We present Multi-Q 2, an isobaric-labeling quantitation tool which can yield the largest quantitation coverage and improved quantitation accuracy compared to three state-of-the-art methods. Multi-Q 2 supports identification results from several popular proteomic data analysis platforms for quantitation, offering up to 12% improvement in quantitation coverage for accepting identification results from multiple search engines when compared with MaxQuant and PatternLab. It is equipped with various quantitation algorithms, including a ratio compression correction algorithm, and results in up to 336 algorithmic combinations. Systematic evaluation shows different algorithmic combinations have different strengths and are suitable for different situations. We also demonstrate that the flexibility of Multi-Q 2 in customizing algorithmic combination can lead to improved quantitation accuracy over existing tools. Moreover, the use of complementary algorithmic combinations can be an effective strategy to enhance sensitivity when searching for biomarkers from differentially expressed proteins in proteomic experiments. Multi-Q 2 provides interactive graphical interfaces to process quantitation and to display ratios at protein, peptide, and spectrum levels. It also supports a heatmap module, enabling users to cluster proteins based on their abundance ratios and to visualize the clustering results. Multi-Q 2 executable files, sample data sets, and user manual are freely available at  Among several quantitation techniques, isobaric labeling-based quantitative proteomics has gained increasing attention because of its multiplexed capability, allowing for absolute and relative protein quantitation in multiple samples within a single run3. For example, a number of research groups in CPTAC 5 use isobaric labeling experiments, such as iTRAQ (isobaric Tags for Relative and Absolute Quantitation) or TMT (Tandem Mass Tag), to quantify thousands of proteins for cancer tissue samples from hundreds of patients.Mass spectrometry-based proteomics has become a dominating approach for identification and quantitation of proteins from complex biological samples6 and jTraqX7 exclusively support Mascot; MaxQuant8, PatternLab9, and OCAP10 exclusively support Andromeda11, Comet12, and X!Tandem13, respectively. The quantitation coverage for these tools could be limited because it has been reported that combining multiple search engines can markedly increase the numbers of identified peptides and proteins14.Two major objectives of bioinformatics analysis of isobaric labeling experiments are enlarging quantitation coverage  and improving quantitation accuracy. Enlarging quantitation coverage increases the likelihood of finding important biomarkers. To date, a number of isobaric-labeling quantitation software tools support identification results from only a single database search engine for quantitation. For example, IsobariQ16 on quantitation accuracy. Protein ratio calculation takes a set of identified PSMs as input to infer protein ratios. Common approaches include the use of mean17, median18, weighted average21, and 20% trimmed mean17 of the ratios at the spectrum level (PSM ratios) to determine protein ratios. Another common approach aggregates or sums the reporter ion intensities  across different PSMs, and then infers protein ratios based on the aggregate values22. Instead of deriving protein ratios directly from PSMs, some other methods adopt a hierarchical two-stage procedure, i.e., PSM ratios to infer peptide ratios (stage one), and peptide ratios to infer protein ratios (stage two). Commonly used two-stage quantitation algorithms adopt weighted average23 and median24 for both stages.For proteomics experiments in search of biomarkers, improving quantitation accuracy decreases the possibilities of false positives  and false negatives . Isobaric-labeling quantitation workflow usually consists of three major components: calculation of ratio of protein abundances in two samples (termed protein ratio), normalization, and reducing the effect of ratio compression17, median20, or summation17 of intensities across all the spectra. Normalization can also be applied at the level of peptide or protein ratio based on the assumption that the median of log transformed peptide or protein ratios is zero23. Variance stabilizing normalization is also proposed to address the issue of heterogeneity of variance among peaks of varying intensities25. Ratio compression arises from the presence of coeluting peptides within a precursor isolation window, resulting in systematic underestimation of actual protein and peptide abundance variations29. Using triple-stage mass spectrometry (MS3)31 or dual isolation width acquisition32 can mitigate the negative impact of these interfering signals, but they require modifications in the experimental settings or the instrument control code and are not applicable to the majority of existing isobaric labeling data sets. On the other hand, an algorithm that corrects compressed ratios based on calculated signal-to-interference ratios has been proposed33, offering an attractive solution to ratio compression.Normalization is usually applied at reporter ion level, in which reporter ion intensity of each channel is normalized according to its mean35. We further demonstrate that while searching for differentially expressed proteins, a set of six selected algorithmic combinations produce 70% to 90% common candidate proteins, suggesting that using algorithmic combinations of complementary rationale simultaneously in search of differentially expressed proteins can be a reasonable strategy to increase either sensitivity or precision.Quantitation results depend on the combination of algorithms for protein ratio calculation, normalization, and correction of ratio compression. In spite of great efforts being made to devise the above-mentioned algorithms, there is a lack of systematic evaluation of all the algorithmic combinations with various scoring functions. In light of the situation, we develop a standalone and installation-free software tool, Multi-Q 2, which is equipped with six protein ratio calculation algorithms, four peptide ratio calculation algorithms, three normalization algorithms, and the ratio compression correction (RCC) algorithm. With Multi-Q 2, we generate up to 336 algorithmic combinations and systematically evaluate them with standard data sets using various evaluation measures. Our analyses reveal that different algorithmic combinations have different strengths and are suitable in different scenarios. To be specific, algorithmic combinations that better quantify proteins of larger fold changes tend to sacrifice the accuracy for proteins of smaller fold changes, and vice versa. Thus, it is preferable that a software tool provides the flexibility of customizing quantitation algorithms for different purposes. With proper selection of algorithmic combinations, Multi-Q 2 can achieve better quantitation accuracy than MaxQuant, PatternLab, and Libra35, PeptideShaker36, and the commercial Proteome Discoverer, offering up to 12% improvement in coverage compared with MaxQuant and PatternLab, both of which are limited to identification results of a single database search engine. Multi-Q 2 provides interactive graphical user interfaces to perform quantitation and to display protein, peptide, PSM ratios as well as raw and processed reporter ion intensities. Moreover, a heatmap module is implemented to cluster proteins based on the calculated ratios using hierarchical clustering, K-means, and fuzzy C-means, facilitating users to perform further investigations.Multi-Q 2 is a Windows-based software tool designed with great flexibility. It supports identification results from Trans-Proteomic Pipeline (TPP)As illustrated in Fig. 37. To ensure correct PSMs for further quantitation, Multi-Q 2 takes the spectra satisfying an FDR of 1% at peptide and protein levels by default and extracts their reporter ions. Isotope impurity correction on reporter ions is then performed based on the correction matrices provided by reagents’ manufacturers23. Multi-Q 2 includes preset matrices for iTRAQ-4, iTRAQ-8, TMT-6, TMT-8, and TMT-10. User-defined correction matrix is also supported.Multi-Q 2 accepts MS spectra files in mzML or mzXML format. It accepts statistically validated search results from three popular proteomics data analysis systems: (1) pep.xml and prot.xml files from TPP, (2) xls files from PeptideShaker, and (3) pep.xml and prot.xml files from Proteome Discoverer. Statistical validation is usually performed with a target-decoy search strategy which provides estimation of false discovery rate (FDR) for given PSMs and thus can distinguish correct PSMs from incorrect PSMs under a specified FDR33 and is shown to improve quantitation accuracy without sacrificing quantitation coverage as spectra filtering approach does33. This RCC algorithm is implemented in Multi-Q 2. The assumption of the RCC algorithm is that the total percentage of noise from co-eluting interferences in the