XL-MSDigger: a deep learning-based, versatile solution for cross-linking mass spectrometry

Domain: neuroscience
Published: 2026-02-10
Editorial outcome: major_revision

Abstract
Cross-linking mass spectrometry (XL-MS) technology plays an important role in protein structure and protein-protein interaction (PPI) studies. However, there are serious shortcomings in the data processing and analysis methods of XL-MS that limit its ability to perform in-depth analysis. Here, we built a deep learning-based XL-MS versatile platform, XL-MSDigger, to address the bottlenecks of XL-MS technology. The foundation of this platform is a deep learning-based multidimensional information prediction tool, Deep4D-XL, for cross-linked peptides. This tool is capable of accurately predicting retention time, collisional cross-section, and fragment ion intensity information of cross-linked peptides. Through the multidimensional information prediction, we develop rescoring algorithms and workflows for DDA and DIA analysis data, which improve the coverage of DDA-based XL-MS identification, and realize the evaluation of false discovery rate and high-reliability identification of DIA-based XL-MS analysis. In addition, XL-MSDigger enables DIA-based XL-MS analysis using predicted spectral libraries, allowing improved detection of protein–protein interactions in targeted or moderate-scale interaction analyses. We believe that the XL-MSDigger platform can be widely used as a general solution to enhance the performance of XL-MS analysis.

Introduction
The structure of proteins and their interactions influence their properties and functions. In recent years, cross-linking mass spectrometry (XL-MS) has evolved into a crucial tool for studying protein structures and protein-protein interactions. XL-MS employs chemical cross-linkers to covalently bond amino acid residues within a certain spatial range, thereby capturing the conformation and interaction interfaces of proteins in their native environments.

The primary targets of XL-MS experiments are cross-linked peptides, composed of two peptides linked by a cross-linker. These peptides exhibit more complex structures and mass spectrometric fragmentation behaviors compared to linear peptides in typical proteomics experiments. The resolving of MS data for these peptides requires consideration of a greater variety of fragment ion types. Due to the unique structure of cross-linked peptides, database searches used in proteomics face higher computational complexity, often leading to vast search spaces and an elevated risk of false positives. As research progresses, various specialized cross-linked peptide analysis software have been developed, including StavroX, Kojak, Xilmass, Merox, Xolik, pLink2 and Scout, among others. For instance, pLink2 utilizes a fragment index and a two-step open search strategy to perform proteomic-level cross-linked MS analysis within a shorter timeframe. However, almost all such software relies only on the m/z information of precursor and fragment ions, which may increase the likelihood of random false matches in peptide-spectrum matches (PSMs) when faced with complex XL-MS data and enormous search spaces.

Recently, post-processing tools like MSBooster and DeepRescore have enhanced the sensitivity of PSM identification in regular proteomics by using deep learning-based prediction of fragment ion intensity, retention time (RT), and collisional cross-section (CCS) in PSM rescoring. The core of these tools is the ability to accurately predict multidimensional peptide information. Since the development of the pDeep, researchers have successively developed various models capable of predicting properties for regular peptides, such as Prosit, DeepMass, DeepDIA and Deep4D for fragment ion intensity prediction, and DeepRT, DeepLC, and AutoRT for RT prediction. Mann and colleagues have also developed a model for predicting the CCS of peptides. However, the deep learning-based prediction model for cross-linked peptides is very rare due to their structural complexity. Currently, only the xiRT for predicting the RT and pDeepXL for predicting fragment ion intensity are available. To date, a deep learning-based model capable of predicting multidimensional information for cross-linked peptides is lacking.

On the other hand, most XL-MS analyses are currently performed in data-dependent acquisition (DDA) mode. Compared to DDA, data-independent acquisition (DIA) techniques, which fragment precursors in an unbiased manner across predefined windows, can enhance precursor coverage and repeatability. DIA has become a mainstream method in proteomics and has demonstrated high identification performance, but DIA-based XL-MS methods are just beginning to emerge. We developed 4D-diaXLMS, a DIA-based workflow that supports proteome-wide cross-linking analysis. However, current methods still rely on sample-specific experimental spectral libraries derived from DDA experiments, primarily leveraging DIA’s quantitative capabilities rather than maximizing its advantages in identification coverage. DIA-based regular proteomics has demonstrated that the use of predicted peptide libraries derived from the species’ proteome can effectively eliminate the need for time-consuming experimental library construction and expand the identification coverage. Nevertheless, the DIA analysis for cross-linked proteomics based on predicted spectral libraries is still restricted by the tools capable of predicting multidimensional information specific to cross-linked peptides.

In this study, we aim to develop a comprehensive deep learning-based solution to address the key issues currently facing XL-MS analysis, including deep mining of DDA data, FDR control for DIA analysis, and DIA analysis based on predictive spectral libraries. We develop a deep learning-based model, Deep4D-XL, which can accurately predict multidimensional information, including RT, CCS, and fragment ion intensity of cross-linked peptides. A versatile workflow XL-MSDigger is further developed for in-depth XL-MS analysis, supporting both DDA- and DIA-based methods. Compared to existing XL-MS technologies, XL-MSDigger offers several key advancements: 1) by utilizing multidimensional information predicted by Deep4D-XL and a deep neural network-based rescoring model, it can comprehensively extract more information on inter-protein cross-linked peptides and protein-protein interactions (PPI) from DDA-based XL-MS data; 2) it establishes a systematic framework for FDR evaluation in DIA XL-MS analysis and reduces the elevated FDR observed in current DIA XL-MS workflows through optimized rescoring; and 3) it enables DIA-based XL-MS analysis using predicted spectral libraries, thereby enhancing the identification depth of both intra- and inter-protein cross-linked peptides.

Results
Construction of Deep4D-XL model
Deep4D is a deep learning model with robust predictive performance for the multidimensional information (RT, CCS, and fragment ion intensity) of linear peptides and phosphorylated peptides. However, due to significant structural differences between cross-linked peptides and linear peptides, the Deep4D model could not be directly applied to cross-linked peptides. Therefore, we have specifically developed a dedicated model for cross-linked peptides based on the foundational framework of Deep4D, named Deep4D-XL. In this model (Fig. 1a), we employed a Siamese network architecture in the encoder module to characterize the information of the two linear peptides within the cross-linked peptides, followed by a cross-attention module that merges the feature representations of both peptides. Finally, the decoder module, consisting of a convolutional neural network (CNN) and fully connected layers, converts the tensor output from the cross-attention module into RT, CCS and fragment ion intensity.

To evaluate the effectiveness of the Deep4D-XL model, we first compared its performance with xiRT in predicting the RT of cross-linked peptides. Specifically, we trained Deep4D-XL on the same published dataset used in the xiRT and evaluated its performance against the results reported for xiRT (Supplementary Data 1). Deep4D-XL achieved an R² of 0.96 and a median absolute error (MAE) of 1.61 min (Supplementary Fig. 1a), outperforming xiRT, which yielded a lower R² of 0.93 and a higher MAE of 2.29 min on the same dataset (Fig. 1b, c). In addition, we trained and tested both xiRT and Deep4D-XL on three other independent retention time datasets. Across all datasets, Deep4D-XL consistently exhibited lower prediction errors and higher coefficients of determination than xiRT. Specifically, Deep4D-XL achieved MAE of 2.06, 2.45, and 3.92 min with corresponding R² of 0.970, 0.967, and 0.963, respectively (Supplementary Fig. 1b–d), whereas xiRT showed higher MAE (3.03, 4.00, and 13.30 min) and lower R² (0.946, 0.950 and 0.950) on the same datasets (Fig. 1b, c). These results demonstrate that Deep4D-XL provides more accurate and stable RT predictions across diverse experimental settings, motivating us to further explore the potential of the Deep4D-XL model in predicting additional properties of cross-linked peptides.

Dataset construction and multidimensional prediction performance for cross-linked peptides
To enable the Deep4D-XL model to predict additional properties of cross-linked peptides, we first constructed a large-scale, high-quality dataset for training and testing, as no such dataset currently exists. We conducted a deep fractionation of cross-linked peptide samples (40 fractions) from the HeLa cell proteome. These samples were then analyzed using ddaPASEF mode on a timsTOF pro mass spectrometer, and the resulting data were processed with pLink2. In total, 90,116 cross-linked PSMs were identified across all sample fractions (Supplementary Fig. 2). For each identified peptide, we retained the highest-scoring PSM in each observed charge state to extract complete RT, CCS, and MS/MS spectral information. This resulted in 34,115 charge-specific unique cross-linked peptides, thereby generating a large-scale four-dimensional (4D) dataset of cross-linked peptides (Fig. 2a). The theoretical spatial distances of intra-protein cross-linked peptides in the steric structures of proteins were calculated within our dataset. The results showed that, of the 12,580 intra-protein cross-linked peptides that could be matched to protein structures, 9841 peptides (78.2%) had amino acid residue distances within the range constrained by the disuccinimidyl suberate (DSS) cross-linker (Supplementary Fig. 3), indicating the high reliability of this XL-MS dataset.

Next, we randomly divided the dataset into training, validation, and test sets in a ratio of 8.1:0.9:1, and then trained and tested the corresponding models for predicting RT, CCS, and fragment ion intensity. For RT prediction, the trained model demonstrated accurate prediction on the test set (Supplementary Data 1), with a mean absolute error of 2.06 min (Fig. 2b), approaching the performance of the Deep4D model for linear peptides. For CCS prediction, the trained model achieved a median relative error (MRE) of 1.52% on the test set (Fig. 2c), with accuracy nearly comparable to that for linear peptides. This result demonstrates that Deep4D-XL enables accurate CCS prediction for cross-linked peptides using a deep learning framework (Supplementary Data 1).

For the prediction of fragment ion intensity, the complex and varied fragment ion types of cross-linked peptides pose significant challenges. In addition to considering the b and y ions of each linear peptide, it is necessary to consider fragments containing the cross-linked site (see “Methods” section for details). Despite this complexity, the trained model performed well on the test set, achieving a median dot product of 0.88 between predicted and experimental spectra (Supplementary Data 1). In addition, we separately calculated the dot products between the predicted and experimental spectra for fragment ions originating from each of the two peptides, as well as for fragment ions containing the cross-linking site (Fig. 2d). Figure 2e, f show the prediction performance using two cross-linked peptides as examples. The results show that the predicted spectra for both cross-linked peptides are very similar to their corresponding experimental spectra, again demonstrating the reliability of the prediction.

To demonstrate the broad applicability of the Deep4D-XL model, we further evaluated its generalization across different instruments and cross-linker types. From an Orbitrap–based DSS-crosslinked dataset, comprising 14,300 cross-linked PSMs, the model was trained and tested, achieving a median dot product of 0.844 (Supplementary Fig. 1e) between predicted and experimental spectra, indicating broad adaptability to different instrument platforms. We also evaluated its performance on other non-cleavable cross-linkers. From an Orbitrap-based PhoX-cross-linked dataset comprising 22,306 cross-linked PSMs, the model achieved a median dot product of 0.917 (Supplementary Fig. 1e) between predicted and experimental spectra. To further enhance versatility, we also analyzed an Orbitrap–based cleavable DSBU-crosslinked dataset, which yielded 20,446 cross-linked PSMs. To accommodate the unique fragmentation characteristics of cleavable cross-linkers, the output dimension of the Deep4D-XL model was adjusted accordingly. The trained model achieved a median dot product of 0.853 on the test set (Supplementary Fig. 1e).

Overview of XL-MSDigger
After developing and validating the Deep4D-XL model, we built a versatile computational pipeline for in-depth analysis and mining of XL-MS data, called XL-MSDigger, centered on that model. The main functions of XL-MSDigger are shown in Fig. 3, which includes two primary functional modules for analyzing both DDA and DIA XL-MS data. In DDA data analysis, the workflow begins with the use of the pLink2 software to perform a database search of DDA data to obtain preliminary results. Subsequently, the Deep4D-XL model performs multidimensional predictions for all identified cross-linked peptides, which were used to compute multiple features for each PSM, including ΔRT, ΔCCS, MS/MS similarity and other information. These features are then utilized by a deep neural network to rescore cross-linked peptide results, enhancing the identification of cross-linked peptides. The experimental spectral library generated from DDA results can also be used for subsequent DIA analysis.

In DIA data analysis, a decoy spectral library is first generated based on the target spectral library, and the two libraries are merged. The merged library is then analyzed using DIA-NN software to perform initial DIA analysis. Subsequent rescoring of the DIA-NN search results is conducted using a deep neural network, followed by FDR evaluation to obtain the final identification results (see “Methods” for details). For spectral library construction, predicted cross-linked spectral libraries can also be generated based on the Deep4D-XL model, which enhances the identification scope of DIA analysis. The specific performance of each function of XL-MSDigger are detailed in the following results.

Rescoring of DDA-based XL-MS data to improve the coverage of inter-protein crosslinks
The rescoring method for DDA-based XL-MS data in XL-MSDigger includes two main steps: 1) feature extraction for cross-linked peptides based on the Deep4D-XL model; 2) rescoring based on a deep neural network.

