Personalized anticancer therapy requires continuous consolidation of emerging bioinformatics data into meaningful and accurate information streams. The use of novel mathematical and physical approaches, namely topology and thermodynamics can enable merging differing data types for improved accuracy in selecting therapeutic targets. We describe a method that uses chemical thermodynamics and two topology measures to link RNA-seq data from individual patients with academically curated protein-protein interaction networks to select clinically relevant targets for treatment of low-grade glioma (LGG). We show that while these three histologically distinct tumor types  may share potential therapeutic targets, the majority of patients would benefit from more individualized therapies. The method involves computing Gibbs free energy of the protein-protein interaction network and applying a topological filtration on the energy landscape to produce a subnetwork known as persistent homology. We then determine the most likely best target for therapeutic intervention using a topological measure of the network known as Betti number. We describe the algorithm and discuss its application to several patients. The overriding principle of personalized medicine is the uniqueness of each individual patient, creating an equally unique molecular signature of the patient's cancer. After more than half a century of cancer treatment based on non-specific chemotherapy and radiation, oncologists are beginning to embrace precision oncology as means of incorporating these distinctive, patient-specific cancer molecular signatures. The goal of precision medicine is to select the best, i.e. an individual specific, therapy. It recognizes that based on the genetic and phenotypic background of an individual, a different biological pathway may be engaged in tumor initiation and progression. In most cancers more than one genomic and proteomic alteration is identified exposing our inability to establish the importance of one molecular alteration over another. Much too often the oncologist faced with the dilemma of multiple molecular targets ends up enrolling the patient on one of the available Phase 1 clinical trials, “matching” no more than a single mutation. Not infrequently a patient may be placed on the wrong pharmacological agent if the Phase I trial that targets a less important genomic alteration. Furthermore, because most present clinical trial designs allow for testing of a single agent per trial only, in cases where more than one genomic alteration is present – the other activated pathways will not only remain active, their activity may get further escalated by inhibiting a single target. Most cancer signaling pathways show a large degree of redundancy, which precludes the possibility of finding a “silver bullet”. For successful therapy it is important to recognize and preserve the eco-evolutionary forces within the tumor microenvironment [http://thebiogrid.org), first described by Breitkreutz et al. in 2002 [These protein-protein interaction networks reflect cell dynamics, and mirror the well-coordinated and controlled interactions within a cell. A set of all known interactions gives rise to a network, which can be characterized and analyzed using rigorous mathematical and physical methodology. A state-of-the-art example of a PPI network database is Biogrid  to improve the quality of present-day clinical decisions. The application of mathematics in molecular systems biology, and the descriptions and conjectures about the application of group theory and abstract algebra in molecular networks, have been well-reviewed previously , 5. For similarity in protein sequence or structure; mathematicians use this term to describe similarity in topological surfaces. As such, the term persistent-homology describes a topological surface feature that is observed despite the presence of noise or surface roughness. In this manuscript, we use the term persistent homology as a topological measure on Gibbs free energy surfaces for protein-protein interaction networks. We combine the concept of Gibbs energy on PPI networks to compute the persistent homology, and then use Betti number to compute a therapeutic target or targets according to a set of rules described below.We surmise that the eventual development of reliable clinical tools enabling clinical oncologists to correctly analyze and apply an individual's genomic information is likely to require a much wider array of mathematical and physical tools, but we contend that the best present computational approach should involve a combination of Gibbs free energy , 9 and hhttp://cancergnome.nih.gov). We will introduce a novel method for superimposing transcription information from individual patients (or the extensive RNAseq data available through The Cancer Genome Atlas - TCGA - http://cancergnome.nih.gov) onto a human protein-protein interaction network with the goal of selecting targets for therapeutic intervention.In the subsequent paragraphs, we introduce the theoretical background for this method, using the extensive microarray and RNAseq transcription information available in The Cancer Genome Atlas  is an ill-defined subgroup of glial tumors, associated on the basis of their clinical features (slow growth) and some histological features (GFAP and low proliferative fraction). There are three main histological subtypes: low grade astrocytoma, oligoastrocytoma, and oligodendroglioma. While these may represent very distinct molecular entities, their biological behavior is sufficiently similar for this grouping. Most importantly, because these slow growing tumors have a very low proliferative fraction and do not respond to chemotherapy and radiation, there are no existing effective therapeutic interventions. The identification of molecularly guided targeted therapies, which do not depend on the proliferative fraction in the tumor, would provide viable therapeutic strategies for poor prognosis cancers such as DIPG or low-grade thalamic gliomas.p < 0.0001), and there is a trend to statistically significant difference between astrocytoma and oligoastrocytoma (p = 0.0746).Using the TCGA data we computed the Gibbs free energy for the homology subnetwork of each patient with LGG, and found statistically significant differences in energy between the three different cell types Figure . The GibA Pareto chart ranking the “best therapeutic targets” for these 514 patients with LGG available from TCGA Figure  shows thInterestingly, the analysis of the homology networks for patients in whom elimination of HSPA8 leads to most significant changes in complexity revealed similarities in the homology subnetworks despite the differences in tissue type. This is likely due to the observation that the protein neighbors of HSPA8 within a PPI network are the same in the different tissue types  and the expression of HSAP8 is determined by the degree entropy rather than by the tissue type. For example, the astrocytoma patient  by a comparable amount. Because reducing complexity or Gibbs free energy can be correlated with increased probability of 5-year survival , 8, we ehttps://david.ncifcrf.gov/) and KEGG (http://www.genome.jp/kegg/). This allowed us to obtain the disease pathways known to be associated with these proteins. We found for example, EGFR is involved in colorectal cancer, pancreatic cancer, endometrial cancer, prostate cancer, melanoma, bladder cancer and non-small cell lung cancer, and it has been previously considered a good therapeutic target in glioma [In order to determine what role HDAC4 and HSPA8 along with their similar energetic neighbors play in cancer, we submitted the list of proteins to DAVID  and Betti numbers (which quantify the presence of rings in a network) can identify the pathways most important for the growth and dissemination of the patient's tumor. It is likely that in a not-too-distant future, similar mathematical and physical tools may be used prospectively for designing biopsy-guided therapy. However, as we show, a retrospective analysis of genomic profiles of patients enrolled in clinical trials may reveal which patients were exposed to therapeutically appropriate targets, and provide a unique window of understanding for our failures to successfully implement targeted therapies. It is likely that with careful retrospective analysis, many “failed” agents may be returned to our pharmacopeia, because even though some patients may have a therapeutic target similar to other patients, most patients have a unique molecular signature requiring a medicine , 21 repr®. The energetic state of a cell can therefore be described by the sum of the chemical potential (Gibbs free energy) of all interacting pairs of proteins within the network; and the perturbations and variations in chemical energy can be graphically represented by a rugged energy landscape such as the one illustrated in Figure The energy between interacting molecules (interaction energy) is referred to in statistical thermodynamics as a chemical potential. Whenever the concentration of one molecular species changes, the reactions in which this molecular species participates is therefore affected as well. Thus, a change in one protein concentration will percolate through the network affecting multiple other molecular species, and changing the network's chemical potential. The concept is applicable to any large-scale molecular network, including established biological protein-protein interaction networks such as Biogrida priori what content to place on the arrays, the RNA-seq, which does not use probes or primers, needs to convert mRNA (and other RNAs) to cDNA, which is then used as the input to a next-generation sequencing library. The RNA-seq has the ability to uncover new and rare driving mutations, but it is only as good as the ability to use the most appropriate library. Until it is established that RNA-seq derived transcription information is comparable to microarray methods, and until there is a sufficient number of studies comparing gene expression levels by microarrays vs. those obtained using RNA-seq, the two may be best analyzed separately. Yet, a large-scale comparison of gene expression levels by microarrays and RNA-seq using TCGA data for fourteen different cancer types found a Spearman correlation of about 0.8 [We have previously described how to use RNA transcription data and protein- protein interaction data to compute the Gibbs free energy for various types of cancers represented by their PPI networks , 9. It sbout 0.8 , and thebout 0.8 , which gGiven the close correspondence of microarray and RNA-seq data, we can use either of these data types as surrogates for protein concentration estimates. Koussounadis et al.  show thaWe combine this surrogate “protein concentration” with the PPI and create an energetic landscape represented by chemical potential of protein-to-protein interactions Figure . Complexi, or individual protein, is given by:c i is the concentration of the protein, or the normalized  expression of protein i. The sum in the denominator of Eq. j in the neighborhood, including i. The natural logarithm of this dimensionless number in conventional chemical thermodynamics represents the Gibbs free energy for an individual protein in the network [We compute Gibbs free energy for a given cellular population as described previously , 10. The network . The ovepersistent landscape structure that remains even in presence of noise, but the concept remains valid even in absence of noise. Consider a horizontal plane (a filtration plane) moving upwards from the bottom as depicted in Figure filtration plane moves up, it cuts through more and more energy wells, capturing increasingly more minima. Since these energy wells represent Gibbs free energy of the network, the small