electron density or positive omit difference density can be reconstructed and no significant correlation between observed and calculated model density exists. In addition and as expected, when both purported complex structures (PDB entries 1n7q and 1n7r ) are used to calculate the mF_o - DF_c difference electron-density maps, the entire substrate-molecule density coincides with negative density peaks, indicating the absence of the substrate (cf. Fig. 2). Despite the high B-factor values of the ligand molecules in these models already indicating an absence of meaningful density, negative difference density is still observed at levels that are significantly higher than expected for a ligand that actually contributes to the observed structure factors. Upon refinement, the B factors of the hexasaccharide molecules (130 Å²) substantially exceed those of the surrounding protein atoms (35 Å²). In fact, this difference is also present in the deposited models (although it is smaller: 110 versus 50 Å²). When the hexasaccharide is removed from the model and the enzyme model is refined, the resulting electron-density maps contain no discernible positive difference density indicative of the ligand (Fig. 10). In agreement with vanishing real-space correlation, bias-minimized electron-density maps reveal no ligand density. Consistent with this observation, the original publication provided no electron-density figure.

Figure 10 Missing ligand density, ligand omit map. The active site of S. pneumoniae hyaluronate lyase shows no meaningful density for the entire hexasaccharide molecule in the structure (PDB entry 1n7q ; Nukui et al., 2003). Disaccharide unit labels are consistent with the original publication. The 2.3 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

Another earlier paper published by the same group describes hyaluronate lyase from S. agalactiae (Li & Jedrzejas, 2001). This protein is 50% sequence identical to the S. pneumoniae ortholog and it is therefore not surprising that the structural models are also similar. Given the high degree of similarity between the two proteins, the authors anticipated corresponding similarity of the catalytic mechanism. To verify the role of the corresponding residues and regions of the structure, the disaccharide-complex structure (PDB entry 1i8q ) is presented. The structure of the protein part of the model alone (PDB entry 1f1s ) appears to be refined correctly in general, except for a few disordered loops. It is claimed that two product molecules were found in the electron density. We have recalculated the electron density consistent with the EDS density using the deposited structure and experimental data with the disaccharide molecules removed. No significant positive density is observed beyond solvent within the active site to justify the placement of these molecules. With the disaccharides placed in their reported positions, despite the corresponding B factors (110 Å² upon refinement) being much higher than the surrounding atoms (30 Å²) and indicating the absence of significant model density contributions, negative density peaks are still observed in the difference map, while the omit maps show no evidence that the ligand molecules are present (Fig. 11).

Figure 11 Missing ligands. Two disaccharide molecules in the structure of hyaluronate lyase from S. agalactiae (PDB entry 1i8q ; Li & Jedrzejas, 2001) are not supported by the omit electron-density maps. The 2.2 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

The conclusions provided in Li & Jedrzejas (2001) are based exclusively on the purported complex structure 1i8q . Given the absence of the saccharide, the conclusions are unsubstantiated extrapolations from what is known about the S. pneumoniae homolog and are unsupported by crystallographic evidence. In the paper, a figure of a 2F_o - F_c electron density without an indication of levels or specification of Fourier coefficients is provided. We were unable to reproduce this figure.

This work was further extended in a subsequent publication (Mello et al., 2002). Here, the authors present the structure of the hyaluronate lyase complex with the hexasaccharide (PDB entry 1lxm ), followed by a discussion of the role played by different regions of the enzyme and modelling of its dynamics. Similar to the case of the S. pneumoniae homolog, structural findings supposedly explain the specific details of how the enzyme achieves the processivity of the substrate degradation.

The problems that we have found with the experimental data in this case are identical to all the other examples and are dramatic. If the hexasaccharide molecule is removed from the model (PDB entry 1lxm ), the recalculated electron density shows a completely empty active site. With the substrate in place, negative density is observed in the difference map (Fig. 12) and the B factors of the substrate molecule (135 Å²) significantly exceed those of the surrounding atoms (30 Å²) (this is also evident from the statistics table included in the paper, although the B factors of the ligand are somewhat lower at 100 Å²). We thus conclude that the experimental data in this case once again do not support the presence of any hexasaccharide molecule in the active site. No electron-density figure is provided in Li & Jedrzejas (2001), consistent with the experimental evidence of low real-space correlation and high B factors.

Figure 12 Absent ligands. The active site of hyaluronate lyase from S. agalactiae, PDB entry 1lxm (Mello et al., 2002), does not contain the electron density needed to justify the presence of the hexasaccharide ligand. (a) shows difference density from the EDS contoured at -2, coinciding with the location of the ligand in the deposited model. (b) shows the omit maps and no electron density is observed that would allow ligand placement. (b) shows the 2.2 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue). Maps were calculated for a refined model with the ligand atoms omitted.