Cross-linked peptides are categorized into two types: intra-protein and inter-protein cross-links. In the target-decoy approach, due to the larger search space for inter-protein cross-linked peptides, most of the matched decoy PSMs are inter-protein cross-links, which can negatively impact the identification of target inter-protein cross-links during FDR evaluation. Additionally, inter-protein cross-links are usually less abundant and more challenging to identify, often resulting in very low identification rates. Therefore, we aimed to explore whether the rescoring method based on Deep4D-XL could help improve the identification of inter-protein cross-linked peptides. Here, we used Deep4D-XL to predict RT, CCS, and fragment ion intensity information for all candidate peptides (including both target and decoy cross-linked peptides) found in the search results, extracting 12 features related to them. Together with the four original search result features, a total of 16 features were used as input for the rescoring model (Supplementary Table 1). In choosing the rescoring model, we evaluated the performance of support vector machines (SVM) and deep neural networks (DNN). pLink2 continued to be used as the search software for DDA-based XL-MS analysis, and DDA data from seven yeast cross-link samples were analyzed. The results show that pLink2 identified 461 inter-protein cross-linked PSMs across the seven samples (Supplementary Fig. 4), while the proposed SVM and DNN rescoring results included 852 and 956 inter-protein cross-linked PSMs, respectively, representing an increase of 85% and 107% in identification quantity compared to the original pLink2 results. These preliminary results demonstrate that the rescoring method based on predictive information from the Deep4D-XL model can enhance the identification of target cross-linked PSMs.

To further validate the effectiveness of the rescoring method in DDA-based XL-MS analysis, we applied it to the aforementioned 40 HeLa cross-linked proteome fraction datasets. The results show that after rescoring, the identification of inter-protein cross-linked PSMs in 37 out of the 40 datasets exceeded the number originally identified by the pLink2 software, with only three datasets showing a slight decrease in the number of inter-protein cross-linked PSMs identified after rescoring (Fig. 4a). The total number of inter-protein cross-linked PSMs identified by the rescoring was 106.9% higher (2326 vs. 1224) compared to the original results from pLink2 software results (Fig. 4b), and the corresponding protein-protein interactions (PPIs) also increased by 76.3% (610 vs. 346) (Supplementary Data 2).

Furthermore, under the assumption that the target PSMs meeting the FDR threshold in the original search results were authentic, the objective of rescoring was twofold: to mine as many target inter-protein cross-linked PSMs as possible from those not meeting the original FDR and to retain as many PSMs as possible that met the FDR restrictions initially. Therefore, we defined sensitivity to indicate the proportion of original FDR-compliant PSMs included in the rescoring results relative to all originally FDR-compliant PSMs. Our findings revealed that 1140 of the 1224 inter-protein cross-linked PSMs identified in the original pLink2 results appeared in the rescoring results (Fig. 4b, Supplementary Fig. 5), achieving a sensitivity of 93.1%. Additionally, the sensitivity of the identified PPIs before and after rescoring was similarly high at 88.8% (Fig. 4b). These results demonstrate the reliability of our rescoring algorithm.

We further incorporated the E. coli proteome as an entrapment database to provide an additional layer of quality assessment for the identification results. The proportion of inter-protein cross-linked PSMs involving E. coli proteins was 1.0% before rescoring and 0.97% after rescoring (Supplementary Data 2), indicating that the quality control of our rescoring approach is comparable to that of pLink2.

Subsequently, we analyzed the confidence scores of all protein–protein interactions (PPIs) in the initial and rescoring results using the STRING database (Supplementary Data 2, Supplementary Fig. 6). The results show that XL-MSDigger not only outperforms in the number of identified interactions but also improves result credibility. Among PPIs uniquely identified by XL-MSDigger, 49% lack STRING scores, which is lower than the 61% observed for PPIs uniquely identified by pLink2 (Supplementary Fig. 6a). This indicates our method prioritizes interactions supported by known databases. These PPIs, currently unsupported by STRING data, may include previously unreported discoveries with potential biological significance or interactions within database coverage blind spots. In addition, among uniquely identified PPIs with available STRING annotations, 78% of those recovered by XL-MSDigger have STRING scores above 0.4, compared to only 64% for pLink2 (Fig. 4c, Supplementary Fig. 6b, c). This further demonstrates the ability of the proposed method to uncover more high-confidence results among well-documented interactions.

To evaluate the contribution of individual subscores to the overall rescoring performance, we conducted ablation experiments on 40 DDA datasets by sequentially removing the RT, spectral similarity, and CCS features. The results showed that excluding RT, spectral similarity, and CCS reduced the number of identified PSMs to 74%, 86%, and 99.6% of the full rescoring results, respectively (Supplementary Fig. 7). These findings indicate that RT contributes the most to model performance, followed by spectral similarity, while the CCS feature has only a minimal effect. This observation is consistent with the results reported in the MSBooster study, which demonstrated that CCS values are highly correlated with precursor m/z and charge, leading to nearly identical CCS distributions between target and decoy peptides at the current ion mobility resolution.

Furthermore, to assess the applicability of XL-MSDigger to different mass spectrometry types and cross-linkers, we applied our rescoring method to the previously mentioned Orbitrap-based DSS-, PhoX-, and DSBU-cross-linked datasets (Supplementary Data 5). Specifically, we analyzed subsets of data files from these datasets using pLink2 (for DSS and PhoX) and Scout (for DSBU). For the DSBU-cross-linked dataset, the number increased from 126 to 241 (Fig. 4d); for the DSS-cross-linked dataset, the number of inter-protein cross-linked PSMs increased from 254 to 476 (Fig. 4e); and for the PhoX-cross-linked dataset, the number increased from 152 to 317 (Fig. 4f). These results demonstrate the good versatility and applicability of XL-MSDigger across different experimental settings.

FDR control for DIA-based XL-MS analysis by the rescoring algorithm improves identification reliability
For low-abundance cross-linked peptides, the semi-stochastic selection of the precursor ions in the DDA method may result in the loss of MS/MS information, leading to poor reproducibility in identification. In contrast, the DIA method with unbiased fragmentation of precursors can effectively address this issue. However, a primary challenge facing current DIA-based XL-MS analysis is the lack of a specific FDR assessment method for cross-linked peptides. This is because current DIA-based proteomics methods typically rely on decoy spectral libraries for FDR evaluation, yet there are no tools available for constructing decoy cross-linked peptide spectral libraries. Both our previously published 4D-diaXLMS method and the method by Rappsilber et al. are DIA-based approaches based on sample-specific DDA experimental spectral libraries, which primarily leverage the quantitative capabilities of the DIA-based analysis. In addition, due to the absence of an FDR evaluation method for cross-linked peptides, the authenticity of DIA results cannot be guaranteed once nonspecific cross-linked peptide information is introduced into the spectral library.

Based on the Deep4D-XL model, an FDR evaluation module was added in XL-MSDigger. The Deep4D-XL model was used to predict the multidimensional information of all decoy cross-linked peptides to construct a decoy spectral library, which is then merged with the target experimental spectral library to form an integrated spectral library (Supplementary Fig. 8). A library search is then performed based on the library, and the FDR is calculated based on the number of target and decoy peptides in the search results. This approach was further validated by evaluating diaPASEF data from 20 cross-linked samples using the 4D-diaXLMS method. First, all identification results were ranked based on the score output by DIA-NN, and the false discovery rate (FDR) was calculated. Using an FDR threshold of 5%, a total of 5379 target cross-linked precursors were identified across 20 DIA datasets. However, analysis of the DIA-NN score distributions for target and decoy precursors revealed poor separation between the two groups (Fig. 5b). Most of the decoys were of the TD type, which contain one target linear peptide. Because Deep4D-XL can generate fragment ions identical to those of true cross-linked peptides, these ions may coincidentally match experimental spectra, leading existing scoring algorithms to assign spuriously high scores to decoy cross-linked peptides and thereby inflate the FDR. Addressing this issue will require the development of scoring algorithms specifically optimized for cross-linked peptides to achieve more accurate FDR control in DIA-based XL-MS analysis.

To address the limitations of existing scoring algorithms for DIA-based XL-MS method, we developed a rescoring method inspired by the rescoring approach in DDA analysis. This rescoring algorithm incorporates 20 features (Supplementary Table 2), including those extracted from the theoretical and experimental relationships of multidimensional information of cross-linked peptides, along with multiple outputs from DIA-NN, and employs a deep neural network for rescoring. The effectiveness of the DIA rescoring method of XL-MSDigger was validated using 20 previously analyzed DIA datasets. We validated the effectiveness of this DIA rescoring method in XL-MSDigger using 20 previously analyzed DIA datasets. As shown in Fig. 5a, applying an FDR threshold of 5% resulted in the identification of 25,269 target cross-linked precursors, representing approximately a five-fold increase compared with the results prior to rescoring. Moreover, the score distributions of target and decoy precursors (Fig. 5b) exhibited clear separation after rescoring, indicating that our algorithm effectively distinguishes true targets from decoys. We further plotted the relationship between FDR thresholds and the number of identified target precursors, revealing that XL-MSDigger consistently yields higher identifications across the entire FDR range (Fig. 5c), demonstrating the robustness and superior sensitivity of the proposed rescoring approach.

In-depth DIA-based XL-MS analysis with predicted spectral library
Current DIA-based XL-MS methods rely on a spectral library obtained based on sample-specific DDA analysis, which can limit the overall coverage of DIA analysis because mass spectral information for some cross-linked peptides is not included in the library. In principle, our Deep4D-XL model, together with the DIA rescoring algorithm and FDR control of XL-MSDigger, enables the DIA-based XL-MS analysis using predicted spectral libraries. However, generating a proteome-wide theoretical cross-linked spectral library is computationally impractical due to its massive scale, making such an approach unfeasible at this stage. Therefore, we adopted a compromise strategy, constructing moderately scaled predicted spectral libraries for selected proteins or PPIs, allowing the implementation of 4D DIA XL-MS analysis under current computational constraints.

The feasibility was first evaluated by using a predicted spectral library to identify intra-protein cross-links. For this purpose, 100 proteins identified from the HeLa cross-linking proteome with available 3D structures were selected to generate predicted spectral libraries for all possible intra-protein cross-linked peptides (Supplementary Data 3). The DIA analysis was then conducted on 20 cross-linked sample fractions. To manage the spectral library size, we randomly divided the 100 proteins into five equal groups and constructed separate predicted spectral libraries for each group. The sizes of these libraries ranged from 1.06 to 1.94 million, with an average of 1.37 million. As a result, 90 intra-protein cross-linked peptides not identified by the DDA approach were identified using this workflow (Supplementary Data 3).

We then calculated the theoretical spatial distances of the cross-linked peptides within their 3D protein structures to assess the reliability of these identifications. Distance information was available for 88 peptides, of which 81 (92%) had residue distances within the constraints of the DSS cross-linker (Fig. 6a), comparable to the 85% observed for all identified cross-linked peptides with DDA analysis (Fig. 6b, Supplementary Data 3). The structures of two example proteins, GMPS and RUVBL1 and their cross-linking sites illustrate the advantage of the high coverage of the predictive library-based DIA approach in protein structure analysis (Fig. 6c). In addition, we calculated the distances between all possible intra-protein cross-linking sites for these 100 proteins and found that only 26.7% of the cross-linking sites met the distance constraint (Supplementary Fig. 9), which is much lower than our identified results. Furthermore, when constructing the predicted spectral library, we included an additional set of 100 randomly selected E. coli proteins as an entrapment control to further assess the quality of the identifications. The results showed that, at an FDR threshold of 5%, among 88 identified intra-protein cross-linked precursors, only two originated from E. coli. (Supplementary Data 3). These findings indicate that, with FDR assessment, DIA XL-MS using predicted spectral libraries achieves reliability and protein conformation analysis capabilities comparable to DDA.

To evaluate the performance of predicted spectral libraries in uncovering low-abundance cross-linked peptides, we selected 100 proteins with only one cross-linked peptide identified in DDA analysis and generated predicted spectral libraries for them (Supplementary Data 3). These libraries were then used for in-depth DIA analysis of 20 HeLa cross-linked protein samples. At a 5% FDR threshold, we identified 36 additional intra-protein cross-linked peptides that were not detected in the DDA results (Supplementary Data 3). Of these, 19 mapped to known 3D protein structures, and 15 met the theoretical distance constraints of the DSS cross-linker. These results demonstrate that the 4D DIA XL-MS with predicted spectral libraries enhances the detection of low-abundance intra-protein cross-linked peptides from DIA data.

We further evaluated the effectiveness of predicted spectral libraries in identifying inter-protein cross-links, focusing on HSP90AA1, a key molecular chaperone protein. Using the STRING database, we selected 17 proteins with the highest interaction confidence with HSP90AA1 and used these 17 PPIs to construct a predicted spectral library for DIA analysis. In the previous DDA results from the HeLa cross-linked proteome, only 3 of these 17 PPIs were identified. However, our analysis of DIA data from 20 HeLa samples using the predicted library identified 10 of these PPIs (Fig. 6d, Supplementary Data 4). To further assess the reliability of the identifications, we introduced an additional 17 E. coli proteins to form entrapment PPIs with HSP90AA1 during library construction. The entrapment experiment was randomly repeated ten times, and at an FDR threshold of 5%, only 5 out of a total of 109 identified cross-linked precursors (4.6%) corresponded to entrapment PPIs (Supplementary Data 4). These results further confirm the robustness and reliability of our DIA-based XL-MS analysis using predicted spectral libraries. Similarly, we studied HSPD1 and HSPA1B, selecting their interaction partners from STRING for spectral library construction and DIA analysis. While the DDA results show only 0 and 1 PPIs for HSPD1 and HSPA1B, respectively, the DIA analysis detected 4 and 7 PPIs (Supplementary Fig. 10, Supplementary Data 4). These results demonstrate the higher coverage of the DIA-based XL-MS analysis with predicted multidimensional spectral libraries compared to DDA, providing much more information on inter-protein cross-links and PPIs.

