At a low interaction level, proteins function together in small, stable complexes and at a higher level, in sets of interacting complexes. All interaction levels are crucial for the living organism, and one of the challenges in proteomics is to measure the proteins at their different interaction levels. One common method for such measurements is immunoprecipitation followed by mass spectrometry (IP/MS), which has the potential to probe the different protein interaction forms. However, IP/MS data are complex because proteins, in their diverse interaction forms, manifest themselves in different ways in the data. Numerous bioinformatic tools for finding protein complexes in IP/MS data are currently available, but most tools do not provide information about the interaction level of the discovered complexes, and no tool is geared specifically to unraveling and visualizing these different levels. We present a new bioinformatic tool to explore IP/MS datasets for protein complexes at different interaction levels and show its performance on several real–life datasets. Our tool creates clusters that represent protein complexes, but unlike previous methods, it arranges them in a tree–shaped structure, reporting why specific proteins are predicted to build a complex and where it can be divided into smaller complexes. In every data analysis method, parameters have to be chosen. Our method can suggest values for its parameters and comes with adapted visualization tools that display the effect of the parameters on the result. The tools provide fast graphical feedback and allow the user to interact with the data by changing the parameters and examining the result. The tools also allow for exploring the different organizational levels of the protein complexes in a given dataset. Our method is available as GNU-R source code and includes examples at  Proteins in a living cell interact and build functional units to play their role in the cellular machinery –4. TheseCharacterizing protein complexes in a cell sample is still a delicate task, although the research field has progressed considerably and proteins can now be identified and quantified using high–throughput methods, such as immunoprecipitation followed by mass spectrometry (IP/MS) , 8, 9. IIn the context of IP/MS data, proteins are considered “similar to each other” when they occur together across experiments and have similar abundance values. This often holds for proteins that build a complex together; however, the different characteristics of protein complexes lead to different similarity levels of their proteins in the data. This phenomenon is shown in The similarity of interacting proteins in IP/MS data makes it possible to detect protein interaction and complexes with clustering tools , which cDifferent protein complexes at a specific interaction level, such as complex cores, do not always appear at the same similarity level in IP/MS data . Most coWe overcome these limitations with a new strategy that takes into account that protein complexes exist at different interaction and similarity levels. Our strategy is a hierarchical version of the 4N algorithm from  that we Like previous methods, HC4N assigns proteins that are similar to each other to clusters. In addition, our method provides information about why proteins were clustered together and where these clusters can be split into smaller clusters of more similar proteins that represent complexes at a lower interaction level. This divide-and-conquer strategy makes it possible to capture different interaction levels from large sets of complexes down to the stable cores each complex is built of. New graphical result representation methods are part of HC4N. They visualize at which similarity level complexes are found in the data and make predictions about their interaction level possible. They also help in adjusting the method’s parameters to fit different IP/MS datasets and finding different types of complexes.Several IP/MS datasets from yeast and humans are used to study the properties of our method and for comparison with other methods. Together with the IP/MS data, species–specific reference protein complexes are needed for the evaluation. We used the large–scale yeast IP/MS dataset that was presented by Gavin et al.  and two The human IP/MS dataset of Malovannaya et al.  is the lA satisfying reference for human protein complexes is still difficult to obtain. The best–known database for human interactions is CORUM . HoweverHC4N is based on the 4N method , which wThree global threshold parameters, one for each of the three above–mentioned similarity types, are used to set the strictness for calculating the near neighbor networks. The co-occurrence threshold parameter denotes in how many IPs two proteins need to co-occur relative to the number of IPs where any of them occur. The set–wise completeness parameter denotes how exclusive a near neighbor network needs to be. A low threshold allows for overlapping near neighbor networks, while a high threshold produces near neighbor networks that occur exclusively in this configuration. The abundance similarity is defined by the cosine similarity between two proteins.The 4N method can set the thresholds for co-occurrence and set–wise completeness automatically to the strictest setting at which no proteins are lost, and it also returns the values as user feedback. The abundance similarity parameter is of minor importance (and not applicable for 0/1 data) and set by hand to 40 in all experiments. At low strictness settings, proteins with at least low similarity are assigned to large clusters that then represent a high protein interaction level. Proteins with high similarity are assigned to clusters when 4N is applied with high strictness settings, and they represent a low interaction level. Clusters that overlap by a certain percentage  are joined to larger clusters, creating the final result of 4N.The HC4N strategy uses the ability of 4N to capture clusters at different similarity levels. It starts by applying 4N with low strictness to the IP/MS dataset. The resulting clusters are at level 1 in the result hierarchy tree; see The parameters of HC4N are set manually for the first level (see the result section for details). A manual setting of the parameters for all levels would be impossible as the total number of parameters can get very large. Therefore, the parameters for the higher levels are set automatically to the highest values where all proteins from the current subset are assigned to at least one cluster. As each subset is divided into smaller subsets of more similar proteins in a step, the HC4N strategy automatically captures a higher protein similarity level than before. Clusters of one step can have proteins in common. This facilitates, for example, that a core with different attachments can appear as a different cluster for each combination of core and attachments.The result of HC4N is a tree–structured graph where the root node (level 0) contains all proteins in the IP/MS dataset. The root node has a child node for each level–1 cluster. Each node contains a cluster that is calculated from the subset of the previous node in the hierarchy. A node is a leaf when its cluster is not split further or an inner node with child nodes when its cluster is split into smaller clusters. The protein similarity of each cluster is judged using the minimum co-occurrence of its proteins. A cluster with a low co-occurrence represents proteins with low similarity at a high interaction level. Clusters with a high co-occurrence represent a low interaction level. Child nodes of an inner node have a higher co-occurrence than their parent node, as they were built by splitting the parent node into proteins of higher similarity.Visualization of the HC4N result is crucial for interpreting the results and can be done in different ways. One way is the “hierarchical cluster plot” . They appear in the HC-plot as large squares with complex inner structures as shown in SOIs are small, which makes it possible to analyze them with other methods for which the full dataset would be too large. We will discuss the SOI analysis with the methods Biclust , HICLAS K clusters creates K protein clusters and K IP clusters. In the model, an I × J protein by IP dataset D is approximated by a model matrix M of the same size. M is composed as M = A ⊕ B, where A is a I × K binary matrix with Ai, k denoting whether protein i is in protein cluster k, B is a J × K binary matrix with Bj, k denoting whether IP j is in IP cluster k and ⊕ is a binary matrix multiplication operator where each result > 0 is set to 1, for example, 1+1 = 1. HICLAS minimizes the residuals function f over the matrices A and B, where f denotes the sum of squared differences between the model matrix M and data matrix D asThe HICLAS  , 32 algoWe applied HICLAS in our tests with different numbers of clusters and examined the residuals of each analysis to find the optimal number of clusters. We used the possibility to weight negative residuals differently