Comparative Modeling

The structure of a target protein can be predicted with comparative modeling, if experimental X-ray crystallography or NMR structures of a homologous template protein exist. Out of the 94 proteins that were purified from the PP2A interaction network [6], only 8 (2AAA_HUMAN, 2A5G_HUMAN, 2ABA_HUMAN, PP2AA_HUMAN, SGOL1_HUMAN, SET_HUMAN, MST4_HUMAN, DYL1_HUMAN) had partial or complete structural information from X-ray crystallography experiments. For a subset of 15 proteins comprising all remaining PP2A core subunits and the eight TRiC chaperonin proteins, high quality comparative models were generated using various homologous template structures (see Table 1) and the following workflow (see also Figure 1A). The typical execution time of the workflow is about 5 CPU days per protein.

• 1.1 Run HHpred [27] (http://toolkit.tuebingen.mpg.de/hhpred/) on the target sequence to determine the best template structure.
• 1.2 Download the template structure from the Protein Data Bank(http://www.pdb.org).
• 1.3 Extract the sequence alignment between target and template protein from the HHpred output. Note, that the template sequence in HHpred corresponds to the SEQRES sequence and not to the ATOM coordinate sequence. In cases in which the template structure is predetermined and has a high sequence identity to the target protein, as was the case for the PP2A and TRiC proteins, one can also use the global sequence alignment application needle from the EMBOSS package v6.2.0 [28] with default command-line flags.
• 1.4 Generate fragment files for the target protein using the ROBETTA server [29] (http://robetta.bakerlab.org).
• 1.5 Predict the secondary structure of the target protein using PSIPRED [30] (http://bioinf.cs.ucl.ac.uk/psipred).
• 1.6 Using the input files from above, run ROSETTA’s minirosetta application on each target protein using following command line flags:
  • -database {rosetta_DB_dir}
  • -run:protocol threading
  • -run:shuffle
  • -in:file:fasta {protein.fasta}
  • -in:file:psipred_ss2 {protein.ss2}
  • -in:file:template_pdb {template.pdb}
  • -in:file:alignment {protein-template.aln}
  • -out:overwrite
  • -out:nstruct 200
  • -out:shuffle_nstruct 200
  • -cm:aln_format general
  • -idealize_after_loop_close
  • -out:file:silent_struct_type binary
  • -loops:extended
  • -loops:build_initial
  • -loops:remodel quick_ccd
  • -loops:relax relax
  • -loops:frag_sizes 9 3 1
  • -loops:frag_files {fragments9} {fragments3} none
  • -frag9 {fragments9}
  • -frag3 {fragments3}
  • -relax:fast
  • -relax:default_repeats 2
  • -silent_decoytime
  • -random_grow_loops_by 4
  • -select_best_loop_from 1
  • -in:detect_disulf false
  • -fail_on_bad_hbond false
• 1.7 Predict at least 200 models per target.
• 1.8 Create a tab delimited text file (xls.txt) holding the list of all intra-protein cross-links and mono-links in a Xwalk specific distance file format (see also http://www.xwalk.org/cgi-bin/help.cgi#vXLtable):
  • 1 protein.pdb LYS-1-C-CBLYS-2-C-CB

where the 1^st column is an incremental index, the 2^nd column is the PDB file name and the 3^rd and 4^th columns are dash delimited PDB information about first and second cross-linked atom, respectively. The PDB information should list the residue name, residue number, chain ID and atom name. Mono-links are described with the first three columns only.

• 1.9 Calculate the SAS distance for each intra-protein cross-link using Xwalk [26] (http://www.xwalk.org) on each model with following command

$> java Xwalk -infile {model.pdb} -dist {xls.txt} –bb –radius 2.0–mono.

• 1.10 Choose models that satisfy the largest number of intra-protein cross-links and mono-links.
• 1.11 If multiple models satisfy the same number of cross-links and mono-links, or if none of the models satisfy any cross-link, select the model with the lowest Root Mean Square Deviation (RMSD) to the template structure as the best model.

Alternatively, distance information from XL-MS data can also be exploited as distance restraints within the scoring function (see next section), which for the PP2A project was omitted to keep the modeling unbiased for validation purposes.