Methods
Sample preparation of cross-linked peptides
HeLa cells and yeast were each analyzed as a single biological sample. Briefly, the cell pellet was resuspended in cross-linking buffer (20 mM HEPES, 150 mM NaCl, 2.5 mM MgCl2, pH 7.5) containing 1× EDTA-free protease inhibitor cocktail and lysed by sonication on ice. Yeast was first ground in cross-linking buffer using a grinder before sonication. Cell debris was removed by centrifugation, protein concentration of the supernatant was determined by Bradford assay and adjusted to 1 mg/mL. Cross-linking reaction was performed using 2 mM DSS at 37°C for 1 h and quenched with 50 mM Tris-HCl (pH 8.0). Cross-linked proteins were denatured with 8 M urea followed by reduction and alkylation. Samples were diluted by four times using 50 mM NH4HCO3 and digested with trypsin at an enzyme-to-protein ratio of 1:50 (w/w) at 37°C overnight. The resulting peptides were desalted using C18 cartridges (Waters, USA), dried and stored at −80°C for further use.

Strong cation exchange (SCX) fractionation of cross-linked peptide was performed on a PolySULFOETHYL A SCX column (3 µm, 300 Å, 2.1 mm i.d. × 150 mm, PolyLC, USA). SCX solvent A consisted of 0.1% TFA in 30% ACN, SCX solvent B consisted of 0.1% TFA, 0.5 M NH4Cl in 30% ACN. The flow rate was set as 200 µL/min. The digested products of 2 mg protein were dissolved with SCX solvent A and then loaded to the column. The SCX gradient was set as follows: 0–0.01 min (0–2% B); 0.01–8.01 min (2–3% B); 8.01-14.01 min (3–8% B); 14.01–28 min (8–20% B); 28–38 min (20–40% B); 38–48 min (40–90% B); 48–54 min (90% B); and 54–60 min (0% B). A total of 40 fractions with high proportions of cross-linked peptide were collected, with the eluent of 1 min as an individual fraction from 18 to 38 min. The fractions were named as F1, F2, F3 until to the last fraction of F40 in order of their elution time. All fractions were dried, de-salted using home-made C18 tips, dried and stored at −80°C until LC-MS/MS analysis.

LC-MS/MS analysis
All the LC-MS/MS analysis of peptides were performed on a timsTOF Pro mass spectrometer (Bruker Daltonics, Germany) in PASEF or diaPASEF mode separately for DDA or DIA analysis via a CaptiveSpray nano-electrospray ion source (Bruker Daltonics, Germany) coupled with an EASY-nLC 1200 system (Thermo Fisher Scientific, USA). Samples were re-dissolved in mobile phase A and loaded onto a 20 cm in-house packed capillary column (75 µm inner diameter packed with 1.9 µm Venusil XBP C18 silica beads, Agela Technologies, China). The mobile phase for gradient elution consisted of mobile phase A (ddH2O mixed with 0.1% formic acid) and mobile phase B [ACN-H2O (8:2, v/v) mixed with 0.1% formic acid]. The chromatographic gradient program for both PASEF and diaPASEF analysis was set as follows: 2–28% B at 0–90 min, 28–46% B at 91–100 min, 46–95% B at 101–110 min, 95% B at 111–120 min.

For MS analysis operated in ddaPASEF mode, 1 survey TIMS-MS and 10 PASEF MS/MS scans were acquired during cycle time of 100 ms. Precursor ions for MS/MS analysis were isolated with a 2 Da window for m/z < 700 and 3 Da for m/z > 800 in a total m/z range of 100–1700. The collision energy was lowered linearly as a function of increasing ion mobility starting from 75 eV at 1/K0 = 1.6 Vs·cm−2 to 25 eV at 1/K0 = 0.6 Vs·cm−2. For analysis of cross-linked peptides, precursors with charge states of ≥3+ and ≤6+ were selected for fragmentation, while precursors with charge states ≥1+ and ≤6+ were selected for fragmentation of regular peptides.

For MS analysis operated in diaPASEF mode, a 2D polygonal filtering window was used for precursor selection, with m/z ranging from 400–1600, 1/K0 ranging from 0.74–0.84 at m/z of 400 and 1.22–1.58 at m/z of 1600. The m/z windows were divided to 80 sub-windows with m/z width set as 15. The collision energy was lowered linearly as a function of increasing ion mobility starting from 75 eV at 1/K0 = 1.6 Vs·cm−2 to 25 eV at 1/K0 = 0.6 Vs·cm−2.

DDA and DIA software parameters
pLink2 and pLink3 were used with the following parameters: precursor tolerance, 20 ppm; fragment tolerance, 20 ppm; enzyme, trypsin; number of missed cleavages, 3; peptide mass, [600, 6000]; peptide length, [6, 60]; fixed modification, carbamidomethylation (+57.021 Da) for cysteines; no variable modifications; filter tolerance, ±10 ppm; FDR, 1% at PSM level.

Scout (1.6.3) were used with the following parameters: fragment m/z, [200, 1800]; crosslinker, DSSO; reaction residuals, k; enzyme, trypsin; enzyme specificity, FullySpecific; Isotopic possibilities precursor, 1; peptide length, [6, 60]; max variable modification per peptide, 2; peptide mass, [500, 6000]; max miscleavages, 3; ppm error on MS1 level, 10; ppm error on MS2 level, 20; static modification, Carbamidomethyl; variable modification, Oxidation on Methionine; FDR 100% on all level.

DIA-NN (1.8.1) was run with the following parameters: Mass accuracy, 10 ppm; MS2 accuracy, 15 ppm; scan window, 6; use isotopologues; no shared spectra; neural network class, double-pass model; quantification strategy, robust LC; precursor FDR, 1%.

Peptide encoding
We encoded each peptide of a cross-linked peptide separately. Each peptide was converted into a letter sequence where each amino acid was represented by its corresponding one letter code, such as A for alanine and K for lysine. Each amino acid was then encoded as a 23-dimensional one-hot vector, with the first twenty dimensions representing the 20 standard amino acids, the 21st and 22nd dimensions reserved for potential PTMs which were not used in this paper, and the 23rd dimension indicating crosslinking sites. The maximum length of a peptide was set to 50. For a peptide containing M amino acids, the M×23 one-hot tensors were zero-padded to 50×23.

Deep4D-XL model
Deep4D-XL builds upon the Deep4D model with enhancements tailored to cross-linked peptides, incorporating Siamese network structures and cross-attention mechanisms. The framework comprises encoding and decoding modules. Specifically, shared parameter encoding modules characterize each peptide in a cross-linked pair. A cross-attention mechanism then integrates the outputs of the encoding modules of both peptides. Finally, the decoding module processes the output from the cross-attention module to generate predictions. Detailed specifications of the encoding and decoding modules are provided below.

Encoding module. The encoded representation tensor of the peptide is first embedded through a 500-dimensional fully connected layer. Then the embedding tensor is put into several serial sub-encoders, two sub-encoders for CCS prediction and three sub-encoders for retention time and fragment ion intensity prediction. Each sub-encoder consists of 5 layers, and each layer is composed of multi-head attention and a fully connected feed-forward network, with residual connection and layer normalization. The number of heads and the dimension of the feed-forward network are set to 5 and 1200.

Decoding module. The decoder consists of a convolutional neural network and a fully connected feed-forward network. The output tensor of the Encoder was put into a convolutional neural network. For CCS and intensity ion prediction, the convolutional neural network contains 2 batch normalization layers, 2 convolution layers and 2 max pooling layers. For retention time prediction, the convolutional neural network contains 3 batch normalization layers, 3 convolution layers and 3 max pooling layers. Then, the 3D output tensor of the convolutional neural network was converted to 1D and put into a fully connected feedforward network to obtain the final predicted CCS, RT or fragment ion intensity.

We trained or fine-tuned our models on a machine with one NVIDIA Tesla V100 GPU. The Adam optimizer was used with beta1 = 0.9, beta2 = 0.999 and eta_min = 10−9. Learning rate was set to 1e−4 for pre-training and 1e−5 for fine-tuning, with adjustment managed by the Cosine Annealing Warm Restarts method. The CCS and RT models were trained using the MSE loss function, while the MS2 model utilized a normalized spectral contrast loss function. Training was conducted for 70 epochs with early stopping based on the validation set.

DDA rescoring
The workflow includes 4D prediction, feature extraction, rescoring and FDR evaluation. 4D prediction of cross-linked peptides using Deep4D-XL: The Deep4D-XL model is first fine-tuned using 4D information of all intra-protein cross-linked peptides. Subsequently, PSMs of all cross-linked peptides, including TD and DD decoys, were extracted from the pLink2 result file. CCS, RT, and MS/MS spectra of these PSMs are predicted using a fine-tuned Deep4D-XL model.

Feature extractions. All 4D information predicted values and experimental values of cross-linked peptide PSM are used for feature extraction. There are a total of 16 features, including Charge, Original_score, Length 1, Length 2, RT_AE, CCS_RE, Match_num, Match_num1, Match_num2, Both_num, Both_num1, Both_num2, Cosine, SA, Pearson, and Spearman (Supplementary Table 1).

Rescoring using deep neural networks. The deep neural network consists of four layers of fully connected networks, with corresponding neuron numbers of 100, 1000, 100, and 1. First, all target cross-linked peptides that initially meet the FDR criteria of the pLink2 software were labeled as 1, and all decoy cross-linked peptides as 0. A subset of target cross-linked peptides that did not meet the FDR criteria remained temporarily unlabeled. Subsequently, all target and decoy cross-linked peptides labeled as 1 or 0 are evenly divided into n parts for n-fold cross-validation. Using this approach, n models are trained, with each model being trained on n-1 parts and tested on the remaining part. During training, part of the data is selected from the training set as the validation set, and the evaluation metric of the validation set is the median absolute error. Based on the evaluation metric, the best model parameters are selected for the rescoring of the test set and unlabeled cross-linked peptides.

DIA FDR evaluation
The FDR evaluation was based on the identification results of diaPASEF cross-linked mass spectrometry data in DIA-NN software. A sample-specific 4D experimental spectral library was constructed based on the DDA identification results of cross-linked peptides. Here, we defined the cross-linked peptides in the experimental spectral library as TT, meaning that both peptides in the cross-linked pair were target peptides. For each target cross-linked peptide, its corresponding decoy cross-linked peptides are generated by reversing one or two independent linear peptide sequences it contains (excluding the terminal amino acid). The decoy cross-linked peptides include two types: TD, which contains one target and one decoy peptide, and DD, which contains two decoy peptides. Next, use the Deep4D-XL model to construct a decoy spectral library, and merge the experimental spectral library and the decoy spectral library into a comprehensive spectral library (Supplementary Fig. 8). Finally, use this spectral library with DIA-NN software to perform DIA analysis on the diaPASEF cross-linked mass spectrometry data. Calculate the FDR based on the numbers of target and decoy peptides at a given score threshold, using the formula:

FDR = (#TD + #DD) / #TT

#TD and #DD respectively represent the number of two types of decoy peptides passing the score threshold, while #TT represents the number of target cross-linked peptides identified above the same threshold.

DIA rescoring
The workflow includes the construction of a spectral library and DIA analysis, feature extraction of cross-linked peptides, and rescore based on deep neural networks and FDR assessment.

Construction of spectral library. The spectral library consists of three parts: the sample-specific experimental spectral library, the decoy spectral library, and the theoretically predicted spectral library. Among these, the sample-specific experimental spectral library and decoy spectral library are mandatory options, while the theoretical predicted spectral library is optional and only needed for DIA analysis based on theoretical predictions.

Feature extraction. Based on the experimental information of the cross-linked peptide in the identification results and the prediction information of Deep4D-XL, the following features are extracted: Evidence, CScore, Q.Value, PEP, Average_corr, Pep1_num, Pep2_num, Pep1_num_matched, Pep2_num_matched, Spec_frag_num, Spec_frag_num1, Spec_frag_num2, Pep_cosine, Pep_entropy_smi, Pep1_cosine, Pep2_cosine, Pep1_entropy_smi, Pep2_entropy_smi, RT_AE, and CCS_RE (Supplementary Table 2).

Rescoring based on deep neural networks. Similar to the rescoring method in the previous DDA, a deep neural network is also used here as the rescoring model. The model consists of four fully connected layers with neuron counts of 100, 2000, 100, and 1, respectively. Initially, all cross-linked peptides identified by DIA-NN software are labeled, marking all decoy cross-linked peptides as 0. Then, an equal number of target cross-linked peptides from the experimental spectral library are randomly selected and marked as 1. These two datasets are combined for training the rescoring model. Remaining cross-linked peptides from the experimental spectral library are not labeled. If a theoretical prediction spectral library is added to the combined spectral library, then the cross-linked peptides from the theoretical prediction spectral library are marked as ‘test’. The model training and rescoring are performed using cross-validation. In each training session, 10% of the training set is selected as a validation set, with the evaluation metric being the median absolute error. The best model parameters, selected based on the evaluation metric of the validation set, are used after training to rescore the cross-linked peptides in the test set. The cross-linked peptides labeled as 1 or 0 are rescored using the model output when they were part of the test set in cross-validation. For all unlabeled or ‘test’ cross-linked peptides, the rescoring result is based on the average output of the model during cross-validation.