than positive residuals .The method apComplex , 31 usesThe tree–shaped graphs from our HC4N method contain more information than just the clusters themselves; however, no comparison method that takes this additional information into account is available. To make the comparison possible, we removed the tree information from the result and joined clusters that were overlapping by more than 60%. The same joining step was applied to the results of the other methods for a fairer comparison. This joining step increased the quality of all methods because they often produce numerous, very similar small clusters that, when joined, represent the reference complexes better.We used the method by Brohée and van Helden  to evaluOne shortcoming of this method is that the accuracy does not decrease when a prediction method produces too many clusters that contain proteins from the reference complexes, as just the best matching cluster for each reference complex is taken into account. Hence, a score called separation is provided by the method in addition, denoting how many predicted complexes represent one reference complex. The separation score is 1 when each predicted complex covers exactly one reference complex.In our comparison, not all analysis methods could be applied to all datasets. For apComplex, the large datasets do not produce results due to memory problems when running on a PC with 12 gigabytes of memory. Both Biclust and HICLAS did not produce results on the large sets within a reasonable amount of time.The HC4N performance depends on optimal parameters for level 1. To find these parameters, we initially allowed HC4N to create the level–1 clusters with automatic setup where the thresholds for co-occurrence and set–wise completeness are set as high as possible so that each protein is still assigned to at least one cluster.We examined the HC-plot for the result to determine at which protein co-occurrence level the first clusters appear. When the clusters were too large, we set the co-occurrence threshold slightly higher than before, and when they were overlapping too much, we set the set-completeness parameter higher. For the SOI analyses, we have set the co-occurrence threshold and set-completeness parameter slightly lower than in the automatic setup to detect the interaction level of complex–complex interactions (see below). A scheme for how to use HC4N is located in The results are summarized in When compared to other methods, HC4N does not always yield a larger separation score see . In thesThe HC-plot from the Gavin2006 analysis shows subsets of interest, and we analyzed the green–framed SOI see  as an exAnalyzing the dataset starts by running HC4N with automatic setup and inspecting the HC-plot. The plot shows complexes but only a few connections between them, as shown in www.string-db.org) 36]. We aThe dataset was also analyzed with apComplex and HICLAS see . We wereFinding protein complexes in IP/MS data is a difficult task. Protein complexes can be found at different organizational levels in IP/MS data, and these levels must be explored together. The task is twofold: i) finding the complexes at different levels and ii) visualizing the result in a way that makes the different levels visible. In essence, this is a data exploration and visualization problem, and we designed our method, HC4N, to address that problem.Exploratory data analysis is a partly subjective task, e.g., by selecting parameters during analysis. While most software tools come with default parameters, understanding their effect on the result remains a problem. Our method not only supports automatic and manual parameter settings but also allows the user to retrace the effect of parameter changes with visual feedback. The change of parameters is very insightful because it enables exploring the different levels of organization of the protein complexes in a given dataset.A major problem for all complex finding tools is noise in the IP/MS data, leading to many false positives. While HC4N cannot actively remove noise, its built–in visualization tools help in detecting noise. In noisy data, HC4N will find many small, possibly false-positive clusters at low co-occurrence levels when applied with automatic parameters. Detected true-positive clusters may not have a fundamentally higher co-occurrence than the false positives. This leads to characteristic HC-plots without the typical clusters of high co-occurrence that appear when analyzing low-noise datasets. The behavior is demonstrated with examples in We have shown in this manuscript that protein complexes occur at different interaction and similarity levels, even in the same IP/MS dataset. Our new method, HC4N, is able to find complexes of different types and has been validated thoroughly using several datasets and comparisons with existing methods. The philosophy behind HC4N is to provide an interactive exploratory tool for analyzing IP/MS data that can be used (and tuned) by the biologists.S1 TableReference from Malovannaya et al..(PDF)Click here for additional data file.S2 TableSeparation scores of HC4N in comparison with the other methods.(PDF)Click here for additional data file.S1 TextDetails for 4N, HC4N and the hierarchical cluster plot. pseudocode for all modules.(PDF)Click here for additional data file.S2 TextUsage and parameter selection strategy for HC4N.(PDF)Click here for additional data file.S3 TextHC4N analyses on the large–scale datasets.(PDF)Click here for additional data file.S4 TextAnalysis of Gavin2006-SOI and Malovannaya-SOI with Biclust, apComplex, HICLAS.(PDF)Click here for additional data file.S5 TextHC4N result graph for the Malovannaya-SOI analysis.(PDF)Click here for additional data file.S1 FigAll proteins of the Gavin2006-SOI dataset as string-DB network.(TIFF)Click here for additional data file.


Biologists generally interrogate genomics data using web-based genome browsers that have limited analytical potential. New generation genome browsers such as the Integrated Genome Browser (IGB) have largely overcome this limitation and permit customized analyses to be implemented using plugins. We illustrate the use of a plugin for IGB that exploits advanced visualization techniques to integrate the analysis of genomics data with network and structural approaches.We show how visualization technologies that combine both genomics and network biology can facilitate the selection of the key amino acid contacts from protein-protein and protein-drug interactions. Starting from the MDM2-P53 interaction, which is a high-value target for cancer therapy, and Nutlin, the parent small molecule of an MDM2 antagonist that is currently in clinical trials, we show that this method can be generalized to analyze how drugs and mutations can interfere with both protein-protein and drug-protein networks. We illustrate this point by two additional use-cases exploring the molecular basis of tamoxifen side effects and of drug resistance in chronic myeloid leukemia patients.Combined network and structure biology approaches provide key insights into both the genetic and the edgetic roles of variants in diseases. 3D interactomes facilitate the identification of disease-relevant interactions that can then be specifically targeted by drugs. Recent advances in molecular interaction and structure visualization tools have greatly simplified the mapping of mutated residues to molecular interaction interfaces. Such approaches can now also be integrated with genome visualization tools to enable comparative analyses of interaction contacts.The online version of this article (doi:10.1186/s12859-016-0908-x) contains supplementary material, which is available to authorized users. The wealth of available genomics data has created an analysis bottleneck; efficient means of candidate gene prioritization that permit the integration, comparison and interpretation of genome-scale molecular information are therefore urgently needed. In particular, network and structural biology criteria must be applied to candidate genes in order to pinpoint their contribution to the development of cancer-specific phenotypic traits and to evaluate their druggability. In general terms, the former can be evaluated by studying the connectivity of candidate genes with bona-fide cancer genes in protein-protein interaction (PPI) networks, while the latter can be deduced from structural information on the protein of interest.Disease networks (networks of disorders and disease proteins) facilitate the identification of connections between disease-causing gene defects , 2 and mKnowledge of the structures of proteins and PPIs is required to understand the mechanism of action of drugs and how they interfere with protein networks. The Protein Data Bank (PDB)  containsCombining data on protein structures and genomic screens for integrated analysis is a non-trivial task. We have recently developed a plugin for IGB  that useThe PDB contains structures for 5387 human proteins from UniProt (02/2015) . Those s2, see methods). We identified 1253 ligands