De Novo Modeling

If experimental structures are missing for a target protein and its homologs, the structure of the target protein can be predicted from its primary amino acid sequence using de novo modeling. The human IgBP1 protein had no crystal structure available in the Protein Data Bank (PDB) [31]. Structural coordinates existed only for the N-terminal domain from a mouse homolog (PDB-ID: 3CQ1). To generate a full-length model of IgBP1, we applied the following de novo modeling workflow (see also Figure 1B), which required about 14 CPU years of computation.

• 2.1 Generate fragment, PSIPRED, alignment files as described in the comparative modeling workflow above.
• 2.2 In addition, create a ROSETTA constraints file holding the list of intra-protein cross-link information in the following format (see also http://www.rosettacommons.org/manuals/archive/rosetta3.4_user_guide/de/d50/constraint_file.html):
  1. AtomPair {atom name1} {residue number1, chain ID1} {atom name2} {residue number2, chain ID2} FLAT_HARMONIC {x0} {standard deviation} {tolerance}

The flat harmonic function guarantees that models are penalized only if the Euclidean distance between two cross-linked atoms exceeds 30.0 Å. The function takes the Euclidean distance dist and three parameters that for a DSS cross-link were heuristically chosen to be x₀ = 15.0, tolerance = 15.0 and standard deviation σ = 1.0:

• 2.3 Run ROSETTA’s nonlocal application with the input files described above and the following command line flags:
  • -database {rosetta_DB_dir}
  • -in:file:fasta {protein.fasta}
  • -in:file:psipred_ss2 {protein.ss2}
  • -in:file:template_pdb {template.pdb}
  • -in:file:alignment {protein-template.aln}
  • -out:overwrite
  • -out:nstruct {n}
  • -cm:aln_format general
  • -frag3 {fragments3}
  • -frag9 {fragments9}
  • -abinitio::relax
  • -abinitio::no_write_failures
  • -abinitio:increase_cycles 1
  • -abinitio:rg_reweight 0.25
  • -nonlocal:builder star
  • -nonlocal:mode semirigid
  • -nonlocal:gap_sampling_extension 5
  • -jumps:ramp_chainbreaks
  • -jumps:overlap_chainbreak
  • -jumps:increase_chainbreak 0.5
  • -constraints:cst_fa_file {template.cst}
  • -constraints:cst_file {template.cst}
• 2.4 Generate at least 100,000 models.
• 2.5 Generate a Xwalk input file listing all cross-links and mono-links (see step 1.8) and run Xwalk (see step 1.9).
• 2.6 Choose top models as described in step 1.10. Choose the lowest scoring 500 models if more than 500 models should satisfy the largest number of cross-links.
• 2.7 Calculate an all against all Cα coordinate RMSD matrix among the top models.
• 2.8 Perform a hierarchical clustering with the complete clustering method using R [32] and the following R script:
  • rmsd.dat<-read.table(“rmsd_allVsAll.txt”, row.names = 1)
  • rmsd.dist<-as.dist(rmsd.dat)
  • rmsd.hist = hclust(rmsd.dist)
• 2.9 Cut the hierarchical cluster tree at an RMSD threshold value of 10 Å in the same R script:
  • rmsd.cut<-cutree(rmsd.hist, h = 10.0)
  • write.table(rmsd.cut, file = ”rmsd_cluster.txt”, quote = FALSE, col.names = FALSE, row.names = TRUE, sep = “\t”)
• 2.10 Pick the lowest scoring model from the largest cluster as the best model. If the clustering should retrieve only singletons, pick models that have the smallest RMSD value compared to the template structure as the best models.

Protein-protein Docking

The catalytic subunits of PP2A were docked against best full-length models of IgBP1 (see previous section) using the following workflow (see also Figure 1C). The workflow requires a computation time of around 100 CPU days.

