PDB_REDO: constructive validation, more than just looking for errors
Developments of the PDB_REDO procedure that combine re-refinement and rebuilding within a unique decision-making framework to improve structures in the PDB are presented. PDB_REDO uses a variety of existing and custom-built software modules to choose an optimal refinement protocol (e.g. anisotropic, isotropic or overall B-factor refinement, TLS model) and to optimize the geometry versus data-refinement weights. Next, it proceeds to rebuild side chains and peptide planes before a final optimization round. PDB_REDO works fully automatically without the need for intervention by a crystallographic expert. The pipeline was tested on 12 000 PDB entries and the great majority of the test cases improved both in terms of crystallographic criteria such as Rfree and in terms of widely accepted geometric validation criteria. It is concluded that PDB_REDO is useful to update the otherwise `static' structures in the PDB to modern crystallographic standards. The publically available PDB_REDO database provides better model statistics and contributes to better refinement and validation targets.
A crystallographic experiment and the ensuing process of phasing, model building and refinement (hopefully) culminates in a three-dimensional structure model that fits both the experimental X-ray data and our prior knowledge of macromolecular chemistry. Validation helps to guide this process and enables crystallographers to produce high-quality structure models suitable for biological interpretation. Validation software routines have been available since the early 1990s (Laskowski et al., 1993; Hooft et al., 1996; Davis et al., 2004). These check many aspects of crystallographic (or other) structures, typically with a strong focus on macromolecules and specifically on proteins. Validation of nucleic acid structures is also available, for example in MolProbity (Chen et al., 2010; Richardson et al., 2008). Validation software for other chemical entities is available as well, e.g. PDB-care (Lütteke & von der Lieth, 2004) for carbohydrates and WASP (Nayal & Di Cera, 1996) for metal ions. Various validation tools are also available directly through graphical model-building software such as O (Jones et al., 1991) and Coot (Emsley & Cowtan, 2004; Emsley et al. 2010).
While finalizing a crystallographic structure, validation can be used constructively to detect anomalies in the model and the crystallographer can either remove the anomaly or confirm that it is real, i.e. by assuring that there is sufficient (experimental) evidence for a model with this anomaly. This process has many complications. For example, large overall bond-length deviations typically arise from wrong or erroneous restraint settings; however, they can also be the result of errors in the experimental determination of unit-cell parameters and should not be resolved by tightening the restraints but rather by updating the unit-cell parameters.
Most validation tools focus on the identification of outliers: residues which are, based on statistical measures of our growing empirical knowledge of macromolecular structure, not similar to other residues in known structures. Focusing on outliers is sensible because these residues are most likely to be either interesting or wrongly modelled, but it takes away attention from the rest of the model. This becomes a problem when the absence of outliers is seen as a confirmation that the model is optimal. Side-chain rotamers are a good example: having no (or few) outliers does not mean all the rotamers are optimal with respect to the experimental data.
After a crystallographic structure has been finalized, deposited in the PDB and released, the atomic coordinates are set in stone. The Protein Data Bank (Bernstein et al., 1977; Berman et al., 2003) is a historical archive and does not change the atomic coordinates, although their annotation may be updated (Henrick et al., 2008) to deal with the changing needs of depositors and users. The static nature of structure models in the PDB has many implications. The obvious consequence is that models that are several decades old often lack the accuracy and precision that modern crystallographic software offers, while they also lack the benefit of constructive validation which was either lacking or less `mature' at the time these older models were constructed. This way, the users of the PDB often have access to models that are suboptimal by modern-day criteria. In addition, a less obvious consequence is that even when a user validates an existing PDB entry or uses ready-made validation reports as provided by, for example, the PDBREPORT data bank (Hooft et al., 1996; Joosten, te Beek et al., 2011), validation is no longer constructive: any anomalies found do not lead to an improved structure model because most PDB users do not have the crystallographic expertise to make the structure better before using it. In this context, validation may lead to the outright rejection of a structure model when an alternative with better validation results is available. This situation not only affects the older models in the PDB, which were accumulating at a slower pace (more crystallographic structures have entered the PDB in the last three years alone than in its first thirty years): a model submitted now will simply be an old model in a few years time, as crystallographic methods are still improving at an appreciable pace.