Validation and analysis of the cross-links. The high-resolution structures of the protein were obtained from RCSB PDB. The latest known PPI database STRING was used for PPI validation. 3D protein structure visualizations have been generated with PyMOL Open-Source 2.5.0.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Summary\nChen et al. developed a crosslinking MS software framework with two major focuses: rescoring of crosslink identifications\nfrom a standard data-dependent acquisition (DDA) workflow, and enabled crosslink identifications via library-free data-\nindependent acquisition (DIA) using predicted spectral libraries.\nFor this, they developed an algorithm that predicts retention time (RT), collisional cross-section (CCS) and crosslinked MS2\nspectra for DSS-crosslinked peptides. Their evaluation showed high predictive accuracy, demonstrating a general reliability\ncomparable to linear peptides in their dataset. Using these features, rescoring improved inter-protein crosslink identifications\nby 107% in a HeLa DSS dataset.\nAs a second aspect, the authors acquire a DIA dataset of HeLa DSS lysate and use their software to rescore the\nidentifications and state that they implement a more strictly controlled FDR. They also showed proof-of-concept for DIA\nsearches using predicted spectral libraries, identifying additional low-abundance crosslinks.\nDIA analysis is an important aspect in future crosslinking MS developments and this work claims promising initial results.\nHowever, there are essential controls and evaluations missing to fully judge the quality of the identifications. Especially the\nFDR calculation in the DIA results needs to be supported by additional analyses or controls. In addition, the claimed\nversatility is not given, as the work is entirely limited to one crosslinker and does not mention integration of the standard\ninput or output formats.\nTherefore, the work in its current state is only of limited use for the field and is not suitable for a publication in Nature\ncommunications.\nMajor concerns\nLack of proper controls\nThe controls used in this paper are not up to current field standards. The authors report an increase in identification numbers\nbut do not show sufficient evidence that these results are reliable.\nWhile possibly a good first impression, the use of residue-residue crosslink distances has been shown to drastically\nunderestimate the error (Yugandhar et al. 2020) and is unsuitable. For all of the optimisations shown, additional controls\nneed to be employed. Appropriate controls are for example the use of an entrapment database by searching the same\nnumber of proteins of a different species (Lenz et al. 2021) or datasets that have a built in experimental control (Clasen et al.\n2024; Matzinger et al. 2022; Stieger, Doppler, and Mechtler 2019; Lenz et al. 2021). I also want to highlight a recent preprint\nevaluating FDR evaluation for linear proteomics: (Wen et al. 2024, https://doi.org/10.1101/2024.06.01.596967).\nThis extra negative control needs to be employed on all the results from Figure 4 to 6.\nUnderstanding of DIA FDR\nThere seem to be major flaws in some of the conclusions drawn from the DIA FDR calculation. The authors appear to\nconfuse “rescoring” and “FDR calculation” and use them as interchangeable approaches (line 270: “Specifically, the\nrescoring method achieved a significantly low average FDR”). In fact, these are two separate concepts: rescoring adjusts\nand improves the final score, based on which the FDR is estimated and a cutoff is applied. The FDR threshold is defined by\nthe user and stays constant. Rescoring under a working FDR estimation improves the separation of true and false matches,\ntherefore the overall number of matches passing the same FDR threshold improves. It does not reduce the overall error.\nThis section therefore needs to be rephrased, extra controls need to be implemented and methodological details need to be\nclarified or changed.\nI assume that the error calculation as presented in the DIA-NN results (Fig 5) is already flawed in some way, but there is\ninformation lacking in the manuscript for a full picture:\nHow does the FDR calculation on the y-axis differ from DIA-NN’s internally calculated FDR (e.g., q-values)?\nThe spectral library generated by the authors includes TT, TD, and DD spectra. Are both TD and DD labeled as decoys\nwhen subjected to DIA-NN?\nWhat is the distribution of DIA-NN’s q-values (and scores) for these decoy matches?\nWas the FDR calculated the same way for DIA-NN and XL-MSDigger results? It’s unclear to me why the error is reduced if\nthe FDR was calculated the identically, as mentioned above, rescoring is not a suitable explanation for this.\nRelated to this, the authors test FDR thresholds of 1% and 0.1% and conclude the false positives decrease. However, the\nrelative error is much higher for the 0.1% cutoff. For example, F1 has an error of 14% for the desired 1% FDR (14-times\nincrease), while at 0.1% this relative error is 93-times higher than the desired 0.1%. This fact needs to be considered when\nevaluating the results.\nAlso it is crucial to know what FDR was set for the XL-MSDigger result. Was it 5% as reported? Please use the same\ncutoffs for both DIA-NN and XL-MSDigger.\nFor the decoy spectra generation, are both possible target-decoy spectra generated? It is unclear based on the text. I think\nit’s essential to generate both spectra since the identification quality is typically different depending on the peptide. Also, the\ndifferent sizes of random search space is the assumption for the FDR formula used in this manuscript.\nInclude an entrapment database or other negative control as mentioned above and report this error. See (Lenz et al. 2021;\nWen et al. 2024) for examples how to do it for crosslinking or DIA, respectively.\nThe manuscript lacks clarification regarding the level (spectrum, peptide pair, residue pair, protein) at which the results are\nreported and FDR is calculated, as it is my understanding that the rescoring would happen on spectrum level, while the\nauthors mention crosslinked peptides in their results. It has been established in the field that the error needs to be calculated\non the level that is being reported (Fischer and Rappsilber 2017; Lenz et al. 2021), and this might be one source of their\ninflated error.\nLimited crosslinker choice\nIn this work, the authors solely use DSS crosslinked datasets. While I understand that an optimised implementation might\nrequire more work, a tool that claims to be versatile needs to be adapted to a variety of crosslinkers, as right now, it is only a\nsoftware for the use with DSS.\nThere is no mention of adapting the workflow to non-cleavable crosslinkers of different masses. This should be an easy\ntweak in the algorithm and needs to be included.\nEspecially for PPI detection, the current field standard are cleavable crosslinkers. Even though the fragmentation behavior is\ndifferent, the fundemental behavior is similar (Kolbowski et al. 2022), and a basic implementation of cleavable crosslinkers is\nfeasible in my opinion, especially for the scope of a publication in Nature Communications.\nVersatility and standard outputs\nThe authors rely on implementing pLink2 for their workflow. For a versatile tool as claimed by the authors, it needs to work\nsearch software independent and field standard outputs (mzIdentML) (Rappsilber et al. 2025,\nhttps://doi.org/10.48550/arXiv.2504.06824) need to be accepted as well as outputted.\nUse of datasets\nThe work would significantly benefit from more datasets being incorporated. While I am aware that most published datasets\ndo not contain CCS information, retention time prediction and spectral prediction should still be valid and tested. In relation\nto this, I would like to see the spectral prediction efficiency depending on machine type and MS2 resolutions, or at least a\ncomment on them.\nMinor\nThere is information missing on the different types on fragments in typical crosslinking MS spectra for the evaluation of the\nspectral prediction.\nInformation needs to be added for fragments that contain the second peptide (“crosslinker containing fragments”). These\nneed to be highlighted in Fig. e and f.\nThe experimental spectra in Fig. 2 e+f seem to be cleaned and only show fragments of the peptides. Please specify this in\nthe caption and show the full spectra in the supplement.\nPlease add the detected fragments to the peptide sequences as it is usually shown (Fig. 2e+f).\nFig 2d should include the dot product of only those crosslinker containing fragments.\nTypically one of the two crosslinked peptides fragments much better than the other. Fig. 2d should also include separate dot\nproducts for each of those peptides.\nPlease add an evaluation of the impact of the different subscores on the rescoring. I.e. is the spectral prediction more\nimportant than the CCS? This helps the user to estimate which things to focus on for optimisation.\nFigures 4a and 5: The use of individual fractions from the same sample as individual results is unclear to me. If these are\nmeant to represent distinct sets of peptides, I find it insufficient, as a substantial peptide overlap between fractions is likely.\nInstead, I recommend the use of different datasets (see above), even if they lack CCS information.\nDetails on the pLink2 and DIA-NN settings are lacking (line 107 / methods): e.g. what FDR was set, on which level was it\ncalculated, information on search settings and version.\nAs shown in Fig. 4c, the STRING database contains many low confidence interactions. In my understanding, this amount\nwill vary based on the protein selection. Therefore, I would like to see the percentage of PPIs shown in 4c also for PPIs of\nproteins identified in pLink2 / XL-MSDigger only.\nFor the predicted spectral library, how are crosslinking sites handled? Will all possible sites be included for the same\npeptide pair?\nThe authors should cite recent work of the Sinz lab for DIA in crosslinking MS (Rojas Echeverri et al. 2024).", "reviewer_2": "Review: XL-MSDigger: A Deep Learning-1 Based Versatile Solution for Cross-Linking Mass Spectrometry\nThis work is focused on the growing area of cross-linking mass spectrometry to provide increased informatics intended to\nincrease the depth of analysis that is possible. The authors train models to predict chromatographic retention time, gas\nphase collisional cross-section (CSS), and fragment intensities of peptide pairs cross-linked with the non-cleavable cross-\nlinker DSS. They then use these models to re-score pLink2 cross-link identifications, to generate predicted spectral libraries,\nand with the use of a decoy spectral library, to predict the FDR of DIANN DIA results. This work is of value and these\nprograms could have potential benefit to the cross-link community.\nGeneral comments:\nMany labs that are focused on advanced cross-linker mass spectrometry studies with complex systems are employing\ncleavable chemical cross-linkers since the ID strategies are more straightforward. However, the programs developed in this\nwork could also benefit these labs and increase the impact of the present work. Therefore, additional documentation on\nGitHub to illustrate how to use the software and train models for data of cross-linkers other than DSS and analyzed with\nsoftware other than pLink2 is needed. In the GitHub Deep4D section, there are instructions for training the RT, CCS,\nfragment models, but not in the Deep4D-XL section.\nThe presented analysis is applied only to pLink2 results and with rescoring, improves its numbers of identifications. How\ndoes this compare with other software programs such as Kojak? A concern is that the improvements in rescoring may only\nbe relevant to previous software, pLink2, developed by the authors. If so, it would seem the potential advances of the present\nwork are limited, only helpful to labs that use pLink and therefore, less appropriate for a broad impact journal, such as Nature\nCommunications. It’s also possible that other programs like Kojak already perform as well as the presented improvements to\npLink2 and this would be important to evaluate for a larger audience.\nRetention time, CCS, and fragment intensities are used to re-score pLink2 results. For a broader impact on the community,\ndiscussion on how much each of those features individually contribute to increased numbers of cross-link identifications is\nneeded. For instance, many in the XL-MS community may not have CSS available so how much could they expect to benefit\nfrom RT or fragment ion intensities? It would be useful to assess the use of all subsets of those features in comparison to\ndetermine their contributions and benefits.\nValidation of additional identifications is done only with STRING. An improvement is needed that includes analysis of the\nDDA data with Kojak or something similar to illustrate that re-scoring yields everything that Kojak identified but not identified\nwith pLink2.\nTo validate the DIA analysis, the authors should first assess what fraction of the DDA library entries (most assuredly in the\nsample) are identified. This should be close to 100%.\nReproducibility of DIA. Coverage is a benefit proposed for DIA. This should be tested directly on sets of both technical and\nbiological replicates. What is the frequency for identifying library entries in each number of replicates after rescoring DIANN\nresults with controlled FDR?\nSpecific items:\np. 2 line 65: the word ‘powerful’ is unclear and should be omitted.\np. 3 line 73: You state ‘DIA XL-MS analysis tools’ yet you only consider one tool, DIANN, in this manuscript.\np. 3 line 83: ‘Siamese network architecture’ should be defined or referenced.\np. 3 line 84: ‘cross-attention module’ also should be defined or referenced.\np. 3 line 86: ‘MLP’ should be defined or referenced (Make sure Methods explains the above 3 steps in detail).\np. 3 line 92: The increased R2 against a single test dataset versus xiRT is not very large and should be compared against a\nset of test datasets, if possible, to show mean and error R2 values and the assessed statistical significance of their\ndifference.\np.3 line 96. Figure 1a. What is meant by the various shades of blue and green in the one-hot and positional\nencodings?\np. 4 line 107. How were the data filtered to ensure high quality? What fraction were inter-protein cross-links?\np. 6 line 139. You state ‘We also validated the model performance on a dataset of linear peptides MS/MS spectra derived\nfrom pLink2 results’ , yet your model requires two cross-linked peptides as input, doesn’t it? How then can it work on\nindividual peptide id’s?\np. 9 line 208: ‘under the assumption that the target PSMs meeting the FDR threshold in the original search results were\nauthentic’ but you later show that the pLink2 FDRs were much higher than the reported. If that’s the case, then you should\nideally never achieve 100% sensitivity.\np. 12 line 269: ‘Does the re-scoring of DIANN results use the DDA library or also the predicted library?\np. 12 line 272: ‘meeting the commonly accepted 5% FDR threshold in the field of XL-MS research’. Can one filter the output\nto achieve any desired FDR, for example 1%? Is there an overall score by which to rank all results in order to know how far\ndown the list one can go before reaching that FDR value? For example, are there calculated qvalues?\np. 14 line 333: Would it be worthwhile to also make libraries of pairs of proteins that are by no means expected to interact\nand see how many you identify in your HeLa DIA runs?\np. 14 line 344: How do the predicted spectral library entries compare with their corresponding DDA based ones? Do they\nhave good agreement (via DOT product)?