reporter ions of an MS2 scan is consistent with the percentage of noise of co-eluting interferences versus the total ion signals in its precursor isolation window. The authors calculate the signal-to-interference (S2I) measure as the abundance of a precursor and its isotope cluster divided by the sum of all ion signals observed within the isolation window. S2I ranges from zero to one and a smaller value indicates a higher degree of interferences caused by co-fragmented peptide ions. RCC calculates the total amount of noise in reporter ions as the product of 1-S2I and the summation of all the reporter ion intensities, thereby inferring putative noise for each channel. The putative noise is then deducted from the raw reporter ion intensity of the corresponding channel, and the resulting corrected intensity is used for quantitation in Multi-Q 2.An algorithmic solution to the ratio compression issue has been proposed in Savitski et al.Multi-Q 2 calculates PSM, peptide and protein ratios between two selected channels in an experiment at PSM, peptide, and protein levels, respectively. Given a PSM, the corrected reporter ion intensities of the two channels in the spectrum are used to calculate the PSM ratio. Multi-Q 2 supports the following four different approaches to calculate peptide ratios from PSMs: (1) LinearRegression: collect paired reporter ion intensities of two selected channels across all PSMs of a peptide, and use the slope of the linear regression model as the peptide ratio; (2) SumPsmIntensity: sum up the reporter ion intensities across all PSMs of a peptide, and use these aggregate values to derive peptide ratios; (3) MedianPsmRatio: use the median of PSM ratios as the peptide ratio; (4) WeightedPsmRatio: use the weighted average of PSM ratios to derive peptide ratios, in which the weight of a PSM ratio is proportional to the summation of its reporter ion intensities.To calculate protein ratios, the following six algorithms are supported: (1) SumPsmIntensity: sum up the reporter ion intensities across all PSMs assigned to the protein, and use these aggregate values to derive protein ratios; (2) MedianPsmRatio: use the median of the PSM ratios as the protein ratio; (3) WeightedPsmRatio: same as the WeightedPsmRatio approach for peptide ratio calculation except for the use of all the PSMs assigned to the protein; (4) TrimmedMeanPsmRatio: remove 20% of the largest and the smallest PSM ratios, respectively, and calculate the mean of the remaining PSM ratios as the protein ratio; (5) MedianPepRatio: use the median of the calculated peptide ratios as the protein ratio; (6) WeightedPepRatio: use the weighted average of peptide ratios to derive protein ratios, in which the weight of a peptide ratio is defined as the median of the weights of PSM corresponding to the peptide.Multi-Q 2 supports three different levels of normalizations. Normalization at the reporter ion level adjusts reporter ion intensities of respective channels so that their median intensities are identical based on the assumption that the sample amounts across different channels remain constant. Based on the assumption that the amounts of most of peptides (proteins) across different channels, e.g., channels corresponding to samples of patients with different states of a disease, remain the same, normalization of peptide (protein) ratios is to multiply the ratios by the reciprocal of the median peptide (protein) ratio so that the normalized peptide (protein) ratios have a median of 1.38, a data set of Erwinia carotovora lysate with four standard proteins at varying ratios, (2) Hultin-iTRAQ839, a standard data set of human A549 cell lysate with known abundance ratios at 2:2:1:1:2:2:1:1, (3) NCI-740, a TMT-10 data set from seven cancer cell lines, and (4) Chen-iTRAQ841, a data set of samples from anaerobic thermophilic eubacterium. Detailed descriptions of the data sets can be found in Supplementary Text Four data sets were obtained from public domain to evaluate various ratio calculation algorithms and normalization approaches of Multi-Q 2. These are (1) Gatto-TMT642 for searches, followed by statistical validation using PeptideShaker, where the first seven methods used a single search engine, including MyriMatch43, Andromeda, OMSSA44, Tide45, Comet, X!Tandem and MSGF+46, and the eighth method adopted combined searches using Comet, X!Tandem, and MSGF+. The ninth method used Comet and X!Tandem searches in TPP followed by PeptideProphet47, iProphet48, and Mayu49 for statistical validation. NCI-7 was processed by Comet and X!Tandem searches using SearchGUI and statistical validation using PeptideShaker for protein identification. Chen-iTRAQ8 was processed by Comet, X!Tandem, and MSGF+ searches in TPP followed by PeptideProphet, iProphet, and Mayu. All of the operations in TPP were performed via WinProphet50, a software system for proteomic pipeline creation and management. All of the database search parameters were identical to the settings reported in their original papers. Identified proteins and peptides were validated with FDR no greater than 1%.Gatto-TMT6 and Hultin-iTRAQ8 were processed by nine different database search methods and statistical validation tools in order to investigate the coverage of the identified proteome. The first eight methods used search engines in SearchGUI21. To generalize the concept, we devise a measure called area under the curve of coverage vs deviation (AUCCD), in which a curve is generated on a 2D plane with x-axis denoting deviation of protein ratios, ranging from 0 to 100% to the ideal values, and y-axis denoting coverage of protein ratios within the deviation. A large AUCCD indicates larger coverage of protein ratios within the specific range (0–100% in our design) of deviation and implies higher accuracy of quantitation. We also use two additional measures: average relative error (ARE), defined as the average of |xi−yi|/yi over all the protein ratios, and root mean square error (RMSE), defined as the square root of Σi(xi−yi)2/m, where xi and yi denote calculated and ideal ratios at protein level, respectively, and m is the total number of ratios at protein level. Particularly for ARE, since one of our data sets, i.e., Gatto-TMT6, contains standard proteins and background proteins, we further distinguish ARE_Std and ARE_Bg to denote the ARE of ratios for all standard proteins and for all background proteins, respectively. AUCCD focuses on the percentage of protein ratios within a specific range of deviation to their ideal values and ignores the ratios far from the ideal values. RMSE, in contrast, produces much larger penalties for protein ratios of the latter case. ARE assigns larger  tolerance for protein ratios of larger  ideal values so that ratios at different scales can be considered on the same basis. The three evaluation measures are designed based on different rationale and are used integrally to provide a more comprehensive understanding for quantitation results.The coverage of ratios at protein level under a deviation of a certain amount from the ideal value has been used to evaluate the accuracy of quantitation results. Previous studies compare the coverage at 10%, 20%, and 30% deviation for different quantitation tools46 and validated by PeptideShaker; notably, Hultin-iTRAQ8 shows an increase of 7.4% or 177 proteins (from 2378 to 2555 proteins) being identified. The results suggest validation tools can be a significant factor affecting the coverage of the identified proteome. This phenomenon highlights an advantage of Multi-Q 2—the capability of accepting multiple database search results from several popular proteomic data analysis systems including TPP, PeptideShaker, and Proteome Discoverer. Because of the largest coverage, the identification results based on TPP were used by Multi-Q 2 to perform quantitation for further benchmark analysis.Since quantitation tools accept identification results for further quantitation, we first compared identification results of two standard data sets, Gatto-TMT6 and Hultin-iTRAQ8, from using a single search engine or multiple search engines, followed by validation using different tools. Supplementary Figs. To evaluate different algorithmic combinations of Multi-Q 2, we used the standard data sets Gatto-TMT6 and Hultin-iTRAQ8 since the ideal protein ratios are known and can be used as the ground truth. There are various algorithms in the workflow of Multi-Q 2, including four algorithms for peptide ratio calculation, six algorithms for protein ratio calculation, and two possibilities of RCC (enabled or disabled). In addition, we used seven different normalization approaches: no normalization, reporter ion level normalization only, peptide level normalization only, protein level normalization only, reporter ion plus peptide level normalization, reporter ion plus protein level normalization, and all three levels of normalization.A large-scale systematic benchmark experiment was conducted on Gatto-TMT6 by exhaustively generating all 336 (4 × 6 × 7 × 2) possible combinations of different