To keep PDB models up to date, we decided to apply some of the latest crystallographic methods to all PDB entries for which experimental X-ray data are available (Joosten, Salzemann et al., 2009) and created the PDB_REDO software pipeline that takes atom coordinates and X-ray data from the PDB and re-refines the structure model in REFMAC (Murshudov et al., 1997, 2011). A strong focus was placed on automation in order to deal with the tens of thousands of PDB entries, which meant dealing with the problems the PDB still had (at the time) with inconsistent annotation of coordinate and reflection files. The most important strength of automation is that it allowed us to optimize the weight between the X-ray data and the geometric restraints, something that is a lot of work to do by hand even for a single structure model. In our re-refinement we consistently used TLS models for anisotropic atom movement (Schomaker & Trueblood, 1968; Winn et al., 2001), which has only recently been made accessible to macromolecular crystallography, thus using the latest developments in refinement for all PDB entries. The resulting structure models showed an improvement in terms of Rfree (Brünger, 1992), and model validation showed a substantial improvement in overall model-quality estimators such as the Ramachandran plot (Ramachandran et al., 1963) Z score, which compares the combination of backbone torsion angles for each residue with a residue-type and secondary-structure specific distribution in high-quality protein structure models (Hooft et al., 1997), and the number of atomic clashes or bumps. A notable result was that very recent PDB entries also improved, although in most cases the improvement was not as great or as common as in older PDB entries.
Making the improved structure models available to the PDB user community through the PDB_REDO data bank (Joosten & Vriend, 2007) was an initial step towards a constructive form of structure validation of deposited structure models. However, it was clear that local fitting errors and other problems in structure models could not be resolved by the approach we used (Joosten, Womack et al., 2009). A much more comprehensive approach that incorporates real-space model rebuilding was needed.
Algorithms for real-space fitting and rebuilding parts of the structure model have existed for decades (Diamond, 1971; Jones, 1978). The problem lies in deciding how they should be applied and where in the structure. The typical approach has been to manually update the structure model using molecular graphics, with a validation report to hand. The program OOPS (Kleywegt & Jones, 1996) provided a significant speed-up of this process by automating the where part of the problem: it used validation results from O (Jones et al., 1991) and WHAT_CHECK (Hooft et al., 1996) and turned them into a `macro' for O that takes a user through the flagged parts of the structure model automatically. Similar implementations are available to interface MolProbity (Chen et al., 2010) with Coot (Emsley et al., 2010). Solving the how part of the problem still remains a challenge in structure validation: finding an anomaly is often easier than understanding what caused it.
We recently described two programs (pepflip and SideAide) that rebuild structure models using a strategy that incorporates both the where and the how in a single decision-making framework (Joosten, Joosten et al., 2011). Instead of improving crystallographic structures just by rebuilding the parts of the model flagged by validation routines, the main chain and side chain of every residue is rebuilt and validated; if rebuilding leads to an improved fit to the crystallographic maps, then the model is updated with the new conformation. Instead of specifically looking for errors, this approach focuses on improvable features of the structure model and therefore has much greater coverage of the structure model than validation-based methods. The algorithms are fully automated and not particularly computationally intensive, enabling us to incorporate them in the PDB_REDO pipeline.
The main challenge in automation lies in decision making. Decisions, and the priority they are given, are often taken based on statistic measures, but also on personal preference, experience or gut feeling, or even on dogmatic principles. Many decisions are taken without even realising it, e.g. by applying default values to many parameters. Fully automated software pipelines need to formalize all these decisions to a closed set of rules. Here, we discuss PDB_REDO as a decision-making framework, showing the choices we face and how we resolved them, and also present an extensive test on 12 000 PDB entries.
The different model-quality metrics used in the decision-making process of model optimization are described in Table 1. The software programs used in the procedure are discussed in the text and summarized in Table 2.
‡Calculated by REFMAC before refinement.
§Calculated during TLS refinement in REFMAC directly after resetting the B factors.
¶Used as a cutoff value for picker.
††Complex refers to the model with the most (B-factor-related) parameters and simple to the model with fewest.
‡‡Calculated by REFMAC after the final refinement.
§§The terms are swapped to compensate for the `lower-is-better' nature of Rfree.
¶¶Calculated by WHAT_CHECK for the input PDB file.
†††Calculated by WHAT_CHECK for the final model.