\np. 14 line 345: Do you ever describe in detail your training dataset of identified cross-links? How many non-redundant cross-\nlinks did they include? How many instances of each? How many do you think are required to train models of a cleavable\ncross-linker? What is the effect of having as many as 10% false positives in your training data set?", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_4": "Chen et al. present Deep4D-XL, a deep neural network predictor for the RT, CSS, and MS/MS spectra of crosslinked\npeptides. They use this predictor to rescore pLink2 results of DDA data, so that pLink2 crosslink assignments that were\npreviously below the confidence threshold may now be reported as hits, apparently within the same set FDR. The\nmanuscript then probes the potential of the predictor to build libraries for DIA analysis of XL-MS data. Results of intra-protein\ncrosslinks in a pre-selected set are presented showing an improvement of ~10% (?) in identification. Also presented are\nresults of DIA analysis for inter-protein crosslinks within a set of pre-selected proteins.\nWhile the ability of deep NN predictors to find the RT of crosslinked peptides was previously demonstrated (ref. 26), the\nauthors demonstration of CSS and MS/MS spectra predictions for crosslinked peptides is novel.\nI have several concerns about the results:\n1) What is the real availability of this predictor to the XL-MS community? My understanding is that currently a new predictor\nmust be TRAINED for the use of each research group, because of differences in instrumentation, analytical columns, LC\ngradients, crosslinking reagents and even preference of analysis software (pLink, Xi, Merox, etc.). Specifically, the authors\ntrained a predictor on the data of ref. 26, and then trained ANOTHER predictor on their own data. If this is indeed the case,\nthen the usability of the rescoring scheme to the XL-MS community is low, since most research group will not be willing to\ndabble in deep NN training. To show the general usability of the approach, I think the authors should benchmark it on\ndatasets other than their own, such as Bartolec et al. (ref. 3) and Wheat et al. (PMID: 34349018).\n2) The rescoring scheme in the DDA context is doing rather dramatic changes in the reported crosslink list, and perhaps not\nall of them for the better. I think that the author’s statement of 2x increase in PSM and PPI yield (Fig. 4b) is too superficial and\nshould be examined more closely. For example, looking at Data Set 2 on all the entries for which gene1 starts with the letter\n“L”:\nThe original pLink2 list shows 6 inter-protein crosslinks. The rescored list shows 9 inter-protein crosslinks that are VERY\ndifferent: two confident interactions from the pLink2 list are now missing (LIN9-LIN37 and LARP7-PABP4) ; one highly\nsuspect interaction (LSM4-FINC) is added ; a homodimer interaction that are always suspect as artefact (LMNA- LMNA) is\nadded 3 times as the same peptide pair, and so on.\nThe authors should clean their data of same peptide-pair redundancies, and assess more closely what biological insights are\nactually gained (if at all) from the rescoring.\n3) The idea of DIA analysis to find low-intensity XL-MS signal at the proteome-level is very intriguing, even if it is currently\ncomputational prohibitive, as the author rightly explain. I think the authors should better substantiate their claims regarding\nits possible merits. Specifically:\na. Can at least some of the new crosslinks that were identified by DIA (both intra- and inter-, Fig. 6a and 6d) be now\nidentified by DDA using targeted reaction monitoring?\nb. Many of the new DIA intra-links are consecutive peptides, which are often common mis-assigment artefacts. Can the\nauthors state how many non-consecutive peptides were in the DDA and DIA analyses.\nc. What was the negative control in running the DIA of Figures 6d and S9? Can the authors choose 17 proteins that are\nabsolutely not connected to HSP90AA1 and see that they don’t get an inter- crosslink? Can they do it 100 times, and see\nwhat are the statistics of getting an inter- crosslink with HSP90AA1 by chance?"}, "author_response": "Response to Reviewers’ Comments\nReviewer 1:\n1. Lack of proper controls. The controls used in this paper are not up to current field standards. The authors report\nan increase in identification numbers but do not show sufficient evidence that these results are reliable. While\npossibly a good first impression, the use of residue-residue crosslink distances has been shown to drastically\nunderestimate the error (Yugandhar et al. 2020) and is unsuitable. For all of the optimisations shown, additional\ncontrols need to be employed. Appropriate controls are for example the use of an entrapment database by\nsearching the same number of proteins of a different species (Lenz et al. 2021) or datasets that have a built in\nexperimental control (Clasen et al. 2024; Matzinger et al. 2022; Stieger, Doppler, and Mechtler 2019; Lenz et al.\n2021). I also want to highlight a recent preprint evaluating FDR evaluation for linear proteomics: (Wen et al. 2024,\nhttps://doi.org/10.1101/2024.06.01.596967). This extra negative control needs to be employed on all the results\nfrom Figure 4 to 6.\nReply: We sincerely thank you for the professional suggestion. We agree that controls are essential to further\nevaluate the reliability of the results. Therefore, we added new results in the revision.\nFor the DDA results (Fig. 4), we employed an E. coli proteome as an entrapment database combined with the\noriginal search database. Among the 1,298 inter-protein XL peptide PSMs identified by pLink2, 13 contained E. coli\npeptides, while after rescoring, 1,759 PSMs were identified, including 17 E. coli-derived PSMs. This comparable\nentrapment ratio indicates that the rescoring maintains the same level of reliability as the original search.\nThis experimental results have been added to the revised manuscript and Supplementary data. Please see lines 227-\n230 in the main text, and Supplementary Data 2.\nFor the DIA results, our DIA analysis already included rigorous negative controls during the library construction\nstep, where both TD (target–decoy) and DD (double–decoy) types of decoy XL peptides were generated for all\ntargets. Thus, the rescoring and FDR estimation were based on a built-in negative control framework. Nevertheless,\nwe further evaluated the results using an entrapment strategy.\nFor intra-protein DIA analysis (Fig. 6), 100 E. coli proteins were randomly selected and merged with 100 human\nproteins to build the predicted spectral library. At 5% FDR, among 88 newly identified intra-protein XL precursors,\nonly two originated from E. coli. Similarly, when combining 100 E. coli proteins with 100 low-abundance human\nproteins, two E. coli precursors were found among 34 new identifications, demonstrating robust FDR control\n(Supplementary Data 3). This experimental results have been added to the revised manuscript and\nSupplementary data. Please see lines 330-333 in the main text, and Supplementary Data 3.\nFor inter-protein DIA analysis (Fig. 6), following Reviewer #4’s suggestion, we randomly selected 17 E. coli proteins\nthat are unrelated to HSP90AA1 and combined them with HSP90AA1 to construct additional negative PPIs. We\nconducted 10 independent random trials under a 5% FDR threshold. Across these analyses, a total of 109\nprecursors were identified, among which only five (4.6%) involved E. coli proteins (Supplementary Data 4). These\nresults indicate that the probability of obtaining false inter-links with HSP90AA1 by chance is very low, confirming\nthe reliability of our DIA-based rescoring results. This experimental results have been added to the revised\nmanuscript and Supplementary data. Please see lines 360-365 in the main text, and Supplementary Data 4.\nTogether, these entrapment and decoy-based validations demonstrate that our rescoring method substantially\nincreases the number of identifications while maintaining high result reliability.\n2. Understanding of DIA FDR. There seem to be major flaws in some of the conclusions drawn from the DIA FDR\ncalculation. The authors appear to confuse “rescoring” and “FDR calculation” and use them as interchangeable\napproaches (line 270: “Specifically, the rescoring method achieved a significantly low average FDR”). In fact, these\nare two separate concepts: rescoring adjusts and improves the final score, based on which the FDR is estimated\nand a cutoff is applied. The FDR threshold is defined by the user and stays constant. Rescoring under a working\nFDR estimation improves the separation of true and false matches, therefore the overall number of matches\npassing the same FDR threshold improves. It does not reduce the overall error. This section therefore needs to be\nrephrased, extra controls need to be implemented and methodological details need to be clarified or changed.\nI assume that the error calculation as presented in the DIA-NN results (Fig 5) is already flawed in some way, but\nthere is information lacking in the manuscript for a full picture: How does the FDR calculation on the y-axis differ\nfrom DIA-NN’s internally calculated FDR (e.g., q-values)? The spectral library generated by the authors includes\nTT, TD, and DD spectra. Are both TD and DD labeled as decoys when subjected to DIA-NN? What is the distribution\nof DIA-NN’s q-values (and scores) for these decoy matches? Was the FDR calculated the same way for DIA-NN and\nXL-MSDigger results? It’s unclear to me why the error is reduced if the FDR was calculated the identically, as\nmentioned above, rescoring is not a suitable explanation for this. Related to this, the authors test FDR thresholds\nof 1% and 0.1% and conclude the false positives decrease. However, the relative error is much higher for the 0.1%\ncutoff. For example, F1 has an error of 14% for the desired 1% FDR (14-times increase), while at 0.1% this relative\nerror is 93-times higher than the desired 0.1%. This fact needs to be considered when evaluating the results. Also\nit is crucial to know what FDR was set for the XL-MSDigger result. Was it 5% as reported? Please use the same\ncutoffs for both DIA-NN and XL-MSDigger. For the decoy spectra generation, are both possible target-decoy\nspectra generated? It is unclear based on the text. I think it’s essential to generate both spectra since the\nidentification quality is typically different depending on the peptide. Also, the different sizes of random search\nspace is the assumption for the FDR formula used in this manuscript.\nReply: We thank the reviewer for these insightful and professional comments. We acknowledge that our previous\ndescription of the DIA section was confusing and did not clearly distinguish between the rescoring and FDR\ncalculation steps. We have now rewritten this section to clarify the workflow and ensure conceptual consistency.\nIn our analysis, DIA-NN was used only as an initial scoring engine to generate preliminary peptide-spectrum match\n(PSM) scores for TT, TD, and DD cross-linked peptides (generated at a ratio of 1:2:1). All three peptide types were\ntreated as target entries within the DIA-NN spectral library. The FDR estimation was then performed externally,\nbased on the score distributions of TT, TD, and DD peptides output by DIA-NN.\nIn the previous version, we referred to “DIA-NN 1%” and “DIA-NN 0.1%” conditions, which corresponded to\nrunning DIA-NN with internal Q-value thresholds of 1% and 0.1%, respectively, and then recalculating the FDR\nfrom the output. We agree that this terminology was confusing and have removed it in the revision. Instead, we\nnow rank all precursor identifications using DIA-NN scores and XL-MSDigger scores separately, compute FDRs\nusing the same target–decoy scheme, and compare the two methods at identical FDR thresholds (5% FDR in\nrevised Fig. 5a). The updated results show that rescoring markedly improves the separation between true and\nfalse matches. At an FDR of 5%, the number of identified cross-linked precursors increases from 5,379 (DIA-NN)\nto 25,269 (XL-MSDigger).\nFurthermore, the new Joint Density Plot (revised Fig. 5b) demonstrates that DIA-NN scores cannot effectively\nseparate target and decoy peptides, whereas XL-MSDigger scores achieve a clear bimodal distribution. The\naccompanying FDR-versus-identification curve (revised Fig. 5c) further confirms that XL-MSDigger consistently\nyields higher identifications across the entire FDR range. These results demonstrate that rescoring improves the\noverall quality of the scoring function and strengthens the separation between target and decoy identifications.\nConsequently, more confident matches can be obtained at the same FDR threshold.\nThese experimental results have been added to the revised manuscript. Please see lines 269-304 on page 11-13\nand Figure 5 in the revised manuscript.\n3. The manuscript lacks clarification regarding the level (spectrum, peptide pair, residue pair, protein) at which\nthe results are reported and FDR is calculated, as it is my understanding that the rescoring would happen on\nspectrum level, while the authors mention crosslinked peptides in their results. It has been established in the field\nthat the error needs to be calculated on the level that is being reported (Fischer and Rappsilber 2017; Lenz et al.\n2021), and this might be one source of their inflated error.\nReply: Thank you for your comment. In our study, the FDR was calculated at the PSM level for DDA data and at\nthe precursor level for DIA data. To avoid potential confusion, we have revised the manuscript to replace the term\n“cross-linked peptide” with more precise expressions such as “cross-linked PSM” and “cross-linked precursor”,\nas appropriate.\n4. Limited crosslinker choice. In this work, the authors solely use DSS crosslinked datasets. While I understand that\nan optimised implementation might require more work, a tool that claims to be versatile needs to be adapted to\na variety of crosslinkers, as right now, it is only a software for the use with DSS. There is no mention of adapting\nthe workflow to non-cleavable crosslinkers of different masses. This should be an easy tweak in the algorithm and\nneeds to be included. Especially for PPI detection, the current field standard are cleavable crosslinkers. Even\nthough the fragmentation behavior is different, the fundemental behavior is similar (Kolbowski et al. 2022), and\na basic implementation of cleavable crosslinkers is feasible in my opinion, especially for the scope of a publication\nin Nature Communications.\nReply: Thank you very much for your valuable suggestion. We fully agree that extending the method to include\nnon-cleavable cross-linkers of different masses as well as cleavable cross-linkers would further enhance the\nversatility and applicability of our framework.\nTo evaluate the generalizability of our model across non-cleavable cross-linkers with different masses, we first\nanalyzed an Orbitrap-based dataset generated using the non-cleavable cross-linker PhoX (PXD029034; Angew.\nChem. Int. Ed. 2022, 61, e202113937). Using pLink, this dataset yielded 22,306 cross-linked PSMs. After splitting\nthe data into training, validation, and test sets at an 8:1:1 ratio, Deep4D-XL achieved a median dot product of\n0.917 on the test set (Supplementary Fig. 1c in the revised Supplementary Information).