sets of energy wells captured by the filtration plane at each energy threshold represent specific subnetworks. The subnetworks, which represent the deepest  of Gibbs free energy, are called a persistent homology, and we will hereinafter refer to these energetic subnetworks as Gibbs homology networks.Each node in the network has an associated real negative number representing its respective Gibbs free energy creating a schematic of a complex network mapped onto a rugged landscape Figure . PersistWe can now use the analogy of flooding a landscape as a way to intuit the dynamics of energy landscapes, a concept well explored in the past . The deehttp://cancergnome.nih.gov), and well-described in the past [Homo sapiens, 3.3.99, March, 2013) from BioGrid (http://thebiogrid.org) containing 9561 nodes and 43,086 edges [We collected RNA-seq data for low grade glioma (LGG) from The Cancer Genome Atlas (TCGA) hosted by the National Institutes of Health  and maximum (emax) of the individual patient dataset, and the log transformed data for each gene, ei in that RNA-seq or transcriptome vector is then processed as:ci represents the rescaled value and is used in Eq The workflow for the calculations of the Gibbs-homology and determination of the potential protein target(s) for therapeutic intervention is shown in the flowchart of Figure This rescaling is justified from both a mathematical perspective and a chemical physics perspective. Negative values in the argument of the natural logarithm of Eq. The rescaled dataset is then analyzed at a set energy filtration threshold Figure . The selWhen the energy threshold is low , the complexity of the subnetwork is also low, and removing any individual protein will drop the Betti number by the same amount resulting in as many as eight or more equivalent targets. In contrast, at high-thresholds  typically only one node leads to a large drop in the Betti number. The energy filtration threshold was optimized by identifying the best targets through a systematic  application of energy thresholds between 8 and 128 . We found the most clinically relevant information is to be derived at threshold of 32, where an average of about 1.514 equivalent targets (SD+/− 0.915) is found. At this level, for the majority of patients one or two potential targets are found, but there may be up to three equivalent targets. This provides a good margin for selection of treatment options aimed at inhibiting these proteins as targets for pharmacological agents.At each threshold, and for each patient in the population of patients, we computed Gibbs homology, total Gibbs energy  for the homology subnetwork, and the nominal Betti number for this Gibbs homology. The information for each patient in the set therefore included Gibbs homology subnetwork, Gibbs energy, and Betti number. We then sequentially removed (with replacement) each protein from the Gibbs homology subnetwork, recomputed the total Gibbs energy of the subnetwork, and determined the respective change in Betti number. This provided us with an array of protein targets and their respective changed Betti numbers, as well as the respective change in Gibbs energy for each patient in the set. By searching this array for the smallest Betti number (the most reduced Betti), which corresponds to the biggest reduction in complexity of the homology subnetwork we could make specific personalized predictions for the best potential therapeutic targets. We re-iterated this process for each patient in the set, and kept track of the lowest Betti number(s) and respective target(s) (See Table


Gene fusions are common cancer-causing mutations, but the molecular principles by which fusion protein products affect interaction networks and cause disease are not well understood. Here, we perform an integrative analysis of the structural, interactomic, and regulatory properties of thousands of putative fusion proteins. We demonstrate that genes that form fusions  tend to be highly connected hub genes, whose protein products are enriched in structured and disordered interaction-mediating features. Fusion often results in the loss of these parental features and the depletion of regulatory sites such as post-translational modifications. Fusion products disproportionately connect proteins that did not previously interact in the protein interaction network. In this manner, fusion products can escape cellular regulation and constitutively rewire protein interaction networks. We suggest that the deregulation of central, interaction-prone proteins may represent a widespread mechanism by which fusion proteins alter the topology of cellular signaling pathways and promote cancer.  •Parents of fusion proteins occupy central positions in protein interaction networks•Parents are rich in interaction-mediating features, which are often lost via fusion•Fusions preferentially join proteins with no previous connection in protein networks•Fusion proteins escape regulation by losing post-translational modification sites The molecular mechanisms of fusion-mediated interactome disruption are currently unclear. Latysheva et al. find that fusion-forming proteins occupy central positions in interaction networks. They lose much of their extensive interaction-mediating ability and capacity for regulation upon fusion. These findings provide insights into how fusion proteins could rewire networks in cancer. TMPRSS2-ERG fusion is the most frequent genetic aberration in prostate cancer , and highlight novel fusion hubs   was anal2 = 29.5, df = 1, and p = 5.7 × 10−8)   D and are× 10−16) E. AlthouParent genes were grouped into OG parent genes, TSG parent genes, and all other parent genes A. Parent−16; Next, the role of parent proteins in tissue-specific protein interaction networks  was exam−4; and pairwise Wilcoxon rank-sum tests with Holm multiple testing correction), TSG parents 1.15 × (p = 1.5 × 10−3), and other parents 1.13 × (p < 2 × 10−16) higher disorder compared to non-parents. Parent OGs and TSGs are approximately equally disordered as non-parent OGs and TSGs . There is a slight tendency for parent OGs to have higher IMD densities than non-parent OGs   D. We exa−5; Structural interfaces in fusion proteins were identified by analyzing the Protein Interfaces, Surfaces, and Assemblies (PISA) database, which houses macromolecular interfaces  in the Protein Data Bank (PDB). Parent proteins in the PDB contain more interface-forming residues C. On ave−16), TSG parents 7.1× (p < 2 × 10−16), and other parents 1.3× (p = 8.0 × 10−10) the LM density of non-parents. Parent TSGs have slightly higher LM densities compared to non-parent TSGs (Linear motifs (LMs) are short sequence motifs, usually <10 residues, often found in intrinsically disordered regions . Using 1ent TSGs G. Fusionent TSGs F. Parentent TSGs . Similarent TSGs G, thoughent TSGs H. Intereent TSGs H. Either−16; We mapped putative interaction-regulating PTMs . This suggests that the function, stability, and subcellular location of parent proteins are extensively regulated by PTMs. Further, on average, parent OGs have 1.5× (p = 7.5 × 10−3) the PTM content of non-parent OGs, and parent TSGs have 2.1× (p = 1.4 × 10−5) the PTM content of non-parent TSGs , subcellular localization , and protein function . Parent proteins have significantly more PTMs J compareent TSGs K. PTMs aent TSGs K. The seTSGs −4; K. ParentTSGs −4; , while pNext, we examined the PTM profiles in included and excluded fusion protein segments L. CertaiEWSR1-FLI1 gene fusion from Ewing’s sarcoma (ATP50-TGFB1 fusion (Ubiquitination (UB) sites are of particular interest since their loss and gain upon fusion could “upregulate” OG activity or “downregulate” TSG activity, due to the role of UB sites in mediating protein stability and degradation. We find 14 fusion proteins in which OGs lose ≥5 UB sites and ten fusion proteins in which a TSG gains ≥5 UB sites . As an i sarcoma A. The sp sarcoma . Convers1 fusion B, which 1 fusion . OG pare1 fusion  could be2 fold change between diseased and healthy samples). The targets of TFs had significantly  higher DGE values in five of the eight paired breast cancer samples when compared to all other genes (2) DGE of which is 2.0× the mean DGE of all other genes (−5). Across the eight available biospecimen pairs, the average DGE of TF targets is 1.41× (mean) and 1.45× (median) the DGE of all other genes.To investigate the potential downstream network rewiring effects due to fusion events, we investigated whether fusions involving transcription factors (TFs) are associated with downstream expression changes in the TFs’ regulatory targets. TCGA tumor samples with TF-containing fusion transcripts and paired normal controls were identified . The reger genes . For exaMany disease states result from altered dynamics of complex regulatory and signaling interactions. Representing interactions as networks provides a conceptual framework for understanding how mutations in proteins can affect entire cellular systems and cause disease , especiaAlthough it is likely that not all of the analyzed fusion proteins drive disease . Examining specific cases of fusion-mediated loss and gain of molecular features A–3L, as RARα) encodes a LM that acts as a phosphorylation-dependent switch for binding Pin1. RARα forms driver fusion proteins in acute promyelocytic leukemia, for which Pin1 suppression is used as a treatment . A fusion network of all gene fusions was constructed using Cytoscape. Throughout this study, gene sets were tested for enrichments of GO-Slim molecular functions and protein classes using PantherDB . Scores range from 0 to 1, where higher scores indicate a higher propensity toward intrinsic disorder. Intrinsic disorder was calculated for genes  and for specific included and excluded segments as an average over either the protein or segment length.Residue-by-residue predictions for disorder for each protein in the human proteome were generated using the IUPred program  retained in fusion proteins. DDIs were deemed to be “retained” if at least one fusion protein incorporated at least 90% of the IMD. Novel interactions created as a result of the transfer of IMDs were between protein A and B if there existed at least one fusion protein B-C, where C normally interacts with A and at least 90% of C’s IMD was retained. Novel links were those that did not appear in a set of known PPIs .Pairwise shortest path lengths (geodesics) between all protein pairs in a PPI network  were calhttp://www.ebi.ac.uk/pdbe/pisa/). Interface residues were identified and their positions converted into Ensembl protein coordinates. PISA residue densities were calculated by counting unique positions and dividing by protein lengths. Differences in the distributions of interface-forming PISA residue densities were analyzed as before. Biological process and protein class enrichments for parent genes that donate ten or more interface-forming residues to fusion proteins were calculated.Structures of proteins in complex with proteins, DNA, or RNA molecules were obtained from the PDB and PISA database (A set of 1,410 experimentally validated  and 1,03PTM sites, which are candidate sites for regulating protein interactions, were acquired from the PTMcode v2 data set . Differe2 fold change between the diseased and healthy samples. The regulated target genes of TFs were acquired from the TRRUST database (Fusion transcripts in TCGA samples  were fildatabase . DGE valStudy Conception and Design: N.S.L., R.J.W., and M.M.B.; Acquisition of Data: N.S.L., L.M., M.E.O., J.G., and R.J.W.; Analysis and Interpretation of Data: N.S.L., L.M., M.B., R.J.W., T.F., and M.M.B.; Manuscript Writing: N.S.L. and M.M.B.; and Critical Inputs to Manuscript: N.S.L., L.M., T.F., M.E.O., R.J.W., M.B., and M.M.B. The project was led by N.S.L. and supervised by M.M.B.