quantitation and normalization algorithms. Similarly, on Hultin-iTRAQ8 48 (4 × 6 × 2) algorithmic combinations were exhaustively generated with no normalization because the sample proportions across different channels in this data set are not of equal amount. Note that some of the combinations can have identical quantitation results at protein level regardless of any peptide ratio calculation method used. For example, if protein ratios are directly derived from PSM ratios, altering peptide ratio calculation algorithm does not change protein ratios.Benchmark results of 336 algorithmic combinations on Gatto-TMT6 are shown in Supplementary Table When sorting Supplementary Table Benchmark results of the 48 algorithmic combinations on Hultin-iTRAQ8 are reported in Supplementary Table We used Multi-Q 2 to quantify a total of 10,524 proteins  in NCI-7. Six protein ratio calculation methods were used for benchmark analysis, where the two methods based on peptide ratios are particularly chosen to be MedianPepRatio-LinearRegression and WeightedPepRatio-WeightedPsmRatio based on our previous analyses on Gatto-TMT6 and Hultin-iTRAQ8. For all the six methods, RCC can be enabled or disabled, resulting in 12 different algorithmic combinations. Normalization was disabled because of the unequal abundance ratios  among channels. Performance evaluation of the quantitation results from the 12 algorithmic combinations is illustrated in Fig. The experiment results show that several algorithmic combinations, instead of a single combination, can achieve the best performance. In general, the algorithmic combination most suitable for quantifying proteins of significant fold changes  sacrifices its accuracy for proteins of insignificant fold changes . Enabling RCC does to some extent remedy ratio compression, but inevitably decreases the quantitation accuracy for background proteins because it tends to pull protein ratios away from one. To quantify a data set with equal amounts of samples across different channels, algorithmic combinations with normalization achieve better AUCCD, ARE_Bg, and ARE_Std compared to those without normalization, as shown in the results of Gatto-TMT6. Using one, two, and three different normalization methods can all achieve the lowest ARE_Bg and the highest AUCCD. For NCI-7, altering protein ratio calculation algorithm has marginal impact on AUCCD and ARE. Enabling RCC does lead to a slight decrease in AUCCD and a slight increase in ARE, both are in good agreement with the observations of background proteins from Gatto-TMT6 and Hultin-iTRAQ8.To evaluate the performance of Multi-Q 2, we compared its performance with those of PatternLab, MaxQuant, and Libra on Gatto-TMT6. In addition to AUCCD and ARE, we use root mean square error (RMSE), mean, and standard deviation (SD) to evaluate protein ratios of background proteins.For quantitation, Libra uses the same identification results as Multi-Q 2 , and PatternLab and MaxQuant use their built-in Comet and Andromeda, respectively, for database searches, followed by their own statistical validation algorithms. The numbers of quantifiable proteins of Multi-Q 2, PatternLab, MaxQuant, and Libra are 456, 406, 418, and 440, respectively. Multi-Q 2 has the largest coverage because it benefits from the use of multiple database search engines and its flexibility in supporting various protein and peptide validation systems, as mentioned earlier.No single algorithmic combination is the best for all situations under all evaluation measures according to the previous analyses. For the purpose of performance comparison, two algorithmic combinations of Multi-Q 2 were selected. The first, denoted by MTQ_alg1, stands for MedianPepRatio-LinearRegression with normalization at reporter ion level and RCC enabled . The second, denoted by MTQ_alg2, stands for WeightedPepRatio-WeightedPsmRatio with normalization at peptide level and RCC disabled . Relative errors of the four standard proteins for the compared tools are illustrated in Fig. 2 between 0.93 and 0.96; slope between 0.88 and 0.96) though a small portion of protein ratios are distant to the diagonal.Multi-Q 2, PatternLab, MaxQuant, and Libra quantified 2528, 2285, 2315, and 2486 proteins, respectively. Again, Multi-Q 2 has significantly larger coverage in quantifiable proteins than MaxQuant and PatternLab because it benefits from the use of multiple search engines . We then evaluated the four tools on the 2023 commonly quantifiable proteins, and the results are summarized in Table It is evident no single algorithmic combination can be claimed to be the best for all the situations. Even though the two algorithmic combinations, MTQ_alg1 and MTQ_alg2, were selected from rigorous experiments using various evaluation measures, there is no guarantee the two are the best for other data sets. The best algorithmic combination of a given data set can be dependent on a number of factors including instrument, spectrum quality, the complexity of samples, the definition of ratios (numerators and denominators), and evaluation measures. Optimization of algorithmic combinations or providing guidelines for the selection of quantitation algorithms for a given data set is a complicated issue and is beyond the scope of this study. Nevertheless, compared to other tools mostly based on a fixed quantitation method, the flexibility of Multi-Q 2 provides clear advantage in quantitation accuracy. The previous benchmark analyses demonstrate that Multi-Q 2 can outperform existing tools with proper selection of algorithmic combinations.When proteins are differentially expressed in different states, e.g., tumor vs. normal tissue samples, acquiring a list of candidate biomarkers, namely, proteins of high fold changes across different states, is usually crucial for further biological discovery. Thus in this subsection, we further use Chen-iTRAQ8 to evaluate different algorithmic combinations of Multi-Q 2 in search of differentially expressed (temperature-dependent) proteins, which are defined as proteins with at least a ratio above 1.5  by Multi-Q 2. Twelve algorithmic combinations of six protein ratio calculation methods used for NCI-7 with RCC enabled and disabled are used to analyze Chen-iTRAQ8 for finding temperature-dependent proteins. Normalization is applied at reporter ion level. The number of temperature-dependent proteins of these methods are shown in Supplementary Fig. 51, defined as the size of the intersection divided by the size of the union of the two lists. The results are illustrated in Fig. We then evaluated the similarity of two lists of temperature-dependent proteins obtained from any pair of the six algorithmic combinations with RCC enabled by Jaccard indexFurthermore, examining the pairwise similarity of algorithmic combinations with RCC disabled, we observed overall decreases (ranging from 0.01 to 0.1) in all the pairwise similarities except for SumPsmIntensity vs WeightedPsmRatio, as illustrated in Supplementary Fig. Multi-Q 2 was implemented with Visual Studio C# and can be run on the Windows platforms  with a prerequisite of .net framework 4.0 or newer versions. A quantitation wizard, as shown in Supplementary Fig. In addition to the main window, Multi-Q 2 supports a heatmap module, through which users can cluster proteins of similar ratios using different clustering algorithms—hierarchical clustering, K-means, and fuzzy C-means—based on different distance measures—Euclidean distance, Manhattan distance, Pearson’s correlation coefficient, and covariance. An example of heatmap is illustrated in Supplementary Fig. We present Multi-Q 2, a versatile software tool for isobaric labeling quantitation. Multi-Q 2 supports identification results from TPP, PeptideShaker, and Proteome Discoverer, offering up to 12% improvement in coverage compared with MaxQuant and PatternLab. Multi-Q 2 is implemented with popular quantitation, normalization, and ratio compression correction algorithms, supporting up to 336 algorithmic combinations. Our benchmark analyses show that Multi-Q 2 is capable of generating the largest quantitation coverage and improved quantitation accuracy compared with state-of-the-art software solutions. More importantly, we show that there is still no single algorithmic combination that outperforms others in all evaluation measures under all circumstances. It is therefore beneficial for a software tool to provide the flexibility of customizing quantitation algorithms. We further demonstrate that using algorithmic combinations of complementary rationale simultaneously in search of candidate biomarkers can be a reasonable strategy to improve either sensitivity or precision. Multi-Q 2 is a standalone and installation-free Windows program. It provides friendly graphical interfaces for users to perform quantitation and follow-up analysis, such as clustering and heatmap visualization. We believe that Multi-Q 2 can be of great help in searching for potential biomarkers from complex proteomic samples.Supplementary Table S1.Supplementary Table S2.Supplementary text and figures.