The PDB_REDO software pipeline uses the PDB file with the deposited crystallographic structure coordinates and the associated reflection file containing the X-ray diffraction data.
The reflection file is standardized with Cif2cif (Joosten, Salzemann et al., 2009), which writes out Miller indices and amplitudes (or intensities if amplitudes are not given) for each reflection. σ values and Rfree-set flags are written out if available. Only the first data set in the reflection file is used. Some basic sanity tests are performed as follows.
The PDB file is parsed with Extractor to extract cell dimensions, space group, waters and special residues that are involved in chemical interactions (as marked in LINK records in the PDB header). Parameters about refinement are also extracted at this stage: the R factor and the Rfree from the PDB header (Rhead, Rfree,head), TLS-group selections and tensors, and the type of solvent model. The following records are removed from the PDB file by the program Stripper, mostly to ensure proper restraint generation for refinement: explicit H atoms, atoms with occupancy < 0.01, superfluous O atoms in carbohydrates, if detected by PDB-care, unknown ligands (UNLs), side-chain atoms beyond Cβ for unknown residues (UNKs), inter-symmetry LINK and SSBOND records, fields containing atomic distances in LINK records, unknown atoms (UNXs) and any other atoms of element X since no scattering factors can be assigned.
The original structure is validated using WHAT_CHECK. REFMAC is then used (without any refinement) to calculate Rcalc and Rfree,calc in five steps.
To get the most out of refinement in REFMAC, many parameters should be optimized. In the original PDB_REDO pipeline we only optimized the geometric restraint weight. Despite the presence of a robust and reliable option to automatically weight X-ray data and geometry in newer versions of REFMAC, we find that our search method can have advantages. We use the geometry-weight optimization and also systematically explore the usage of many other refinement strategies, as follows.
Our previous PDB_REDO results showed that re-refinement could benefit from making the search space for the geometric restraint weight resolution-dependent. We have performed this by assigning each input model to one of six different categories (Table 3) based on the resolution of the data and the number of X-ray reflections per atom. The latter is important because at a given data resolution the number of reflections per atom varies greatly depending on the solvent content: for example, at 3.0 Å resolution values of between 1.9 and 7.8 reflections per atom are observed. In addition to assigning the geometric restraint-weight search space, the `resolution' categories are also used for determining the B-factor restraint-weight search space and the application of `jelly-body' restraints (Murshudov et al., 2011), which we use to stabilize the re-refinement of structures belonging to the two lowest resolution categories (`vlow' and `xlow').
‡In these categories only resolution cutoffs are used.
The re-refinement results in a structure model with new (difference) electron-density maps. These maps are used to rebuild the structure model in four steps.
The rebuilt model is refined in REFMAC one last time. The TLS model (if used) is updated, followed by restrained refinement with the previously established refinement parameters but with three different geometric restraint weights: the optimal weight from the re-refinement, a slightly tighter restraint weight and a slightly looser one. The final model is selected using the same selection algorithm as used in the re-refinement.
The final model is validated with WHAT_CHECK. The validation scores and the R and Rfree values are combined to give a web page for the PDB_REDO data bank and an unformatted file that can be used for data mining. Three-dimensional scenes are created that show the model atoms coloured by atomic movement, with warmer colours marking increasing atomic shifts with respect to the original structure model (Fig. 1), and the model atoms coloured by TLS group. The scenes can be visualized in the free viewer version of YASARA (Krieger et al., 2002). A plug-in for Coot (Emsley et al., 2010) is available to download and visualize PDB_REDO optimized structure models and their electron-density maps.
To be able to apply the PDB_REDO pipeline to the entire PDB, it was necessary to create decision-making algorithms that can deal with the many choices available when optimizing structure models without supervision or user input. Here, we show the result of our developments in the five main decision-making algorithms.
The introduction of the Rfree metric (Brünger, 1992) was an important step in macromolecular crystallography as it helped to detect overfitting and overrefinement of the model. However, until the mid-1990s many structures were refined without using Rfree. Properly dealing with Rfree sets is therefore essential for structure-model optimization; PDB_REDO deals with Rfree sets using the following procedure.
The atomic displacement factors, commonly referred to as B factors, can be parameterized to represent various levels of detail: anisotropic B factors require nine parameters per atom, isotropic B factors four and a single B factor for all atoms only three. In PDB_REDO we assign the type of B-factor model based on the number of X-ray reflections per atom (RPA) using the following successive criteria.