that bind at the interface of 1123 human binary PPIs (meaning that at least one contact is shared with PLI). The interactions are based on 473 complete experimental structures and 650 complete homology models (>80 % coverage) or partial experimental structures or models.We started by retrieving the list of structures from PDB that include a compound and extracted all contacts between proteins and ligands Fig. . Then, wp-value: 7e–19), in response to stimulus , and they are mainly membrane proteins  may be irrelevant when looking for molecules that may alter the PPI network. Therefore, we restricted the list of ligands in PDB to include only small molecules approved by the U.S. Food and Drug Administration (FDA) listed in DrugBank  see Met. Of the By intersecting the structural protein-protein and protein ligand networks above, we observed that many small molecules, including several approved drugs, could potentially compete with other proteins for binding at interaction sites. However, these analyses required programming skills, the download of datasets with diverse formats from external repositories, and basic knowledge of network and structural biology. To overcome these issues, and make the tool more accessible to a broader scientific user base, we have integrated the analysis pipeline into a single visualization tool as an IGB plugin called Molecular Interaction (MI) bundle . SeveralHere we used this plugin to visually investigate several examples of drug-PPI interactions, and to integrate mutations and drug-ligand data in order to identify gatekeeper mutations (mutations that abrogate binding of drugs to their targets).Choose drug target and select the corresponding gene in IGB,Select PDB and small molecules in the MI-Bundle to obtain a list of structures with ligands,Select Interactome3D to obtain a list of PPIs with either a structure or a model,Create a new track for each single interaction of interest: the PLI and the PPI by clicking on the “create track” button on the selected row in the result table,Select tracks of interest and calculate the intersection using basic IGB functionalities.The analyses can be done in 5 steps Fig. :Choose dWe illustrate this pipeline with the examples of the p53-activating drug Nutlin, the estrogen receptor modulator Tamoxifen, and the development of resistance to Imatinib in chronic myeloid leukemia patients  is overexpressed in a large fraction of human tumors, and exerts its activity primarily via inhibition of P53 (uniprotkb: P04637). The N terminus of P53 is required for its activity as a transcription factor; it is also the critical domain required for binding to MDM2 . Once boMDM2 gene , which was identified during screening of a compound diversity set performed by Roche . The resMDM2 is involved in three additional interactions for which a structure is available. We created a new track to display the contacts with each of those: MDM2, USP7 (uniprotkb:Q93009) and MDM4 (uniprotkb:O15151). Interestingly, the MDM2 homo-dimerization site intersects with the MDM2-Nutlin interface, suggesting that Nutlin may also interfere with MDM2 homodimerization. Conversely, the contacts that MDM2 makes with USP7 and MDM4 are distinct from the ones with Nutlin: The MDM2/USP7 and MDM2/MDM4 interactions may not be affected by this ligand, suggesting an edgetic effect of this compound. Our prediction that Nutlin does not interfere with the MDM2/MDM4 interaction is supported by data showing that MDM2 and MDM4 co-immunoprecipitate following Nutlin treatment, which is consistent with Nutlin-stimulated, MDM2-dependant degradation of MDM4 , 19.In order to determine whether Nutlin might perturb other interactions in which MDM2 participates, we repeated the previous query with Interactome3D resulting in the extension of the 3D coverage of the MDM2 network with models for interactions with three E2 enzymes (Ubiquitin-conjugating enzyme E2), UBE2D1 (uniprotkb:P51668), UBE2D2 (uniprotkb:P62837), and UBE2K (uniprotkb:P61086). Based on the models, none of those interactions share contact regions with Nutlin; those models nevertheless confirm the importance of the C-terminal MDM2 RING domain in mediating its E3 ubiquitin ligase activity . It is wIntriguingly, our modeling suggests a novel PPI target for Tamoxifen, a small molecule that is used in the clinic to treat estrogen-dependent breast cancer . TamoxifAlthough many effective anticancer drugs have been developed, advances are often hampered by the development of drug resistance. There are several mechanisms that cause drug resistance, including target cell extrinsic mechanisms, tumor microenvironment, and gene polymorphisms that affect gene expression, for instance . GatekeeA search for ligands of ABL1 in PDB indicates that the structure of this protein in contact with Imatinib has been resolved (PDB: 2hyy and 3pyy). A new track can be created to display the residues that are actually in contact. We also downloaded from COSMIC  a list oGenomics and molecular analysis tools are now widely available and sufficiently user friendly to allow cross-disciplinary investigation of the impact of genomic variants on biological systems. In this manuscript, we have used an extension for the IGB to illustrate the identification of key residues for the binding of MDM2 to P53, of Tamoxifen to NR1H4, and of gatekeeper mutations inducing resistance to Imatinib. Our IGB plugin greatly simplifies the integration of genomics data with network and structural analyses of both protein-protein and PLIs.The particular example of the MDM2-P53 interaction is derived from the intersection of 3D protein-protein and protein-ligand networks. Nevertheless, the structural coverage of the protein network is largely incomplete. The compound-binding proteins we have identified in this work are involved in many interactions for which no structure is available. Thus, we are likely missing additional interactions that may be targeted by small molecules. However, it is possible to increase the structural coverage of the protein network with Interactome3D, which includes PPI models for interaction supported by experimental evidence. Although indirect interactions  are excluded from the underlying experimental PPI network in Interactome3D, false positives may still limit the accuracy of the pipeline. The score implemented by the MI bundle may help to identify the most reliable interactions.By looking at the intersection between protein-ligand contacts and protein-protein contacts, we were able to identify small molecules that may interfere with PPIs. To be clear: our aim with this modeling approach is not to diminish the importance of the conventional approaches to discover the mode of action of those drugs. However, we suggest that our integrated tool can be exploited to generate new hypotheses. It may also be useful for the identification of drugs or molecular scaffolds that can be repurposed in order to block PPIs.Here, we focused on approved small molecules. Nevertheless, many other ligands have been crystalized together with target proteins and deposited in PDB, including experimental molecules and biotech drugs . By extending the analyses to these additional compounds, we believe that it will be possible to generate predictions regarding their effects on disease-relevant PPI networks.Our analyses are restricted to human proteins. It will be interesting to extend it to other species, both model organisms (many structures are generated based on the homologs of human proteins), and in host-pathogen interactions. To this end it may be useful to model not only PPIs, but also PLIs.For our initial validation and testing, we have focused our analyses solely on contact residues, considering that one contact may be enough to imply a steric clash when the two partners are superimposed. We didn’t assess the extent of cases in which the protein structure of a PLI includes a protein interface that is significantly different from the interface between the same protein and another protein (PPI). We would increase the accuracy of the method by checking the number of clashing atoms. Indeed, in the examples based on the MI-bundle, we were able to visually verify that the respective proteins and drugs share several residues. This current limitation will also be restrained by extending the intersection analysis to the entire interaction interface. Employment of other tools and databases may be useful in this regard , 28. In We have shown that all our analyses can be done without prior bioinformatics skills by using IGB together with the MI bundle. The software allows loading, visualization, comparison, and analysis of protein-protein and PLIs. Importantly, such analyses are not limited to the current knowledge deposited in public databases. The MI-bundle allows a local copy of an Interactome3D directory to be used. Any user that generates new protein networks (e.g. by yeast two hybrid) can submit them to the Interactome3D server and download the resulting structural network. Consequently, the user will be able to apply the plugin to their own data to discover new putative drug-PPI interactions.As a genome browser, IGB accepts a large number of genomic formats, such as BED, VCF or GTF; it can also communicate directly with DAS servers , such asFinally, we did not consider the features of PPIs that may influence the success of an inhibitor in this manuscript. In a recent review, Smith and Gestwicki  have anaWe used the mapping file available at  to assocWe used the mapping between Uniprot and PDB provided by the SIFTS initiative .We worked on a local mirror of the PDB database updated on May 2015. For PPIs, we downloaded the representative human dataset from Interactome3D, version 2015_05. The structures in Fig. 2. Parsing of PDB files and calculation of the available surface area was done with the BioJava libraries version 4.1 [In order to identify the contacts between the pairs of proteins or the pairs of protein-compound identified in the previous step, we measure the available buried surface area as described in . We conssion 4.1 .We have downloaded the VCF file of all coding mutations in Cosmic  version The network figures have been generated with Cytoscape version 3.2.0 .We used the BINGO plugin  for CytoWe downloaded and installed IGB and the MI-Bundle as described at . All ana