Here, we present the ANCA, an interactive Web server for Amino Acids Network Construction and Analysis based on a single structure or a set of structures from the Protein Data Bank. The main purpose of ANCA is to provide a portal for three types of an environment-dependent residue contact energy (ERCE)-based network model, including amino acid contact energy network (AACEN), node-weighted amino acid contact energy network (NACEN), and edge-weighted amino acid contact energy network (EACEN). For comparison, the C-alpha distance-based network model is also included, which can be extended to protein–DNA/RNA complexes. Then, the analyses of different types of AANs were performed and compared from node, edge, and network levels. The network and corresponding structure can be visualized directly in the browser. The ANCA enables researchers to investigate diverse concerns in the framework of AAN, such as the interpretation of allosteric regulation and functional residues. The ANCA portal, together with an extensive help, is available at  With the increasing number of high-resolution 3D structures of biomolecules, including proteins, protein–DNA complexes, and protein–RNA complexes, the development of rapid and efficient methods to perform large-scale analysis for them is needed. A variety of structure-based computational tools and methods is developed to satisfy the new challenges , such asNowadays, several Web tools that construct different types of AANs have facilitated progress in this area of research. RING2.0 constructs an AAN based on the physicochemical interactions between the residues, which include covalent and non-covalent interactions . ProteinIn this paper, we developed a Web server called ANCA  for construction and analysis of our previously proposed ERCE-based network models AACEN and NACEN. To refine our ERCE-based models, we also added the edge-weighted amino acid contact energy network (EACEN) model in our Web server using the ERCE as link weights. Moreover, a C-alpha distance-based network  model was also included in our ANCA for two purposes. Firstly, the C-alpha model can be used as the comparison network for our ERCE-based models for proteins or protein complexes. Secondly, ANCA also provides the construction and analysis for single and multiple protein–DNA/RNA complexes based on the C-alpha model. The organization of our portal ANCA was shown in The ANCA Web server is comprised of two core modules entitled “single structure” and “multiple structures.” The single-structure module provides the construction and analysis for one structure with any one of the AAN models at a time, while in the multiple-structures module, the structures can be analyzed in batches using any of the four types of AAN models. The former module is more suitable for carrying out a detailed analysis for one structure (either a PDB code or a PDB file). The latter module can be used for comparison analysis of different structures. Both modules support four types of AAN construction, analysis, and visualization. Moreover, ANCA can provide the option of distance-based AAN construction for protein–DNA/RNA complexes.eij between residues i and j was defined as in our previous studies , mass, hydrophobicity, polarity, or user-self defined node weights .In EACEN, the links between residues were weighted by ERCE and the adjacent matrix AM of EACEN was defined as:wij is the normalization of the contact energy eij between i and j:Where ∗(sugar group), and C2 (base group) atoms to represent each nucleotide of the DNA or RNA  and two weighted AANs (NACEN and EACEN). The C-alpha model can be used not only for protein and protein–protein complex but also for protein–DNA/RNA complex. But since the network is constructed just based on the distance between C-alpha atoms, it is a relatively coarse model. AACEN is an ERCE-based network model that can be used just for protein or protein complex but provide more detailed information by considering the local environment of the residues , and it http://sysbio.suda.edu.cn/anca/.ANCA can be used for the network analysis of proteins, protein–protein complexes, and protein–DNA/RNA complexes from the node level, edge level, and network level. The detailed definition of the parameters was listed in Lnet). Moreover, for NACEN, we also calculated the weighted degree, betweenness, and closeness centralities based on the node weights. Their definitions were in our previous work , and the results showed that the top 3 residues were PHE337, TYR392, and PHE340 as shown in Postsynaptic density-95/Discs large/Zonula occludens 1 (PDZ) protein domain family is a protein–protein interaction module, which is involved in dynamic regulation of signaling pathways and scaffolding and has emerged as a paradigmatic model system for intra-domain allostery . Here weAt this part, we constructed and analyzed all the four types of network, including AACEN, NACEN, EACEN, and C-alpha network for two structures, PDZ3 in case 1 and protein–RNA complex MDA5 double-stranded RNA Filament (PDB 6G19) with default parameters at one time. Then, ANCA portal gave the results page with summary information for each network and the link of the network in the column “Run Status.” The links point to the page containing detailed information for each network as described in case 1.ANCA is a comprehensive portal for the construction and analysis of network representations of protein and protein–protein/DNA/RNA complexes to explore and understand the macromolecules at different levels of organization. It can help in the management of heterogeneous information sources, such as structural, sequence, physicochemical, and dynamical information of residues. Another advantage of our portal is that it also allows scientists to address diverse questions by choosing different network models. For example, NACEN is more suitable to identify the functional residues in the structures, while EACEN can capture the intramolecular information flow to help in understanding the allosteric regulation.http://sysbio.suda.edu.cn/anca/.Publicly available datasets were analyzed in this study. This data can be found here: WY and BS conceived and designed the Web server. CY performed the server front-end and back-end. WY carried out the case studies. JZ and JC contributed to the Web server testing. WY, CY, and JC wrote the manuscript. JC polished the language and gave many constructive suggestions. BS critically reviewed and edited the manuscript. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Conformational transitions are implicated in the biological function of many proteins. Structural changes in proteins can be described approximately as the relative movement of rigid domains against each other. Despite previous efforts, there is a need to develop new domain segmentation algorithms that are capable of analysing the entire structure database efficiently and do not require the choice of protein-dependent tuning parameters such as the number of rigid domains.We develop a graph-based method for detecting rigid domains in proteins. Structural information from multiple conformational states is represented by a graph whose nodes correspond to amino acids. Graph clustering algorithms allow us to reduce the graph and run the Viterbi algorithm on the associated line graph to obtain a segmentation of the input structures into rigid domains. In contrast to many alternative methods, our approach does not require knowledge about the number of rigid domains. Moreover, we identified default values for the algorithmic parameters that are suitable for a large number of conformational ensembles. We test our algorithm on examples from the DynDom database and illustrate our method on various challenging systems whose structural transitions have been studied extensively.http://azifi.tz.agrar.uni-goettingen.de/webservice/.The results strongly suggest that our graph-based algorithm forms a novel framework to characterize structural transitions in proteins via detecting their rigid domains. The web server is available at  Proteins are molecular machines that are involved in a large variety of biological processes. Protein function is often driven by large-scale structural transitions . ExperimGiven the large number of available protein structures, we need computational methods that identify structurally conserved domains in a set of alternative structures in an automated fashion with minimal user intervention. For example, one could use the software to study molecular dynamics trajectories at the level of rigid domains to gain an understanding of large-scale movements, or identify important active sites located at the interface between rigid domains.A number of computational methods for detecting rigid domains in protein structures have been developed. Dyndom  identifiA more ambitious goal is to predict rigid domains from a single structure by, for example, molecular dynamic simulation or an elastic network model that can both be used to generate a set of alternative conformational states. HingeProt  and DomaDespite the rich literature on methods for rigid-domain detection in protein structures, all of the existing methods require the initial number of rigid domains in their calculation. Thus, there is still a need for algorithms that are robust, reliable, able to handle high-throughput data and yet do not require extensive parameter tunning. Here, we introduce a graph-based method that infers a binary labeling that encodes if pairs of amino acids belong to identical or different rigid domains. Our algorithm proceeds in two stages: first, we construct a protein graph based on spatial proximity, which we cluster using the Louvain algorithm to obtain a coarse-grained graph of reduced size. Second, edges in the reduced graph are labeled by applying a line graph transformation along with the general Viterbi algorithm. We benchmark our algorithm on 487 entries of the DynDom database and find a high agreement with the reference segmentation. In addition, we also present a detailed analysis of various proteins that show a large variety of conformational transitions and compare our results to other methods.To validate our algorithm, we first segment conformations of Adelynate Kinase (ADK). We then perform a benchmark on 487 proteins