Several catalysis, cellular regulation, immune function, cell wall assembly, transport, signaling and inhibition occur through Protein-Protein Interactions (PPI). This is possible with the formation of specific yet stable protein-protein interfaces. Therefore, it is of interestto understand its molecular principles using structural data in relation to known function. Several interface features have beendocumented using known X-ray structures of protein complexes since 1975. This has improved our understanding of the interfaceusing structural features such as interface area, binding energy, hydrophobicity, relative hydrophobicity, salt bridges and hydrogenbonds. The strength of binding between two proteins is dependent on interface size (number of residues at the interface) and thus itscorresponding interface area. It is known that large interfaces have high binding energy  vdW, H-bonds,electrostatics). However, the selective role played by each of these energy components and more especially that of vdW is not explicitlyknown. Therefore, it is important to document their individual role in known protein-protein structural complexes. It is of interest torelate interface size with vdW, H-bonds and electrostatic interactions at the interfaces of protein structural complexes with knownfunction using statistical and multiple linear regression analysis methods to identify the prominent force. We used the manuallycurated non-redundant dataset of 278 hetero-dimeric protein structural complexes grouped using known functions by Sowmya et al.(2015) to gain additional insight to this phenomenon using a robust inter-atomic non-covalent interaction analyzing tool PPCheck. This dataset consists of obligatory , immune and nonobligatory(enzyme and regulator inhibitors) complexes. Results show that the total binding energy is more for large interfaces.However, this is not true for its individual energy factors. Analysis shows that vdW energies contribute to about 75% ± 11% on averageamong all complexes and it also increases with interface size (r2 ranging from 0.67 to 0.89 with p<0.01) at 95% confidence limitirrespective of molecular function. Thus, vdW is both dominant and proportional at the interface independent of molecular function.Nevertheless, H bond energy contributes to 15% ± 6.5% on average in these complexes. It also moderately increases with interface size(r2 ranging from 0.43 to 0.61 with p<0.01) only among obligatory and immune complexes. Moreover, there is about 11.3% ± 8.7%contribution by electrostatic energy. It increases with interface size specifically among non-obligatory regulator-inhibitors (r2 = 0.44). Itis implied that both H-bonds and electrostatics are neither dominant nor proportional at the interface. Nonetheless, their presencecannot be ignored in binding. Therefore, H-bonds and (or) electrostatic energy having specific role for improved stability in complexesis implied. Thus, vdW is common at the interface stabilized further with selective H-bonds and (or) electrostatic interactions at anatomic level in almost all complexes. Comparison of this observation with residue level analysis of the interface is compelling. The roleby H-bonds (14.83% ± 6.5% and r2 = 0.61 with p<0.01) among obligatory and electrostatic energy (8.8% ± 4.77% and r2 = 0.63 with p<0.01) among non-obligatory complexes within interfaces (class A) having more non-polar residues than surface is influencing ourinference. However, interfaces (class B) having less non-polar residues than surface show 1.5 fold more electrostatic energy on average.The interpretation of the interface using inter-atomic  interactions combined with inter-residuepredominance (class A and class B) in relation to known function is the key to reveal its molecular principles with new challenges. Protein complexes play an important role in catalysis, regulation,immunity, protein assembly, transport and inhibition throughprotein-protein interaction (PPI). This is fundamental todemonstrate a well-designed communicating network inbiological systems. Interfaces are relevant in the context of targetsdefined for several diseases. The HIV-1 ENV GP160GP120/GP41) trimer spike 0/GP41 tr and supeWe used a dataset of 278 protein complexes as describedelsewhere by Sowmya et al. (2015) . It consPPCheck  (freely available at http://caps.ncbs.res.in/ppcheck/) , 26 is aInterface size (number of interface residues) and energiesassociated with various interactions were calculated using PPCheck for each of 278 complexes. Thisdata is presented as supplementary material It should be noted that electrostatic energy was positive orunfavorable in few entries  and 4. TWe performed multiple linear regression analysis of interface sizewith vdW, H-bonds, electrostatics and its total interface energiesusing Microsoft® Office Excel (version 2003) statistical analysistool (regression). Its co-efficient of determination (r2), a predictivepower score, was estimated with assessment of significance using statistical ANOVA test at 95% confidence limit.PPI is an important phenomenon among several biologicalprocesses. It is associated with catalysis (e.g. phospho-rylation),regulation , biologicalassembly (e.g. regulate motility), immune response (e.g. RNASEA / Ab CAB-RN05) and inhibition (enzyme inhibitor (e.g. inhibitkinase activity) and regulator inhibitor (e.g. produce killertoxins)) as shown in There are 278 interfaces in the dataset and it is non-redundant,comprehensive and representative. Each interface is different inits absolute view. However, there are common patterns orfeatures among them. Gleaning their common features acrossdifferent interfaces is the bottleneck. The binding of two proteinsis related to interface size (number of interface residues involvedin binding)  and its The importance of H-bonds (14.83% ± 6.5% and r2 = 0.61) amongobligatory and electrostatic (8.8% ± 4.8% and r2 = 0.63) amongnon-obligatory within interfaces (class A) having more non-polarresidues  is addinPPI is an important phenomenon in biological events such ascatalysis, regulation, signaling, protein assembly, immunefunction and inhibition. Therefore, it is interest to understand itsmolecular principles using known structural complexes withdefined molecular functions. The interface size (correspondinglyinterface area) is primarily deterministic of protein-proteinbinding. Inter-atomic level analyses show that vdW is the majorcontributor independent of molecular function. However, Hbondsare pronounced among obligatory and immune complexesunlike non-obligatory regulator inhibitor complexes with fittingelectro-static energy. Thus, vdW is common at the interfaces withstabilizing H-bonds and electrostatic interactions with inferredspecificity to molecular function. The corresponding strength ofH-bonds and electrostatic interactions to interface size and its relation to grouped molecular function is of significance. Theproportional presence of H-bonds in obligatory complexes andelectrostatic in non-obligatory complexes among non-polarinterfaces (class A) helps to integrate our interpretation to refineand design interfaces in the context of genetic variation, mutationand evolution in future investigations. The 150% increase inelectrostatic energy among polar interfaces (class B) is providingbetter clarity to residue level analysis. It should be that PPcheckoffers analysis of vdW, H-bonds and electrostatics energy inprotein-protein interfaces. Hence, the overlap of vdW with Hbondsand electrostatics should be resolved in future. The degreeof concurrence between vdW and hydrophobic effects shouldalso be established for an integrated understanding of thephenomenon. We foresee more unambiguousness withadditional structural data with known molecular function usingimproved analytical techniques.This manuscript analyzes the relationship between the size ofprotein interaction interfaces and several biophysicaldeterminants of molecular interaction strength, namely van derwaals forces, hydrogen bonds and electrostatics. To do this, theauthors analyze a set of 278 interfaces published in 2015 bySowmya et al. First, interfaces are annotated using an online toolcalled PPCheck, which returns interface size in amino acids, vander waals, hydrogen bond and electrostatic forces. Finally, theauthors use regression to study the relationship between interfacesize and the different forces.This work expands upon work published by Sowmya et al. byfurther investigating the relationship between interface size andcomponents of binding energy, with van der waals andelectrostatic forces not having been previously explicitlyanalyzed. In addition, the authors have further categorized the278 interfaces as obligatory and non-obligatory, thereby allowinga new grouping of the proteins according to broader functionaldesignation. The interface size calculated by PPCheck appears tobe given in terms of number of amino acids rather than in termsof surface area as was used by Sowmya et al. (2015). Over all, thepaper seems to reach many of the same conclusions as Sowmya et al. with new findings that van der waals forces correlate withinterface size independent of molecular function, while hydrogenbonds and electrostatic forces appear to be correlated withinterface size in different functional classes of proteins.Overall, it is necessary to do something to further distinguish thecurrent work from the previous work by Sowmya et al. Theauthors comment on the future knowledge to be gained fromapplying similar analyses to larger datasets. Based on thepreliminary finding that the relationship between interface sizeand electrostatics has implications for protein function, why notdownload all co-crystal structures from the PDB, run themthrough PPCheck, then perform an unsupervised analysis togroup complexes according to interface features, or therelationships between those features. Then the different groupscan be surveyed to see which align to the functional groups thatare currently being analyzed and the clustering can also be usedto look for other common functional themes that might exist. Thiswould potentially significantly extend the analysis without theneed to carefully manually curate all of the complexes and groupthem prior to doing the analysis.The authors provide p-values for the regressions, but do notdirectly compare two groups and test the difference in forcecontributions statistically. The authors observe that van der waalsforces are not different between groups, but h-bonds are morepronounced in obligatory and immune complexes andelectrostatic energy is more correlated with interface size in nonobligatorycomplexes. These differences should be evaluatedstatistically to show that they would not be expected under a nullmodel that these interface size to force relationships are the sameacross groups. It is not clear whether the findings based on the278 interfaces studied here will generalize to other complexeswhen grouped by similar functional category.