Computational approaches aided by computer science have been used to predict essential proteins and are faster than expensive, time-consuming, laborious experimental approaches. However, the performance of such approaches is still poor, making practical applications of computational approaches difficult in some fields. Hence, the development of more suitable and efficient computing methods is necessary for identification of essential proteins.In this paper, we propose a new method for predicting essential proteins in a protein interaction network, local interaction density combined with protein complexes (LIDC), based on statistical analyses of essential proteins and protein complexes. First, we introduce a new local topological centrality, local interaction density (LID), of the yeast PPI network; second, we discuss a new integration strategy for multiple bioinformatics. The LIDC method was then developed through a combination of LID and protein complex information based on our new integration strategy. The purpose of LIDC is discovery of important features of essential proteins with their neighbors in real protein complexes, thereby improving the efficiency of identification.Saccharomyces cerevisiae and Escherichia coli showed that LIDC outperformed classical topological centrality measures and some recent combinational methods. Moreover, when predicting MIPS datasets, the better improvement of performance obtained by LIDC is over all nine reference methods .Experimental results based on three different PPI(protein-protein interaction) networks of LIDC is more effective for the prediction of essential proteins than other recently developed methods. Proteins are vital parts of living organisms, functioning as the main components of the physiological metabolic pathways of cells, and form densely connected modules to perform various biological functions. With the development of proteomics research in the post-genomic era, several protein-related topics, including discovery of the structures and functions of proteins, detection of interactions among proteins, and identification of essential proteins or protein complexes and functional modules, have become the major focus of many researchers. Essential proteins are those proteins that, if deleted, result in lethality or infertility . Some reGenerally, two types of methods are used to identify essential proteins. The first is experimental techniques, such as single gene knockout , RNA intAs a new modality for the identification of essential proteins, computational approaches focus on the topological properties of biological networks according to the centrality-lethality rule , and grau in a given protein complex sets. They have only discussed the ratio of a single essential protein in a given protein complexes[Existing results suggest that there is a correlation between essentiality and the degree of proteins in PINs, e.g., according to the centrality-lethality rule; this is also perhaps the main reason that most computational approaches must be sensitive to the topological structures of PINs. Additionally, subsequent experiments and analyses, e.g., yeast two-hybrid (Y2H) analyses, have shown that this type correlation may be too weak for binary or transient protein interactions , 18. Morcomplexes. Li et acomplexes. Zhong ecomplexes. We consSaccharomyces cerevisiae and Escherichia coli, which are representative model organisms, downloaded from the DIP and MIPS databases.To overcome the limitations of existing computational approaches in current research on prediction of essential proteins, we have explored the interaction relationships among nodes in real protein complexes based on protein and protein interaction information, we partition proteins in a protein interaction network to two type nodes: interactive nodes and isolated nodes as described in section Definition of the problem and analyses. This kind of partition to proteins in complexes we proposed is different from the in-degree measure of one complex used by some existing studies mentioned above. And then we proposed a new identification method, local interaction density combined with protein complexes (LIDC), which is composed of three components. The first is a new centrality measure based on the local topological properties of proteins in protein complexes, called the local interaction density (LID); the second is the biological information of protein complexes, called the in-degree centrality of complex (IDC); and the third is a new integration strategy for combining LID and IDC. LID is expected to facilitate the identification of essential proteins from their neighbors, which interact with other neighbors. LIDC was applied to three PIN datasets of Compared to nine conventional methods, i.e., degree centrality (DC) , betweenMost existing prediction methods are built on the centrality-lethality rule and the topological centrality of PINs; even recent multi-information fusion measures, which often perform better than purely topological centrality methods, usually include one type of topological centrality measure. To further improve the prediction capability of multi-information fusion measures, we may be confronted with two problems: 1) discovery of new topological centralities, and 2) development of more effective integration strategies.With regard to existing topological centrality, we have learned that most high-degree hub nodes are not essential in yeast PINs . The corThrough statistical analysis of the identification methods mentioned above, we noticed that some proteins have the same centrality score in a given ranking range predicted by one method, and these proteins may not be distinguished clearly, regardless of whether the protein is essential or nonessential. These limits may reduce the overall performance of existing identification methods. In order to achieve improved performance of identifying essential proteins, we even more present a new integration strategy that combines LID and information of protein complexes so as to construct LIDC, which achieved better performance in these ranking ranges: top 100, top 200, top 300, top 400, top 500 and top 600.G = , which consists of a node set V and an edge set E. One node v ∈ V represents a unique protein, while one edge  ∈ E represents an interaction between protein u and protein v. The adjacency matrix is written as A of G, and the matrix (an N × N symmetric matrix) is written as A = au,v, where the variable N is the total number of nodes in a PIN; thus,A PIN is generally described as an undirected graph GNB(u) = (VNB(u),ENB(u)) is the adjacency subgraph of a protein u, i.e., a source node u of GNB(u) in a PIN, where VNB(u) is the node set in GNB(u), and ENB(u) is the edge set in GNB(u). VNB(u) is the union of two neighbor node subsets, VNB_ISO(u) and VNB_INT(u), while ENB(u) is also the union of two neighbor edge subsets, ENB_ADE(u) and ENB_INT(u). Edges in ENB_ADE(u) are called adjacency edges and are interactions between a source node u and all of its neighbors; edges in ENB_INT(u) are called interactive edges and are those interactions among neighbor nodes of u. Nodes in VNB_ISO(u), called isolated neighbors, are nodes that only have adjacency edges to the source node u, while nodes in VNB_INT(u), called interactive neighbors, are nodes that have both adjacent edges to u and interactive edges among them, as shown in u is a star node if its VNB_INT(u) is empty and the topological structure of its adjacent subgraph is a star, e.g., protein YDL171C, as shown in In order to analyze the correlations between interactive neighbors and essential proteins in terms of modularity, we first examined nodes in a real protein complex dataset based on our partition of