\nFurthermore, we analyzed an Orbitrap-based dataset generated using the cleavable cross-linker DSBU\n(PXD012546; Anal. Chem. 2019, 91, 10236-10244). This dataset contained 20,446 cross-linked PSMs. To\naccommodate the distinct fragmentation characteristics of cleavable cross-linkers, we adjusted the output\ndimensionality of the Deep4D-XL model. After training, the model achieved a median dot product of 0.853 on the\ntest set (Supplementary Fig. 1c in the revised Supplementary Information). In addition, a retention-time\nprediction model trained on 2,981 DSBU-cross-linked peptides from the same dataset reached a mean absolute\nerror of 3.92 min (over a total gradient time of 240 min). These results have been added to the revised\nmanuscript and Supplementary Information. Please see lines 149-163 in the main text.\nWe then applied rescoring to representative subsets of data files from these datasets using pLink2 (PhoX) and\nScout (DSBU). For the PhoX-cross-linked dataset, the number of inter-protein cross-linked PSMs increased from\n152 to 317, and for the DSBU-cross-linked dataset, the number increased from 126 to 241 (Supplementary Fig. 7\nin the revised Supplementary Information). These results have been added to the revised manuscript and\nSupplementary Information. Please see lines 250-256 in the main text.\nThese results demonstrate that Deep4D-XL and XL-MSDigger can be readily adapted to different types of cross-\nlinkers, including both non-cleavable and cleavable reagents. We will continue to expand the range of supported\ncross-linkers and further optimize the algorithm in future updates.\n5. Versatility and standard outputs. The authors rely on implementing pLink2 for their workflow. For a versatile\ntool as claimed by the authors, it needs to work search software independent and field standard outputs\n(mzIdentML) (Rappsilber et al. 2025, https://doi.org/10.48550/arXiv.2504.06824) need to be accepted as well as\noutputted.\nReply: Thank you for your suggestion. In the latest version, we have extended the Deep4D-XL model to support\ncleavable cross-linkers and incorporated compatibility with the widely used cleavable XL-MS search software\nScout into our workflow, enabling XL-MSDigger to handle both uncleavable and cleavable XL-MS analyses. Using\nsix DSBU datasets from PXD012546, we found that XL-MSDigger substantially increased the number of inter-\nprotein PSMs from 126 to 241 after rescoring the Scout results (Supplementary Fig. 7a in the revised\nSupplementary Information), demonstrating a substantial enhancement in identification depth. We appreciate\nyour suggestion regarding the use of field-standard formats such as mzIdentML. While the current version mainly\nfocuses on rescoring results generated from existing search engines (pLink and Scout), we are already evaluating\npractical solutions for mzIdentML input/output compatibility in upcoming updates to better align with community\nstandards.\n6. Use of datasets. The work would significantly benefit from more datasets being incorporated. While I am aware\nthat most published datasets do not contain CCS information, retention time prediction and spectral prediction\nshould still be valid and tested. In relation to this, I would like to see the spectral prediction efficiency depending\non machine type and MS2 resolutions, or at least a comment on them.\nReply: Thank you for this helpful suggestion. In addition to the Orbitrap-based DSBU dataset mentioned in our\nresponse to Comment 4, we also analyzed the Orbitrap-based DSS dataset PXD017620 (Mol. Cell. Proteomics 2020,\n19, 1161-1178) to further evaluate the generalization of our model. This dataset contains 14,300 cross-linked\nPSMs identified using pLink2, which we randomly divided into training and test sets at a 9:1 ratio. After training,\nthe Deep4D-XL model achieved a median dot product of 0.844 on the test set (Supplementary Fig. 1c in the\nrevised Supplementary Information), indicating strong spectral prediction performance on a dataset acquired\nunder different MS2 resolution and instrument settings.\nFurthermore, we trained a retention time prediction model on 1,470 cross-linked peptides from the same dataset\n(training:test = 9:1). The model achieved a mean absolute error of 2.45 min (Supplementary Fig. 1a in the revised\nSupplementary Information), confirming that Deep4D-XL maintains robust prediction accuracy across different\ninstrument platforms and acquisition conditions.\n7. There is information missing on the different types on fragments in typical crosslinking MS spectra for the\nevaluation of the spectral prediction.\nInformation needs to be added for fragments that contain the second peptide (“crosslinker containing fragments”).\nThese need to be highlighted in Fig. e and f.\nThe experimental spectra in Fig. 2 e+f seem to be cleaned and only show fragments of the peptides. Please specify\nthis in the caption and show the full spectra in the supplement.\nPlease add the detected fragments to the peptide sequences as it is usually shown (Fig. 2e+f).\nFig 2d should include the dot product of only those crosslinker containing fragments.\nTypically one of the two crosslinked peptides fragments much better than the other. Fig. 2d should also include\nseparate dot products for each of those peptides.\nReply: We have revised the figures according to your request.\n8. Please add an evaluation of the impact of the different subscores on the rescoring. i.e. is the spectral prediction\nmore important than the CCS? This helps the user to estimate which things to focus on for optimisation.\nReply: Thank you for your helpful suggestion. To assess the contribution of different subscores to the rescoring\nperformance, we conducted ablation experiments on 40 DDA datasets by individually removing RT, spectral\nsimilarity, and CCS features. The results showed that excluding RT, spectral similarity, and CCS reduced the number\nof identified PSMs to 74%, 86%, and 99.6% of the original rescoring results, respectively (Supplementary Fig. 6 in\nthe revised Supplementary Information). This indicates that RT has the largest impact on model performance,\nfollowed by spectral similarity, whereas the CCS feature contributes only marginally.\nThis observation is consistent with the MSBooster study (Nat. Commun. 2023, 14, 4539), which reported that CCS\nis highly correlated with precursor m/z and charge, resulting in nearly identical CCS distributions between target\nand decoy peptides under the current ion mobility resolution. We speculate that the CCS dimension may play a\nmore significant role in the identification and differentiation of certain isomeric peptides. Overall, these results\nsuggest that RT and spectral similarity are the most influential features to prioritize during further optimization.\n9. Figures 4a and 5: The use of individual fractions from the same sample as individual results is unclear to me. If\nthese are meant to represent distinct sets of peptides, I find it insufficient, as a substantial peptide overlap\nbetween fractions is likely. Instead, I recommend the use of different datasets (see above), even if they lack CCS\ninformation.\nReply: To further evaluate cross-dataset applicability, we tested our framework on six BS3 datasets from the public\ndataset PXD017620. Using pLink2, 254 inter-protein XL-peptide PSMs were initially identified; after applying our\nDDA rescoring module, the number increased to 393 inter-protein XL-peptide PSMs (Supplementary Fig. 7b in the\nrevised Supplementary Information), including 241 overlapping with the original results (~95% sensitivity).\nThese results demonstrate that our approach is effective not only on our in-house data but also on independent\npublic datasets, indicating good generalizability and practical usability for the broader community.\n10. Details on the pLink2 and DIA-NN settings are lacking (line 107 / methods): e.g. what FDR was set, on which\nlevel was it calculated, information on search settings and version.\nReply: Thank you for pointing this out. We have now added detailed information about the pLink2 and DIA-NN\nsearch settings in the revised Methods section. Please see page 17 in the manuscript.\n11. As shown in Fig. 4c, the STRING database contains many low confidence interactions. In my understanding,\nthis amount will vary based on the protein selection. Therefore, I would like to see the percentage of PPIs shown\nin 4c also for PPIs of proteins identified in pLink2 / XL-MSDigger only.\nReply: Thank you for your valuable comment. As suggested, we analyzed the STRING confidence scores for the\nXL-MSDigger-only PPIs (101 PPIs) and the pLink2-only PPIs (11 PPIs). Our analysis showed that over 90% of the\nPPIs identified exclusively by pLink2, exclusively by XL-MSDigger, or by both methods had STRING confidence\nscores greater than 0.4. These comparable proportions indicate that the newly identified PPIs by XL-MSDigger\nexhibit a similar level of biological plausibility to those identified by pLink2, thereby supporting the reliability of\nour extended identifications. We have also updated Fig. 4c in the revised manuscript accordingly.\n12. For the predicted spectral library, how are crosslinking sites handled? Will all possible sites be included for the\nsame peptide pair?\nReply: When constructing the predicted spectral library, we considered all possible cross-linking site combinations\nfor each peptide pair, including all lysine residues and protein N-termini. This comprehensive enumeration\nensures that the predicted library fully covers all theoretically possible cross-linked configurations of the same\npeptide pair.\n13. The authors should cite recent work of the Sinz lab for DIA in crosslinking MS (Rojas Echeverri et al. 2024).\nReply: Thank you for your suggestion. The referenced work has been cited in the revised manuscript (Ref. 30).\nReviewer 2:\n1. Many labs that are focused on advanced cross-linker mass spectrometry studies with complex systems are\nemploying cleavable chemical cross-linkers since the ID strategies are more straightforward. However, the\nprograms developed in this work could also benefit these labs and increase the impact of the present work.\nTherefore, additional documentation on GitHub to illustrate how to use the software and train models for data of\ncross-linkers other than DSS and analyzed with software other than pLink2 is needed. In the GitHub Deep4D\nsection, there are instructions for training the RT, CCS, fragment models, but not in the Deep4D-XL section.\nThe presented analysis is applied only to pLink2 results and with rescoring, improves its numbers of identifications.\nHow does this compare with other software programs such as Kojak? A concern is that the improvements in\nrescoring may only be relevant to previous software, pLink2, developed by the authors. If so, it would seem the\npotential advances of the present work are limited, only helpful to labs that use pLink and therefore, less\nappropriate for a broad impact journal, such as Nature Communications. It’s also possible that other programs\nlike Kojak already perform as well as the presented improvements to pLink2 and this would be important to\nevaluate for a larger audience.\nReply: Thanks for your helpful suggestions. We have now added detailed instructions on the training process of\nthe Deep4D-XL model to our GitHub repository.\nTo further enhance the versatility of our tool, we have also extended model support to cleavable cross-linkers and\nsoftwares. Using the DSBU-crosslinked dataset PXD012546 (Anal. Chem. 2019, 91, 10236-10244), we obtained\n20,446 PSMs, which were split into training, validation, and test sets in an 8:1:1 ratio. To accommodate the specific\nfragmentation patterns of cleavable XL peptides, we modified the model output dimensions accordingly. The\ntrained model achieved a median dot product of 0.853 on the test set (Supplementary Fig. 1c in the revised\nSupplementary Information). In addition, we trained an RT-prediction model for 2,981 DSBU cross-linked\npeptides (training:test = 9:1), which achieved a mean RT error of 3.92 min over a 240-min gradient\n(Supplementary Fig. 1a in the revised Supplementary Information). We then applied rescoring to the\nidentification results generated by the Scout software for subsets of data files from the PXD012546 dataset, which\nincreased the number of inter-protein cross-linked PSMs from 126 to 241 (Supplementary Fig. 7 in the revised\nSupplementary Information).These results have been added to the revised manuscript and Supplementary\nInformation. We plan to continuously expand the range of supported cross-linkers in future updates.\nTo evaluate the general applicability of our approach beyond pLink2, we reanalyzed 40 DDA datasets using the\nKojak module within the TPP pipeline. We compared the results among Kojak, pLink2, and pLink2_rescore at the\ninter-protein XL-peptide level (figure below). The results show that pLink2 and Kojak yielded comparable total\nidentifications (565 and 597 XL peptides, respectively), with 212 shared identifications. After Deep4D-XL rescoring,\npLink2_rescore identified 983 XL peptides in total, including 86 additional peptides that were originally found only\nby Kojak, and 377 unique peptides not identified by either pLink2 or Kojak. Although some non-overlapping\nidentifications remain due to differences in the intrinsic scoring and validation strategies of the two software tools,\nthese results demonstrate that Deep4D-XL rescoring effectively improves identification coverage for inter-protein\nXL peptides.\n2. Retention time, CCS, and fragment intensities are used to re-score pLink2 results. For a broader impact on the\ncommunity, discussion on how much each of those features individually contribute to increased numbers of cross-\nlink identifications is needed. For instance, many in the XL-MS community may not have CSS available so how\nmuch could they expect to benefit from RT or fragment ion intensities? It would be useful to assess the use of all\nsubsets of those features in comparison to determine their contributions and benefits.\nReply: Thanks for your suggestion. To assess the contribution of different subscores to the rescoring performance,\nwe conducted ablation experiments on 40 DDA datasets by individually removing RT, spectral similarity, and CCS\nfeatures. The results showed that excluding RT, spectral similarity, and CCS reduced the number of identified\npeptides to 74%, 86%, and 99.6% of the original rescoring results, respectively (Supplementary Fig. 6 in\nthe revised Supplementary Information). This indicates that RT has the largest impact on model performance,\nfollowed by spectral similarity, whereas the CCS feature contributes marginally.\nThis observation is consistent with the MSBooster study (Nat. Commun. 2023, 14, 4539), which reported that CCS\nis highly correlated with precursor m/z and charge, resulting in nearly identical CCS distributions between target\nand decoy peptides under the current ion mobility resolution. Overall, these results suggest that RT and spectral\nsimilarity are the most influential features to prioritize during further optimization.\nAlthough the CCS feature does not show a major contribution in current proteomics rescoring workflows, its ability\nto distinguish structural and conformational isomers has been well demonstrated in multiple studies (Nat.\nCommun. 2023, 14, 6671; Angew. Chem. Int. Ed. 2025, 64, e202507483). With the continuous improvement of ion\nmobility resolution and instrumentation, CCS is expected to play an increasingly important role in proteomics,\nproviding more orthogonal and discriminative information that complements retention time and spectral\nsimilarity. Moreover, ion mobility-based acquisition strategies such as PASEF have been shown to significantly\nenhance MS sensitivity, further highlighting the growing potential of CCS-related features in future proteomic\nresearch.