CDH1) was associated with a collateral loss of members of the adherens junction complex, an effect we validated using an engineered model of E-cadherin loss.Protein complexes are responsible for the bulk of activities within the cell, but how their behavior and abundance varies across tumors remains poorly understood. By combining proteomic profiles of breast tumors with a large-scale protein-protein interaction network, we have identified a set of 285 high-confidence protein complexes whose subunits have highly correlated protein abundance across tumor samples. We used this set to identify complexes that are reproducibly under- or overexpressed in specific breast cancer subtypes. We found that mutation or deletion of one subunit of a co-regulated complex was often associated with a collateral reduction in protein expression of additional complex members. This collateral loss phenomenon was typically evident from proteomic, but not transcriptomic, profiles, suggesting post-transcriptional control. Mutation of the tumor suppressor E-cadherin (  •Identified a set of 285 complexes coherently expressed across breast tumor proteomes•Identified complexes over- or underexpressed in specific breast cancer subtypes•Loss of one subunit often associated with reduced expression of a co-regulated complex•CDH1) mutation causes reduced expression of an adherens junction complexE-cadherin ( Ryan et al. develop an approach to identify co-regulated protein complexes from breast tumor proteomic profiles and demonstrate that genomic loss of one subunit is often associated with a reduction in the protein expression of an entire complex. Multi-subunit protein complexes are responsible for the bulk of the functionality of the cell . DespiteLargely for technical and economic reasons, the large-scale molecular profiling of tumors performed over the past decade has focused on characterizing changes at the genomic and transcriptomic level. Transcriptomic measurements are often used as a proxy measurement for protein expression, but most genes display only a moderate correlation between their mRNA and protein expression levels . MoreoveWe first wished to assess whether known protein complexes are coherently regulated across tumor proteomes. Using the CORUM manually curated set of human protein complexes  and 77 p−6) suggesting increased post-transcriptional control of protein complex subunits.Although co-expression calculated over the same number of samples suggested a significant advantage of proteomic profiles over mRNA profiles, the number of existing tumors with mRNA profiles far exceeds the number with proteomic profiles. We found that even with all TCGA breast tumor samples included (∼14 times as many mRNA profiles as proteomic profiles), the proteomic profiles still outperformed mRNA in predicting co-complex membership A. This sWhile in general the expression of different subunits within the same CORUM complex was highly correlated, this was not the case for all complexes examined, suggesting that not all complexes are coherently regulated to a similar degree in breast cancer D. MoreovWe hypothesized that by integrating large-scale protein-protein interaction networks with proteomic profiling, we could identify protein complexes coherently regulated in breast tumors. We first constructed a large network of protein-protein interactions by integrating literature-curated interaction databases  with rec−16, Fisher's exact test) and to display similar patterns of conservation across species .The majority of BrCa-Core complexes have significant overlap with specific Gene Ontology Cellular Component and Biological Process terms, suggesting common localization and functionality, respectively  . Like knAs our method exploited the correlation between protein expression profiles to identify complexes, we expected the average correlation across the TCGA proteomes within the BrCa-Core complexes to be high. This was indeed the case; the observed correlation (0.63) was higher than the average of pairs in our integrated protein interaction network  or pairs within CORUM complexes (0.20). To rule out the possibility that we were merely overfitting our results to a single proteomics dataset, we assessed whether the same higher correlation could be observed in two additional breast tumor proteomic datasets . In bothThe tendency of pairs of proteins within the same complex to display similar phenotypes when inhibited has been well established in the literature . To asse−16, Fisher's exact test) as were pairs always found in the same CORUM complex .The BrCa-Core complexes contain complete or partial coverage of 538 CORUM complexes (average percent of CORUM complex members included in the corresponding BrCa-Core complex is 57%) corresponding to 39% of the CORUM complexes represented in the proteomic dataset . We note that this is larger than the number of BrCa-Core complexes that significantly overlap with CORUM complexes (138) due to the heavily overlapping nature of CORUM complexes. In CORUM, the average protein belongs to three distinct complexes, while by design, in BrCa-Core, each protein was assigned to a single complex based on highly correlated expression with other members. The subset of CORUM co-complex pairs we identify in BrCa-Core have higher average protein co-expression (average correlation 0.65) than those not identified in BrCa-Core (average correlation 0.16). One explanation for this is that we have preferentially identified complex cores or modules . Many pr−/PR−/HER2+), ER+ (ER+/PR+/HER2-), and triple negative (ER−/PR−/HER2−).At the molecular level, breast cancer is a very heterogeneous disease, with each tumor displaying a unique genetic and epigenetic profile. Despite this heterogeneity, molecular biomarkers can be used to classify tumors with similar molecular profiles into subtypes that display different survival outcomes and different responses to targeted therapies . The bio−8), suggesting that with larger sample sizes, additional associations between subtype and complex abundance could be replicated. Examples of replicated differentially expressed complexes are presented in + tumors were associated with decreased expression of two complexes involved in antigen processing (BrCa-Core 59 and 193) consistent with data suggesting that expression of antigen presentation human leukocyte antigen molecules is lower in the ER+ subtype (+ tumors were associated with increased expression of two complexes involved in Golgi-transport-associated vesicle coating (BrCa-Core 25 and 42). It is not immediately obvious why HER2 amplification would be associated with an increased expression of complexes involved in vesicle transport, but the association is evident across both patient cohorts  of 10% . At the  subtype . HER2+ t cohorts .Figure 2trans) of protein expression of other subunits or indeed the entire complex (CDH1 (E-cadherin), PBRM1, CYFIP2, GLUD1, EXOC2). We then asked whether mutation or deletion of these genes was also associated with overall reduction in protein expression of the complex that they belong to. In all five cases, we found that loss of one subunit was associated with a reduction in the protein expression of additional complex subunits. For instance, homozygous deletion or mutation of EXOC2 was associated with decreased proteomic abundance of EXOC2 and an overall reduction in the protein expression of multiple members of the exocyst complex (BrCa-Core 27)   to whichCore 27) B. While NA level A, suggesNA level B, suggesCOPS3 is associated with a reduction in the protein expression of all subunits  deletions in tumors are frequent, and the majority of BrCa-Core member genes were hemizygously deleted in three or more tumor samples . We identified 308 BrCa-Core complex members whose hemizygous deletion was associated with a reduction in the expression of their encoded protein   C and S3CCore 30) D and fou samples C. In con samples D. None oproteins A but onlproteins A.Figure CDH1 is associated with reduced expression of other E-cadherin-associated subunits, but it does not demonstrate a causal effect. It is of course possible that some additional factor causes reduction in expression of the entire adherens junction complex rather than the mutation of a single subunit such as CDH1. To establish causality, we used mass spectrometry to measure differential protein expression in a pair of isogenic breast cancer cell lines (MCF7) with CRISPR-Cas9 engineered CDH1 loss  and selected one for further study that exhibited loss of E-cadherin protein expression  . To test whether our approach missed additional collateral loss events associated with CDH1 mutation, we assembled a list of 95 E-cadherin protein-protein interaction partners from CORUM (18 co-complexed subunits), BioGRID (89 protein-protein interaction partners), and HINT (15 co-complex interaction partners). Aside from the five members of the adherens junction complex in BrCa-Core, none of the known E-cadherin interaction partners displayed a significant reduction in protein abundance in the E-cadherin-defective model. This suggested that our data-driven approach effectively identified the specific subunits of the adherens junction complex whose expression is reduced by CDH1 mutation in breast cancer.A limitation of our analysis of tumor proteomes is that it identifies correlative rather than causal associations; it demonstrates that mutation of DH1 loss . We recepression . We perfpression . We founpression B, suggesadherin) B, perhapadherin) . The decWe found that, in general, correlation between protein expression profiles predicts co-complex membership better than correlation between mRNA expression profiles. One factor that contributes to this improved correlation is the collateral loss phenomenon we observe; when one subunit of a complex is lost via deletion or mutation, a collateral loss in the protein expression of additional complex members is observed. This collateral loss is typically not observed at the mRNA level, and consequently complexes that experience collateral loss display higher correlation at the protein than mRNA level. There are likely many other factors that contribute to maintaining the coherent expression of protein complexes across tumors, including dosage compensation of copy-number-amplified genes .We have not addressed here the mechanisms responsible for the collateral loss phenomenon, although the observation that the reduction in protein expression levels is not evident at the mRNA level suggests post-transcriptional mechanisms must be responsible. Perhaps the simplest explanation is that loss of one subunit prevents a complex from assembling, and consequently there is an increase in the proteasomal degradation of unbound subunits. Our analysis of hemizygous deletions suggests that complete loss of protein expression is not necessary for the collateral loss phenomenon. Similarly, we note that work in mice suggests that regulatory mutations that affect the mRNA expression of individual protein complex subunits may also cause a collateral loss in the expression of their interaction partners .We note we did not always observe perfect agreement between the genotype calls in tumors and protein expression; in some instances, copy-number analysis suggested a homozygous deletion but substantial protein expression was still observed. This could reflect errors in calling the deletions, limitations of mass spectrometry protein identification, or simply heterogeneity between the portion of the tumor sample assessed for proteomic profiling and the portion assessed for genotypic profiling.We have exclusively focused on the behavior of coherently expressed protein complexes across breast tumor samples. This approach has a number of advantages; in particular, it allows us to see how different complexes behave as a single unit within molecularly defined groups of tumors. A disadvantage of this approach is that we cannot identify when different variants/isoforms of a protein complex become more or less abundant in specific conditions. We have overlooked such events here, but recent work in cancer cell lines and mouse fibroblasts suggest that they may be relatively common and merit further investigation .We expect that the BrCa-Core complexes will be useful for the analysis of additional proteomic and functional datasets and make the full list of complexes available in colm.ryan@ucd.ie).Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Colm J. Ryan  supplemented with 10% fetal bovine serum (Gibco) and 1% L-glutamine (Gibco).CDH1 gene in MCF7 cells was CRISPR-Cas9 mutagenised using the Edit-R-CRISPR-CAS9-gene engineering kit (GE Dharmacon) according to the supplier’s instructions. A crRNA sequence targeting exon 7 of CDH1 was used. Briefly, MCF7 cells were transfected in 24 well plates with tracrRNA, crRNA and Cas9 plasmid. 72 hours after transfection, cells were plated in 15 cm dishes and continuously cultured until colonies formed. Colonies were recovered and profiled using PCR and Sanger sequencing to determine the presence of CDH1 gene mutations. Loss of E-cadherin expression in the selected clone was confirmed using western blotting  supplemented with protease inhibitor tablets (Roche) and phosphatase inhibitors  (Sigma-Aldrich). Lysates were subjected to sonication (Syclon ultrasonic cell disrupter), boiling  and placed on ice for 10-15 min prior to centrifugation . The supernatant was transferred to fresh eppendorfs and samples were subsequently placed on ice for a further 10-15 min to allow the SDS to precipitate and re-centrifuged. Supernatant was transferred to fresh eppendorfs and protein concentration was measured using the Pierce BCA protein assay kit as per manufacturers instruction (Thermo Scientific), using a SpectraMax M3 (Molecular Devices). Once quantified, DL-DTT (DTT) was added to the lysates at a final concentration of 0.1 M DTT. Subsequently, lysates were boiled . Detergent was removed from the lysates prior to MS analysis using the Filter Aided Sample Preparation (FASP) procedure incorporating Vivacon spin ultracentrifugation units with a molecular weight cutoff of 30 kDa (Sartorius)(4HC03). After the final wash step, filter units were transferred to a new collection tube and a multi-step digestion method was employed as described by Wisniewski and Mann , 20 mM Tris-HCl pH 7.5, 150 mM NaCl, 1 mM MgClartorius). Brieflyand Mann . In the and Mann . StageTi6, MIT 60ms while scan parameters for MS2 were: Resolution 17,500, AGC 5e4, MIT 250ms, NCE 27.0, Isolation window 1.6m/z. The exclusion list parameters contained no entries and charge exclusion was set to un-assigned and singly charged. Both MS1 and MS2 were recorded as profile data. Data were acquired in automatic data-dependent switching mode, with a high-resolution MS scan (300-1600 m/z) selecting the 12 most intense ions prior to tandem MS (MS/MS) analysis. Each biological sample (n=3) was run in technical duplicate.Mass spectrometry analysis was performed on a Q-Exactive mass spectrometer (Thermo Scientific), connected to a Dionex Ultimate 3000 (RSLCnano) chromatography system (Thermo Scientific) incorporating an autosampler. Five microliters of Lys-C/tryptic peptides was loaded onto a fused silica emitter ), packed with 1.8μ 120Å UChrom C18 packing material (NanoLCMS Solutions) and separated using an increasing acetonitrile gradient of 2 – 35%, with a 180 min reverse phase gradient at a flow rate of 250 nl/min. The instrument was operating in positive ion mode and with a capillary temperature of 320°C, coupled to a potential of 2300V applied to the column. Scan parameters for MS1 were as follows: Resolution 70,000, AGC 3eIdentifiers in all protein-protein interaction networks, protein expression datasets, and validation sets were converted to ENTREZ gene IDs. In cases where a particular gene or protein could not be matched to an ENTREZ gene ID it was discarded from further analyses.For the primary analysis we used the breast tumor proteomics dataset from the TCGA CPTAC project . Only saWe assembled an integrated protein interaction network from multiple sources. From the HINT database  we incluOur goal was to identify sets of proteins (complexes) such that each complex consisted of a set of proteins whose expression profiles were highly similar across tumor profiles and that were densely connected on the protein interaction network. Other formulations are possible, but we chose to focus on disjoint complexes, such that each protein could only belong to a single complex. We did not require that every protein be assigned to a complex.There are three components to our approach 1) choosing a score to evaluate the similarity of the expression profiles of a set of proteins 2) the identification of a similar score to evaluate the connectivity of a set of proteins on an interaction network, and 3) the identification of sets of proteins that score well on both datasets.1) Scoring complexes using expression profilesWe calculate the Pearson’s correlation coefficient between each pair of expression profiles  and use this to compute a log-likelihood ratio that A and B belong to the same protein complex versus the likelihood that they are unrelated. This can formalized as follows:expression = Pwithin / PbackgroundLLRwithin is calculated using logistic regression trained on CORUM co-complexed pairs  as the sum of all LLRexpression scores for all unordered pairs  in the set S.For each set of proteins (S) we calculate the total LLR2) Scoring complexes using the protein-protein interaction networkFor the protein-protein interaction network we sought to score each pair of proteins based on how likely they are to form part of the same complex. While direct protein-protein interaction provides an indication that two proteins may be part of a protein complex, previous work has demonstrated that taking into account the fraction of interaction partners shared by two proteins can provide additional support of co-complex membership . Based ointeraction) by comparing the probability of observing a particular score within a protein complex to the probability of observing it among all pairs of proteins. For each set of proteins (S) we calculate the total LLRinteraction(S) as the sum of all LLRinteraction scores for all unordered pairs  in the set S.As with the protein expression correlation, this score was transformed into log-likelihood ratio (LLR3) Identifying complexes supported by both data sourcesintegrated(S), which is equal to the sum of LLRexpression(S) and LLRinteraction(S). We found that this LLRinteraction score predicted co-complex membership better than co-expression alone .Our challenge is the identification of sets of proteins with high LLRWe identify high-scoring sets of proteins using an approach resembling agglomerative hierarchical clustering. Similar approaches have been used previously to identify complexes supported by genetic interaction and protein interaction networks in budding yeast  and alsointegrated for all pairs of proteins that directly interact in the protein-protein interaction network. We also evaluate scores for all possible 3-cliques  in the protein-protein interaction network. The highest scoring pair or 3-clique is taken as an initial cluster, and all overlapping pairs or 3-cliques are then removed from consideration. The second highest scoring pair or 3-clique is then assigned as a cluster, and any overlapping pairs or 3-cliques removed from consideration. This continues until no pairs or 3-cliques with positive LLRintegrated scores remain. At the end of the process proteins that have not been assigned to any cluster are assigned to their own single element cluster. We then apply an iterative approach to improve these clusters. At each iteration we consider three possible moves – merging, removal and switching. Each pair of clusters  is evaluated for merging into a single cluster (m1 U m2) and assigned a score LLRintegrated. For every protein in every cluster with multiple proteins we also calculate a LLRremove score that reflects the change in the log likelihood resulting from removing that protein from the cluster, and an LLRswitch score that calculates the change in likelihood from switching a protein from one cluster to another. At each iteration max is taken as the next move. To prevent the identification of clusters supported by only one data source (e.g. highly correlated expression but not densely connected on the protein interaction network) we only permitted moves in cases where the move resulted in an increase in the LLR score for both the expression and the protein interaction networks. Iterations continue until no move that increases the LLR score on both sources is identified. The end result is a list of clusters with an associated LLR score.To initialize our clusters we first evaluate LLRexpression and LLRinteraction scores. To remove potentially spuriously detected clusters we compared the clusters we identified to those identified using 100 randomized versions of the input - the same protein interaction network and expression set, but with the gene IDs on the expression set shuffled. These randomized networks allowed us to empirically estimate the False Discovery Rate as we could see for a given LLRintegrated score how many genes would be assigned to complexes in the randomized networks compared to the genes assigned to complexes in the real network. We chose an FDR of 10% for defining the BrCa-Core set of complexes.We assume that by chance some proteins that interact on the protein interaction network would have high co-expression scores and consequently we could identify clusters with positive LLRTo assess the overlap between BrCa-Core complexes and existing annotation sets  we used the gProfiler tool . Only geWe calculated the average Pearson correlation between complex subunits using the dataset of Tyanova et al  and PoznFrom the STRING database  we extraTo identify protein complexes differentially expressed in specific breast cancer subtypes we used a variant of the 1D annotation enrichment test proposed by Cox and Mann . For eacSequence, copy number and mRNA expression profiles for were all obtained through the cBioPortal  . To idenTo assess how genetic variants altered the overall abundance of protein complexes to which they were associated, we first converted the quantitative measurements of protein expression into rank orders. In each sample we then calculated the mean rank of all complex members, and tested if samples harboring the alteration of interest displayed lower mean rank than samples without the alteration using a one-sided Mann Whitney U test. The mean rank was calculated with the deleted gene excluded . For deletions (homozygous or hemizygous) complex members on the same chromosome as the altered gene were also excluded from the mean rank calculation.Mass spectra were analyzed using MaxQuant software (version 1.5.0.25) containiCDH1 wild-type) and CDH1-defective cell lines. Two technical replicates were obtained for each biological replicate and these were averaged prior to further analysis. Missing values were imputed using the minimum observed intensity for each sample, based on the assumption that missing proteins could be absent or below the detection threshold of the instrument. Log2 transformed LFQ (Label Free Quantification) values were used for analysis. A two-sided heteroscedastic t-test (Welch’s t-test) was used to identify differentially expressed proteins and the Benjamini-Hochberg approach was used to estimate the False Discovery Rate (Proteomic profiles were generated for three biological replicates of the parental (ery Rate .PXD007543. Python code for the complex identification method, along with necessary input data, can be obtained from: https://github.com/cancergenetics/brca-coreThe MCF7 CDH+/- mass spectrometry proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository with the dataset identifier C.J.R. conceived and designed the study, wrote all code, and drafted the manuscript. D.M. and S.K. performed and analyzed proteomics experiments. I.B. and C.J.L. created the CDH1 model. All authors aided interpretation of the results, provided input on the manuscript, and read and approved the final manuscript.