from the DynDom database. Finally, we compare our method with other domain segmentation algorithms on a number of test cases ranging from medium to large scale conformational changes.We first run our algorithm for rigid domain segmentation on Adenylate Kinase (ADK) for which multiple experimental structures showing different conformations are available . ADK catFigure Unlike DynDom, our method also works with multiple conformational states. To study this feature, we ran our algorithm again but on 100 ADK conformations generated by morphing between the open and closed state . The algAn advantage of our method is that it allows users to integrate prior knowledge to improve the segmentation. For example, for the default parameter setting, our method incorrectly assigned fifteen amino acids of the NMP-binding and LID domain to the core domain. Yet with some prior knowledge about the rigid domains, we can improve the rigid-domain segmentation. Suppose we are given ADK’s segmentation calculated from Spectrus  with \doWe benchmarked our method on the DynDom database  reduced Figure To study the impact of the edge cutoff used in the definition of the protein graph, we ran experiments with varying cutoff values. Table We ran our method on various proteins studied in  showing Pyruvate phosphate dikinase (PPDK) is a large biomolecular complex that catalyzes the reversible conversion of PEP, AMP, and  and ATP . We appl and ATP  and by o and ATP . Our seg and ATP . TypicalT7 RNA polymerase is involved in the initiation and elongation of RNA transcription. Our segmentation is highly consistent with the results from DynDom,  and the The chaperonin GroEL  providesWe also benchmark our method on proteins undergoing medium-scale structural transitions. Aspartate aminotransferase (AST) is an enzyme involved in amino acid metabolism that catalyzes the reversible transfer of an lutamate . For thiOur results demonstrate that segmentation of protein conformations into rigid domains can be achieved with a graph-based algorithm that solves the rigid segmentation problem with an edge-labeling strategy. Let us discuss the key features of the algorithm and the impact of algorithmic parameters. To measure the efficiency of the graph construction and coarse graining, we use a metric that we call inconsistency error. The inconsistency error quantifies the heterogeneity of clusters weighted by their size. Let all conformations, and to weight the edge by the reciprocal exponentiated variance computed over all conformations . Additional file We first study different ways to construct a protein graph from multiple conformations. There are many reasonable options for constructing a protein graph. For example, one possibility is to create an edge if the distance between two vertices is smaller than a cutoff in at least one conformation, and to assign as a weight the number of such conformations. Another possibility (detailed in Methods) is to create an edge if its distance is smaller than the cutoff in We also studied various options for the coarse-graining step. In all tests, we used the Louvain algorithm for fitting Potts models  for coarhttps://www.ebi.ac.uk/Tools/msa/clustalo/). Our segmentation on Lysozyme completely agrees with Spectrus [RMSDs are 1.6 and 4.9 Å, respectively.Moreover, we ran our algorithm on Lysozyme , an enzySpectrus  and NguySpectrus  where alRMSDs are 0.6 and 1.6 Å, respectively. This segmentation is stable against variations in the rigidity threshold and does not require the execution the merging procedure. When we reduced the threshold to define the protein graph to 4.5 Å, we obtained two different domains: a small domain (amino acids 193–246) and a large domain (amino acids 1–192 and 247–337) whose RMSDs deteriorated to 2.7 and 3.0 Å, respectively.Our method is also applicable to study rigid domains in membrane proteins. For instance, the chemokine receptor CCR5  located To avoid duplication of features involving vertices and edges, we modify the construction of the line graph by discarding an edge if its two end vertices are connected as well. That way, features extracted from edges add new information. Finally, we use a merging routine with heuristic criteria to merge two domains. One may ask if we could skip the labeling step  and apply the merging routine directly to the clusters found by coarse graining. This simplified version of our algorithm achieves good results on proteins showing a large-scale movement, but fails on more subtle cases. Overall, post-processing via the merging procedure compensates for segmentation errors involving small fragments.The running time of our algorithm depends on the size of the protein, the density of the protein graph, and the rigidity of the conformational change. Additional file Indeed, the running time strongly depends on how often the Viterbi algorithm is executed in the recursion and how quickly a big, non-rigid graph is segmented into several subgraphs. The worst scenario occurs when many Viterbi calculations are required for a protein with densely connected protein graph and with a high degree of flexibility such as intrinsically disordered proteins . In thesOther segmentation methods and ours all require 3D protein structures which are not always available. In our graph-based framework, we may resolve this shortcoming by estimating a protein graph as follows. First, from a given protein primary sequence, we may use its protein contact map predicted, for example, by AlphaFold  to constWe present a new algorithm to characterize structural transitions in proteins. Our graph-based algorithm constructs a graph from a set of protein conformations and detects rigid domains via an edge labeling strategy. A key feature is that the number of rigid domains is determined automatically. Yet the algorithm allows users to relax the rigidity definition of domains and thereby increase or decrease the number of rigid domains. Segmentations produced by our algorithm agree strongly with segmentations found by other methods such as DynDom , 28 and Our approach has several advantages over other rigid segmentation methods. First, there is no limitation on the number of protein conformations. In fact, a larger number of conformations should result in a better signal and thereby a superior performance of the algorithm. Second, by using the graph-based model along with a binary labeling of edges, we overcome the need to choose the number of rigid domains, which is necessary for many of the existing methods. Moreover, our method performs well with default parameter settings, which saves the user from parameter tweaking. Another appealing aspect of our method is that it can be used to produce a good initial segmentation for other segmentation algorithms. For instance, the 6 method  requiresWe organize the “nth atom in the mth conformation. Every conformational state gives rise to a symmetric Our algorithm aims to infer a rigid-domain segmentation from M structures through a protein graphk, l belongs to the edge set We encode the conformational variability across all a et al.  suggest a et al. , which an (RMSD)  between enchmark .are small enough to include, with a few exceptions, amino acids that are part of the same rigid domain . However, we obtained very poor results with this approach due to the small number of inter vertices/edges. Therefore, we only consider the distribution of values from intra vertices/edges and treat values of inter vertices/edges as outliers.Motivated by these observations, we denote by an MAD) [P vertices Q edges To identify outliers, we use the algorithm developed by  that detMAD) . MAD is Outliers are characterized by a mean variance that is larger than any other mean variance. The set of outliers can be enlarged by including non-outliers located at the end of the array. By such expanding, it is important to notice that the indices of outliers are always bigger than ones of non-outliers.sites and observations. i by an edge in I: e and Let us consider a graph I of size s in c is the maximum clique size. For every clique size s. Under very weak assumptions the feature-based exponential models coincide with the class of conditional random fields where at every site i the label is conditionally independent of the labels outside A pair The labeling problem is solved by computing a labeling sequenceailed in  is able edges in the coarse-grained graph, whereas the Viterbi algorithm estimates optimal vertex labels. Thus, it is not suitable to directly apply the Viterbi algorithm to the coarse-grained graph. Instead, we apply the generalized Viterbi algorithm on a line graph derived from the coarse-grained graph. This gives us a binary labeling of line graph vertices, which equivalent to a binary labeling of edges in the coarse-grained graph.A shortcoming of existing rigid-domain detection methods such as , 8, 28 iunnormalized probability” or “scoring function” interchangeably.Thus, we consider a line graph as a site graph described above. In a pairwise CRF, one only considers cliques formed by vertices and edges. Consequently, Eq.  can be rv along with its label In our rigid domains detection problem, we define a feature function for a vertex e and its predicted label Given an edge Case “Two values amongare equal toCase “For any other combination ofandHence, for any labeling of the line graph ity Eq.   via Eqs.ity Eq.  –14) and and\docuThis subsection provides pseudo code for our graph-based prediction of rigid domains in proteins. We denote the rigidity threshold as There is no guarantee that this algorithm always converges. However, we experienced fast convergence within a few iterations in most of our experiments. We also added a limitation on the number of recursions. The final result of our algorithm is a list of disconnected subgraphs of the coarse-grained graph.Our graph-based method for rigid-domain detection described in the Sect. Let After termination of the Merging Algorithm, Additional file 1: The support information includes the follows. The first section is the analyses of inconsistency error of reduced graph. The second section is the analyses of signal enhancement by coarse graining. The third section contains PDB codes of Lysozyme protein. The fourth section is the analyses of the running time.