nodes. In a yeast protein complex dataset containing 408 complexes and 1920 nodes, without considering the overlap among complexes  (whose iLIDC is a multi-information fusion measure proposed in this paper that is composed of three parts as follows.u (LID(u)) is defined as the density of interactions among its interactive neighbors:u is protein YJL143W, and we then have |ENB_INT(u)| = 2 and |VNB_INT(u)| = 4, such that LID(u) = 0.5. Obviously, LID(u) will be larger if there are fewer neighbors of node u, resulting in denser interactions among the nodes.The LID of a node u in a protein complex set is defined as:u) denotes a set of protein complexes that include protein u, and IN-Degree(u)i is the in-degree value of protein u in ith protein complex that belongs to ComplexSet(u). IN-Degree(u)i is computed as:u)i is the degree value of protein u in complex i, which is ith element in ComplexSet(u).Protein complexes are stable macromolecular assemblies that perform many diverse biochemical activities essential to cell homeostasis, growth, and proliferation; proteins within these complexes appear at the same time and in the same location, and more some proteins participate in more than one complex. At the network level, protein complexes are usually substructures in PINs. In our design, we may compute the IDC of a protein to identify the essential proteins. The IDC of a protein The purpose of our new integration strategy is to overcome the constraints of existing identification methods, such as existing identification methods lack sufficient flexibility to adapt to various network structures of PINs. The construction of topological centrality measures is based on a special dataset, generally becoming the innate deficiency in multiple datasets, indicating that the performance of this type of identification method is sensitive to the structures of PINs. There are two types of integration strategies used to combine multi-information fusion measures. The first is that the prediction score of proteins is the product of values of multifeature information, such as PeC, CoEWC and UC, and the second is that the predicting score of proteins is the linear sum of values with some coefficients of multifeature information, such as ION and WDC. The way of product increases the network structure dependence of those methods than the linear sum way without sufficient guarantee of the quality of the dataset, leading to high false positives and false negatives of interactions among proteins. On the other hand, the pattern of the linear sum contains some coefficients that adjust the proportions of feature values for each type of information in the predicting score of the proteins, and however many of these coefficients are constants, which, in most cases, depend on a given PIN, thereby increasing the network structure sensitivities of these methods as well. Therefore, we consider a new integration strategy to pursue good performance in all six ranking ranges at the same time in order to improve flexibility in the context of multiple PINs.u) be the order number of the descending sort of protein u according to LID(u) in a PIN. According to the modularity of proteins and the integrating strategy, there are four cases to show some biological meanings of our LIDC. The first case is when LID(u) is larger and IDC(u) is larger, LIDC(u) is also larger which means neighbors of protein u have more interactions among them so that protein u and its neighbors have more modularity and the probability of protein u be an essential protein also is increased. The second case is when LID(u) is smaller and IDC(u) is smaller, LIDC(u) is smaller which means neighbors of protein u have fewer interactions among them so that protein u and its neighbors have smaller modularity and the probability of protein u be an essential protein is decreased. The third case is when LID(u) is larger and IDC(u) is smaller, LIDC(u) mainly depends on LID values which means we maybe predict some new protein complexes around protein u from the perspective of biology. The forth case is when LID(u) is smaller and IDC(u) is larger, LIDC(u) depends on IDC values which means we maybe find out some new interactions among protein u and its neighbors.The new integration strategy we consider here has the advantages of the topological centrality measure LID and the prediction method IDC. Let RANK(u) is the order number of the descending sort of protein u according to LID(u) depended on a given PIN, which means RANK(u) will be changed with different PPI networks. The flexibility of our new integrating strategy will improve the expansibility of LIDC.On the other hand, LIDC with our new integrating strategy is a more soft computing method than those integrating ways with fixed coefficient style for multi information used in PeC, ION, WDC and UC because RANK(u can be computed as:u) is the value of the LID, IDC(u) is the value of IDC of the protein complex of protein u, and N is the number of proteins in the current PIN. RANK(u) is the order number of the descending sort of protein u according to LID(u) in the current PIN, which can vary with different datasets such that LIDC can be more flexible and adjustable than traditional, simple, empirical, single-parameter patterns.After summarizing and analyzing the experimental results of most topological centrality measures, including our new centrality LID, we found that there was no single centrality measure that could predict all essential proteins correctly and completely in a given PIN. Therefore, we should construct multi-information fusion measures in order to improve the performance of identification synthetically. Thus, we chose the IDC as our second biological information source in our new identification method because of the modularity of protein function, as mentioned above. Therefore, the LIDC of protein From the definition and analyses of LIDC above, LIDC may identify essential proteins more effectively than existing identification methods.Saccharomyces cerevisiae (yeast) as one of experimental materials because this model organism has relative complete, reliable PPI and essential protein data. The PPI network of Saccharomyces cerevisiae was downloaded from two databases: the DIP database [S. cerevisiae was gathered from several databases, including MIPS [To evaluate the performance of our proposed LIDC method, we considered PPI data of database S1 Text)Saccharomdatabase   into one comprehensive protein complex set. Of the four protein complexes datasets, only complexes with a size of more than two nodes were kept. CM270 is the gold standard protein complex set and was downloaded from the MIPS database . It contNext, we constructed two yeast PINs firstly for evaluating LIDC from two PPI datasets whose nodes represented proteins and edges represented interactions among proteins. The first network downloaded from the DIP database, marked YDIP_5093, included 5093 proteins and 24743 interactions. Its average degree was about 9.72. The second network downloaded from the MIPS database, marked YMIPS_4546, included 4546 proteins and 12319 interactions. Its average degree was about 5.42. The numbers of interactions in the two PINs were counted after removing self-interactions and duplicate interactions. With regard to the essentiality of proteins in a PIN, nodes were grouped into three subsets in a network: essential proteins, nonessential proteins, and unknown proteins covered by neither the essential protein set nor the nonessential protein set. We incorporated the unknown protein set into the nonessential protein set for the sake of easier discussion in this paper. There were 1167 essential proteins and 3926 nonessential proteins in network YDIP_5093 and 1016 essential proteins and 3530 nonessential proteins in network YMIPS_4546. The proportion of essential proteins in each PIN was nearly equal, which helped us to examine the precision of LIDC rationally. The details of nodes within the two PINs are shown in The global characteristics of the two PINs were similar for most items in From local topological characteristics of PINs shown in In general to evaluate the overall performance of LIDC, we first ranked the results of LIDC in descending order and then chose proteins in six different ranking ranges (top 100–600) as essential protein candidate sets of the two PINs. The more essential proteins were identified in each potential set for the given method, the better the performance of the method.SN = TP / (TP + FN); specificity was defined as SP = TN / (TN + FP); positive predictive value (PPV) was defined as PPV = TP / (TP + FP); negative predictive value (NPV) was defined as NPV = TN / (TN + FN); F-measure was defined as F = 2 × SN × PPV / (SN + PPV); accuracy was the proportion of correct prediction results of all the results, which is defined as ACC = (TP + TN) / (Posi + Nega), where Posi and Nega are the total number of essential proteins and nonessential proteins, respectively. The precision-recall curve has been finished in which Precision = TP / (TP + FP) and Recall = TP / (TP + FN). In addition, identification of essential proteins was also considered a classification problem; therefore, the area under the receiver operating characteristic (ROC) curve (AUC) was a suitable measure used to estimate the performance of our new method in which TPR = TP / (TP + FN) and FPR = FP / (FP + TN), and then may be computed through trapezoidal integration methods.And then for assessing the effectiveness and accuracy of LIDC, we selected the top 20% of ranking results from LIDC which were regarded as an essential protein candidate sets, and the rest part of the results which were considered nonessential protein sets for computing some statistical results. We then calculated several parameters, including the values of true positives (TPs), true negatives (TNs), false positives (FPs), false negatives (FNs), and obtained the outcomes of six common statistical methods using these values , which are usually used to evaluate the effectiveness of an algorithm. Sensitivity was defined as In order to validate the performance of LIDC, a comparison was carried out with nine classical identification measures: DC, BC, NC, LID, PeC, CoEWC, WDC, ION and UC. Among these, DC and BC are classic local and global topological centrality measures, respectively, and have been used by many researchers in various fields , 13, 26.Experimental dataset section. The numbers of essential proteins predicted by LIDC and the other nine methods in the two yeast networks are shown in Figs For the purpose of performance testing of LIDC after ranking proteins in descending order based on their LIDC values and other methods, the six ranking ranges (from the top 100 to the top 600) were chosen as essential candidates, and finally, the essentiality of the proteins was checked through the collection of essential proteins described in the As shown in As shown in The jackknife methodology  has beenIn order to evaluate the overall performance of LIDC synthetically, we took advantage of six statistical analysis parameters, including sensitivity, specificity, PPV, NPV, F-measure, and accuracy. The top 20% selected from the ranking results of all methods was regarded as the essential protein candidate set, while the remaining results were considered the nonessential protein set . The sensitivity, specificity, PPV, NPV, F-measure, and accuracy of LIDC were higher than those of the eight other methods for both PINs, especially in YMIPS_4546 PIN , and rouThe identification of essential proteins may be considered a two-class classification problem, rather an approximate imbalanced classification problem because there are usually two or three more nonessential proteins than essential proteins in PINs. For example, there were 1167 essential proteins and 3926 nonessential proteins in YDIP_5093 and 1016 essential proteins and 3530 nonessential proteins in YMIPS_4546. Hence, AUC is a suitable measure for estimating the efficiency of classifications between LIDC and other reference methods. The top 20% selected from the ranking results of all methods was regarded as the essential protein candidate set, while the remaining results were considered the nonessential protein set . The AUC of LIDC was better than those of nine reference methods in the YMIPS_4546 PINs (0.62 for YMIPS_4546), while 0.66 for YDIP_5093 is very close to the best AUC(0.67) of those results in other reference measures. The performance of LIDC for this imbalanced two-class classification for identification of essential proteins was best in YMIPS_4546 PIN as shown in To assess the effects synthetically of the new integration strategy on LIDC in YDIP_5093 and YMIPS_4546 PINs, we analyzed the relative increasing ratio as a measure for evaluating performance, using LID as the reference method in 12 rank ranges top 100–600 and top 1%-25%. LID is a topological centrality measure whose performance was poorer than NC, a core component in PeC, CoEWC, and WDC, of the six comparisons for each PIN, as shown in Figs From u) will be changed with different PINs, thereby changing RANK(u) and LIDC(u). This type of change may increase the flexibility of LIDC when analyzing different PINs.Above all, our new strategy may contribute to the enhancement of the LIDC identification method for proteins whose centrality values were located in the middle part of ranking ranges after descending sorting. The second advantage of this new strategy is that it decreases the number of unidentified proteins that have the same centrality scores, improving the performance of LIDC. For example, there were 2705 proteins whose NC centrality measures were 0 and 2734 proteins that had 0 score using the PeC multi-information fusion method on the same DIP dataset; in contrast, there were 2430 proteins with 0 values using our LIDC method, a 10% reduction in the number of unidentified proteins. The third advantage of this integration strategy is that LID because we expected the protein modules predicted by ClusterONE to possess stronger biological significance, with the module size detected in more than two nodes. And seven top 100 network structures among LIDC and the six other methods are shown in Figs Proteins rarely act alone; instead, proteins function in groups, i.e., protein complexes or functional modules, to perform their tasks in biological systems. Hence, protein modularity may be an appropriate approach to evaluate the rationality of essential proteins identified by LIDC in some biological sense. In order to explore the modularity of proteins predicted by LIDC and six other methods , whose probability to be essential were higher, each of seven small PINs were constructed based on the top 100 proteins detected by LIDC and the six reference methods in YDIP_5093 and YMIPS_4546. Each network consisted of the top 100 proteins ranked by LIDC and the six other methods. Next, we used clustering with the overlapping neighborhood expansion (ClusterONE)  to detecAs shown in Additionally, ClusterONE have detected seven functional modules in the PIN of LIDC, and LIDC yielded the best results in all seven top 100 PINs in YDIP_5093. We found that the more functional modules were in the more sparse top 100 PIN, which was identified by the LIDC method. Moreover, the same results were observed for the seven top 100 PINs of YMIPS_4546. Therefore, essential proteins predicted by LIDC possessed more obvious modularity than those identified by the six other methods in YDIP_5093 and YMIPS_4546 PINs. We still need to concern the effect of orthologous information of proteins for essential protein prediction according to performance of ION and it may be a reasonable way to combine LIDC and orthologous information based on our integrating strategy reported in this manuscript.Escherichia coli PIN. The PPI data of E. coli is downloaded from DIP database[E. coli has been collected from database DEG[To further assess the performance of LIDC, we have taken used of it to predict essential proteins in  database called Eabase DEG which coEscherichia coli PIN yet, we consider LIDC will be simplified to a pure LID measure to take part in comparative experiments with three reference measures which are PeC, CoEWC, WDC. The main reason for the choice of these three measures is the lack of necessary bioinformatics information for other rest reference multi information fusion methods.Due to we have not obtained the real protein complex data of Escherichia coli has been downloaded from [The gene expression data of ded from  which coFor evaluating the performance of LIDC in EDIP_2727 after ranking proteins in descending order based on their LIDC values and other methods, the six ranking ranges (from the top 100–600) were chosen as essential candidates. As shown in For the sake of evaluate the overall performance of LIDC synthetically in EDIP_2727, we also have taken advantage of the same six statistical analysis parameters who include sensitivity, specificity, PPV, NPV, F-measure, and accuracy. The top 20% (545 proteins) selected from the ranking results of four measures were regarded as the essential protein candidate set, while the remaining results were considered the nonessential protein set (1282 proteins). The sensitivity, specificity, PPV, NPV, F-measure, and accuracy of LIDC were higher than those of the three other methods . These dEscherichia coli, AUC also has been consider a suitable measure to examine the power of LIDC on two-class classification in a PIN because it is an approximate imbalanced dataset of EDIP_2727 PIN where are 245 essential proteins and 1282 nonessential proteins. The AUC of LIDC (0.64) with respect to all proteins in EDIP_2727 PIN was the second best result among four prediction methods shown in To better understanding the performance of LIDC in protein interaction networks of Escherichia coli, we also has considered the protein modularity as an appropriate approach, and then explored the modularity of proteins predicted by LIDC and three other methods . Each of four small PINs were constructed