Curiously, the structure presented in the paper is that of the wild-type enzyme and not an enzymatically inactive mutant. The authors do not discuss the fact that it would therefore be expected that upon long incubation the substrate would have been digested, even considering the reduced activity of the enzyme in the crystalline form.

4.2. Protein-ligand complex structures with unjustified ligands

The examples of problematic ligands in the crystal structures described below all share the same set of features. Namely, (i) no electron density is found in the (2mF_o - DF_c) maps that would justify the ligand placement, (ii) when the derivative model with ligands excluded is subjected to refinement no interpretable positive difference electron density is found in the (mF_o - DF_c) omit maps and, finally, (iii) when the ligands in the original locations are re-refined their B factors increase to levels that are incompatible with the surrounding protein atoms. In the cases where the deposited models do have B factors of ligand atoms that match the surrounding protein, there is distinct negative difference electron density overlapping with ligands in the maps calculated from the deposited models without modification. All of these observations indicate a lack of experimental evidence for the proposed ligands. What the presented examples have in common is that they originate from the same laboratory. We clearly cannot specifically address what may have led to the erroneous models. Possible explanations are consistent erroneous deposition of incorrect structure factors and/or incorrect structure models. Given the evidence, one cannot exclude the possibility of a pattern of flawed methodological approaches routinely used by the researchers working at the laboratory in question.

4.2.1. `The structural basis for the prevention of nonsteroidal anti-inflammatory drug-induced gastrointestinal tract damage by the C-lobe of bovine colostrum lactoferrin'

In this paper (Mir et al., 2009), the authors described four crystal structures of bovine lactoferrin determined using crystals prepared from samples that contained four different nonsteroidal anti-inflammatory drugs (NSAIDs). The authors inferred the binding constants from tryptophan fluorescence quenching and found apparent binding affinities in the submillimolar range. They further report that for four NSAIDs they observe `reasonably characteristic electron densities at the ligand binding sites'. This finding is directly contradicted by the electron-density maps produced by the EDS and our own calculations (Fig. 13). In fact, only the complex with indomethacin shows any electron density at all near the reported ligand-binding site, yet this density is uninterpretable. Even assuming that this density can be attributed to the ligand, it only covers part of the indomethacin molecule and hence placing the latter in the structure is problematic (there is also no density above the 3 level in the difference omit map). Only the aspirin molecule has relatively low B factors as deposited; the model however overlaps with negative difference density, confirming its potential status as an artifact.

Figure 13 Absent ligands. Four protein-ligand complex structures presented in Mir et al. (2009) include ligands that are not supported by electron density. All panels show the omit maps for complex structures with the following ligands: (a) indomethacin (PDB entry 3ib1 ), (b) diclofenac (PDB entry 3ib0 ), (c) aspirin (PDB entry 3iaz ) and (d) -methyl-4-(2-methylpropyl)benzeneacetic acid (PDB entry 3ib2 ). The 2.2 Å (a), 1.4 Å (b), 2.0 Å (c) and 2.29 Å (d) resolution mFo - DFc maps contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit maps contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

4.2.2. `Polysaccharide binding sites in hyaluronate lyase - crystal structures of native phage-encoded hyaluronate lyase and its complexes with ascorbic acid and lactose'

Mishra and coworkers presented the crystal structures of hyalouronate lyase from Streptococcus pyogenes in its apo form and in complex with lactose and ascorbic acid (Mishra et al., 2009). These crystal structures were determined at a resolution of 3 Å, which in itself makes the reliable identification of a small-molecule ligand difficult. At the time of writing, the experimental data were available only for the ascorbic acid complex; therefore, we cannot evaluate the validity of the complex with lactose. As far as the complex with ascorbic acid is concerned, the placement of the ligand does not appear to be justified by the experimental data (Fig. 14).

Figure 14 Absent ligand. The ascorbic acid molecule as placed in the structure of hyalouronate lyase from S. pyogenes, PDB entry 3eka (Mishra et al., 2009), is unsubstantiated by the difference omit map. The 3.1 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

4.2.3. `Carbohydrate-binding properties of goat secretory glycoprotein (SPG-40) and its functional implications: structures of the native glycoprotein and its four complexes with chitin-like oligosaccharides'

Kumar and coworkers presented structures of SPG-40 in complex with four oligosaccharides of different lengths (Kumar et al., 2007). The authors reported that the `ligands were included only when they were well defined by unbiased |F_o - F_c| maps'. This is not confirmed by the electron-density maps calculated with oligosaccharides excluded from the model (Fig. 15). Only in the pentasaccharide complex is there a continuous electron density that appears to cover three of the five sugars of the ligand, although this particular structure was determined at a significantly lower resolution (2.9 Å) than the others (2.1-2.5 Å).