Saccharomyces cerevisiae (yeast) and Homo sapiens (human) with state-of-the-art approaches in terms of clustering, biological metrics and execution times, as well as three gold standards for yeast and two for human. Furthermore, we analyze false positive predicted complexes searching the PDBe (Protein Data Bank in Europe) database in order to identify matching protein complexes that have been purified and structurally characterized. Our analysis shows that more than 50 yeast protein complexes and more than 300 human protein complexes found to be false positives according to our prediction method, i.e., not described in the gold standard complex databases, in fact contain protein complexes that have been characterized structurally and documented in PDBe. We also found that some of these protein complexes have recently been classified as part of a Periodic Table of Protein Complexes. The latest version of our software is publicly available at http://doi.org/10.6084/m9.figshare.5297314.v1.Many proteins work together with others in groups called complexes in order to achieve a specific function. Discovering protein complexes is important for understanding biological processes and predict protein functions in living organisms. Large-scale and throughput techniques have made possible to compile protein-protein interaction networks (PPI networks), which have been used in several computational approaches for detecting protein complexes. Those predictions might guide future biologic experimental research. Some approaches are topology-based, where highly connected proteins are predicted to be complexes; some propose different clustering algorithms using partitioning, overlaps among clusters for networks modeled with unweighted or weighted graphs; and others use density of clusters and information based on protein functionality. However, some schemes still require much processing time or the quality of their results can be improved. Furthermore, most of the results obtained with computational tools are not accompanied by an analysis of false positives. We propose an effective and efficient mining algorithm for discovering highly connected subgraphs, which is our base for defining protein complexes. Our representation is based on transforming the PPI network into a directed acyclic graph that reduces the number of represented edges and the search space for discovering subgraphs. Our approach considers weighted and unweighted PPI networks. We compare our best alternative using PPI networks from  Understanding biological processes at a cellular and system levels is an important task in all living organisms. Proteins are crucial components in many biological processes, such as metabolic and immune processes, transport, signaling, and enzymatic catalysis. Most proteins bind to other proteins in groups of interacting molecules, forming protein complexes to carry out biological functions. Berggård et al.  showed tTechnological advances in biological experimental techniques have made possible the compilation of large-scale PPI networks for many organisms. Given the large volume of PPI networks, many mining algorithms have been proposed in recent years for discovering protein complexes. Research on PPI networks has shown that these networks have features similar to those of complex networks based on topological structures, such as small world  and scalDisease Module Identification DREAM Challenge for subchallenge 1 , which we call DSDCluster. DSDCluster is a method that first applies the DSD algorithm  is a function that maps an edge to a real number between 0 and 1 that represents the probability that an interaction is real.Since the interactions among proteins in a PPI are symmetric, these networks are usually modeled as undirected graphs, where proteins are vertices and interactions between proteins are edges. We represent a PPI network with adjacency lists, where each adjacency list contains the set of neighbors of a protein. In order to find complexes, we represent each undirected edge {Node ordering algorithm, such as random, lexicographic, by degree, BFS traversal, and DFS traversal, among others.We first represent a protein-protein interaction network as a graph, where the protein names of the network are represented as vertices in the graph with numeric ids. Thus, each protein name must be mapped to a unique numeric id. Mapping protein names to numeric ids can be done using any DAPG, which is built from the input PPI network.Our algorithm for finding dense subgraphs looks for cliques and complete bipartite subgraphs in the PPI network. The process of finding good dense subgraphs is run over an acyclic graph called Definition 1 Directed Acyclic Prefix Graph (DAPG)Given a graph G = , a set V′ ⊆ V and a total order ϕ ⊆ V × V, we define a directed acyclic graph DAPG = , as follows:N = ⋃v′ ∈ V′adjlistϕ(v′),A = { ∈ N × N, ∃v′ ∈ V′, u1and u2are consecutive in adjlistϕ(v′)},adjlistϕ(v) = 〈u ∈ V,  ∈ E〉 is the adjacency list of node v in G = , listed in the total order ϕ.where ϕ for the adjacency lists of G ensures that DAPG has no cycles. We consider two possible total orders ϕ: ID sorts the nodes by their ids, whereas FREQUENCY sorts them by their indegree, or number of times they appear in all the adjacency lists of V′. Using a total order u′ is the parent of u in DAPG iff  ∈ A, and call root a node with no parents. A path is a sequence of nodes in DAPG,  ∈ A, with i = 1, …, n − 1.We say that a node u ∈ N in DAPG based on the input graph G = , as follows:In addition, we define attributes for any node label: a unique identifier given to a node v ∈ V in G.vertexSet(u) = {v ∈ V′,  ∈ E}.vertexSet of a node u ∈ N is the set of vertices v ∈ V′ pointing to u, that is, whose adjacency lists adjlist(v) contain u. Note that the FREQUENCY order sorts nodes u by |vertexSet(u)|.In words, the Let us now define the types of dense subgraphs we will detect.Definition 2 Dense subgraph (DSG)A dense subgraph DSG of G =  is any graph G′, where S, C ⊆ V, and S × C ⊆ E, that is, it contains all the edges from a subset of nodes S to another subset C. Our implementation removes possible self-loops.S = C) and bicliques , but also more general subgraphs where S ∩ C ≠ 0.Note that Definition 2 includes cliques , a path P =  in D, and a set R ⊆ P, a valid dense subgraph DSG =  is defined as S = ⋂u∈RvertexSet(u) and C = R.u, we define an inverse traveler function, as follows.In order to find a promising path in DAPG starting from a given node Definition 3 Inverse traveler functionAn inverse traveler in DAPG is a partial function t: N → N, such that t(u) is a parent of u in DAPG. It gives no answer only when u is a root in N.u, the nodes in the path Pu are be determined by applying the function t repeatedly on u: u → t(u) → (t ∘ t)(u) → … → root.An inverse traveler function traverses a set of nodes in DAPG, moving from a node to one of its parents, up to a root. Therefore, given a node Pu we determine a set Ru ⊆ Pu, with u ∈ Ru, that maximizes a given objective function fobj defined as follows.Once we have a path Definition 4An objective function is a functionwhereis the universe of dense subgraphs of the form H =  based on Definition 2.Objective functions maximize some feature of dense subgraphs, aiming at detecting good ones. The functions used in this work are based on the number of edges in the dense subgraphs, or on a weighted density measure. They are listed in An important advantage of our approach is that it enables the easy extension of new traveler and objective functions. New traveler functions might improve the mining process for discovering dense subgraghs and new objective functions might include biological knowledge to discover subgraphs with biological significance.Our problem can then be formulated as follows.Problem: Detecting Maximal Dense SubgraphsFor a given graph G = , represented by a DAPG , a weight function w: E → , a traveler function t, and a given objective function fobj, output a set of maximal dense subgraphs  of G.G where each protein in the network is a vertex with a numeric id. Mapping protein names to numeric ids can be performed using any node ordering algorithm. In this work, we use six different mappings. First maps protein names to numeric ids in the order in which proteins are read from the PPI network. Lexicographic sorts the protein names and then assigns the numeric ids in that order. Degree sorts the proteins by decreasing degree in the network and then assigns the numeric ids in that order. Random maps protein names to numeric ids randomly. Finally, BFS and DFS map proteins names based on the breadth-first or depth-first search network traversal, respectively.Our algorithm first represents a PPI network as a graph G, using a total ordering function in the adjacency lists. As mentioned, we propose two total ordering functions: ID and FREQUENCY. The second phase consists in discovering dense subgraphs based on optimizing two objective functions: one guides the traversal on DAPG and the other specifies which nodes to choose.The algorithm we propose for discovering dense subgraphs proceeds in two phases. The first phase builds an acyclic graph DAPG from P, finding all the possible sets R in the path requires time exponential in the number of nodes in the path. Finding the best paths P in DAPG is also exponential-time. Instead, we design an efficient mining heuristic for discovering dense subgraphs in DAPG.Lemma 1 enables the detection of dense subgraphs from DAPG, however, even for a given path Pu =  so that u1 is a root in DAPG. We find a promising path in DAPG starting from a given node u using an inverse traveler function given in Definition 3.The main mining heuristic is based on finding at most one dense subgraph starting at each node in DAPG. This approach enables us to find dense subgraphs that might overlap. The heuristic is based on finding a promising path v in DAPG and walks its way to the previous node in the path up to a root. Along the path, we maintain in set S the intersection of the