Protein‐protein interactions are critical to protein function, but three‐dimensional (3D) arrangements of interacting proteins have proven hard to predict, even given the identities and 3D structures of the interacting partners. Specifically, identifying the relevant pairwise interaction surfaces remains difficult, often relying on shape complementarity with molecular docking while accounting for molecular motions to optimize rigid 3D translations and rotations. However, such approaches can be computationally expensive, and faster, less accurate approximations may prove useful for large‐scale prediction and assembly of 3D structures of multi‐protein complexes. We asked if a reduced representation of protein geometry retains enough information about molecular properties to predict pairwise protein interaction interfaces that are tolerant of limited structural rearrangements. Here, we describe a reduced representation of 3D protein accessible surfaces on which molecular properties such as charge, hydrophobicity, and evolutionary rate can be easily mapped, implemented in the MorphProt package. Pairs of surfaces are compared to rapidly assess partner‐specific potential surface complementarity. On two available benchmarks of 185 overall known protein complexes, we observe predictions comparable to other structure‐based tools at correctly identifying protein interaction surfaces. Furthermore, we examined the effect of molecular motion through normal mode simulation on a benchmark receptor‐ligand pair and observed no marked loss of predictive accuracy for distortions of up to 6 Å Cα‐RMSD. Thus, a shape reduction of protein surfaces retains considerable information about surface complementarity, offers enhanced speed of comparison relative to more complex geometric representations, and exhibits tolerance to conformational changes. Knowledge of the participating protein‐protein interfaces involved in forming these complexes is thus critical for understanding and perturbing protein function in a cellular context. Most of our understanding about the contact surfaces by which proteins interact has been from direct experimental determination using techniques such as X‐ray crystallography and electron microscopy,Importantly, the prediction of protein‐protein interaction interfaces is of substantially lower computational complexity than the problem of predicting or folding a 3D protein structure based on its linear amino acid sequence, as interface predictions  are limited to 6° of rotational and translation freedom and a sampling of accompanying intramolecular motions that might occur upon binding.Such predictions are complicated by the fact that protein‐protein interactions may take quite different forms, and interactions can be categorized in various ways, including obligate and non‐obligate, permanent and transient, and strong and weak.Computational approaches for determining how proteins interact include predictions of interaction interfaces or docking of protein structures, where the former informs the latter. It has been shown that knowledge of an interaction interface can greatly improve the prediction of the conformation of the proteins that are interacting.Sequence‐based predictors utilize protein sequence information to either feed different amino acid properties into a machine learning classifier or sequence alignment tools. Sequence alignment methods assume that proteins of similar sequences have similar binding partners and therefore binding sites.n closest residues where n depends on the size of the protein or a set size for all proteins.Structure‐based predictors utilize structural information from either experimental data or homology modeling as a constraint in formulating their prediction. Previous studies showed that the quality of the prediction is dependent on the quality of the structure and that homology models produce less accurate predictions.Partner‐specific interface predictors, which account for all participating proteins in the interaction are less common but have the benefit of considering complementarity between specific proteins. Partner‐specific predictors use structures or sequences of two proteins that are assumed to interact in predicting the interaction interface for each protein.Currently, many partner‐specific approaches exist for predicting interactions. A majority of these methods use the primary sequence and homology searches to make predictions. PAIRpred utilizes a support vector machine classifier for predicting partner‐specific interaction interfaces.One important challenge that remains for partner‐specific, structure‐based predictors is accounting for conformational changes that occur upon binding. The performance of these methods decreases with increasing conformational rearrangements and dynamics of the protein pairs upon binding.22.1To evaluate the quality of the interaction interface predictions from MorphProt, we used a benchmark set of known protein complexes. The benchmark data set for this method was version 5.0 of the widely used protein‐protein interaction docking benchmarks.In addition to the protein docking benchmark 5.0, we used the protein docking gold standard, the Critical Assessment of PRedicted Interactions (CAPRI) score set.2.2The properties that were used in these analyses were charge, hydrophobicity, and evolutionary rate. The atomic charge was calculated using PDB2PQR.The Wimley‐White hydrophobicity valuesFinally, the evolutionary rates were obtained from the ConSurf Database.2.3To reduce the dimensionality of the intricacies of protein shape, we performed a shape reduction of the 3D atomic structure into a simplified representation. To perform these calculations, we have created a Python library, MorphProt. The input for these calculations is a PDB file (either an atomic structure or homology model), a PQR file, and a conservation file produced by Consurfx, y, and z coordinate as 6 biased start centroids, k = 6. MorphProt uses SKLearnx and y direction and the k‐means is recalculated. We also test an initialization of the protein structures by taking the first three principal components, corresponding to the major axes, to orient the protein in an optimized start position.After the atomic coordinates of the surface are extracted, MorphProt took the maximum and minimum for each 2.4We computed a 2D cross‐correlation, a common pattern recognition and image processing tool, to predict areas of the protein surface with maximum interaction between properties. The cross‐correlation was calculated using MorphProt. Because each protein is reduced to a total of six matrices, we calculated a total of 36 2D cross‐correlations for each pairwise interaction between the six faces of each protein for a given initialization. In addition, we sampled all 10° rotations to account, in an approximate fashion, for different orientations or positions of the initial protein structures.We then calculated the sum of the top 10 scores for the unrotated and rotated initialization positions. The top score for interactions driven by evolutionary rate and hydrophobicity is the maximum score; however, because complementary charge interactions involve a pairing of negative and positive numbers, the top score is the minimum. The start position with the top score is used as the optimal start position. Predicted interfaces are calculated independently for each of the properties. However, to determine the most likely interface, we determine consistency for the top 10 interfaces predicted for each property. If each of the top 10 interface predictions is a different subset of the same two faces (matrices), then this can be considered a consistent prediction and is selected as the top interface. For antibody complexes, we took the top charge score due to the variable binding region that would not be captured with evolutionary rate or the hydrophobic interaction between the heavy and light chains.After identifying the top score in the cross‐correlation matrix, we determine the position of the two matrices that produced the score. We use the position of the high score within the cross‐correlation matrix to identify the alignment of the two matrices and extract any overlapping regions between the two. Once the areas of the two matrices that are interacting are identified, we map this back to the protein structures themselves.2.5F1 score are defined accordingly:To evaluate our predictions, we calculated a confusion matrix to classify predicted interface residues as true positives, false positives, false negatives, and true negatives based on the predicted and actual classes. We defined a residue to be on the interaction interface if any atom from the residue is within 5 Å of an atom from the protein it is in complex with. We then evaluated our confusion matrix where the precision, recall, accuracy, and Additionally, we have integrated an extreme value calculation to validate the “uniqueness” of the atomic properties. This demonstrates that placement along the interface is not a random distribution of points but a clustering of some property contributing to an interface. To calculate this, we randomly shuffled the properties associated with each atom and recalculated scores. We repeated this shuffle and scoring 1000 times to generate a distribution. If the score was an extreme value in the distribution, then the score is statistically significant and represented a clustering of a property at that location.2.6http://bioportal.weizmann.ac.il/promate/. The default configuration was used. The proteins that had no predicted interface atoms were assigned statistics of 0. The SPPIDER predictions were run at: http://sppider.cchmc.org, using the predict interface from unbound structures option. The tradeoff between sensitivity and specificity used was 0.5 . The PredUS 2 predictions were run at: https://bhapp.c2b2.columbia.edu/PredUs/index_omega.html, using all default settings. The PIER predictions were run using the server at: http://abagyan.ucsd.edu/PIER/. The suggested cutoff score of 30 was used to predict the interface residues.MorphProt was compared to four different structure‐based prediction tools: Promate 2,2.7To simulate structural distortion in the crystal structures from the test set we used elNémo3We wished to test if a highly simplified geometric representation of a 3D protein surface embedded with properties was sufficient to predict protein‐protein interactions, while being tolerant of possible molecular motions relevant to the interaction. We wanted to consider protein surface properties and how opposing surfaces complement each other when forming an interface, largely independent of protein shape. For this reason, we began with a reduction of the irregular shape of a protein by considering atoms near the surface of the protein, thus excluding the atoms that play a role in stabilizing the protein core and presumably make less of a contribution to protein‐protein interactions.3.1Our simplified representation is as follows: The solvent accessible surface of the protein is computed and reduced into a simplified geometric representation proportional to the size of the protein Figure . The redThese reduced protein surfaces are images, making them suitable for several image processing techniques. To build a partner‐specific predictor that considers surface property‐complementarity, we