• 3.1.1 Prior to docking calculations, crystal structures from the PDB (e.g. PP2AA) need to be relaxed. For relaxation, run ROSETTA’s relax protocol with following command line flags:
  • -database {rosetta_DB_dir}
  • -in:file:s {protein.pdb}
  • -relax:sequence
  • -constrain_relax_to_start_coords
• 3.1.2 Prepare a ROSETTA constraint file holding a list of all inter-protein cross-links (see step 2.2).
• 3.1.3 Using the constraint file, run protein-protein docking calculations with ROSETTA’s docking_protocol application in low-resolution centroid mode using following command line flags:
  • -database {rosetta_DB_dir}
  • -in:file:s {protein.pdb}
  • -constraints:cst_file {inter-xl.cst}
  • -out:overwrite
  • -out:nstruct {n}
  • -out:file:o {model.pdb}
  • -docking:low_res_protocol_only
  • -docking:randomize1
  • -docking:randomize2
  • -docking:spin
  • -docking:docking_centroid_outer_cycles 10
  • -docking:docking_centroid_inner_cycles 50
  • -docking:dock_lowres_filter 10 1
• 3.1.4 Generate at least 100,000 models.
• 3.1.5 Prepare a Xwalk input file that holds all intra-protein and inter-protein cross-links and mono-links (see step 1.8). Standard docking software and cross-link guided docking protocols utilize only inter-protein cross-links. But Xwalk ability to mimic cross-links by its shortest path and SAS distance calculation, allows it to additionally employ intra-protein cross-links and mono-links as post-docking filters. Predicted docking models that bury intra-protein cross-links or mono-links within their binding interface are thus detected by Xwalk and removed (see Discussion).
• 3.1.6 Assess the number of cross-links and mono-links satisfied by each model. To speed up calculations, apply first Xwalk’s Euclidean distance measure and subsequently the SAS distance measure (see step 1.9) on each model.
• 3.1.7 Select models satisfying to the highest number of cross-links. Should their number be higher than 500 or should none of the models satisfy any cross-link, select those 500 models with the lowest ROSETTA energy score.
• 3.1.8 Analyze the binding interface size of the selected models, which is equivalent to the buried surface area (BSA):

where SASA() is the solvent accessible surface area of the protein complex or its protein components. The SASA can be calculated with NACCESS [33] (http://www.bioinf.manchester.ac.uk/naccess/).

• 3.1.9 Select further only models with a sufficiently large binding interface with BSA(complex) ≥900 Ų [34].
• 3.1.10 Choose a large number of models with the shortest mean SAS distance over all cross-links. (In the case of the IgBP1-PP2AA, we selected the 300 models with the shortest mean SAS distance). The shortest mean distance leads to a preference for models with overall shorter cross-link distances that in most cases show distance ranges similar to Figure S1.
• 3.1.11 Calculate an all against all Cα coordinate RMSD matrix among the top models. Note, that the RMSD should be computed only on the smaller protein (ligand) and not on the larger structure (receptor), as the latter remains fixed during the docking calculations and has an RMSD of 0 among all selected models. The RMSD among the smaller proteins is also known as the ligand RMSD (L-RMSD).
• 3.1.12 Perform a hierarchical clustering as described in step 2.8.
• 3.1.13 Cut the hierarchical cluster tree at a L-RMSD threshold value of 20 Å (see step 2.9).
• 3.1.14 Pick the lowest scoring model from the largest clusters as best models.

We would like to emphasize that the workflow described above is only one of two strategies for cross-link guided protein docking. It was developed to highlight the impact of XL-MS data on docking calculations and visualize the set of conformations that satisfy a large number of distance information from XL-MS. For a biophysically more meaningful prediction, the workflow above can alternatively be extended after step 3.1.6 with a high-resolution refinement docking stage as follows:

• 3.2.1 Run steps 3.1.1–3.1.6.
• 3.2.2 Select models that satisfy most cross-links. Should their number be higher than 500 or should none of the models satisfy any cross-link, select those 500 models with the lowest ROSETTA energy score.
• 3.2.3 Filter the 500 models by binding interface size (see step 3.1.8 and 3.1.9).
• 3.2.4 Apply Quality Threshold (QT) clustering on models passing the interface size filter. A QT cluster is defined by the translational and rotational distances between a reference and referred ligand structures, where the distance must be smaller than 3 Å and 8°, respectively. The distance thresholds correspond to translational and rotational perturbations that will be applied during local-refinement docking, and thus, in contrary to RMSD based clustering, will allow a seamless transition between global and local docking calculations. Rotational and translational distances can be calculated with the Superimpose application (http://cleftxplorer.googlecode.com/files/cX.zip), which is part of the CleftXplorer software package [35], [36]:
  • java –cp cX.jar:colt.jar:cdk-1.0.2.jar cX/Superimpose -dir <dir> -chain A:A -dock -xseq -ca –r –ta 3∶8

The colt.jar and cdk-1.0.2.jar JAVA libraries are required by the Superimpose application and can be downloaded from http://acs.lbl.gov/software/colt/colt-download/releases/colt-1.2.0.zip and http://sourceforge.net/projects/cdk/files/cdk/1.0.2/cdk-1.0.2.jar, respectively. The Superimpose application will read in all PDB files from the directory <dir> and output an all against all dissimilarity matrices. The dissimilarity matrix holds 0′s for similar model pairs whose translational and rotational differences are smaller than the threshold values, and 1′s for distinct models.