\n3. Validation of additional identifications is done only with STRING. An improvement is needed that includes\nanalysis of the DDA data with Kojak or something similar to illustrate that re-scoring yields everything that Kojak\nidentified but not identified with pLink2. To validate the DIA analysis, the authors should first assess what fraction\nof the DDA library entries (most assuredly in the sample) are identified. This should be close to 100%.\nReply: We appreciate the reviewer’s insightful comments. As mentioned in the response to Comment 1, our\nrescoring strategy (pLink2_rescore) successfully recovered 78 additional peptides that were originally identified\nonly by Kojak. This result indicates that the rescoring process not only improves sensitivity but also effectively\nbridges the gap between different search algorithms.\nAlthough in theory DIA methods are capable of covering all possible peptides present in a sample, in practice the\ninjected DIA samples are usually more complex than those used for DDA library construction. This is because DIA\nanalyses are often performed with fewer fractions, and the higher spectral complexity together with matrix effects\ntypically limit the coverage of the DDA-derived spectral library. For example, in the study by the Matthias Mann\nlab (Mol. Cell. Proteomics 2022, 21, 100279; https://doi.org/10.1016/j.mcpro.2022.100279), a sample-specific\nDDA spectral library containing 124,155 peptides was generated, but the corresponding DIA analysis identified an\naverage of 76,214 peptides—approximately 61% of the DDA library. In our case, we would like to clarify that our\ncomplexity compared with the individual DDA runs. Using the experimental DDA spectral library and applying a 1%\nDIA-NN Q-value threshold, we identified approximately 70% of the target cross-linked peptides contained in the\nDDA library. This recovery rate indicates that the coverage achieved by our method is well within an acceptable\nrange for DIA analyses.\nTo further validate the reliability of our DIA-based identifications, we adopted a negative control strategy\nsuggested by Reviewer 4. Specifically, we randomly selected 17 proteins from the E. coli proteome that are\nunrelated to HSP90AA1 and combined them with HSP90AA1 to construct additional in silico negative PPIs. We\nconducted 10 independent random trials under a 5% FDR threshold. Across these analyses, only 5 inter-links out\nof 109 total identifications (4.6%) were found as false (negative) PPIs (Supplementary Data 4). This very low false-\nlink probability demonstrates that the chance of obtaining spurious inter-links with HSP90AA1 by random\ncombination is minimal, thereby providing strong orthogonal evidence for the specificity and reliability of our DIA-\nbased analysis.\n4. Reproducibility of DIA. Coverage is a benefit proposed for DIA. This should be tested directly on sets of both\ntechnical and biological replicates. What is the frequency for identifying library entries in each number of\nreplicates after rescoring DIANN results with controlled FDR.\nReply: Thanks for your suggestion. Regarding technical reproducibility, we have previously investigated this aspect\nin our published 4D-diaXLMS study (Anal. Chem. 2023, 95:14077-14085). As described in that work, the proportion\nof reproducibly identified XL peptides across three technical replicates was 83%, which is substantially higher than\nthe 38% reproducibility observed for DDA XL-MS replicates.\nTo further evaluate biological reproducibility and the impact of rescoring, we analyzed data from another ongoing,\nunpublished project currently being conducted in our laboratory. This dataset consists of three biological\nreplicates of RAW 264.7 cell line samples, each separated into 10 fractions. A spectral library was constructed\nusing target cross-linked peptides identified from DDA experiments, together with corresponding TD and DD\ndecoy cross-linked peptides. First, we obtained the initial results by setting the DIA-NN Q-value threshold to 5%.\nWe then recalculated the actual FDR based on the proportion of decoy peptides and filtered the identifications at\nFDR < 5%, resulting in 7,756 target peptides, with 2,850 shared across the three replicates (36.7% reproducibility)\n(see figure below). After applying rescoring and filtering again at FDR < 5%, the number of identified target cross-\nlinked peptides increased to 13,158, with 6,623 reproducibly detected across the three replicates (50.3%\nreproducibility). These results clearly demonstrate that rescoring substantially improves both the total number of\nconfident identifications and their reproducibility under the same controlled FDR threshold.\n5. Minor concerns:\np. 2 line 65: the word ‘powerful’ is unclear and should be omitted.\np. 3 line 73: You state ‘DIA XL-MS analysis tools’ yet you only consider one tool, DIANN, in this manuscript.\np. 3 line 83: ‘Siamese network architecture’ should be defined or referenced.\np. 3 line 84: ‘cross-attention module’ should be defined or referenced.\np. 3 line 86: ‘MLP’ should be defined or referenced (Make sure Methods explains the above 3 steps in detail).\nReply: The manuscript has been revised accordingly.\n6. p. 3 line 92: The increased R2 against a single test dataset versus xiRT is not very large and should be compared\nagainst a set of test datasets, if possible, to show mean and error R2 values and the assessed statistical significance\nof their difference.\nReply: We thank the reviewer for this valuable comment. Our initial intention was to ensure a fair comparison\nbetween our model and xiRT; therefore, we used the same dataset reported in the original xiRT publication,\ntrained and tested our Deep4D-XL model on it, and directly compared our results with the reported xiRT\nperformance metrics.\nWe fully agree with you that evaluation across multiple datasets provides a more comprehensive assessment.\nAccordingly, we further trained and tested both xiRT and Deep4D-XL on three additional datasets: (i) the retention\ntime dataset constructed in our study, (ii) PXD017620 (Mol. Cell. Proteomics 2020, 19, 1161-1178), and (iii)\nPXD012546 (Anal. Chem. 2019, 91, 10236-10244). For each dataset, both models were trained and tested using\nthe same data splits. The resulting mean absolute errors (MAE) of Deep4D-XL were 2.06, 2.45, and 3.92 min,\nwhereas the corresponding MAE values of xiRT were 3.03, 4.00, and 13.26 min, respectively (Supplementary Fig.\n1a and 1b in the revised Supplementary Information). These results clearly demonstrate that Deep4D-XL achieves\nsuperior retention time prediction accuracy compared with xiRT across all evaluated datasets.\n7. p.3 line 96. Figure 1a. What is meant by the various shades of blue and green in the one-hot and positional\nencodings?\nReply: The different shades of blue and green in Figure 1a are only used to visually distinguish the two peptide\nsequences for illustration purposes. The color depth has no quantitative meaning and does not represent any\nspecific numerical value or feature intensity.\n8. p. 4 line 107. How were the data filtered to ensure high quality? What fraction were inter-protein cross-links?\nReply: To ensure high data quality, we set the FDR threshold at 1% in the pLink2 search results. For each identified\npeptide, the highest-scoring PSM in each observed charge state was retained for extracting retention time (RT),\ncollision cross section (CCS), and MS/MS spectral information. This is described in lines 108–112 in the revised\nmanuscript. Among the 34,115 database-identified cross-links, 738 were inter-protein cross-links.\n9. p. 6 line 139. You state ‘We also validated the model performance on a dataset of linear peptides MS/MS spectra\nderived from pLink2 results’, yet your model requires two cross-linked peptides as input, doesn’t it? How then can\nit work on individual peptide id’s?\nReply: In our model architecture, the two peptide encoders share parameters through a Siamese network\nstructure. For linear peptides, we used the same encoder to generate their representations. The cross-attention\nmodule was slightly modified such that both of its inputs were set to the same encoder output, effectively\nfunctioning as a self-attention mechanism in this case. We agree that the original description may have caused\nsome confusion. Following Reviewer 1’s comment, we have removed the prediction results on linear peptide\nMS/MS spectra from the revised manuscript. Instead, to more comprehensively characterize the model’s\nperformance on cross-linked peptide spectra, we now report the dot products between the predicted and\nexperimental spectra for (i) fragment ions originating from each of the two peptides, and (ii) fragment ions\ncontaining the cross-linking site. These revised evaluations more accurately reflect the model’s capability in\npredicting cross-linked MS/MS spectra. Please see lines 143–145 on page 6 and Fig. 2 in the revised manuscript.\n10. p. 9 line 208: ‘under the assumption that the target PSMs meeting the FDR threshold in the original search\nresults were authentic’ but you later show that the pLink2 FDRs were much higher than the reported. If that’s the\ncase, then you should ideally never achieve 100% sensitivity.\nReply: Thank you for this comment. We believe there may be a misunderstanding regarding the origin of the\nhigher FDR values shown later in the manuscript. The assumption that “the target PSMs meeting the FDR threshold\nin the original search results were authentic” refers specifically to the DDA pLink2 search results, which were used\nas the ground-truth labels in the rescoring framework. This is a common and widely adopted practice in rescoring\napproaches (Nat Methods 4, 923–925 (2007)), where the target PSMs passing the original FDR threshold serve as\npositive examples to train a model that aims to recover additional true targets from those originally below the\ncutoff.\nIn contrast, the higher FDR values discussed later in the manuscript correspond to the DIA identifications produced\nby DIA-NN, not to the DDA pLink2 results. As we detail in lines 269–304 of the revised manuscript, in DIA analysis\nthe initial DIA-NN scores do not sufficiently separate target and decoy precursors, resulting in inflated apparent\nFDRs. After applying XL-MSDigger rescoring, the updated scores provide much better target–decoy separation and\nthus substantially reduce the DIA-level FDR.\n11. p. 12 line 269: ‘Does the re-scoring of DIA-NN results use the DDA library or also the predicted library?\nReply: In our DIA-NN rescoring analysis, all target peptides were derived from the experimental library, while all\ndecoy peptides were generated from the predicted library. As we detail in lines 269-272 on page 11 of the revised\nmanuscript and the supplementary Figure 8.\n12. p. 12 line 272: ‘meeting the commonly accepted 5% FDR threshold in the field of XL-MS research’. Can one\nfilter the output to achieve any desired FDR, for example 1%? Is there an overall score by which to rank all results\nin order to know how far down the list one can go before reaching that FDR value? For example, are there\ncalculated qvalues?\nReply: We thank the reviewer for this insightful question. In our rescoring framework, each precursor in the DIA\nresults is assigned a continuous score, and all precursors are ranked according to this score to calculate the\ncorresponding FDR. Therefore, the output can be filtered at any FDR threshold, such as 1%. To illustrate this\nflexibility, we have additionally included a curve showing the relationship between FDR and the number of\nidentifications in Fig. 5c in the revised manuscript.\n13. p. 14 line 333: Would it be worthwhile to also make libraries of pairs of proteins that are by no means expected\nto interact and see how many you identify in your HeLa DIA runs?\nReply: Thank you for this valuable suggestion. Reviewer 4 also raised a similar point. To further validate the\nspecificity of our DIA-based rescoring approach, we randomly selected 17 E. coli proteins that are biologically\nunrelated to HSP90AA1 and combined them with HSP90AA1 to construct additional negative PPI libraries. We\nthen performed 10 independent random trials under a 5% FDR threshold. Across these analyses, a total of 109\nprecursors were identified, among which only five (4.6%) involved E. coli proteins. These results indicate that the\nlikelihood of obtaining false inter-links with HSP90AA1 by random chance is very low, thereby supporting the\nreliability and specificity of our DIA-based rescoring results. This experimental results have been added to the\nrevised manuscript and Supplementary data. Please see lines 360-365 on page 15 in the main text, and\nSupplementary Data 4.\n14. p. 14 line 344: How do the predicted spectral library entries compare with their corresponding DDA based\nones? Do they have good agreement (via DOT product)?\nReply: We thank the reviewer for raising this question. In our spectral library, the DDA-based portion was directly\ntaken from the experimental library. The predicted part included theoretically generated intra- and inter-protein\ncross-linked peptides corresponding to proteins or PPIs of interest, as well as all decoy cross-linked peptides. For\nthese predicted spectra, no experimental spectra were available for direct comparison.\n15. p. 14 line 345: Do you ever describe in detail your training dataset of identified cross-links? How many non-\nredundant cross-links did they include? How many instances of each? How many do you think are required to\ntrain models of a cleavable cross-linker? What is the effect of having as many as 10% false positives in your training\ndata set?\nReply: In our constructed dataset, a total of 34,115 cross-links were included, comprising 25,910 non-redundant\ncross-linked peptides with charge states of 3, 4, or 5. For each non-redundant cross-linked peptide under the same\ncharge state, only the PSM with the highest score was retained to ensure data quality. These details are described\nin lines 108-112 on page 4 of the main text and illustrated in Fig. 2a.\nFor the cleavable cross-linker, we used a public DSBU dataset (PXD012546, Anal. Chem. 2019, 91, 10236-10244)\nand built a dataset containing 20,446 cross-links. The data were split into training, validation, and test sets in an\n8:1:1 ratio. On the test set, the model achieved a dot product similarity of 0.853 (Supplementary Fig. 1c in the\nrevised Supplementary Information) between the predicted and experimental spectra. We believe that the\nprediction performance can be further improved as larger and more diverse training datasets become available\nin the future.\nTo further evaluate the effect of false positives in the training data, we performed a controlled simulation by\nreversing the peptide sequences of 10% of cross-linked peptides in the training set to generate synthetic false\nexamples. After retraining, the model achieved a median dot product of 0.80 on the test set, compared to 0.88\nfor the original model, suggesting a moderate but measurable decline in performance (see figure below). This\nanalysis demonstrates that while the model shows reasonable tolerance to limited noise, expanding high-quality\nand diverse training datasets will be essential for further improving prediction accuracy in the future.