performed cross‐correlation of images from two partner proteins to find an area of maximum similarity between the two images by computing a dot product at each position after rotation and translation Figure . Cross‐c3.2P value: .007). These results further support the notion that the shape reduction does not cause significant distortions, and cross‐correlation can be used to find the true interface of complementary properties. We then extended this approach to a more complicated scenario of a protein complex with known interaction basis.To address the concern of any distortion by the shape reduction, we demonstrated that interaction interfaces are still detectable with a proof‐of‐concept protein pair, the alpha‐chymotrypsin‐eglin c complex (PDB:1ACB) Figure . We extrα and β supercharged subunits. The top 10 scores accurately predicted two of the charge‐based interfaces between subunits. To further show that the engineered, supercharged GFP produces new charge‐based interfaces, we performed our shuffle analysis on wild‐type GFP to produce 396 000 possible scores and arrangements of the wild‐type residues. The scores from the supercharged GFP fell in the upper tail of the distribution of scores  and the accuracy 0.77 (up from 0.74). In addition, the new CAPRI criterion ranking was 30 high, 41 medium, 81 acceptable, and 20 incorrect.We also classified these predictions according to the CAPRI criterion of high, medium, acceptable, and incorrect ranking.In addition to the protein docking benchmark set, we tested MorphProt's performance on the 13 of the CAPRI targets from the score_set benchmark3.4R2 < .02). However, the ligand distortion shows a slight linear correlation (R2 < .52), with the prediction statistics decreasing as the Cα‐RMSD of the ligand with the native ligand increases. This process was repeated for four additional complexes (eight structures) with similar results  were distorted using normal mode analysis Figure . We used results .4Here, we have demonstrated that by using shape reduction to normalize the highly variable 3D protein structure to a simplified geometric representation, we are able to store layers of information on a 2D representation of a protein surface while preserving atomic neighborhoods. The resulting matrix of values contains the location of surface properties and their proximity to other values and is a direct representation of the spatial coordinates of the 3D atomic structure. We showed that converting the surface properties to an image allows us to identify areas of maximum interaction of surface properties between two proteins via a partner‐specific approach. In addition, MorphProt has the ability to construct large macromolecular assemblies through detecting multiple partner‐specific interfaces.While primary sequences provide information regarding amino acid identity and adjacent residues, it can be difficult to precisely determine from sequence alone which residues reside on the surface of a protein and their relation to each other in its 3D structure. Structure‐based approaches allow us to extract and investigate surface properties, providing a useful first step for interface prediction, as the spatial position of residues is essential for macromolecular recognition.In our approach, patch size is not predetermined; instead, it is dependent on the size of the proteins being tested and the size of overlap between protein faces for each score calculation. Traditional approaches for identifying a surface patch result in fairly uniform patch sizes.F1 score, which combines both precision and recall, went from an average of 0.22 to 0.28. The evaluation criterion is an important consideration and is dependent on the intended use of the prediction.Because our interfaces are defined by a continuous patch of residues and not several interacting residues, it is worth investigating the best method of defining a true interface. In our evaluations, we focused on the CAPRI standard, which defines an interface residue as containing a heavy atom within 5 Å of a heavy atom of the other protein in the bound structure. However, because we are predicting whole interface patches, we have a large number of false positive predictions (residues on the outside of the patch or in concave sections of the surface) that may not be within the 5 Å threshold. By reevaluating our CAPRI predictions using a more forgiving 10 Å true interface threshold, we see the average precision shift from 0.20 to 0.42 . It is ia priori information, either a template that resembles the protein being searched or a training set where a similar protein is represented. This limits these methods from making predictions for proteins that are not well represented experimentally.In our comparison of MorphProt and MorphProt PCA with four other structural predictions, we show that the MorphProt methods are comparable to available methods. MorphProt, however, differs greatly from these methods in its approach. The reduced representation removes emphasis from the shape and shifts it to surface properties and their location relative to each other. Because of this, no information is required aside from the protein structure to generate a prediction. The other programs require some sort of In most structure‐based interaction interface predictors, an interface is identified based on features of a given area on one of the protein surfaces, ignoring properties of a partner when determining how they best fit together. A partner‐specific predictor uses information regarding both proteins of interest. It has been shown that prediction methods that do not employ a partner‐specific approach have lower reliability in predicting transient binding sites,Furthermore, we showed that despite introduced structural distortion, we are still able to predict interfaces based on complementarity. This is increasingly important for predicting interaction interfaces with the widespread use of homology models and lower‐resolution structures. Here, greater weight is put on the neighborhoods of properties on the surface rather than their exact location. The ability to predict the interface for homology models is significant for assembling macromolecular complexes where little is known regarding the structure of the individual subunits. Theoretically, one could produce models for the subunits and then arrange them according to their interaction interfaces to predict the structure for large assemblies. Such analyses would also benefit from protein docking following the interface prediction to improve positioning.While discrepancies between interface prediction and protein docking occur often, the techniques are effective when used in conjunction with one another. Protein‐protein docking is a partner‐specific technique that is highly dependent on shape complementarity and energetics.Another significant application of partner‐specific interaction interface predictors is the screening of small molecule inhibitors or drugs. These often interact via transient interactions,5To address the inherent variability of protein shape, conformational changes, and structural approximations while reducing computation time, we were interested in determining if a simplified geometry retains enough spatial information to predict interaction interfaces based on complementary properties. Specifically, our aim was to develop a pipeline that was robust to molecular motions while gaining computational power to assemble larger multimeric protein complexes. Using MorphProt, we performed a shape reduction of the accessible surface of a protein into a reduced surface representation. This reduced representation allows for easy storage of intrinsic properties of the protein such as hydrophobicity, charge, and evolutionary rate to be embedded within each surface image. The result is a quantitative description of these properties across a protein surface enabling image processing techniques to identify complementarity between the properties of two interacting protein surfaces. We show this method can be useful when one of the above properties is the driving force of the interaction. MorphProt was able to predict interaction interfaces for the unbound CAPRI targets and the protein‐protein interaction benchmark complexes with comparable results to a number of other predictors. Additionally, MorphProt was able to predict interfaces for a large 16‐subunit oligomer, proteins with multiple binding sites, and crystal structures that have been distorted by up to ~6 Å Cα‐RMSD to mimic models built from lower resolution density maps or imperfect homology models. Our algorithm could be integrated into platforms that aim to assemble complicated protein architectures.The authors declare no conflict of interest.6https://publons.com/publon/10.1002/prot.26020.The peer review history for this article is available at AppendixS1. Supporting Information.Click here for additional data file.Figure S1 Score distribution of shuffled wild‐type GFP charge scores. The shuffling method was applied to a wild‐type GFP molecule paired with another wild‐type GFP molecule to show all of the possible scores the two proteins could attain. The charge score was multiplied by −1 to produce positive values here. The scores for the two interfaces predicted in Figure 2D,E are shown with red dots. Both fall in the upper tail of the distribution, showing the engineered GFP scores significantly higher than scores that may be attained with the wild‐type GFP.Figure S2: Considering other consistent predictions improves statistics. The second predicted interface was selected for predictions with precision <0.1 in the protein docking benchmark version 5, shifting the all statistics to the right. This suggests that considering all consistent interfaces might improve the prediction.Figure S3: Interface predictions on additional normal mode analyses. Normal mode analysis was performed on 4 additional complexes, providing 8 more examples of interface predictions of distorted structures. The four complexes were taken from the benchmark set and were distorted up to 10 Å ΔCɑ‐RMSD from the native structure using normal mode analysis. Despite these alternative structures, MorphProt was still able to predict the interaction interface.Figure S4: Statistical shift with change in interface definition. Changing the definition of an interface atom changes the distribution of precision, recall, F1 score, and accuracy. Because MorphProt selects all atoms predicted to be on an interface, not simply those side chains directly interacting with another protein, changing the definition of interface residues from being within 5 Å to 10 Å of a heavy atom of the other protein results in increased precision and F1 score, and decreased recall and accuracy.Table S1: MorphProt predictions for different types of interactions. The table shows average precision, recall, F1 score, and accuracy for the different types of interactions in the protein docking benchmark version 5: antibody‐antigen, antigen‐bound antibody, enzymeinhibitor, enzyme‐regulatory/accessory, enzyme‐substrate, G‐protein, receptor, and miscellaneous.Table S2: Normal modes selected for MorphProt interface prediction. The normal modes that were selected for each PDB to analyze the effect of molecular motions on the interface prediction.Click here for additional data file.