based on the top 100 proteins detected by LIDC and the three reference methods in EDIP_2727 has been clustered with the overlapping neighborhood expansion (ClusterONE) [p-value of less than 0.001 in ClusterONE, and the module size should be more than two nodes.In order to assess the rationality of essential proteins identified by LIDC in some biological sense in sterONE)  to detecAs shown in Escherichia coli. Thus we still have confidences in the better improvement of LIDC in Escherichia coli with the accumulating of relative kinds of bioinformatics data gradually.Although LIDC has a better performance in EDIP_2727 than three reference methods, there is no denying that ION is stronger than LIDC from the results in reference. HoweverIn recent decades, there has been a sharp increase in PPI datasets due to the rapid development of experimental technologies, such as affinity purification. These experimental results may produce various PINs, and the identification of essential proteins at the network level has become a major focus of many researchers. Hence, many prediction methods have been proposed based on topological characteristics and various biological information of PINs. However, experiment datasets for many species are still incomplete, leading to false negative and false positive data. On the other hand, capturing the distinct features of essential proteins to improve the performance of identification is still challenging. These limits decrease the capabilities of existing prediction methods, making the prediction methods sensitive to the network structure of PINs. In order to overcome the constraints mentioned above, we explored real protein complexes to discover new characteristics of essential proteins with their neighbors in complexes, and then found that the essentiality of proteins may have a close relationship with interactions among proteins in the same clustering. As a result, we propose a new identification, LIDC, as a multi-information fusion method constructed by two information features, i.e., the LID and IDC of essential proteins, which represent new topological characteristics of proteins and in-degree information of protein complexes, respectively, based on the new integration strategy designed in this paper, with the goal of improving performance in multiple PINs.S. cerevisiae and E. coli: YDIP_5093, YMIPS_4546 and EDIP_2727. The experimental results indicated that LIDC outperformed recent classical identification methods, including DC, BC, NC, LID, PeC, CoEWC, WDC, ION and UC. In particular, we achieved better improvement in the number of essential proteins identified in YMIPS_4546. Additionally, experimental results also showed that LIDC was quite different from other existing methods and possessed higher accuracy. Moreover, the essential proteins identified by LIDC exhibited stronger modularity, such that the clusters connected by these proteins were also essential for special biological functions, consistent with recent studies [LIDC was applied to three PINs of  studies , 42, 44.S1 Excel(XLSX)Click here for additional data file.S2 Excel(XLS)Click here for additional data file.S1 Text(TXT)Click here for additional data file.S2 Text(TXT)Click here for additional data file.S3 Text(DOC)Click here for additional data file.


All proteins sample a range of conformations at physiologic temperatures and this inherent flexibility enables them to carry out their prescribed functions. A comprehensive understanding of protein function therefore entails a characterization of protein flexibility. Here we describe a novel approach for quantifying a protein’s flexibility in solution using small-angle X-ray scattering (SAXS) data. The method calculates an effective entropy that quantifies the diversity of radii of gyration that a protein can adopt in solution and does not require the explicit generation of structural ensembles to garner insights into protein flexibility. Application of this structure-free approach to over 200 experimental datasets demonstrates that the methodology can quantify a protein’s disorder as well as the effects of ligand binding on protein flexibility. Such quantitative descriptions of protein flexibility form the basis of a rigorous taxonomy for the description and classification of protein structure. Thermally induced conformational fluctuations enable proteins to sample a range of structures under physiologic conditions. In many cases, this flexibility is required for a protein to carry out its prescribed function. Quantitative assessments of protein flexibility would therefore further our understanding of the relationship between protein function and structure.The combination of experiment and computation forms a powerful platform for characterizing protein flexibility. Small-angle X-ray scattering (SAXS), in particular, is one popular experimental method that is often used in this context. Although SAXS typically yields low-resolution information, the combination of SAXS and atomistic simulations can provide insight into conformational changes in proteins and protein flexibility1233a priori, be constrained. The resulting ensemble will therefore depend on the manner in which one chooses to introduce constraints.Many existing approaches for gaining insight into structural flexibility from experimental data belong to a class of approaches that generate a set of structures to agree with a pre-specified set of experimental observations. This process of generating a set of protein structures that fit a given set of experimental measurements, however, is an underdetermined problem because the number of degrees of freedom in the protein is generally much larger than the number of experimental constraints. While this statement is applicable to all proteins, the problem is most egregious for disordered proteins that, by definition, sample a vast region of conformational space. For these systems there are often many different ensembles that agree with a given set of experimental observations681011Consequently, there is a role for structure-free methods that provide information about protein flexibility. Quantitative metrics of protein flexibility calculated from the experimental data alone would facilitate objective comparisons between different proteins, while avoiding the introduction of biases due to the specific choice of structures or simulation protocol. Moreover, metrics that quantify protein flexibility provide a basis for a comprehensive classification scheme for protein structureIn this work we describe a new formalism for quantifying protein flexibility from SAXS data. Our approach distinguishes between proteins that have different degrees of disorder and provides novel insights into ligand-induced effects on protein flexibility.The measured scattering intensity of a protein is the sum of the scattering intensities of all macromolecular conformations within the protein solution. Thus,q is the magnitude of the scattering vector, where q region, where the intensity falls off by about one order of magnitude, the intensity is mainly dependent on the size of the macromolecule, i.e. its radius of gyration. We therefore propose a minimalist model in which the intensity profile of a conformation with radius of gyration Rg is represented by the intensity predicted for a sphere with homogeneous charge density14IS and derive in the To simplify the calculation of the entropy, we propose a model that differentiates conformations based on their radius of gyration, instead of their conformation – a process that reduces the dimensionality of the problem from 3N degrees of freedom to one. Thus, we consider the probabilities of every possible radius of gyration, as opposed to every possible conformation, for our estimation of entropy. The radius of gyration criterion is convenient in SAXS experiments because in the low μ,σ(q), is given byThe scattering intensity in the context of the Radius-of-gyration Distribution (RgD) model, IPμ,σ(Rg) is the probability distribution function (pdf) over the different radii of gyration that a protein can adopt in solution. The model uses a log-normal distribution for the pdf,where Rg, and P(Rg) approaches zero as Rg approaches zero. For practical use, we set P(0) = 0.where μ and σ are the mean and standard deviation of the log-normal distribution. The log-normal distribution has the advantages that it is only defined for positive values of Iμ,σ(q), to the experimental scattering intensity, Iexp(q), we find values of μ and σ that minimize the difference between Iμ,σ(q) and Iexp(q). More information on the minimization method is provided in the To fit the modeled scattering intensity, A consequence of equation [4] is that the entropy has a lower bound of −∞, a fact that distinguishes it from other discrete entropy measures  for which the lower bound is zero. The difference in lower bounds between continuous and discrete probability distributions is emphasized by using the term “differential entropy” for the continuous caseThe RgD formalism uses a spherical