• 3.2.5 Complete the QT clustering by searching within the output file for the model that has the highest number of similar models (i.e. largest number of 0 in a row), declare it as the cluster representative and remove it and all its cluster members from the dissimilarity matrix. If two models have the same number of similar models, then prefer the one with the lower ROSETTA score. Repeat this step two additional times to obtain the cluster representatives of the largest three clusters from the global docking calculations.
• 3.2.6 Run ROSETTA’s docking_protocol application in high-resolution mode with 3.0 Å translational and 8° rotational Gaussian biased random perturbations [37] on the three cluster representative with a ROSETTA constraint file (see step 2.2):
  • -database {rosetta-database}
  • -in:file:s <models.pdb>
  • -constraints:cst_file {inter-xl.cst}
  • -docking:dock_pert 3 8
  • -packing:ex1
  • -packing:ex2aro
  • -docking:dock_rtmin
  • -docking:sc_min
  • -out:nstruct {N}
• 3.2.7 Generate at least 5,000 per cluster representative
• 3.2.8 Run Xwalk on all models as described in step 3.1.6.
• 3.2.9 Select top 500 models as described in step 3.2.2 and 3.2.3.
• 3.2.10 Cluster models as described in step 3.1.11 to 3.1.13.
• 3.2.11 Pick the best models as described in step 3.1.14.

Reference Data Sets for the Modeling Workflows

XLdb: A Database of Literature Curated Intra- and Inter-Protein Cross-links

We collected a non-comprehensive list of 506 intra-protein and 62 inter-protein cross-links from 14 recent publications. In the current form, all cross-links are stored in a database called XLdb, which is based on a Microsoft Excel sheet (Table S1). Figure S1, S2 and S3 provide frequency and probabilities plots for various distance ranges in XLdb (Text S1). Only cross-links that fulfill following criteria were included in the database: 1. XL-MS experiments must have been conducted with the DSS or BS³ cross-linking reagent. 2. Experimental structure on the cross-linked proteins must exist in the PDB. 3. The XL-MS data must have been published. XLdb is besides the recently published Xlink-DB [40] the only database that allows the mapping of cross-links on protein structures and testing of cross-link guided molecular modeling algorithms on a large scale. We hope that as a reference database, it will encourage new method developments in the field of data driven molecular modeling.

Comparative Modeling for Cross-link Validation

We calculated comparative models using the workflow illustrated in Figure 1A for 15 proteins in the PP2A interaction network (Table 1) and 6 proteins from the reference data set (Table 2). Figure 2A shows the RMSD vs. ROSETTA energy scatter plots for all 15 PP2A proteins, where the RMSDs were calculated between the models and the template structure. The models satisfying most DSS based cross-links were furthermore highlighted in green. Two trends can be seen in the plots. First, models satisfying DSS cross-links can span a large RMSD range as evident from the box plots that are located below each scatter plot. There is, however, the tendency that the RMSD of the model with the lowest RMSD score, which nonetheless satisfies the largest number of cross-links, drops with increasing number of cross-links (see Figure 2B). Second, the model that satisfies the largest number of cross-links while being the closest to the template structure is in almost all cases among the top 3 models within the simulations (see Table 1). Thus, comparative modeling can be employed to validate XL-MS data while XL-MS data itself, in combination with a sophisticated scoring function, can aid in identifying native-like conformations. Similar conclusions can be drawn for the reference data set, where a similar range of RMSD values (with respect to their native structures) and rank positions for the best model satisfying most cross-links were observed (see Figure S4 and Table 2).

Two exceptions, namely TRFL_BOVIN and 2ABG_HUMAN showed large RMSD values of 8.5 Å and 19.6 Å, respectively, to their native or template structure. TRFL_BOVIN consists of two flexible C- and N-lobe domains [41]. As a result, some cross-links could have been formed on a conformation that is distinct from the one found in the PDB structure 1BLF. Interestingly 2ABG_HUMAN is a regulatory subunit of PP2A and has a WD40 propeller fold. It was found co-purified and cross-linked to the TRiC chaperonin complex as a substrate. We speculate therefore that some of the intra-protein cross-links stemmed from B regulatory subunits that were in a stable intermediate folding state while bound to the TRiC chaperonin complex. And indeed selecting for the lowest scoring model that satisfies most cross-links (13/18) shows only a partially folded WD40-propeller fold with an RMSD of 19.5 Å to the folded template structure (see Figure 3). Additional XL-MS experiments on affinity purified TRiC subunits that would provide a clean list of only intra-protein cross-links from 2ABG while in complex with TRiC, remain to be conducted.