Figure 15 Absent oligosaccharides. The omit maps of the four oligosaccharides from Kumar et al. (2007) are shown for the protein complexed with the following oligosaccharides: (a) trisaccharide (PDB entry 2dt0 ), (b) tetrasaccharide (PDB entry 2dt1 ), (c) pentasaccharide (PDB entry 2dt2 ) and (d) hexasaccharide (PDB entry 2dt3 ). The 2.45 Å (a), 2.09 Å (b), 2.9 Å (c) and 2.28 Å (d) resolution mFo - DFc maps contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit maps contoured at 1 (blue) are shown. Maps were calculated for a refined model with the ligand atoms omitted.

4.2.4. `Design of specific peptide inhibitors of phospholipase A₂: structure of a complex formed between Russell's viper phospholipase A₂ and a designed peptide Leu-Ala-Ile-Tyr-Ser (LAIYS)'

In this paper, Chandra and coworkers presented the structure of Russell's viper phospholipase A₂ in complex with an inhibitory pentapeptide (Chandra et al., 2002). The presence of the ligand is not supported by the experimental data (Fig. 16), although in this case some density is present that is clearly interpretable as discrete water molecules. Curiously, the authors report this interpretation for the second protein molecule present in the asymmetric unit.

Figure 16 Absent inhibitor: the peptide inhibitor in the structure of phospholipase A2 (PDB entry 1jq8 ; Chandra et al., 2002). The electron-density maps downloaded from the EDS show that the placed ligand overlaps with negative difference density below the -3 level (a), while the omit maps do not support the presence of the ligand in the active site of the enzyme (b). (b) shows the 2.0 Å resolution mFo - DFc map contoured at ±3 (green/red) and 2mFo - DFc maximum-likelihood omit map contoured at 1 (blue). Maps were calculated for a refined model with the ligand atoms omitted.

5.1. Proof positive: omit difference density

The proposition that a ligand in a complex structure is in a specific position and exhibits a unique conformation (i.e. is present in a specific pose) is a very strong and powerful statement, and accepted scientific epistemology requires that strong claims are backed by correspondingly strong evidence. It is quite acceptable that the authors of a structural model are free to interpret the electron density derived from the experimental data to their liking, yet consistency with the experimental data is expected. Necessary self-imposed limits include an expectation that most experts would concur with the proposed interpretation. Some of the examples that we have presented in §3 and §4 included deposited structural models in which the ligand molecules (i) have severalfold higher B factors, sometimes combined with partial occupancy, than surrounding protein atoms, (ii) do not correlate with the (2mF_o - DF_c) electron-density map or (iii) do not coincide with any significant electron density in (mF_o - DF_c) difference density maps calculated from the models with the ligand removed, i.e. show no positive omit difference density. In our judgment, clear positive omit difference density (preferably supported by a properly annotated figure stating the exact type of Fourier coefficients used and density levels) would be the minimum requirement to justify ligand placement based on experimental crystallographic data. Very high B factors and low partial occupancies, particularly when combined, in general do not provide sufficient scattering contributions (cf. §1.1), so that a convincing positive difference density cannot be calculated. Problems of structures with entirely absent ligand density (as presented in §4.2) could be easily prevented by simple map inspection, even by a non-expert.

In cases where ligands contain heavier atoms, anomalous difference data can provide clues towards their identification and evidence for their presence. While this is quite obvious for ligands that contain phosphate moieties or metal ions, an educational example of identification of the S atom in HEPES buffer by means of anomalous difference Fourier density is provided in a publicly available tutorial collection (Faust et al., 2008).

5.2. Overinterpretation and missing parts

A large pool of examples consist of ligand molecules resulting from, in our opinion, overly enthusiastic interpretation of the underlying experimental data. Given the importance of ligand placement in a protein-ligand complex for the purposes of `biological interpretation', it appears to be unacceptable to place a ligand of interest into any blob of density that is not protein. It cannot be overemphasized that the vast majority of consumers of crystal structures still remain unacquainted with the methods of macromolecular crystallography and therefore consider deposited structural models to be akin to factual truth written in stone. Hence, a crystallographer must be careful not to include questionable or projected elements of a crystal structure. In the absence of a community consensus or better methods of stating positional uncertainty, the exclusion of model parts that cannot be verified by electron density seems to be preferable over random guesses. It should be remembered that in contrast to (hopefully past) reviewers' opinion, the absence of density is not a sign of a lack of crystallographic ability on the part of the investigator but is inherent to the underlying properties of the material and the nature of the method.