2.2.3. Selecting the number of refinement cycles
A large number of REFMAC refinement runs are performed to try different parameters; thus, the number of internal refinement cycles becomes an important contributor to the time needed to optimize a model. Based on our experience with REFMAC, we use a set of empirical rules to assign the number of refinement cycles.
2.2.4. Selection of the optimal model from a set of refinement results
The TLS-model optimization, B-factor restraint-weight optimization, re-refinement and final refinement require the selection of the best model from a set of refinement results. The program picker selects the model with the best fit to the experimental data while minimizing the risk of overrefinement. To do this, the quality of the starting structure is also taken into account. Picker uses the following procedure.
The first three steps of rebuilding are meant to be comprehensive, so by default all residues are considered. Negative selection is applied to `special' residues for which automated unsupervised rebuilding is too risky or not needed.WHAT_CHECK validation report. However, the negative selectors above still apply.
We attempted to optimize all of the PDB entries with deposited X-ray diffraction data (>53 000) for inclusion in the PDB_REDO data bank. Fewer than 900 PDB entries (<2%) cannot be used at the moment owing to various problems. The reasons for these missing entries are listed in the WHY_NOT data-bank annotation server (Joosten, te Beek et al., 2011). Some of the reasons for the exclusion of structures from the PDB_REDO data bank are as follows.
The new PDB_REDO pipeline was tested with our evaluation data set of 12 000 PDB entries. Table 4 shows a summary of structure-quality metrics for the data set in the original PDB entry, the re-refined structure model and the final re-refined and rebuilt structure model. On average the improvement in Rfree was 1.8%, corresponding to a significant relative improvement of 6.4σ(Rfree). A total of over 70 000 unsatisfied hydrogen-bond donors or acceptors and more than 310 000 atomic bumps were removed. Over 200 000 erroneous water molecules were removed and 57 000 previously missing side chains were built in total. On average, only a single peptide flip was needed in every second model (still accounting for about 7000 wrongly modelled peptides in total). The least common fix of those attempted was explicit chirality fixes of threonine, valine and isoleucine Cβ atoms and leucine Cγ atoms, which were applied only 12 times in the entire data set.
‡Model-normality Z scores from WHAT_CHECK with respect to a test set of 500+ high-resolution structure models. Higher values are better.
To obtain a better perspective on the performance of PDB_REDO on individual PDB entries, we made `traffic-light' diagrams for the structure-quality metrics (Fig. 2). Each diagram shows the percentage of structure models that became better, stayed the same or became worse after re-refinement and rebuilding, according to different metrics. Depending on the metric used, 31–75% of the models improved on re-refinement and 45–86% of the models improved on full optimization including rebuilding. The greatest improvements are found in Rfree and in the side-chain rotamer and Ramachandran plot Z scores (Hooft et al., 1997). The first two are explicitly optimized and such a result would be expected. However, the Ramachandran plot improvement is an independent metric and its improvement is particularly encouraging. The typical distribution of backbone torsion angles in the Ramachandran plot is brought on by steric hindrance; thus, the improvement of the Ramachandran plot Z score is very likely to be the result of using riding H atoms and tight van der Waals restraints in the refinement, which enforce proper steric hindrance. The change in the Ramachandran plot Z score strongly depends on resolution (Fig. 3), with PDB_REDO having a stronger impact at resolutions lower than 2.0 Å. This is partly a natural consequence of the original distribution in Z scores (there is more room for improvement at lower resolution), but the riding H atoms might also play an important role, since it was (and still is) common practice to not use riding H atoms in lower resolution refinement. This practice is particularly strange considering that riding H atoms add no extra parameters to the refinement, but do add extra restraints or, from an alternative perspective, make already existing van de Waals restraints more effective. This leads to an improvement of the effective data-to-parameter ratio, which is especially important at low resolution.
The PDB_REDO pipeline now contains partial model rebuilding and not only re-refinement as in its first implementation. The added value of rebuilding, in combination with a second round of refinement, is made apparent by comparing the distributions in the re-refined and final structure models. In most cases, the rebuilding and extra refinement increases the fraction of models that improve. Interestingly, however, the new steps also increase the fraction of models that become worse according to some of the criteria: this is most evident for Rfree and the number of atomic bumps (an additional 6% of all models became worse according to these criteria).