\nReviewer 4:\n1. What is the real availability of this predictor to the XL-MS community? My understanding is that currently a\nnew predictor must be TRAINED for the use of each research group, because of differences in instrumentation,\nanalytical columns, LC gradients, crosslinking reagents and even preference of analysis software (pLink, Xi, Merox,\netc.). Specifically, the authors trained a predictor on the data of ref. 26, and then trained ANOTHER predictor on\ntheir own data. If this is indeed the case, then the usability of the rescoring scheme to the XL-MS community is\nlow, since most research group will not be willing to dabble in deep NN training. To show the general usability of\nthe approach, I think the authors should benchmark it on datasets other than their own, such as Bartolec et al.\n(ref. 3) and Wheat et al. (PMID: 34349018).\nReply: We thank you for this insightful and professional comment. We agree that generalizability is essential for\nthe broad adoption of our approach within the XL-MS community. To address this, our DDA module includes an\nautomated fine-tuning option, which enables on-the-fly adaptation of the MS/MS and RT prediction models based\non the current DDA results. This allows the predictor to automatically adjust to dataset-specific characteristics—\nsuch as instrument type, LC gradient, and cross-linker—without manual retraining by the user.\nTo further assess cross-dataset applicability, we tested our framework on six BS3 datasets from the public dataset\nPXD017620 (Mol. Cell. Proteomics 2020, 19, 1161-1178). Initially, 254 inter-protein XL-peptide PSMs were\nidentified; after applying XL-MSDigger DDA rescoring module, the number increased to 476 inter-protein XL-\npeptide PSMs (Supplementary Fig. 7b in the revised Supplementary Information). These results demonstrate\nthat our approach is effective not only on in-house data but also on independent public datasets, highlighting its\ngood generalizability.\nTo further demonstrate the broad usability and versatility of our framework, we have extended the Deep4D-XL\nmodel and XL-MSDigger workflow to support cleavable cross-linkers and multiple XL-MS search engines.\nSpecifically, we added compatibility with the Scout search software, enabling XL-MSDigger to process both\nuncleavable and cleavable XL-MS data within a unified workflow. To verify model-level adaptability, we analyzed\nthe DSBU-crosslinked dataset PXD012546 (Anal. Chem. 2019, 91, 10236–10244), which yielded 20,446 cross-\nlinked PSMs. The data were divided into training, validation, and test sets (8:1:1). After adjusting the output\ndimension to accommodate the unique fragmentation behavior of cleavable crosslinkers, the trained Deep4D-XL\nmodel achieved a median dot product of 0.855 on the test set (Supplementary Fig. 1c). In addition, a retention\ntime prediction model trained on 2,981 DSBU peptides reached a mean absolute error of 3.92 min across a 240-\nmin LC gradient (Supplementary Fig. 1a), indicating strong predictive performance. At the workflow level, using\nsix DSBU data, we found that XL-MSDigger increased the number of inter-protein PSMs from 126 to 241 after\nrescoring the Scout results, demonstrating a substantial enhancement in identification depth (Supplementary Fig.\n7a).\nTogether, these results clearly demonstrate that our framework achieves both dataset-level generalizability and\ncross-linker–level adaptability, providing a practical and scalable solution for the broader XL-MS community.\n2. The rescoring scheme in the DDA context is doing rather dramatic changes in the reported crosslink list, and\nperhaps not all of them for the better. I think that the author’s statement of 2x increase in PSM and PPI yield (Fig.\n4b) is too superficial and should be examined more closely. For example, looking at Data Set 2 on all the entries\nfor which gene1 starts with the letter “L”. The original pLink2 list shows 6 inter-protein crosslinks. The rescored\nlist shows 9 inter-protein crosslinks that are VERY different: two confident interactions from the pLink2 list are\nnow missing (LIN9-LIN37 and LARP7-PABP4) ; one highly suspect interaction (LSM4-FINC) is added ; a homodimer\ninteraction that are always suspect as artefact (LMNA- LMNA) is added 3 times as the same peptide pair, and so\non. The authors should clean their data of same peptide-pair redundancies, and assess more closely what\nbiological insights are actually gained (if at all) from the rescoring.\nReply: Thank you very much for your careful observation. First, we would like to clarify that in Data Set 2, the\npurpose of this comparison was to illustrate the changes at the PSM level before and after rescoring. Therefore,\nwe did not remove redundant peptide or PPI entries in this particular table, which explains the repeated peptide\npairs you observed. Following your valuable suggestion, we have now included a deduplicated PPI-level result\ntable for clarity (Supplementary Dataset 2).\nAs our rescoring is entirely based on machine-learning–derived scores, it is possible that a few originally confident\nPPIs may be lost, or a small number of lower-confidence PPIs may be introduced. Nevertheless, according to our\nstatistics, only about 8% of the original PPIs were lost after rescoring, while the number of confidently identified\nPPIs simultaneously increased by 76.3% (Fig. 4b in the revised manuscript).\nTo further assess biological plausibility, we queried all identified PPIs against the STRING database. Our analysis\nrevealed that over 90% of the PPIs identified exclusively by pLink2, exclusively by XL-MSDigger, or by both methods\nhad STRING confidence scores greater than 0.4 (Fig. 4c in the revised manuscript). These results indicate that the\nnewly added PPIs still exhibit a relatively high degree of biological plausibility, suggesting that our rescoring\nstrategy improves coverage without substantially compromising reliability.\n3. The idea of DIA analysis to find low-intensity XL-MS signal at the proteome-level is very intriguing, even if it is\ncurrently computational prohibitive, as the author rightly explain. I think the authors should better substantiate\ntheir claims regarding its possible merits. Specifically: a. Can at least some of the new crosslinks that were\nidentified by DIA (both intra- and inter-, Fig. 6a and 6d) be now identified by DDA using targeted reaction\nmonitoring?\nReply: Thanks for your insightful comment. Unfortunately, the experimental samples used in our study were\ncompletely consumed during the previous analyses, and therefore we were unable to perform additional PRM\nvalidation on the same dataset. To address this point, we instead utilized an unpublished DIA XL-MS dataset from\nanother project in our laboratory, which was generated from RAW264.7 cells. Specifically, we selected ten PPI\npairs involving the protein P07901 from the STRING database to construct a predicted spectral library and\nreanalyzed the DIA data. Based on this library, we additionally identified the cross-linked peptide RGEYIKTWR(6)–\nKKLSELLR(2) corresponding to the P07901–P31750 interaction. To further validate this finding, we performed PRM\nanalysis on the same RAW264.7 sample and successfully detected the corresponding peptide, thereby confirming\nthe DIA-based identification. The representative PRM spectrum is shown below.\n4. Many of the new DIA intra-links are consecutive peptides, which are often common mis-assigment artefacts.\nCan the authors state how many non-consecutive peptides were in the DDA and DIA analyses.\nReply: Thanks for your suggestion. In our DIA analysis, among the 98 newly identified intra-links, 43 (43.3%) are\nnon-consecutive, and 55 are consecutive. For comparison, in our DDA results (analyzed using plink2), the\nproportion of non-consecutive peptides was 62.8%. As our DIA analysis primarily focuses on the machine-\nlearning–based rescoring strategy, we did not separately analyze consecutive peptides.\nTo further ensure the reliability of the DIA results, we followed the guideline proposed by Iacobucci and Sinz\n(Anal. Chem. 2017, 89, 7832-7835), which states that “the assignment of cross-links should always be supported by\nat least one characteristic diagnostic fragment ion for both cross-linked peptides.” Among the 55 consecutive\npeptide intra-links in the DIA results, 22 met this diagnostic-ion criterion. Therefore, even after excluding the\nremaining consecutive links that did not meet this strict requirement, 65 (43 non-consecutive + 22 high-confidence\nconsecutive) newly identified DIA intra-links remain with high confidence.\nWe sincerely thank the reviewer for raising this valuable point. We would like to clarify that our reported results\nalready include the diagnostic fragment-ion evidence for each cross-link (the number of fragment ions containing\nthe cross-linked sites on both peptides), which enables readers to further filter and validate the identifications.\n5. What was the negative control in running the DIA of Figures 6d and S9? Can the authors choose 17 proteins that are\nabsolutely not connected to HSP90AA1 and see that they don’t get an inter-crosslink? Can they do it 100 times, and see\nwhat are the statistics of getting an inter-crosslink with HSP90AA1 by chance?\nReply: Thank you very much for your professional suggestion. In our original DIA analysis, during the library\nconstruction step, we generated both TD (target-decoy) and DD (double-decoy) types of decoy XL peptides for all\ntarget peptides, with TD and DD ratios of 2:1 and 1:1, respectively. Therefore, our rescoring and FDR estimation\nalready included a stringent built-in negative control.\nFollowing your suggestion, we additionally created an external negative control. Specifically, we randomly\nselected 17 proteins from the E. coli proteome that are unrelated to HSP90AA1 and combined them with\nHSP90AA1 to construct additional negative PPIs. Due to the large size of the predicted XL peptide library, each\ncomplete DIA analysis for 20 DIA data requires approximately 3–4 days, so performing 100 iterations would be\nprohibitively time-consuming. Instead, we conducted 10 independent random trials under a 5% FDR threshold.\nThe results showed that across these 10 DIA analyses, among 109 total identified results, 5 inter-links were found\nas negative PPI (4.6%). These results suggest that the probability of obtaining false inter-links with HSP90AA1 by\nchance is very low, further supporting the reliability of our DIA-based analysis.\nResponse to Reviewers’ Comments\nReviewer 1:\n1. A lot of the additional controls and datasets (also those of other reviewers), were simply added to the\nsupplement. In my opinion, some of these results are more fitting to the main text as they demonstrate error\ncontrol and versatility of the algorithm.\nReply: We thank the reviewer for this helpful suggestion. Following this advice, we have reorganized the\npresentation of the results by moving key supplementary analyses into the main text. Specifically, the original\nSupplementary Fig. 1a,b have been integrated into the revised Fig. 1, and the original Supplementary Fig. 7\nhas been incorporated into the revised Fig. 4.\n2. The mzIdentML output needs to be included in the software before publication.\nReply: We thank the reviewer for the suggestion. The mzIdentML output functionality has now been implemented\nin the updated code. Please see the updated GitHub repository and documentation for details.\n3. The figure legend of 2d needs to be updated.\nReply: We thank the reviewer for pointing this out. The figure legend of Fig. 2d has been updated accordingly in\nthe revised manuscript.\nReviewer 4:\n1. The authors did not convince me that all their new PPI hits are plausible. When looking at Data Set 2 (relating\nto Fig. 4): most of their rescore hits have no String value (#N/A), yet they are counted in Fig. 4b, but not shown in\nFig. 4c (where they would make a huge column at the left 0.0 value).\nReply: Thank you for your valuable feedback. Your observation regarding the consistency of data presentation\nbetween Fig. 4b and Fig. 4c is important for refining both our analysis and figure interpretation.\nWe agree that, in the original version, PPIs without available STRING scores (#N/A) were included in the total\ncounts shown in Fig. 4b but were not displayed in Fig. 4c. This is because Fig. 4c was designed to visualize the\ndistribution of STRING confidence scores and therefore included only interactions with available STRING\nannotations. To avoid the misunderstanding, we have re-analyzed and re-visualized all identified PPIs, including\nthose with and without STRING scores, and added the complete STRING score distribution as Supplementary Fig.\n6a. This supplementary figure provides a comprehensive overview of STRING score distributions across different\nPPI identification methods.\nRegarding the reliability of the identified PPIs, we emphasize that XL-MSDigger does not introduce a higher\nproportion of unannotated interactions when compared with pLink2. Specifically, among PPIs identified uniquely\nby XL-MSDigger, 49% lack STRING scores, which is substantially lower than the 61% observed for PPIs identified\nuniquely by pLink2 (Supplementary Fig. 6a). Moreover, within the subset of STRING-supported PPIs, 78% of the\ninteractions identified uniquely by XL-MSDigger have STRING confidence scores greater than 0.4, compared with\n64% for pLink2 (Supplementary Fig. 6c). These results indicate that XL-MSDigger preferentially recovers PPIs that\nare better supported by existing PPI databases, thereby supporting the overall credibility of the identified PPIs.\nWe further note that the absence of a STRING score (#N/A) does not directly equate to an interaction being\nunreliable or biologically meaningless. STRING is a valuable but non-exhaustive database, and missing annotations\nmay arise from incomplete functional characterization, newly discovered interactions, or context-specific\ninteractions not yet incorporated into the database. Therefore, PPIs without STRING annotation may still\nrepresent genuine interactions with potential biological significance.\nIn summary, we believe that XL-MSDigger preserves the overall credibility of PPI identification results while\nexpanding the coverage of cross-linking mass spectrometry–based interaction discovery. These newly discovered\nPPIs, which are currently unsupported by STRING data, may provide novel hypotheses for subsequent biological\ninvestigation. We acknowledge that bioinformatics-based identification alone does not establish definitive\nbiological validity, and experimental validation remains essential. In future work, we will consider integrating\nadditional prior-knowledge databases and developing more sophisticated post-filtering strategies to further\nenhance the biological interpretability of our results.\nWe once again extend our gratitude to the reviewer for your rigorous and insightful comments, which have\nsignificantly aided us in refining the presentation and discussion of this work.\n2. I also find the following sentence in the abstract to be a gross overstatement, since their DIA applicability is\ncurrently limited. Perhaps it should be toned down. “In addition, XL-MSDigger implements 4D-DIA XL-MS analysis\nbased on predictive spectral libraries, which is capable of mapping high-coverage interaction networks in PPI\nanalysis of proteins.”\nReply: We thank the reviewer for this important comment. While XL-MSDigger enables DIA-based XL-MS analysis\nusing predicted spectral libraries, the present implementation is designed for targeted or moderate-scale\ninteraction analyses rather than proteome-wide network mapping.\nTo address this concern, we have revised the corresponding sentence in the abstract to: “In addition, XL-MSDigger\nenables DIA-based XL-MS analysis using predicted spectral libraries, allowing improved detection of protein–\nprotein interactions in targeted or moderate-scale interaction analyses.”"}]

Decision letter