The generation of information, energy and biomass in living cells involves integrated processes that optimally evolve into complex and robust cellular networks. Protein homo-oligomerization, which is correlated with cooperativity in biology, is one means of scaling the complexity of protein networks. It can play critical roles in determining the sensitivity of genetic regulatory circuits and metabolic pathways. Therefore, understanding the roles of oligomerization may lead to new approaches of probing biological functions. Here, we analyzed the frequency of protein oligomerization degree in the cell proteome of nine different organisms, and then, we asked whether there are design trade-offs between protein oligomerization, information precision and energy costs of protein synthesis. Our results indicate that there is an upper limit for the degree of protein oligomerization, possibly because of the trade-off between cellular resource limitations and the information precision involved in biochemical reaction networks. These findings can explain the principles of cellular architecture design and provide a quantitative tool to scale synthetic biological systems. By performing computational analyses of statistical network properties, such as small-world5, scale-freeness6 and transitivity7 , it has been shown that the connectivity of several protein–protein interaction (PPI) networks in living cells  and metabolic networks10 in various organisms  have an inhomogeneous, scale-free network topology. Most proteins  typically have few connections, and only some proteins have many connections with other proteins, and they are considered highly connected hubs. The degree distribution of these protein networks, defined by the probability of one protein to interact with other proteins, has been shown to follow a power law10.A major goal of systems and computational biology is to gain understanding into the design principles underlying the complexity of large-scale biological networks at the organism level14. It has been shown that oligomerization can explain protein binding14, affecting the diversity and specificity of biochemical pathways16, and is associated with the regulation of enzyme activities17, cooperativity18 and stability11. Homo-oligomers often assume symmetric structures19, which allows proteins to form large structures without significantly increasing the genome size20.Proteins in living organisms are often oligomers composed of multiple subunits, which may be identical (homo-oligomers) or different (hetero-oligomers). Homo-oligomers are prevalent in nature and play important roles in biology18. Positive cooperativity increases with the increased affinity of ligands or protein binding and is modeled by the sigmoidal function . It has been shown that Hill coefficients and the sensitivity of biochemical reactions, defined as the ratio between the percentage of change in the input signal divided by the percentage of change in the output signal, are strongly correlated23. This correlation is widely used in the design of gene circuits by tuning their activities in response to external and internal signals. For example, transcription factors with multiple ligand-binding sites have more pronounced sigmoidal behaviors than transcription factors with a single binding site. While nature can utilize other biological mechanisms to increase the sensitivity of regulatory controls25, cooperativity is one means of scaling the complexity of cellular networks and improving their sensitivity18. However, these improvements in information quality are limited by the energy cost of protein synthesis26, and the balance between them can be achieved via cooperativity and protein oligomerization. For example, it has been shown that multiprotein complexes are created in proportion to stoichiometry, and the kinetics of individual proteins are optimized with regard to resource allocation and activity requirements. Similarly, it has recently been shown that a high transcription rate decreases stochastic fluctuations in gene expression but increases protein synthesis costs27.From a biophysical perspective, cooperativity in living cells can be described as the number of identical or nearly identical components that collectively interact with each other to enhance and stabilize biochemical reactions28.In this work, we characterized the protein homo-oligomer frequencies in proteomes and observed that dimers are dominant, while the formation of larger oligomer decreases following a power law. This common oligomer distribution pattern was observed at the levels of both organisms and metabolic pathways and cannot be explained by free-scale network dynamics. Our results indicate that there is an upper limit for protein subunit number, possibly due to the trade-off between the energy cost of protein synthesis and the sensitivity of biochemical reactions. The delineation of the design principles underlying this distribution may reveal new insights into understanding cell functionality and its application in synthetic biology designsE. coli, H. pylori, B. subtilis, D. discoideum, S. cerevisiae, D. melanogaster, M. musculus, D. rerio and H. sapiens) based on UniProt Knowledgebase29 protein lists  with diverse functionality. The dihedral group comprises more stable proteins that have greater potential for interaction because of subunit interface diversity. Therefore, a possible explanation for fewer odd subunit compositions may be that compositions with an even number of subunits have the ability to form both cyclic and dihedral symmetries, while odd compositions tend to form only cyclic structures35. It is important to note the analogy of the subunit distribution with Oddo–Harkins rule37, which states that elements with even atomic numbers are more abundant in nature than elements with adjacently larger and smaller odd atomic numbers. It is assumed that protons in even numbers are paired to enhance nucleon stability by balancing each other’s spin, leading to even atomic number abundance. Moreover, element abundance decreases as the atomic number increases, showing similarity to the subunit number distribution.To explore the large-scale structure of protein oligomers, we characterized the homo-oligomer frequency of nine organisms ) in homo-oligomers with an even number of subunits was fitted by the power law P(k) ~ − k−2.59   PPI networks follows a power law, we generated an undirected graph of protein networks . Here, the p value was used as a measure of the hypothesis suggesting that the power law is a good fit for the data, and p > 0.1 indicates that we cannot reject the hypothesis that the data were sampled from a distribution different than the power law. The network has an average node degree <d> = 23.3, where <d> is the average number of interactions of a protein in the network. In particular, <d> = 2E⁄N, where E is the total number of edges and N is the total number of nodes.To confirm that protein connectivity in rks Fig. b using dd> , did not correlate with the subunit number. In contrast, the connectivity was homogenous across different oligomerization states . Thus, complex computational networks, such as those in the brain or electronics, are optimally evolved or designed based on trade-offs between resource consumption and precision44. The physical resources that a network utilizes for computation include space, time and energy efficiency per time unit (power) per part. These resources are related to each on the following basis45:The development of systems with complex topology can be governed by two design principles, robustness and resource optimization. For example, it was suggested that networks that follow a scale-free power law distribution continue to operate properly even when several nodes are removedfunc(time) in Eq. (func(space) is proportional to the number of devices, nodes and parts needed to perform the computation. The frequency of a protein with k subunits represents the periodical appearance of the k-subunit structure across the proteome (space); therefore, the frequency can be interpreted as the spatial frequency of the k-subunit structure   and reflect the relative number of parts in the calculations performed in a certain cell (space) as follows:fs is the fraction  of a certain part in a specific space , and f is the frequency in time .Equation  is known) in Eq.  describeure Fig. b. This rFrom an evolutionary perspective, specifically from the point of view of unicellular processes in multicellular organisms, time is a continuous and infinite resource for life expression. Thus, for simplicity, we assume that the time is not a degree of freedom and is not included in the resource of energy allocation, and thus, we write:k subunits) synthesis in living cells, for which typically as much as one-third of the total energy is produced during cell replication46. Moreover, there are estimates suggesting that translation consumes more than 70% of cell energy47. The energy cost E(k) was calculated assuming the consumption of 4.5 ATP molecules per amino acid (aa)49 and the average length of a protein, L, to be ~ 360 aa in eukaryotes and ~ 270 aa50 in bacteria, as follows:To explain the power law distribution of protein oligomerization, we fit the resource-precision model Eq.  to moleck (M > 2) statistical arrangements. However, for simplicity, we selected 2k states based on the best empirical fit of our model  in living cells is given by:N is the number of proteins with k identical subunits and NT is the total number of proteins found in an organism. As in Fig. c(k) = fs(k) × k is proportional to the total number of parts that appear in the proteome with k subunits  is equivalent to the number of bits, and M = 2k is the signal level number, where fs is the bandwidth, which is defined as the difference between the upper and lower bounds for signal frequencies. Thus, the product c(k) = fs(k) × k is analogous to information capacity, which explains the trade-off between precision and energy cost. It is also known that the Nyquist information theory of a noise-free channel51 sets a limit on the maximum rate at which information can be transmitted over a communication channel. Such rate limitations arise from a trade-off between computation and communication. Thus, the maximum signal level that the receiver can distinguish is limited by the capacity of a communication channel. Analogously, in biological networks, a DNA promoter or any other protein involved in reactions can act as the receiver. The activity of a promoter containing several binding sites would thus place a substantial metabolic burden on a cell compared to a promoter with a single binding site.In information theory, 54E. coli data set. The protein oligomerization distributions in these essential metabolic pathways also followed a similar distribution pattern  of these pathways was well matched by the model of biological information capacity . Based on this model, we can design complex genetic circuits and compare their performances with common state-of-the art designs. This experiment can also help to find ways to reduce the component number in design and improve efficiency by combining circle parts (proteins) with respect to the frequency pattern observed in the proteome of some organisms.Developing an advanced model that takes into consideration the diffusion, channel noise and analog signals of proteins can be included in future works  = protein connection\total connections). The calculation of the connection probability function for each subunit number k was calculated in the same way, but the proteins were categorized based on homodimer, homotetramer, homohexamer and homo-octamer groups. The data file 511145.protein.actions.v10.xlsx can be found in a protein-homo-oligomer-distribution repository (E. coli folder.The protein–protein interaction probability distribution for pository  in the ESupplementary Information.