For the case of Rfree, there is however a rather simple explanation. If after the first re-refinement PDB_REDO fails to find optimal refinement settings, the model is still rebuilt and refined with automatic geometric restraint weighting. This is likely to explain why the percentage of models with worse Rfree increases in the re-refined and rebuilt set of models. Indeed, for 72% of the models that end up with a worse Rfree, we had failed to find a good re-refinement setting in the first place. This is in sharp contrast to the 11% we find in all test cases (incidentally, this is an enormous improvement over the 33% in the first version of PDB_REDO). The difference that successful re-refinement makes is made clear in Fig. 4. In the cases where re-refinement succeeds, all but five structures end up with better free R factors at the end. In the cases where re-refinement fails, even if Rfree still improves on average regardless of resolution, many structures end up having a higher Rfree than that recorded in the header of the starting PDB file. This means that further development of the pipeline should focus on better dealing with this problem or avoiding the problem as much as possible. The latter can be achieved by increasing the number of restraints, e.g. by applying jelly-body restraints at higher resolutions or by extending the restraint-weight search space. Optimization of the bulk-solvent mask parameters (the probe size and the shrinkage factor) has recently been implemented and this may also improve the re-refinement results. In 12% of the cases with increased final Rfree the initially calculated Rfree was significantly higher than the Rfree reported in the PDB header [Rfree,calc > 5σ(Rfree)calc + Rfree,head], while for the total data set this was 5%. Reproducing R factors is known to be a challenging problem (Kleywegt et al., 2004; Afonine et al., 2010) and many problems can be reduced to a lack of knowledge of the original refinement parameters, e.g. about the treatment of bulk solvent. Because the annotation of new PDB entries has improved substantially, we can now adapt Extractor to obtain a more detailed description of the original refinement settings. These collectively indicate that part of the problem with worsened Rfree is partly artificial.
Deterioration in Rfree does not mean that the model becomes worse in terms of all other quality metrics. In fact, this is very rare and only occurs in 0.5% (58 structures) of the test set (Fig. 4); deterioration of three or more metrics is still rare and occurs in 6% of the test set. The opposite, improvement of all model-quality metrics, occurs in 16% (1934 structures) of the structures (Fig. 4), while improvement of three or more quality metrics occurs in 85% of structures in the evaluation set (Fig. 5).
During high-throughput testing of PDB_REDO on existing PDB entries, more than 800 fixable errors were encountered and were reported back to the PDB. Although mostly trivial annotation problems, these errors can be devastating when structure models are used in automated computational studies. Most issues were resolved at short notice, fixing the problem for all PDB users rather than just for PDB_REDO.
The results shown here are encouraging, but also show that there is still ample room for improvement. For instance, the sulfate ion in Fig. 1(d) was distorted, which was traced back to a problem with chiral volume restraints for the S atom. In real-life chemistry the O atoms are equivalent and the sulfur is not chiral. However, the O atoms are different computationally (they have different names), which makes the sulfur chiral during refinement. This means that a swap of any two O atoms in sulfate inverts the chirality of the sulfur. The chiral volume restraints now erroneously push the refinement towards improving the chiral volume, resulting in a distorted molecule. We are currently testing a new tool, called chiron, that fixes these computational chirality problems. In the long term, chemical chirality problems (where the atomic coordinates do not match the residue name) should also be fixed by either renaming the compound or rebuilding it. However, this can only be performed when reliable information about the chemical nature of the compound can be obtained automatically, and touches on the issue of constructive validation of ligand entries in the PDB, arguably a more important, but also a significantly more complex, task.
The refinement of a structure model with NCS constraints is available in REFMAC and implemented in PDB_REDO. Unfortunately, using this option often requires manual intervention because the so-called MTRIX records that describe strict NCS in PDB files frequently have annotation errors. We are working on a decision-making algorithm that can properly deal with such cases.
Our current rebuilding tools can be improved to allow support for noncanonical amino acids such as methylated lysines. Also, more substantial backbone rebuilding, for instance by building missing or poorly defined stretches of many residues, is a target for further improvement of PDB_REDO. Adding multiple conformations of side chains and of stretches of main chain presents an additional challenge.