vertexSet of the nodes in a subset of the visited nodes , while we maintain in set C the labels of the nodes of the selected subset. Note that, at each point,  is indeed a valid graph. From all those DSGs, we retain only the “best one”. We determine the “best DSG” using and objective function (fobj), which is a configuration parameter.The core of our mining technique starts at each node inverse traveler function, t, to obtain a promising path P in DAPG, and an objective function, fobj, to discover dense subgraphs given by Definition 2. This approach is flexible to favor given features of dense subgraphs, and allows the exploration of different ideas for determining alternative paths to improve the quality of the results.We can customize the core of the mining technique based on an inverse traveler and objective functions defined in We consider the Deepest in maxDepth, which corresponds to the length of the longest path from a root to each node and it is defined as follows.In order to efficiently implement the inverse traveler function Definition 5 MaxDepthGiven a dag DAPG = , then ∀u ∈ N:v.Finally, the algorithm returns the best DSG it could find starting from node u in DAPG, so one DSG is obtained per starting node u. We only collect the maximal DSGs among those .We run the algorithm starting at each node All algorithms are presented in Deepest, fobj = UNONE, using total order functions ϕ sorting by ID (C) and by FREQUENCY (D). With this representation, we are able to discover cliques C1 = , C2 =  and C3 = .n be the number of nodes in DAPG, h ≤ n be the longest path, and e ≤ n be the maximum number of neighbors of a node. Then, our algorithm starts from each node in DAPG, with an initial vertexSet of size at most e, and walks some path upwards to the root, performing at most h steps. At each step it must compute the distance traveler function, which in our examples costs O(1) or O(e) time. It also intersects the vertexSet of the new node with the current candidates, in time O(e), and determines whether or not to keep the current node in the set C. All the criteria we use for the latter can be computed in time O(e). Therefore, the total time of this process is O(nhe).Let m be the maximum number of maximal subgraphs produced along the process. Once the new subgraph is produced, we compare it with the O(m) current maximal subgraphs, looking for those that include or are included in the new one, in order to remove the included ones (or the new one). This costs O(nme) time.Let O(ne(h + m)). This is O(n3) in the worst case, but much less in practice. For example, in Collins we have n = 1,622, e = 127, h = 187, and m = 12, and therefore ne(h + m) is 25,273n, which is 100 times less than n3 = 2,630,884nThe total cost is therefore minSize define the minimum size of a candidate complex. Then, each DSG is considered as a candidate complex with nodes S ∪ C whenever |S ∪ C| ≥ minSize.We define protein complexes from the DSGs we discover in PPI networks. Since we obtain at most one DSG starting at each node in DAPG, our algorithm is able to obtain DSGs that are in overlap. Let a parameter threshold (we used threshold = 0.8).We generate predicted complexes from candidate complexes based on two different filter options: NONE, where a predicted complex is always a candidate complex, and UNION, where a predicted complex is formed by the set union of the complex pairs with overlap score  greater We implemented the algorithms in C++ and executed all the experiments on a 64-bit Linux machine with 8GB of main memory and with an Intel CPU with i7 2.7GHz. All state-of-the-art methods are also executed on the same machine, except COREPEEL, which provide its method through its web site.http://thebiogrid.org). We used human PPI networks Biogrid (version 3.4.138) and HPRD [http://www.yeastgenome.org), and MIPS (obtained from the ClusterONE distribution [We used yeast (Saccharomyces cerevisiae) and human (Homo Sapiens) PPI networks for experimental evaluation. Specifically, we used the following yeast PPI networks: Collins , Krogan and HPRD . We compand HPRD , SGD (avribution ). For huribution  and CORUribution . Table 2http://www.geneontology.org.For biological metrics, we also used current state-of-the-art gene ontology and annotations, available at We considered state-of-the-art complex prediction methods such as ClusterONE , MCL 1212, CFindTo evaluate the effectiveness of our clustering approach we considered clustering and biological metrics. Clustering metrics measure the quality of the complexes in terms of how well the predicted complexes are related to the reference complexes. Biological metrics assess the probability that proteins in predicted complexes form real complexes (given by a reference) based on the relationship among the proteins in terms of their localization and the annotations.pc is the set of vertices forming a predicted complex and rc the set of vertices forming a complex in the reference, we have Proposed methods usually measure the degree of matching between a predicted and a real complex . This meOS ≥ w .We used three clustering evaluation metrics usually found in complex prediction evaluations: FMeasure, Accuracy (Acc) and Maximum Matching Ratio (MMR).FMeasure is defined in terms of Precision and Recall, which depend on the definition of True Positives (TP), False Positives (FP) and False Negatives (FN). TP is the number of predicted complexes with an OS over a threshold value for some reference complex, and FP is the total number of predicted complexes minus TP. FN is the number of complexes known in the reference that are not matched by any predicted complex. Precision and Recall are metrics that measure, respectively, how many predicted complexes are correct with respect to the total number of predicted complexes, and how many reference complexes are correctly predicted. Acc is the geometric mean of Sensitivity Sn and Positive Predicted Value PPV. Sn shows how good is the identification of proteins in the reference complexes in terms of coverage, and PPV indicates the probability of that the predicted complexes are TP. Sn, PPV, and Acc. Tij is the number of proteins in common between the ith reference complex and jth predicted complex; n is the number of complexes in the reference and m the number of predicted complexes; Ni is the number of proteins in the ith reference complex, and Since several research works use FMeasure and Acc as clustering evaluation metrics, we included them as well. However, they are not free of problems. For instance, Acc penalizes predicted complexes that do not match any of the reference complexes, when some of the predicted complexes might indeed be undiscovered complexes.We also used MMR measure, introduced by Nepusz et al.  to avoidrci) to a predicted complex (pcj) that maximizes the average OS over all reference complexes (considering a minimum OS ≥ 0.2).In order to compute the MMR , ClusterOne important feature of PPI networks is that they are incomplete and noisy. Biological processes for discovering protein interactions are not error free. In consequence, PPI networks might miss proteins with their interactions or include interactions that are not real. Algorithms should consider this feature to improve mining results . This faProteins appearing in the PPI and in the reference.Proteins appearing in the PPI, but not in the reference.Proteins appearing in the reference, but not in the PPI.Evaluating mining algorithms for the cases (1) and (2) is straightforward since protein interaction can be captured by the mining algorithm. Complexes found in case (2) might owe to mistakes on the mining algorithm or incompleteness of the reference, therefore this last case might require an analysis of the false positives generated by the mining algorithm. However, finding complexes in case (3) is impossible for any mining algorithm based on clustering. A possible simple solution to evaluate a mining algorithm would be not to consider reference complexes containing proteins unknown in the PPI, but if these protein interactions are missing in large predicted complexes then there might not be a good reason to eliminate the complete complex. Based on these considerations Nepusz et al.  propose Identify all proteins that had at least one known interaction with other proteins in the input PPI.For each complex in the reference, identify its proteins and compute the set intersection with all proteins in the input PPI.If the set intersection size of a reference complex in the previous step is less than half of the size of the complete reference complex, such reference complex is eliminated because too many proteins are missing in the input PPI, and even if this complex is predicted might not be because of the quality of the algorithm.If the set intersection size of a reference complex is greater than half of the size of the complete reference complex, the reference complex is considered but all proteins that are unknown to the PPI are eliminated. This action does not improve the quality of the mining algorithm since all algorithms are assessed on the same reference and those proteins could not be inferred anyways.https://github.com/jboscolo/RH/find/master. Such implementation includes the computation of FMeasure, Acc and MMR.In order to provide a fair way to compare our approach against other proposed methods, we used the implementation just described , availabColocalization and Gene Ontology Similarity (GoSim). Colocalization measures the relationship of proteins based on where they are located in the cell and organism. The idea is that since protein complexes are assembled to perform a specific function, proteins within the same complex tend to be close to each other [GoSim comes from the Gene Ontology Annotations, which basically describe the functions in which proteins work. Since protein complexes are formed to perform on specific functions, proteins forming a complex tend to share similar functionality [Colocalization and GoSim. ProCope is available at https://www.bio.ifi.lmu.de/software/procope/index.html [Besides clustering measures, we consider biological relevance metrics. In this context we used ch other . The ideionality . We useddex.html .We also include a biological measure that measures the biological significance of predicted protein complexes using enrichment analysis. In order to compute the biological significance of predicted complexes we use the same method described in , taking As mentioned in previous sections, we considered clustering metrics used by other clustering strategies such as FMeasure, Accuracy (Acc) and Maximum Matching Ratio (MMR). Specifically, we used the ClusterONE implementation of Acc and MMR metrics and we added support for FMeasure to compare all clustering techniques considered for comparison. ClusterONE implementation eliminates reference complexes that contain more than 50% of proteins that are unknown  and removes unknown proteins of complexes that contain less than 50% of such proteins.First, Random, Degree, Lexicographic, BFS, and DFS.First, we define different node ordering algorithms to map the protein names to unique numeric ids in the graph. We consider the node ordering algorithms already described: Protein Mapping we specify the text file describing the mapping from proteins to numeric ids. With Graph Type we specify the type of graph, which can be undirected unweighted, UNONE, or undirected weighted, USYM. With alternative fobj, we choose an objective function fobj based on weighted density in the mining algorithm. to detect best dense subgraphs . With Sorting we specify the sorting algorithm of adjacency lists; it can be by ID or by FREQUENCY. Finally, Grouping allows us to define how predicted complexes are built based on candidate complexes. Alternatives are UNION, which takes the union Cx ∪ Cy of the complexes where OS > 0.8, and NONE, where predicted complexes are defined as the candidate complexes. Other parameters include the minimum size, minSize, of any complex, the type of dense subgraph (only clique or dense subgraphs) and an alternative mapping for input PPI networks.We compared our results according to the different parameters we have in our algorithms. We present a summary of the main parameters we provide in our approach in GTypeDM-rSorting-fGrouping(Protein Mapping). In this format GType can be UU (undirected unweighted) or UW (undirected weighted), DM can be any of the density measures; Sorting can be adjacency lists sorted by frequency (F) or ID (I); and Grouping is the way we group candidate complexes to generate predicted complexes, defined by the union set (U) or none (N).In order to compare our results we tried different node ordering (protein mapping) algorithms and different parameters in each experiment, given in the following format: DAPGϕ . We observe that using BFS and DFS traversals provides best results in seven of the eight PPI networks we tested. Also the total order function Sorting by ID is very effective with these protein mappings, achieving best results in six of the eight PPI networks.Tables We also explore the impact of adding random edges into a PPI networks. We present these results in fobj = |S ∪ C| and only in DIP-yeast the degree density (WDEGREE) is better. We also obtain best results without merging or combining dense subgraphs, which is given by the grouping option NONE as described in We show our best results in Disease Module Identification DREAM Challenge for subchallenge 1, https://www.synapse.org/#!Synapse:syn6156761/discussion/threadId=1073).In this section we compare our best results with the state-of-the-art techniques such as ClusterONE , MCL 1212, CFindτ = 0.2, K = 1000, λ = 4, T = 400, ρ = 1e − 6) and set repeat_times = 10 instead of the default, which was 100. With this change we could actually get results in a little more than 12 hours for each PPI network. For CFinder the most sensible parameter is t, which is the allowed time to spend in the detection for clique search per node. We used t = 1 and t = 10 and took the best result. Since GMFTP took too much execution time for small PPI networks (over 12 hours) we did not try to run it with larger PPIs. Also, we were unable to execute CFinder with the two largest PPI networks, and with DCAFP we have a memory error with Biogrid-human, therefore we do not report results for these cases. The main parameter for executing DSDCluster is the number of clusters (K). We executed DSDCluster with K between 100 and 700, increasing by 100 in Collins, Krogan Core, Krogan Extended, and Gavin. In DIP-yeast we reach K = 1600. For Bigrid-yeast, HPRD and Biogrid-human we define K = 500, 1000, 1500, 2000, 2500. We obtain the best results with K = 200 in Collins, K = 500 in Krogan Core, K = 700 in Krogan Extended, K = 500 in Gavin, K = 1200 in DIP-yeast, K = 1000 in Biogrid-yeast, K = 2000 in HPRD, and K = 2500 in Biogrid-human.For each method we used the parameters that provided the best results. In the case of GMFTP we use default parameters  obtained when computing the MMR  ≥ 0.2). We also compute the MMR varying the overlap score threshold. Figs In this section we evaluate how well protein complexes in gold standards are matched with predicted complexes. We first evaluated and compared the protein complex overlap as described earlier using cumulative histograms. We compute the cumulative histogram of all pairs of reference complex and predicted complex (OS = 1.0) by DAPG and the state-of-the-art methods. We observed that GMFTP provides the greatest number of perfect matches in all small yeast references, except in Krogan Extended, where we get one more complex. We are second best, except on Krogan Core (where RNSC gets one more complex) and in Biogrid-yeast . Also, in the human PPIs, we are second after COREPEEL.In addition, we show in We also compared our algorithm with the most competitive methods, GMFTP and COREPEEL, based on some patterns we detected in the PPIs. We considered the four following complexes for yeast, described in the gold standard CYC2008.HIR complex: HIR1, HIR2, HIR3, HPC2Phosphatidylinositol (PtdIns) 3-kinase complex (functions in CPY sorting): VPS15, VPS30, VPS34, VPS38AP-3 Adaptor complex: APL5, APL6, APM3, APS3EKC/KEOPS complex: CGI121, BUD32, GON7, KAE1OS > = 0.8 and with a ✘ mark otherwise.Besides, we found two more complexes in DIP-yeast that follow the same pattern, i.e., a clique of four proteins missing an edge in the PPI. In both cases DAPG detects them, but COREPEEL does not. These complexes are:alpha, alpha-trehalose-phosphate synthase complex: TPS1, TPS3, TPS2, TSL1STE5-MAPK complex: FUS3, STE5, STE7, STE11Finally, we performed a comparison based on the ability of the method to detect protein complexes with proteins that participate in more than one complex. We considered complexes in the CYC2008 gold standard. http://www.ebi.ac.uk/pdbe) which contain information about protein complexes that have purified and structurally characterized. Most of the protein complexes in PDBe are small and are absent in gold standards such as CYC2008 and CORUM, mainly because these gold standards have not been updated recently. In addition, PDBe does not have directly available a repository of all the protein complexes it contains. Therefore, here we propose an automated procedure to query the database to find out whether sets of genes are registered as purified complexes in PDBe. Our analysis do not include protein complexes already found in gold standards . In addition, we also include information of protein complexes that have been topologically characterized, a study done by Ahnert et al. [http://www.periodicproteincomplexes.org). However, this periodic table is not up to date. In order to automate the procedure we use the following PDBe related databases.Predicting protein complexes is challenging because PPI networks are noisy and incomplete, and references are also incomplete and not systematically updated. All prediction techniques report false positives , although they can be real complexes not included in references or not discovered yet. In this work, we perform an automatic false positive evaluation of predicted complexes for yeast and human that are absent in available references. Our goal is to see if the reported false positives contain interesting gene sets. In this work, we analyze the reported false positives by looking into curated biological databases such as PDBe . To obtain protein ids related to pdb ids.Uniprot (https://www.ebi.ac.uk/pdbe/docs/sifts/quick.html). To get chain information of proteins.EMBL-EBI Sifts (http://www.ebi.ac.uk/pdbe/pdbe-rest-api). To query for specific PDB id entry summary information .PDBe REST API (http://www.periodicproteincomplexes.org). To query and visualize topology information of heteromeric complexes.Protein Complex Periodic Table  protein complexes in the gold standards. We also provide a post-processing analysis to study false positive complexes that contain proteins in PPI networks that are absent in the gold standards. In order to study false positives, we consider the information available on protein complexes that have been purified and structurally characterized in PDBe. We used this information together with a recent approach that proposes a periodic table for protein complexes that studies different topologies according to the subunits that compose protein complexes. In this study we discovered that more than 50 yeast complexes and more than 300 of false positive human complexes, not present in gold standards, have actually been already characterized and their information is available in PDBe. Many of these complexes have also been found as having an associated type in the periodic table of protein complexes [We compare our results with state-of-the-art techniques and show that we provide good performance in terms of clustering using different gold standards and biological metrics, as well as good execution times. We show that our method is able to achieve very good results in terms of matching perfectly Click here for additional data file.