In the case of a protein model with disordered side chains, one knows that the side chain has to be somewhere but that it is probably split over multiple conformations that could conceivably be populated with occupancies (with their sum constrained to 1.0) according to empirical distributions of the possible conformers. This is not as simple in most ligands, because owing to the lack of covalent bonds to the protein occupancies lower than 1.0 are the norm rather than the exception (cf. §1.1) and often literally hundreds of poses (conformations and locations) in a binding site are more or less plausible a priori, as also shown in virtual ligand screening (An et al., 2005). There may in fact not be a unique pose in a given crystal structure, which is a likely reason for poorly defined density or density where only certain parts of a ligand or, with luck, one or two major conformations are present. Unfortunately, the scattering contributions decrease with lower occupancy, and if additional positional uncertainty for whatever reason contributes to high B factors, no clear and unambiguous density can be observed out of principle. Again, it is not the absence of clear density that blames the crystallographer, but the desire to model what one fancies.

One possibility to reconcile the fact of indetermination with the often expressed concern that providing incomplete models (e.g. by excluding disordered side chains) may be just as misleading could be the establishment of the practice of depositing two types of models. One would be a minimalistic model that only includes the elements firmly supported by the underlying electron density. The secondary model would be just that: a model reflecting the opinion of the researcher as to where the disordered side chains are and which blobs of density may be interpreted as a glimpse of disordered and/or partially occupied ligand sites. It is important to emphasize that difficult-to-interpret electron density should not always be discarded, since it may contain important information, but presenting it in a structural model that noncrystallographers and crystallographers alike will tend to interpret as a hard fact seems to be misleading at best.

5.3. Improved review and validation

It is our hope that in the long term better teaching and training, as outlined in the next paragraph, will reduce the occurrence of overinterpreted ligand structures. In the immediate future, it is only through more competent and better enabled review and validation that this problem can be addressed. We see no technical reason why the PDB or another independent and trusted organization could not provide a tool similar to our Twilight script (Weichenberger et al., 2013), allowing confidential analysis as soon as a structure is deposited in the PDB. Almost all respectable journals already demand the deposition of coordinates with the PDB, and since February 2008 deposition of the associated structure factors in the PDB has also been mandatory. Journal editors could give reviewers (or themselves) confidential access codes to pre-computed electron densities, which would allow even nonspecialists to reach a judgment as to whether or not the electron density supports the ligand pose. We therefore have provided in the Twilight distribution a simple review script that allows any PDB entry with EDS density to be fetched (after the provision of an at this point inactive password). The review script automatically displays the electron density and model beginning with the first bona fide ligand, as summarized in §2 and detailed in Weichenberger et al. (2013).

In addition, having structure entries reviewed for technical accuracy by an independent technical reviewer or body disinvested in their biological importance might likewise be feasible. We also wish to point out that the PDB policy that allows structure factors to be put on hold for longer than coordinate entries should be reconsidered. Suppression of primary evidence is inherently unscientific.

Validation and further review of small-molecular-weight ligands in protein crystal structures may be greatly facilitated if the wwPDB required the deposition of the dictionaries used, corrected atom names where possible, checked these against expected chemistry and returned a report to the depositor as part of the deposition screening. It is also important that these dictionaries are part of the deposition and should be retrieved by anyone who wishes to download the structure.

5.4. Training and teaching

Another significant concern lies with the ever-diminishing training requirements in biomolecular crystallography. We are not proposing that the structural scientists of today spend years learning every intricate detail of the technique before being allowed to deposit their first structure in the PDB. It is difficult to gauge how widespread cases are in which a young researcher is directed to perform protein crystallography without receiving adequate training and expert advice. However, we extrapolate from personal experience and through informal polling that the number of cases resulting from poor supervision by busy and result-oriented principal investigators may not be small. It is undeniable that with the ever-increasing number of structural studies performed today, and with the progressively increasing number of crystal structures deposited in the PDB, delivery of proper training is absolutely necessary to assure that the technique retains its trustworthy status. Efforts at remediation of the deposited crystal structures and quality control from the crystallographic community at large may be helpful, but to reduce errors in the first place by better training seems to be a more desirable long-term solution. The necessary teaching material including data and documented exercises are certainly available, for example, at http://www.helmholtz-berlin.de/bessy-mx-tutorial/ (Faust et al., 2008).

One concerning observation made by the authors during recent poster-viewing sessions at crystallography conferences and structural biology meetings is that only few protein-ligand structure posters do actually show any electron-density figure in support of the ligand pose. This clearly seems to indicate that no emphasis is put on primary evidence, again pointing towards neglect of adequate training and expert advice. Despite all the diagnostics and validation tools available during model building, model refinement, and ultimately upon PDB deposition, one needs to realise and to impress that not the PDB but the individual crystallographer bears the final (and sometimes far-reaching; Petsko, 2007) responsibility for the correctness of the deposited model.