Representation of the optimization results has become much more important now that we are actively changing structure models. We currently use molecular scenes from YASARA to highlight changes in the model, but this requires that installation of software and can only show one thing at a time. An approach such as Proteopedia (Hodis et al., 2008; Prilusky et al., 2011) could be more flexible and could allow the visualization of results directly in a web browser. Such a tool can allow us to highlight peptides that have been flipped or waters that have been removed.
The current model-quality Z scores are robust metrics, but are somewhat less comprehensible by statistically unaware users than, for example, the percentile scores used in MolProbity (Chen et al., 2010); the percentile scores have, besides obvious advantages, some caveats for asymmetric distributions. In addition, the absolute number of bumps that we use in our reports can cause misinterpretation, simply because it does not account for the severity of the bumps. This can lead to misleading results: in absolute terms ten bumps with atomic overlaps of 0.05 Å are worse than a single bump with overlap 0.5 Å even though the former is likely the result of suboptimal restraints and the latter of a fitting error. A new metric for bumps should be developed. Local measures for the fit to the experimental data are not yet included in the PDB_REDO pipeline and should be added.
In the near future, the brief validation reports proposed by the PDB Validation Task Force (Read et al., 2012) are very likely to become the preferred way of presenting PDB_REDO results. The relative metrics that are recommended for adoption in this report (and are under development in the PDB) can and should be implemented comparing PDB_REDO structures both against average PDB structures but also against average PDB_REDO structures.
The PDB_REDO pipeline can also be used to refine structures in the process of finalizing a structure in any laboratory. We now regularly employ PDB_REDO in our laboratory, usually to optimize near-complete models, but sometimes as early as straight after molecular replacement. While the software is available for download at http://www.cmbi.ru.nl/pdb_redo for use in one's own laboratory (see, for example, Peng et al., 2010; Guan et al., 2011), it is admittedly not straightforward to install and has several system dependencies at the moment. We are also working on a PDB_REDO web server that will provide a more user-friendly way to use the PDB_REDO pipeline in the near future.
We encourage the usage of PDB_REDO prior to structure deposition because it can improve the structure model and its interpretation. It must also be noted that PDB_REDO chases a moving target: unlike the PDB models, the PDB_REDO data bank models are not static and must all eventually be replaced or supplemented by a new version incorporating new methodological advances.
Individual entries in the PDB_REDO data bank (http://www.cmbi.ru.nl/pdb_redo ) can be used for any structural biology study, e.g. for homology modelling (van der Wijst et al., 2010; Flueck et al., 2011). Importantly, the collection of models can also be used as a homogeneously treated data set for statistical analysis of structure models. For example, the Ramachandran plot quality (Fig. 3) or average r.m.s.Z(angle) (Fig. 6) distributions in the PDB_REDO differ distinctly from those in the PDB. These distributions can be used to define new refinement targets and new criteria for choosing reliable water molecules or to construct (stricter) validation criteria (Kota et al., 2011). Further development to alleviate all cases in which some models deteriorate according at least to some criteria will be required before the full potential of PDB_REDO can be unleashed for the community.
The natural and constructive follow-up to structure model validation is to improve the model based on the validation results, as is now common practice by competent X-ray crystallographers. The process of improving the model still requires many decisions to be taken by crystallographers. The PDB_REDO pipeline combines refinement and model rebuilding with a decision-making framework that can autonomously optimize structure models. It makes `constructive validation' possible without the need for manual intervention. This is particularly important for structure models in the PDB, which are never updated otherwise. Applying the PDB_REDO pipeline to 12 000 random PDB entries showed that the majority of PDB entries can be improved according to commonly accepted quality criteria. This improvement is resolution-dependent: greater improvement occurs at lower resolution. Real-space model rebuilding has substantial added value to re-refinement, especially for improving geometrical targets. The limiting factors to improving models appear to be in finding optimal refinement parameters, but also in extending the scope of rebuilding to larger portions of the main chain and adding multiple conformations. The final hurdles are likely to be uniform and reliable water modelling, and last (but by no means least) the PDB-wide rebuilding of additional macromolecules (nucleic acids and carbohydrates) and the various hetero-compounds (ligands) bound to protein structures.
The authors thank the National Computing Facilities Foundation (NCF) for the use of supercomputer facilities with financial support from the Netherlands Organization for Scientific Research (NWO). RPJ is supported by a Veni grant from NWO (722.011.011).
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