Cross-link Guided De Novo Modeling

Immunoglobulin binding protein 1 (IgBP1) interacts with the catalytic subunit of PP2A, rendering it inactive and preventing it from proteasomal degradation [42]. As inter-protein chemical cross-links were found between IgBP1 and the catalytic subunit of PP2A, we constructed a partial de novo full-length model of human IgBP1 (see section De novo modeling) and predicted the interface between both proteins using cross-link guided protein-docking calculations (see section Protein-protein docking). For the partial de novo prediction of IgBP1, Cα distance restraints from the N-terminal region of the mouse homolog and 65 intra-protein cross-link distance restraints from our XL-MS experiments were applied [6]. Of the 65 intra-protein cross-links, 18 were found within the C-terminal region, while 32 were found between the N- and C-terminal domains of IgBP1. Crucial for the structure prediction was the application of Xwalk’s SAS distance as a post-processing filter. From around 157,000 structural models that were predicted, over 113,000 models satisfied at least 60 cross-links by means of the Euclidean distance. In contrast, only around 190 models satisfied the same number of cross-links using the SAS distance measure (see Figure 4A). Nevertheless, the structure prediction calculations did not converge as assessed by a RMSD based clustering attempt of the 190 models and thus did not result in an unambiguous fold prediction for the C-terminal domain (see Figure 4). However, the 32 intra-protein cross-links facilitated the localization of the C-terminal domain with respect to the N-terminal domain. Five models that had the lowest RMSD (≤10.0 Å) to the N-terminal domain of the template structure (PDB-ID: 3QC1) had their C-terminal domain co-localized at the same region (see Figure 4B). These five models were chosen as best models of IgBP1 and docked to the catalytic subunits of PP2A as described in the next section.

A similar structure prediction for the pyruvate kinase from the reference data set (see section Comparative and de novo modeling) with only 14 experimental intra-protein cross-links produced models with RMSD values down to 5.93 Å to the native structure while satisfying all 14 intra-protein cross-links. In contrary to the IgBP1 calculation, the simulation for the pyruvate kinase did converge, producing 5 clusters with at least 24 members, of which the lowest scoring models are shown in Figure S5. Thus, our workflow coupled with chemical cross-link data enables the prediction of useful structural information for large proteins with only partial structural data.

Cross-link Guided Protein-protein Docking

We developed a protein-protein docking workflow [6] (see Figure 1C) and applied it to predict the conformation and the binding interface between the catalytic subunits of PP2A and its interactor IgBP1. For the docking calculations 7 inter-protein cross-links, 11 intra-protein cross-links and 10 mono-links were utilized to guide the calculations between PP2AA and IgBP1.

Prior to the docking calculations, we first tested the impact of the number of cross-links on protein-protein docking calculations. For this purpose, 16 protein complexes with experimental structural coordinates in the PDB from a docking benchmark data set were docked and the impact of randomly chosen 1 to 7 inter-protein cross-links was assessed on the docking results (see section Reference data sets for the modeling workflows). The boxplots in Figure 5 show the docking performance of any model that satisfies a certain number of randomly selected virtual cross-links. The performance was assessed by the ligand’s RMSD values (L-RMSD). A clear trend towards higher quality predictions with increasing number of cross-links was observed. On average, the improvement in docking predictions with the SAS distance measure rose by 5 Å L-RMSD per cross-link and leveled off at 5 cross-links in total, which agreed with a similar observation made elsewhere [43]. The Euclidean distance measure had the same tendencies, although less pronounced and with higher median L-RMSD values as compared to the SAS distance measure.

The application of the cross-link guided docking protocol to the IgBP1-PP2AA protein complex (see steps 3.1.x) revealed 4 large clusters of predicted complex models. Despite the high L-RMSD values among the cluster representatives (see Figure 6B), all models revealed similar interface residues as highlighted by the similar location of IgBP1 with respect to PP2AA in Figure 6A. Three amino acids that had been shown in previous studies to form the interface can indeed be found at the interface of the cluster representatives (see Figure 6A).