model to calculate the scattering intensity of a given protein conformation. Modeling protein structures, and conformations within a disordered ensemble, by spheres is admittedly a simplification that does not capture the complexity inherent in the structures of biological molecules. However, we were encouraged by the fact that the use of simplified models of biological polymers has a long and rich history of providing important insights into many biological processes1718192021222324We began by choosing three proteins to study – one representing a folded, compact, protein, another a partially disordered protein, and the third an intrinsically disordered protein. Our overall approach was to construct ensembles for each protein, generate a theoretical ensemble average SAXS profile for each ensemble, and then input these data into our RgD algorithm to determine whether the RgD model can produce entropies that are consistent with our understanding of the relative disorder of these systems. In this sense, the constructed conformational ensembles are “reference ensembles”, from which experimental observables are calculated. For these simulated experiments the goal is not to generate ensembles that agree with some predefined set of experimental data. By contrast, the structural ensembles represent the “ground truth”, which is then used to calculate SAXS profiles. The resulting SAXS profiles are then input to the RgD algorithm to determine whether the method can differentiate proteins according to their flexibility.E. coliFor the folded protein we ran molecular dynamics simulations of the 202 residue bacterial toxin protein CcdB from the control of cell death and quiescence gene in Results are shown in Rflex and is typically represented as a percentage where 100% represents maximum flexibilityIt is important to note that the RgD calculations do not utilize the structural ensembles themselves; i.e., RgD entropies are calculated from the SAXS spectra alone. To determine how our data compare to other structure based estimates that use both the structure and the SAXS profile, we used EOM to compute quantitative estimates of protein flexibility from each of the three model systems we consideredRflex values of the selected ensembles – 40% for CcdB, 55% for CcdA and 88% for K18 – showed a range of flexibilities in agreement with the values obtained with the RgD model; i.e., 2.58 for CcdB, 3.36 for CcdA and 4.41 for tau.We used the EOM algorithm to generate a pool of 10,000 conformations for each system based on their amino acid sequences and then used these sequence-based conformational pools to fit the theoretical SAXS spectra using the genetic algorithm component of EOMRflex are clearly useful for evaluating the flexibility of systems for which the conformational ensemble is unknown, they require the generation of a set of representative structures. Since RgD requires only a SAXS profile to produce an estimate of a system’s flexibility, it can provide additional information that may help guide the choice of structural library to use with structure based methods like EOM; e.g., proteins with large RgD entropies should have a large structural library that contains a wide range of different structures, while proteins with small RgD entropies may be better modeled as compact or folded.While structure-based metrics like I(q) will decay as q−4, whereas the scattering intensity of a flexible Gaussian chain will decay as q−2 or slowerq2I(q) versus q; i.e., a Kratky plot. Compact proteins will have q2I(q) values that approach zero (or baseline) at high q, while unfolded, or disordered, proteins will generally plateau at intermediate angles followed by continuously increasing values of q2I(q) at wide angles130Kratky plots of SAXS intensity data are commonly used for qualitative assessment of protein disorder. For compact proteins, (qRg)2I(q)/I(0) versus qRg. The x- and y-axes of these plots are dimensionless and therefore are independent of the size and molecular weight of the molecule of interest. Hence these normalized or dimensionless Kratky plots are useful for the analysis of SAXS profiles across different systems. An additional advantage of this formalism is that the dimensionless Kratky plot of a well-folded biopolymer will have a local maximum at (qRg)2I(q)/I(0) = 3e−1 = 1.104. Homogeneous solutions of folded polymers therefore have dimensionless Kratky plots that have an identifiable characteristic shapeAn alternate version of a Kratky analysis renders q values less than 0.3 Å−1. This latter requirement ensured that each entry had enough data to perform a meaningful analysis using standard approaches such as a Kratky plot. This screen left a total of 226 experimental datasets for our analysis 2I(q)/I(0) = 3e−1 = 1.104  vs. q4 will achieve a plateau, which is a function of the molecule’s surface area and its electron density contrast with respect to the surrounding solvent3742q where the Porod-Debye law is applicable – the Porod-Debye region – is estimated from the position of the first peak in the corresponding Porod plot  vs q). Proteins that have considerable flexibility decay slower than q4− and therefore do not reach a plateau in the Porod-Debye region.Dimensionless Kratky representations of the three systems are very similar in that all three proteins have a local maximum at  = 1.104 . It is tA Porod-Debye analysis does clarify the role of flexibility to some degree. The unbound protein does not have a clear Porod-Debye plateau , black, The RgD model suggests that binding of both the ground state analog and the transition state analog reduces the flexibility of the protein and that binding of the transition state analog, GDP-A1Fx, is associated with the greatest reduction in flexibility . MoreoveSince GDP-A1Fx binding causes the protein to adopt a closed state, these observations argue that the closed state is the most rigid. The fact that the MnmE-GppNHp complex has an intermediate value for the entropy is consistent with the observation that GppNHp binding leads to an equilibrium distribution of closed and open states40T-cell intracellular antigen-1 (wtTIA-1) plays a crucial role in pre-mRNA splicing and is an important regulator of translation45q4 ≈ 0.184 = 0.001 Å4, the plateau is lost in the bound state (q3I(q)3 vs. q3 for the bound state further demonstrates that I(q) decays as q−3 in the Porod-Debye region instead of the expected q4− for a compact polymer, thereby suggesting that binding makes the protein more flexible 4846Replication protein A (RPA) is multi-domain protein that plays an important role in regulating DNA processing. Recently a combination of SAXS and molecular dynamics simulations was used to study binding of the DNA-binding core of RPA (RPA-DBC) to a 30-nucleotide ssDNA substrateq4 > 0.00025 ≈ 0.1254 Å4, q valuesq the scattering profile of the free protein has larger variations than that of the bound complex .


In a large-scale study using data from the Protein Data Bank, some of the many reported findings regarding the crystallization of proteins were investigated. The Protein Data Bank (PDB) is the largest available repository of solved protein structures and contains a wealth of information on successful crystallization. Many centres have used their own experimental data to draw conclusions about proteins and the conditions in which they crystallize. Here, data from the PDB were used to reanalyse some of these results. The most successful crystallization reagents were identified, the link between solution pH and the isoelectric point of the protein was investigated and the possibility of predicting whether a protein will crystallize was explored. While redundancy is useful for some types of analysis, in other cases it skews the results. We therefore considered the data at different levels of redundancy.Some proteins have been deposited in the PDB many times with different ligands, modifications or crystallization space groups. For example, hen egg-white lysozyme , referred to as PDB-BLAST-reduced  to train the network with two hidden layers, each having two nodes with sigmoid-tangent transfer functions. The trained model was then used to predict sequences found in the PDB.Overton  al. 2008 formed t3.Fig. 23.1.The interactions between a protein and the various chemicals used in crystallization are complex and the number of possible combinations grows exponentially as the number of chemicals at different concentrations is increased , which are used to control pH and are assumed to be otherwise chemically inert with respect to crystallization . For 83 of these 108 chemicals (76%) a protein structure was obtained for the same 3.2.et al., 2014et al., 2012et al., 2012et al., 1989It is well documented that estimating the pH of a crystallization solution as that of the buffer component can be inaccurate  if annotated as having ‘diffraction quality crystals’, but specifically not ‘in PDB’ in the ‘status’ field  would certainly help.10.1107/S2053230X15014892/nj5235sup1.pdfSupplementary Table S1.. DOI: