Pseudomonas aeruginosa and using it to identify a protein that affects pilus-mediated motility. Our method, SCALES , may be useful for interrogating genotype-phenotype relationships in bacteria.Cellular behaviors emerge from layers of molecular interactions: proteins interact to form complexes, pathways, and phenotypes. We show that hierarchical networks of protein interactions can be defined from the statistical pattern of proteome variation measured across thousands of diverse bacteria and that these networks reflect the emergence of complex bacterial phenotypes. Our results are validated through gene-set enrichment analysis and comparison to existing experimentally derived databases. We demonstrate the biological utility of our approach by creating a model of motility in  A fundamental problem in biology is to understand how proteins interact to create a complex phenotype . BiochemUnderstanding how a phenotype emerges from a collection of proteins requires the ability to relate different ‘scales’ of interactions, from pairwise to higher-order. While higher-order interactions can be inferred from pairwise interactions, recent experimental evidence shows that such inferences are incomplete . Using bOGGD, consisted of 7047 proteomes (rows) and 10,177 OGGs (columns), where each entry is the number of times an OGG was observed in a proteome , a generalized form of principal components analysis  explains more data variance than any other component, SVD2 the second most, and so on , a set of singular values, and OGG projections onto right-singular vectors  for all pairs of proteomes within a spectral window  dividing proteinV into five-component spectral windows, and (iii) computing protein-protein spectral correlations  phylogeny, (ii) indirect interactions between proteins reflecting biological pathways, and (iii) direct  interactions between proteins reflecting protein complexes. The workflow for our analysis was as follows. SVD applied to rs VOGG; . We detel window . We deteelations . We thenenchmark . This openchmark . We focuOGGD to account for uneven phylogenetic distributions of bacterial strains in the UniProt database  there is a wealth of previous biological data regarding its constituent parts and interactions and (ii) it is an illustrative example of a global phenotype that emerges from several layers of protein interactions. From the KEGG hierarchy of directed motility in E. coli K12 , there are three levels of molecular interactions. At the lowest levels, physical interactions between proteins create small units of collective structure and function, such as a basal body, rod, ring, motor, and filament. Integration of these structures and their individual functions produces the flagellum, a machine that turns to move the cell. Integration of the flagellum and the chemotaxis system produces directed motility—the ability to move purposefully along a chemical gradient. We used the flagellar filament, FliC, as a ‘bait’ for identifying spectrally correlated proteins in E. coli K12 putatively related to motility. Aside from this, no other biological knowledge was used: that is, no information regarding components or interactions producing complexes or collective structures contributing to directed motility. We found that 75 proteins were spectrally correlated with FliC , ‘flagellum’ (p<10–56), ‘LPS biosynthesis’ (p<10–3), or ‘cyclic di-GMP signaling’ (p<10–21). Progressing to spectral depth of 1000, the subnetworks at 300 fractured further yielding 9 discrete subnetworks. Each subnetwork was significantly enriched for terms related to a specific function such as ‘cyclic di-GMP catabolism’ (p<10–25) and ‘cyclic di-GMP synthesis’ (p<10–13) or ‘chemotransmission’ (p<10–4) and ‘chemoreception’  were represented in the KEGG hierarchy, 28 (37%) were missing from the KEGG hierarchy but supported by prior experimental evidence in the literature, and only 3 (4%) remained unvalidated . This analysis again produced a hierarchical model of motility that (i) recapitulated the corresponding KEGG hierarchy, (ii) identified proteins missing from the KEGG hierarchy that are known effectors of B. subtilis motility, and (iii) identified a small number of putative motility effectors  and ‘bacterial flagellum’ (p<10–21), were evident, consistent with the ability of P. aeruginosa to use pilus or flagellar-based mechanisms of movement  for twitch-based motility mediated by the pilus or flagellar-based motility  (–4 by Dunnett’s multiple comparisons test). This phenotype resembled that of a knockout strain of PilA and was reversed upon trans-complementation. In contrast, flagellar-based motility of the transposon mutants in Q9I5G6 was not significantly different from that of the parent strain , our experimental results represent a statistically significant enrichment . Moreover, the results of our statistical approach shown in To test these predictions, we assayed single-gene transposon mutants of methods) . Transpomethods) . In contMicrobiome science has taught us that diverse bacteria affect human and environmental health. Therefore, there is a critical need to expand our knowledge of biology more broadly beyond the few well-studied model organisms. Comparative genomics has been critical to inferring functionally relevant interaction networks in newly sequenced organisms. However, these methods are limited in their ability to isolate functional and physical interaction networks from each other as well as from the admixed phylogenetic signal and noise due to finite sampling . Our speE. coli K12 proteome as functionally interacting (indirect PPI), physically interacting (direct PPI), or not-interacting . These predictions were based on protein-protein spectral correlations across three different spectral windows chosen to isolate phylogenetic, indirect PPI, and direct PPI information, respectively  that was not represented in OGGD . We computed the precision and recall for our predictions of any (indirect or direct), indirect, or direct PPIs using the experimentally supported PPIs in the STRING database as a benchmark . We compared these results to those produced by the well-established methods of gene co-occurrence, gene neighborhood, and gene fusion by thresholding the corresponding STRING subchannel scores at different confidence levels . E. coli K12 proteome, our approach for predicting PPIs performs as well or better than established methods across different organisms.Our choice of SVD windows used to compute spectral correlations was guided by MI distributions generated using known Mycobacterium tuberculosis H37Rv found in the STRING database as a benchmark, we found that our approach exhibited significantly greater precision and recall whether using the STRING composite score  or the STRING experimental subscores  that infers direct PPIs from proteome-wide amino acid coevolution (AA Coev) . Brieflyscales.cri.uchicago.edu.We developed a statistical method that predicts hierarchical protein interaction networks reflecting the emergence of complex functions in bacteria. This method involves two aspects: (i) spectral decomposition of variation across bacterial proteomes into components enriched for specific biological scales, (ii) relating covariation structure across components to define hierarchical statistical networks. These hierarchical networks closely resembled the known organization for several well-studied bacterial phenotypes. We call our approach SCALES—Spectral Correlation Analysis of Layered Evolutionary Signals. Having shown that SCALES can be useful for guiding biological discovery, we have developed the following resources: (i) a precomputed database of proteome-wide indirect  and direct  PPI predictions for all 7047 UniProt reference bacterial proteomes; (ii) a tool for predicting indirect and direct PPIs for a user-input proteome; (iii) a tool for generating and interrogating a hierarchical model for a query protein of interest. All of these can be found at The admixture of signals arising from phylogeny, function, and noise negatively impact the accuracy of PPI predictions using comparative genomics . One appUnderstanding the origins of complex biological functions requires defining hierarchical relationships describing how protein interactions integrate to create scales of biological organization. While the use of SVD is fundamental to our method, SVD itself does not define hierarchical relationships; SVD defines orthogonal components of variance ordered according to the amount of variance explained. Two results of our study were key for being able to use the SVD spectrum to produce hierarchical models. First, different components contain information regarding different biological scales. Second, the information in different components could be related by tracking the persistence of spectral correlations across components . These two results enabled extracting hierarchical statistical relationships that predict the integration of PPIs into complex structures approximating pathways and phenotypes. To our knowledge, this is a fundamentally new way of constructing hierarchical models. Instead of predicting pairwise interaction networks and then inferring higher-order networks, we infer an entire hierarchy directly from coevolutionary statistics.Recently, Cong and colleagues reported a method, AA Coev, for inferring direct PPIs from bacterial genome sequences. Their method represented a significant advance for two reasons: (i) it considered coevolution at the resolution of amino acids and (ii) it applied DCA, to entire bacterial proteomes. Like our method, AA Coev tries to extract signal related to a specific scale of biology from admixed signals of phylogeny and noise using coevolutionary statistics of genomes. Specifically, DCA is a statistical physical approach that isolates local (i.e. direct) interactions. However, we observed significant differences in quality and breadth of direct PPI inferences, scalability, and ability to reconstruct hierarchical networks.M. tuberculosis with those of AA Coev, we predicted significantly more interactions with significantly greater precision. This was a surprising result given that our approach considers lower-information features—OGGs versus amino acid sequence-level information. One explanation may be that our predictions were derived by explicitly using correlations across three different spectral windows that provided information about three different scales of biology: phylogeny, indirect PPIs, and direct PPIs. In contrast, AA Coev discards signal unrelated to direct PPIs. It may be the case that phylogenetic and pathway-level information provides context clues for enhancing subtle statistical signals related to direct PPIs. In other words, the confidence in assigning a putative physical interaction is increased by additional signals suggesting that the interaction also contributes to a pathway-level function among phylogenetically related bacteria. The power of our method may lie in its ability to simultaneously deconvolute yet leverage information related to these different scales. Further work is needed to better understand the differences between our method and AA Coev and to determine if the observed difference in PPI prediction is consistent across additional organisms outside of M. tuberculosis.When we compared our direct PPI predictions in A striking difference between the two approaches is related to computational scalability. AA Coev is computationally expensive and, as a result, has been applied to just two organisms thus far. In contrast, we note that our approach can compute proteome-wide PPIs in a matter of minutes, enabling us to provide predictions for all 7047 UniProt Reference Proteomes. As identifying and characterizing different strains of bacteria is becoming increasingly important, scalable computational tools becomes a necessity.A final difference between the two methods is how a hierarchy can be constructed. Cong et al. predicted collective units of structure, using a ‘bottom-up’ approach by putting together their direct PPI predictions. However, compared to the networks produced by SCALES, these networks tended to be smaller and less representative of higher-order collective structure, reinforcing results reported by Kuzmin et al. illustrating that building collective organization from pairwise networks results in incomplete hierarchical descriptions of biology. We therefore pose that though SCALES does not consider as information-rich of a feature as AA Coev, it may prove to be a useful framework to extract hierarchical relationships for connecting bacterial genotype with phenotype.E. coli K12 proteins (6.7%). These proteins cannot be assigned to interactions or units of function by our method. Second, many proteins share the same OGGs and appear to interact at all spectral depths. These putative interactions may or may not be related to biological function. We anticipate that ortholog annotations will continue to improve with additional bacterial genome sequences, helping to alleviate these limitations. Moreover, the use of phylogenomic methods that incorporate models of the phylogenetic history of proteins to improve ortholog definition might create superior inputs for the methods developed here  in the 2020_02 release of the Uniprot Reference Proteome database were downloaded on May 20, 2020 . Five different benchmarks were generated corresponding to pairs of proteomes that share identical phylogenetic substrings down to the level of phylum , class , order , family , or genus .NCBI phylogenetic strings were mapped to the NCBI taxonometric IDs for each of the 7047 bacteria represented in E. coli K12 proteome (STRING ID 511145) on July 22, 2019. A benchmark was assembled to include all protein pairs  with a non-zero combined STRING score that did not share a ‘binding’ action annotation. This benchmark was expected to be enriched for indirect PPIs.STRING database annotations were downloaded for the E. coli K12 proteome through the UniProtKB API. A benchmark was assembled containing the 79,794 protein pairs that share at least one GO term annotation. This benchmark likely contained a mixture of indirect and direct PPIs.‘Biological function’ GO term annotations were mapped for the 4391 proteins in the E. coli K12 proteome (STRING ID 511145). A benchmark was assembled comprised of all  protein pairs with a non-zero combined STRING score. This benchmark included a mixture of pairs with  and without (n=5423) a ‘binding’ annotation and therefore is presumed to contain a mixture of direct and indirect PPIs.STRING database annotations were downloaded for the E. coli K12 proteins selected from the set of complexes in the ECOCYC database after intentionally excluding large complexes with greater than 10 proteins to enrich for directly interacting pairs of proteins , and M is the total number of SVD components. Each protein in a proteome may comprise up to several OGGs:where where An example of this process is illustrated in Spectral correlations were computed by first segmenting the top 3000 SVD components into windows comprised of five components each and calculating spectral correlations across all pairs of variables (either proteome-proteome or protein-protein) within each window. Computing the MI between the distribution of spectral correlations within a window and a biological benchmark quantitates how much knowing the distribution of spectral correlations reduces uncertainty about the benchmark. Because spectral correlations within a window comprise a finite distribution (i.e. not infinite), there exists intrinsic uncertainty due to the need to define a bin width in the distribution. The process of computing this uncertainty has been formalized and is calculated as the ‘differential entropy’ :Hρa:b=-∑a to b, ith set of correlation values, c, MI is the difference between the intrinsic uncertainty in spectral correlations, c can be either ‘1’ if two variables share the benchmark (i.e. two proteins share the same phylogenetic classification or two proteins are found to interact in a database) or ‘0’ if two variables do not share the benchmark. The ‘conditional entropy’ of spectral correlations is the differential entropy conditioned on knowledge of the probability distribution of benchmarks. So, The uncertainty in spectral correlations given knowledge of a benchmark is evaluated in the following way. A benchmark p(c=1) and p(c=0) are the probability of observing a ‘1’ or ‘0’ in c respectively; and c=1) and do not share (c=0) a benchmark, respectively. A model of random MI was generated by computing the MI shared between the spectral correlations within row-shuffled versions of OGGU or OGGV and the benchmarks of phylogeny and protein interactions, respectively  shown in wcdf is the value of the cdf at spectral position idataw, MI is the MI observed in window i, irandomMI is the MI produced by random correlations in window i, W is the total number of windows, and 1≤w ≤ W. Because we considered five-component spectral windows within the first 3000 components, W=2997.where 1000 for the proteins encoded in the proteome of E. coli K12. Our rationale was that since the vast majority of proteins do not interact, the distribution of all-by-all spectral correlations approximates correlations between proteins that do not functionally interact. The variance of this distribution decreased rapidly as the correlation window widened until a width of 100 components. This motivated our choice of computing spectral correlations over sets of 100 components . The ontological term with the lowest p-value is indicated for each statistical module shown in P. aeruginosa strains used in this study were ordered from the Manoil Lab. All strains were grown at 37°C on LB supplemented with 25 µg/ml irgasan and gentamicin (75 µg/ml) as necessary. E. coli XL1-Blue was maintained on LB agar plates with gentamicin (15 µg/ml) as necessary.All P. aeruginosa growth was at 37°C on LB supplemented with 25 µg/ml irgasan and gentamicin (75 µg/ml) as necessary. Strains were assayed for subsurface twitching motility as previously described (escribed . StrainsP. aeruginosa strains of interest were grown overnight and concentrated in morpholinepropanesulfonic acid (MOPS) buffer . A 2.5 µl volume of the MOPS buffered bacterial suspension was spotted onto buffered twitching motility plates  and was incubated for 24 hr at 37°C. The twitching zone was measured and imaged.Surface twitching motility assays were performed as previously described . P. aeruSwimming motility was performed as previously described . OvernigP. aeruginosa strains, the complementation vector pBBR1-MCS5-PA0769 was created using Gibson assembly. The vector was transferred to P. aeruginosa by electroporation using 2.2 kV in a 2 mm gap cuvette and subsequent selection using gentamicin.For complementation of genes of interest into E. coli K12 PPIs was assembled and consisted of 72,000 not-interacting, 1226 indirect PPIs, and 72 direct PPIs. All pairs defined as ‘direct PPI’ satisfied three criteria: they shared amino acid level coevolution (Coev+ benchmark), were annotated in the same protein complex in the ECOCYC benchmark, and interacted in the PDB benchmark. All indirect PPIs were selected based on the following criteria: they shared a ‘non-binding’ type interaction annotation in the STRING Nonbinding benchmark, shared a ‘biological function’ interaction in the GO benchmark, and did not share an interaction annotation in any of the benchmarks of direct PPIs . The ‘not-interacting’ pairs did not share an interaction annotation in any of the benchmarks . The not-interacting set was subsampled to exceed the number of physically interacting pairs by 1000-fold  and validation (40%) datasets. Fifty such random partitions were generated to assess the reproducibility of the results of the machine-learning task described below. Our rationale in partitioning the entire dataset randomly, instead of independent partitioning for each interaction class, was to produce fluctuations in the number of positives and degree of class imbalance.E. coli K12 as not-interacting, indirect PPIs, or direct PPIs by feeding the labeled training set examples to the TreeBagger algorithm . This process was repeated for each random partition of the gold-standard dataset yielding an ensemble of 50 RF models per feature. Each trained RF model was subjected to three validation tasks of classifying interaction types for unlabeled pairs of E. coli K12 proteins in the validation portion of the gold standard (40%). The model performance was evaluated by computing an F-score for each interaction type , where F-score is the harmonic mean of precision and recall, precision is the ratio of the number of correctly predicted interactions within a class to the total number of predicted interactions in a class, and recall is the ratio of the number of correctly predicted interactions within a class to the total number of interactions of that class. F-scores for RF models trained on MIWSCs and used to predict the validation portion of the gold standard are shown in The workflow of training and validating RF models on MIWSCs is depicted in E. coli K12 using MIWSCs).For each feature extracted from existing methods described below, RF models were trained and validated using the identical protocol as for MIWSCs , sum log-likelihood scores from an affinity purification mass spectrometry screen , protein interaction scores from an affinity purification mass spectrometry screen , and binary pairs from a yeast-two hybrid screen   .E. coli K12 (STRING ID 511145) were extracted from the STRING database  feature was modeled after the popular phylogenetic profiling method of OGGB is the binary OGG content matrix and has the same dimensions as OGGD.where The phylogenetic profile of an OGG across all 7047 proteomes was defined as:E. coli K12 were similar was computed by averaging the MI between phylogenetic profiles of the OGGs encoded in the protein pair. The MI shared between two phylogenetic profiles was computed using Shannon’s formulation for the MI between two discrete random variables , the mixed indirect/direct PPIs in the GO  and STRING benchmarks , and the direct PPIs in the entire PDB benchmark .Biological interactions are typically sparse: the number of not-interacting pairs of proteins vastly outnumber the number of interacting pairs. As such, we desired to challenge each of the RF models in a validation task reflective of this asymmetry. To do so, each RF model was tasked with predicting classes for all pairs of proteins in the F-scores for RF models trained on MIWSCs, published experimental, or published computational features and used to predict the out-of-bag examples of non-interacting proteins, indirect PPIs, or direct PPIs are shown in E. coli K12 using MIWSCs were used to predict proteome-wide indirect and direct PPIs in the following bacteria : Aliivibrio fischeri ES114 , A. vinelandii DJ , B. subtilis 168 , Caulobacter vibrioides , Helicobacter pylori 26695 , M. tuberculosis H37Rv , Mycoplasma genitalium G37 , Pseudomonas fluorescens F113 , Staphylococcus aureus NCTC 8325 , Streptomyces coelicolor A3(2) , Synechocystis sp. PCC 6803 . For each proteome, a set of consensus PPIs was defined as those for which a majority of the models (>25) produced the same classification of ‘indirect PPI’ or ‘direct PPI’.Each of the 50 RF models trained to classify interactions in OGGD , OGGs were mapped using EggNOG mapper V2 and MIWSCs were extracted using the OGG projections in OGGV . In contrast, their predictions of PPIs in M. tuberculosis were based on AA Coev alone (‘Coev’). Therefore, for a head-to-head comparison, we compared the predictions produced by our RF models trained on MIWSCs with their PPI predictions in M. tuberculosis. We benchmarked these interactions using two strategies. The first strategy mirrored that used by Cong and colleagues, computing the fraction of interactions assigned a STRING combined score of 0, 0–0.4, or >0.4. The second strategy used orthogonal experimental evidence by computing the fraction of interactions assigned a STRING experimental subchannel score of 0 and >0.Cong and colleagues have provided proteome-wide PPI predictions for is H37Rv . Their p Since the inception of comparative genomics, mining phyletic patterns has been a powerful approach for the discovery of previously unknown biological interactions. The authors use a combination of singular value decomposition of the phyletic pattern matrix and random forests classification method to uncover potential protein-protein interactions. The work illustrates the utility of such methods, which are finding increasing application in addressing various computational biological problems, such as predicting protein-protein interactions from genomic information. public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "Defining hierarchical protein interaction networks from spectral analysis of bacterial proteomes" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:E. coli from their 'scales' website (14429 predictions). We could by-and-large confirm the left panel, but for the right panel we got recall values in the 10e-02 range, which is about 1000 times higher. Is this perhaps a mislabeled axis in the plot, or a misunderstanding on our part?1) The basic predictive power of their MIWSC approach is demonstrated in Figure 2C. However, we were surprised by the extremely low recall shown in the right panel. A recall of 10e-5 is very low indeed, and would preclude this method from having much practical value. We went ahead and recomputed both panels in Figure 2C, based on the author's raw prediction data that we downloaded for 2) Also related to Figure 2C: this panel demonstrates specificity and sensitivity, but only for the author's prediction class of "direct" associations. The authors, however, also predict "indirect" associations … these in fact outnumber their "direct" predictions. Is it possible to also show specificity and sensitivity for those, similar to Figure 2C, for the same set of organisms? This could be done by taking KEGG-pathway membership or GO terms as the benchmark; in our own testing we found that the overall prediction power of their "indirect MIWSC" class is less impressive – more in line with previous efforts, which might be of interest to the reader.3) Bacteria tree is not uniformly sequenced. There is an overrepresentation of certain lineages, e.g., of gammaproteobacteria and terrabacteria (Bacillus group) in the starting matrix. This could potentially bias the quality of the correlations that are obtained in the ``mid-range' SVD components.4) The actual biological inferences drawn for the role of the tested gene in twitching mobility might be over-interpreted. Briefly, the authors recover 4 uncharacterized proteins  as part of their T4 pilus sub-graph and infer a general function for them in the twitching mobility. They chose Q9I5G6 because it was the only one with a supposed domain of unknown function (DUF4845). However, it should be noted that Q9I5R2 also contains another such domain DUF805 along with a Zn-ribbon domain. Further, Q9I0G2 is a T2SS secretion platform protein and Q9I0G1i is the ATPase engine for the pilus. Genomic neighborhood analysis by this referee revealed that DUF4845 likely functions with the signal peptidase in secretion. Thus, given the role of the pilus in secretion and mobility, the best one could infer is a role for DUF4845 in pilus function perhaps with a greater intersection with secretion. This could even indirectly affect the mobility function which the authors' experiments are said to support. However, the authors state right in the abstract they have uncovered a twitching mobility effector. At best they could say they have uncovered a potential component that might be functionally linked to the T4 pilus which might affect secretion or twitching mobility. Indeed, the phyletic pattern of DUF4845 does not immediately suggest that all organisms with it also possess definitive twitching mobility.P. aeruginosa. Only one shows positive experimental results. It would be nice to have some idea how general this is, i.e. how many times proteins get associated by the approach, even if they have biologically known but totally distinct functions.5) The authors found 4 proteins of unknown function associated with pilus motility in 6) The authors might experiment with using a matrix that removes closely related gammaproteobacterial, actinobacterial and terrabacterial lineages to see its effects on their training and predictions.7) When the manuscript speaks of scales of protein interactions represented in the spectrum, is this visible in the singular vectors? We would imagine that large-scale properties should correspond to distributed vectors , while local scales should intuitively correspond to localised vectors.8) It is quite evident that the first singular vectors are related to phylogeny, which is known to be a major source of variability between orthologs . What is more interesting is the crossover from phylogenetic to functional information.9) The MI is not really well defined, it would be hard to reproduce on the basis of what is written in the Methods section.10) We have some doubts concerning the gold standard. If non-interacting pairs are randomly chosen, and fractions of interacting and non-interacting pairs are given in their approximate true proportions, the non-interacting set should contain about the same number of actually interacting pairs as given in the positive examples. The choice of so many random pairs to represent non-interacting pairs is therefore dangerous and potentially misleading. It remains also unclear how the extreme bias towards non-interacting pairs in the dataset is handled . When partitioning into training and validation sets, is this done independently for each class, or for the entire dataset? In the latter case, the number of positive examples might fluctuate a lot in the training set.11) The comparison with Cong et al., might be potentially spectacular, but it is hard to understand it from the little paragraph. This should be explained better. One should also keep in mind that Cong et al., use an unsupervised approach as compared to the supervised in the present manuscript.12) The notation in Materials and methods requires revision. To give an example , n is the number of proteomes in the first paragraph, and the number of OGGs in the second. Please use consistent notations!13) Is Figure 1S2B really showing normalized columns? They appear optically to have very different variances, even if they all should be normalized to variance 1.14) The code should be made available.Presentation:1) The paper is very hard to read and to understand. It is written in a semi-technical jargon mixing spectral analysis, machine learning and information theory. Even having expertise in these fields, we had to continuously jump between the main text, the methods and the figure  to follow the argumentation of the paper. This style is not suitable for a journal with a broad and interdisciplinary readership. The authors should make a serious effort to clean up their presentation, such that the main messages become accessible. Currently, even for disciplinary journals in computational biology or bioinformatics, the presentation would require simplifications.2) The general reader would benefit from an opening figure that clearly lays out the steps in the workflow starting with SVD  to random forest training. It can augment what is shown in the current figure 1 and one of the supplements to figure 2.3) The abstract repeats 8 times the word "hierarchy" or "hierarchical". Avoid such excessive repetitions.4) The introduction was a bit short in giving credit to previous efforts in this area. Yes, the founding papers from the 90s are cited, but there have been quite a number of studies in the meantime, including the use of SVD, reviewed for example here: Nagy et al., NAR 2020, https://doi.org/10.1093/nar/gkz1241 or Moi et al., PLoS computational biology 2020, 16 (7), e10075535) The results on motility are really nice. We suggest placing them much earlier in the paper, and do the more technical stuff with random forest etc. later. It could come directly after Figure 1C has been explained.eLife. Your revised article has been evaluated by Aleksandra Walczak (Senior Editor) and a Reviewing Editor.Thank you for resubmitting your work entitled "Defining hierarchical protein interaction networks from spectral analysis of bacterial proteomes" for further consideration by The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:Reviewer #1 (Recommendations for the authors):General Summary:While the authors have made clearly visible efforts to improve the presentation of their manuscript, the major problem remains: while the results are very interesting, the presentation of the technical details is cumbersome, and reading the paper without massive reference to the huge number of supplementary figures is hardly possible. I think another round of simplification is unavoidable.Detailed report:I am still convinced that this paper has very interesting results, which fully merit publication. But in particular, the initial part of the paper is hard to read. In a nutshell, the method is quite simple: (a) extract a large matrix of phylogenetic profiles (here many proteomes annotated via OGGs), (b) perform a standard SVD, and represent OGGs via their projection to the singular vectors, (c) extract proteins having correlated projections in small spectral windows. The innovative part of the paper is a clever use of these spectral windows going from the singular values/vectors describing the large-scale organisation of the data, to smaller and smaller singular values, far beyond the few typically used in PCA, showing that these deep parts of the spectrum contain finer and finer information – here going from large functional categories via pathways to PPI. It should be possible to present this in a simple way.I would like to make a number of more specific points:OGG and VOGG are used in methods but introduced only in Figure 1 Supp. 1. In addition, the left and right singular values are denoted equally as |n>, which is a bit confusing . In general, the authors should revise the paper such that the supplement gives supplementary information, and the paper can be read without having ~50 pages of supplement in your hands.1. The reading is impossible without the massive use of supplementary figures. To give one example (out of many), the singular vectors in U2. The method heavily relies on subjective hyperparameters and thresholds: For the number of singular values considered, for the bin size in the MI calculation, for the size of the spectral window, for the used cutoffs of the spectral depth. Together with the somewhat anecdotal results (concentration mostly on motility), this gives the impression that the biological system and parameters are hand selected to show nicely interpretable results. I sincerely hope this is not the case, but if the authors would, e.g., show the tree generated by changing spectral depth from largest to smallest values, the different levels of organisation could become more evident (in case well-separated levels exist).3. In some cases, it is hard to understand if the results are significant. If one considers Figure 1E, even a uniform MI distribution would have a similar shape as the blue curves, since the cumulative would be linear, and represented with a log-scale of the spectral position.4. In some places, results imposed by the analysis are presented as astonishing findings. The most evident case is the hierarchical structure when changing spectral depth. Since spectral depth is defined as the depth where correlations are for the first time non-significant, the edge set of the graphs at higher spectral depth is necessarily proper subsets of those at lower spectral depth, and thus connected components are proper subsets, too. If all statistically significant correlations in each spectral window would have been taken into account, edges between proteins might disappear at some depth, and reappear at a deeper one, making the network potentially non-hierarchical.5. Heavy but somewhat random statements like "Understanding the molecular basis of a phenotype requires (i) defining interactions that create units of collective function at different biological scales and (ii) relating these scales to create a hierarchical model of emergent phenotype." should be avoided. Essential revisions:E. coli from their 'scales' website (14429 predictions). We could by-and-large confirm the left panel, but for the right panel we got recall values in the 10e-02 range, which is about 1000 times higher. Is this perhaps a mislabeled axis in the plot, or a misunderstanding on our part?1) The basic predictive power of their MIWSC approach is demonstrated in Figure 2C. However, we were surprised by the extremely low recall shown in the right panel. A recall of 10e-5 is very low indeed, and would preclude this method from having much practical value. We went ahead and recomputed both panels in Figure 2C, based on the author's raw prediction data that we downloaded for -2 .We thank the reviewer for bringing attention to this point and recalculating the recall. We indeed found an error in our plot. We have corrected this error and observe similar results as the reviewer with recall on the order of 102) Also related to Figure 2C: this panel demonstrates specificity and sensitivity, but only for the author's prediction class of "direct" associations. The authors, however, also predict "indirect" associations … these in fact outnumber their "direct" predictions. Is it possible to also show specificity and sensitivity for those, similar to Figure 2C, for the same set of organisms? This could be done by taking KEGG-pathway membership or GO terms as the benchmark; in our own testing we found that the overall prediction power of their "indirect MIWSC" class is less impressive – more in line with previous efforts, which might be of interest to the reader.We thank the reviewer for this excellent suggestion. We have now repeated the same analysis for our indirect predictions as well as the combined set of indirect and direct predictions to provide the reader with a more comprehensive understanding of the accuracy of our method. In addition, we considered that applying different confidence thresholds to the established methods might produce different results and therefore have considered various thresholds and reconstructed complete precision-recall (PR) curves for the methods of GC, GN, and GF. These analyses provide a more fair and complete evaluation of our predictions in comparison with standard prediction tools. We have added text in the manuscript to reflect these points (lines 296-308):E. coli K12 proteome, our approach for predicting PPIs performs as well or better than established methods across different organisms.”“We computed the precision and recall for our predictions of any (indirect or direct), indirect, or direct PPIs using the experimentally supported PPIs in the STRING database as a benchmark . We compared these results to those produced by the well-established methods of gene co-occurrence, gene neighborhood, and gene fusion by thresholding the corresponding STRING subchannel scores at different confidence levels . Figure 4B shows this comparison at the ‘medium’ confidence level. Figure 4C summarizes the entire analysis showing the precision-recall curves across all thresholds tested. We found that the sets of any indirect or direct PPIs produced by our method exhibited a higher precision for a given recall compared to the established methods. These results show that though the SVD windows used to compute spectral correlations were chosen based on analysis of PPIs in the 3) Bacteria tree is not uniformly sequenced. There is an overrepresentation of certain lineages, e.g., of gammaproteobacteria and terrabacteria (Bacillus group) in the starting matrix. This could potentially bias the quality of the correlations that are obtained in the ``mid-range' SVD components.We appreciate this comment regarding the over-representation of certain clades in the original matrix. We performed a sensitivity analysis of our results by randomly downsampling the top 4 Phyla represented in the input dataset by 50%. We have included results of our analysis in the manuscript and have added a supplemental figure  to summarize our findings. Below is the text (lines 102-109).OGG to account for uneven phylogenetic distributions of bacterial strains in the input data . These results show that global to local patterns of bacterial covariation reflect an intuitive hierarchy of biological scale—phylogeny, pathway, protein complex .”“Comparing the relative distributions of these different types of information across the SVD spectrum, we observed an order of Phylum, Class, Order, Family, Genus, indirect PPIs, mixed indirect/direct PPIs, and direct PPIs. The ordering of these distributions across the SVD spectrum was robust to sub-sampling DWith respect to the quality of ‘mid-range’ SVD components, we did not observe a striking difference in the MI density when comparing the subsampled matrix versus the initial matrix. However, we did observe more overlap between the ‘Indirect PPI’ benchmark (STRING NB) and the ‘Mixed indirect and direct PPI’ benchmarks . This difference may arise from having fewer SVD components over which information regarding the ‘Indirect PPI’ benchmark can be spread. We interpret these results to indicate that curating an optimally diverse dataset is a difficult problem that warrants future investigation.4) The actual biological inferences drawn for the role of the tested gene in twitching mobility might be over-interpreted. Briefly, the authors recover 4 uncharacterized proteins  as part of their T4 pilus sub-graph and infer a general function for them in the twitching mobility. They chose Q9I5G6 because it was the only one with a supposed domain of unknown function (DUF4845).We believe the text in our manuscript was unclear with respect to how these proteins were selected. We selected these proteins because they were labeled as ‘uncharacterized’ in UniProt. The modified text is found in lines 221-223:P. aeruginosa .”“Four uncharacterized proteins  were identified in the pilus subnetwork that have not previously been associated with PilA in all four proteins individually to look for an effect on both pilus and flagellar motility. Our data revealed that Q9I5G6 affected pilus motility and not flagellar motility. We presented the results of our experiments for all four proteins .We found that these proteins were connected to proteins that collectively reflect the global function of ‘motility’ at a spectral depth of 50. At a spectral depth of 300, these proteins shared connections with proteins that collectively reflect the specific function of ‘pilus-based motility’ but not other proteins that collectively reflect ‘flagellar motility’. We then experimentally interrogated genetic ablation of the genes encoding However, it should be noted that Q9I5R2 also contains another such domain DUF805 along with a Zn-ribbon domain. Further, Q9I0G2 is a T2SS secretion platform protein and Q9I0G1i is the ATPase engine for the pilus. Genomic neighborhood analysis by this referee revealed that DUF4845 likely functions with the signal peptidase in secretion. Thus, given the role of the pilus in secretion and mobility, the best one could infer is a role for DUF4845 in pilus function perhaps with a greater intersection with secretion. This could even indirectly affect the mobility function which the authors' experiments are said to support. However, the authors state right in the abstract they have uncovered a twitching mobility effector. At best they could say they have uncovered a potential component that might be functionally linked to the T4 pilus which might affect secretion or twitching mobility.We agree with the reviewer. Our approach does not infer a mechanism for Q9I5G6. We believe the key takeaway from our results is that there was a measurable effect of Tn-Q9I5G6 on pilus-based motility and not on flagellar motility. Neither our experiments nor our statistical approach were designed to address the nature  of Q9I5G6 with the pilus. We have included text in the manuscript (lines 424-427) to reflect this concept.“Another limitation of the methods developed here is that they are inherently ‘mechanism-free’: they leverage evolutionary constraint without knowledge of the specific pressures driving the selection of interactions. As a result, our methods identify functionally relevant interactors but cannot reveal their collective function or the detailed molecular basis of the interactions.”Indeed, the phyletic pattern of DUF4845 does not immediately suggest that all organisms with it also possess definitive twitching mobility.We agree, merely having DUF4845 does not necessarily mean that the organism has twitching mobility. The phenotype of ‘twitching mobility’ is likely complex and dependent on the interactions between many proteins within individual organisms. Thus, the effect of Tn-Q9I5G6, conditional on the pattern of genetic interactions of strain PAO1, is to affect twitching motility. SCALES predicts an organism-specific, not domain-specific, hierarchical interaction map for Q9I5G6.P. aeruginosa. Only one shows positive experimental results.5) The authors found 4 proteins of unknown function associated with pilus motility in P. aeruginosa PA01 strain, of which 25 appear in the ‘pilus-assembly module’ within the KEGG database  equating to a 0.4% background rate of association. Thus, a hit rate of 25% is substantially statistically significant . However, we note that the hit-rate of our statistical approach is in fact much higher than 25%. We identified 22 proteins that significantly associated with Pilus-motility, 19 of which were validated by prior experiments in the literature or our own experiments (p < 0.0001 by Chi-squared) . We posit that the three proteins that did not show a phenotype in our experimental conditions might in fact affect pilus-based motility but may require different assay conditions to be revealed.We appreciate the reviewer’s concern about the predictive value of our approach. It is worth noting that a ¼ rate of true positives is impressive given the background expectation. Consider that there are 5564 proteins in the We have incorporated our response into discussion within the main text found in lines 236-246:P. aeruginosa that specifically impacts twitch-based motility. Compared to the background expectation of finding a protein that affects twitch motility , our experimental results represent a statistically significant enrichment . Moreover, the results of our statistical approach shown in Figure 3B illustrate a far higher enrichment of association with identifying 19 effectors of twitch motility out of 22 proteins in the ‘Pilus motility module’. As such, these experiments provide a proof of concept of how our hierarchical models may aid in discovering novel genotype-phenotype relationships.”“These results illustrate that Q9I5G6 is a previously unappreciated effector of directed motility in It would be nice to have some idea how general this is, i.e. how many times proteins get associated by the approach, even if they have biologically known but totally distinct functions.We agree with the reviewer’s point; it would be useful to know the overall false-positive rate of our method. However, our data show that a protein can have distinct functions at a lower scale of interaction and share a collective function at higher scales. Thus, a one-to-one mapping between protein identity and its function is not possible—our results illustrate the concept that biological ‘function’ maps onto emergent networks of protein interactions not individual proteins. Nonetheless, we point to our results in Figure 2, Figure 2—supplemental figures 4, 5, and 6, Figure 5, and Figure 5—supplemental figure 1, where all of the statistical modules characterized by GSEA show a statistically significant association with a known biological function. Moreover, the validation of our proteome-wide interaction predictions across diverse organisms  revealed a consistently high precision. Together, we interpret that these results provide a general sense of a low false-positive rate for our statistically connected proteins.6) The authors might experiment with using a matrix that removes closely related gammaproteobacterial, actinobacterial and terrabacterial lineages to see its effects on their training and predictions.We agree with the reviewer’s comment. We have addressed this in our response to Comment #3.7) When the manuscript speaks of scales of protein interactions represented in the spectrum, is this visible in the singular vectors? We would imagine that large-scale properties should correspond to distributed vectors , while local scales should intuitively correspond to localised vectors.We thank the reviewers for bringing up this important point. While the reviewer’s intuition was shared by the authors as well, our data illustrate a different trend. We find that large-scale properties (i.e. protein interactions that reflect broad differences in phylogeny) are highly localized to the shallow components of variation  while local scales are distributed across the entire spectrum of vectors. This is shown in the curves reflecting the relative distributions of mutual information across the spectrum of vectors shown in Figure 1—figure supplement 4.What is the interpretation of this data? Large-scales properties can be ‘compressed’ into just a few variables while ‘local’ properties cannot. Thus, information regarding large-scale properties is increasingly ‘filtered out’ in deeper vectors thereby enriching for more local information. Hence, one of the main results of our analysis is that the order of the spectrum of vectors corresponds to a hierarchy of protein interactions.We have added the above interpretation of our results into the main text in lines 345-352:“Components in different regions of the spectrum were enriched for information about different biological scales—shallow components phylogeny, deeper components pathways, even deeper components protein complexes, and the very deepest noise, thereby signifying a ‘cross-over’ from phylogenetic to functional information. Our interpretation of these results is that while statistical variance reflecting large-scale properties can be ‘compressed’ into just a few shallow components, information about ‘local’ biological scales is distributed broadly across the spectrum. As a result, discarding global components enriched for phylogeny improved prediction of functionally relevant interactions.”8) It is quite evident that the first singular vectors are related to phylogeny, which is known to be a major source of variability between orthologs . What is more interesting is the crossover from phylogenetic to functional information.We are in complete agreement with the reviewer in regard to this point. We have added text in the manuscript to reflect this distinction and explicitly point out the interesting nature of the cross-over from phylogenetic information into functional information (lines 339-348):“One approach to address this problem is to use PCA which assumes that only global covariation is not statistical noise . A known source of variability between orthologs is phylogenetic relatedness. As SVD achieves spectral clustering and phylogenetic reconstruction hierarchical clustering, we do expect some level of coherence between the two approaches. However, our results also illustrate that relevant biological signal is contained throughout the SVD spectrum, including components harboring a minutiae of data-variance. Components in different regions of the spectrum were enriched for information about different biological scales—shallow components phylogeny, deeper components pathways, even deeper components protein complexes, and the very deepest noise, thereby signifying a ‘cross-over’ from phylogenetic to functional information.”9) The MI is not really well defined, it would be hard to reproduce on the basis of what is written in the Methods section.We agree that the strategy we used to compute MI is critical to explain in the manuscript and was unclear in our initial submission. To address this we have added a supplemental figure  that illustrates the process of computing MI between spectral correlations and biological benchmarks step-by-step; we have also rewritten the Methods section to be more readable. The new text can be found in lines 518-562.10) We have some doubts concerning the gold standard. If non-interacting pairs are randomly chosen, and fractions of interacting and non-interacting pairs are given in their approximate true proportions, the non-interacting set should contain about the same number of actually interacting pairs as given in the positive examples. The choice of so many random pairs to represent non-interacting pairs is therefore dangerous and potentially misleading.et al., 2014). While we acknowledge that our gold-standard dataset is not perfect, we do not believe that it is misleading for the following reasons. First, false negatives in the gold-standard benchmark will manifest as false positives in our predictions and the imperfections of the gold-standard benchmark will only decrease model performance. Thus, the F-scores presented in Figure 4B can be interpreted as a conservative estimate. Second, the comparison of methods was performed using the same gold-standard dataset. Because the gold-standard was not selected to favor any one method, we believe the differences in relative performances are valid.We agree with the reviewer’s comment that our random sampling of non-interacting pairs may lead to imperfections in the gold-standard dataset, specifically the mis-classification of true interactors as non-interactors. The strategy we took was an attempt to mimic the true interaction class imbalance noted in biological PPI studies. As we do not know the true class imbalance, we used a previous estimate provided by Rajagopala and colleagues . When partitioning into training and validation sets, is this done independently for each class, or for the entire dataset? In the latter case, the number of positive examples might fluctuate a lot in the training set.As the reviewer notes, class imbalance problems are challenging for many machine-learning algorithms. We purposely made a random partitioning across the whole dataset, not a partitioning independently performed for each class (i.e. stratified random sampling). Our intention was to introduce fluctuations in the number of positives across each iteration of partitioning the dataset and training models. In this way, we could ascertain the sensitivity of the performance estimates to the model class imbalance, addressing the reviewer’s concern above. In addition, we chose to report F-score as this is a valid metric for class imbalance problems. Finally, we computed F-scores for each class individually to ensure that the model accuracy is not limited to the majority class.We agree with the reviewer that these points are critical and have included the following text in the Methods (lines 635-638 and 652-654):“Predicting PPIs is challenging in part because of the inherent class imbalance in biological systems: the number of non-interacting pairs greatly outnumber true interactors. We tried to design a relevant task by modeling this class imbalance using a previously published estimate of the ratio of these classes …Our rationale in partitioning the entire dataset randomly, instead of independent partitioning for each interaction class, was to produce fluctuations in the number of positives and degree of class imbalance.”11) The comparison with Cong et al., might be potentially spectacular, but it is hard to understand it from the little paragraph. This should be explained better. One should also keep in mind that Cong et al., use an unsupervised approach as compared to the supervised in the present manuscript.et al., The new text can be found in lines 373-412:We agree. We have added a section in the Discussion to discuss a comparison between our results and those of Cong “Comparison of our results with AA CoevRecently, Cong and colleagues reported a method, AA Coev, for inferring direct PPIs from bacterial genome sequences. Their method represented a significant advance for two reasons: (i) it considered co-evolution at the resolution of amino acids and (ii) it applied Direct Coupling Analysis, to entire bacterial proteomes. […] We therefore pose that though SCALES does not consider as information-rich of a feature as AA Coev, it may prove to be a useful framework to extract hierarchical relationships for connecting bacterial genotype with phenotype.”12) The notation in Materials and methods requires revision. To give an example , n is the number of proteomes in the first paragraph, and the number of OGGs in the second. Please use consistent notations!We apologize for this error. We have revised the Methods section and now use consistent notations in the resubmitted manuscript. If the reviewers and referees find any more errors, please alert us and we will correct the Methods section immediately.13) Is Figure 1S2B really showing normalized columns? They appear optically to have very different variances, even if they all should be normalized to variance 1.We verified that this matrix is column normalized, however decided that this figure supplement was unnecessary and have removed it from the new version of the manuscript. The column-normalized matrix can be found in Figure 1-source data 1.14) The code should be made available.We agree. The code is publicly available and can be found at https://github.com/arjunsraman/Zaydman_et_alThis information is in lines 814-815 in the manuscript.Presentation:1) The paper is very hard to read and to understand. It is written in a semi-technical jargon mixing spectral analysis, machine learning and information theory. Even having expertise in these fields, we had to continuously jump between the main text, the methods and the figure  to follow the argumentation of the paper. This style is not suitable for a journal with a broad and interdisciplinary readership. The authors should make a serious effort to clean up their presentation, such that the main messages become accessible. Currently, even for disciplinary journals in computational biology or bioinformatics, the presentation would require simplifications.We deeply appreciate this feedback. In the resubmitted version, we have attempted to decrease jargon and focus on a single main message: extracting a hierarchy of PPIs from statistics of evolutionary variation. To this aim, we have rehauled the entire manuscript. This revision includes (i) rewriting the main text to appeal to a broader audience, (ii) reordering the main arguments of the paper, (iii) including three workflow figures  to explain analytical steps pictorially, and (iv) cutting material that was not salient to the main message of the paper. With respect to the latter, we have removed the entire section on domain-based analysis because in the re-written version, it felt unnecessary. We have also consolidated Supplemental Figures from the previous submission to focus on key ideas in the manuscript, decreasing the length of the manuscript from 86 pages to 60. We hope that the reviewer agrees we have taken their feedback seriously and these revisions have improved the readability and presentation of our manuscript.2) The general reader would benefit from an opening figure that clearly lays out the steps in the workflow starting with SVD  to random forest training. It can augment what is shown in the current figure 1 and one of the supplements to figure 2.We agree. We have included text describing SVD in a general way (lines 71-75):OGG using a technique called Singular Value Decomposition (SVD), a generalized form of Principal Components Analysis (PCA) . SVD defines a spectrum of components of covariation (an ‘SVD spectrum’) where component 1 (SVD1) explains more data-variance than any other component, SVD2 the second most, and so on .”“To explore the structure of extant bacterial variation, we analyzed D3) The abstract repeats 8 times the word "hierarchy" or "hierarchical". Avoid such excessive repetitions.We have edited the abstract to remove unnecessary repetitions. The abstract (lines 22-31) reads:Pseudomonas aeruginosa and using it to identify a protein that affects pilus-mediated motility. We anticipate that our method, SCALES , will be useful for interrogating genotype-phenotype relationships in bacteria.”“Cellular phenotypes emerge from layers of molecular interactions: proteins interact to form complexes, pathways, and phenotypes. We show that hierarchical networks of protein interactions can be extracted from the statistical pattern of proteome variation as measured across thousands of bacteria and that these networks reflect the emergence of complex bacterial phenotypes. We validate our results through gene-set enrichment analysis and comparison to existing experimentally-derived databases. We demonstrate the biological utility of our approach by creating a model of motility in 4) The introduction was a bit short in giving credit to previous efforts in this area. Yes, the founding papers from the 90s are cited, but there have been quite a number of studies in the meantime, including the use of SVD, reviewed for example here: Nagy et al., NAR 2020, https://doi.org/10.1093/nar/gkz1241 or Moi et al., PLoS computational biology 2020, 16 (7), e1007553We thank the reviewer for this point. We have revised the manuscript to acknowledge that this is an evolving field and have included additional relevant references including those cited by the reviewer. [Lines: 35-48]“Biochemical and genetic studies have illustrated that complex behaviors emerge from layers of protein interactions: proteins interact to form complexes, complexes interact to form pathways, and pathways interact to create phenotypes . Current strategies for identifying protein-protein interactions (PPIs) span both experiment and computation. Experimental methods are rapidly becoming more high-throughput and comprehensive . Computational methods based on statistical patterns of co-occurrence or co-proximity of functionally related genes first appeared shortly after publication of whole genome sequences . More recent efforts have advanced the state-of-the-art in computational methods by incorporating evolutionary models (phylogenomics), interaction models borrowed from statistical physics, or spectral methods borrowed from signal processing .”5) The results on motility are really nice. We suggest placing them much earlier in the paper, and do the more technical stuff with random forest etc. later. It could come directly after Figure 1C has been explained.We thank the reviewer for this suggestion which we believe has dramatically improved the presentation of our results. To this end, we have reconfigured the order of the manuscript and the figures. The result of a statistically derived hierarchy of PPIs describing bacterial motility is now Figure 2. Figure 3 is the experimental validation of our approach. Figure 4 describes the results of predicting PPIs using RF models. This reconfiguration of the paper serves not only to highlight the motility results earlier on, but also emphasize the main thrust of the study.Reviewer #1 (Recommendations for the authors):General Summary:While the authors have made clearly visible efforts to improve the presentation of their manuscript, the major problem remains: while the results are very interesting, the presentation of the technical details is cumbersome, and reading the paper without massive reference to the huge number of supplementary figures is hardly possible. I think another round of simplification is unavoidable.We appreciate the reviewer’s feedback on improving the presentation of our manuscript, specifically in regard to the need of referencing many supplemental figures while navigating main figures and text. In the resubmitted version, we made several changes to ensure that (i) the main figures reflected results as well as operational processes of how we arrived at the results and (ii) the supplemental figures were not critical for understanding key messages in the manuscript. Specific changes are listed below1. We remade Figure 1 to only show that shallow modes of variance are enriched for phylogenetic information.2. We made a new Figure 2 to describe our statistical workflow.3. What used to be a supplemental figure for showing that deep spectral components are enriched for physical PPIs is now Figure 3A and Figure 3B. These results are grouped together with the finding that deep to shallow spectral components collectively illustrate a progression of biological scale from phylogenetic to functional information .4. Figure 4 describes the process of computing spectral depth.5. What used to be a supplemental figure for describing how we create hierarchical graphs of protein interaction networks is now Figure 5.Together, the incorporation of supplemental figures from the previous version into main figures has demonstrably changed the flow of the manuscript with respect to needing reference to supplemental materials.I would like to make a number of more specific points:OGG and VOGG are used in methods but introduced only in Figure 1 Supp. 1. In addition, the left and right singular values are denoted equally as |n>, which is a bit confusing . In general, the authors should revise the paper such that the supplement gives supplementary information, and the paper can be read without having ~50 pages of supplement in your hands.1. The reading is impossible without the massive use of supplementary figures. To give one example (out of many), the singular vectors in UWe thank the reviewer for this helpful suggestion. We have reconfigured several of the figures as well as incorporated previous supplemental figures into main figures to address the reviewer’s comment and make our manuscript more accessible . In addition, we have attempted to further simplify text to make transitions easier to follow. Specifically, we have introduced simpler transition to help the reader connect between section of the manuscript. Importantly, all the matrices, including the input data matrix and those resulting from SVD, are now described in the main text, please see the specific description below.– In the section: ‘Global to ‘local’ patterns of bacterial covariation progressively reveal phylogeny, pathways, and protein complexes’, we have edited the first paragraph to read (lines 85-90):OGG output three separate matrices: bacterial projections onto left-singular vectors (UOGG), a set of singular values, and OGG projections onto right-singular vectors (VOGG) .”“We analyzed the SVD spectrum for information regarding (i) phylogenetic information, (ii) indirect interactions between proteins reflecting biological pathways, and (iii) direct  interactions between proteins reflecting protein complexes. The workflow for our analysis was as follows. SVD applied to D2. The method heavily relies on subjective hyperparameters and thresholds: For the number of singular values considered, for the bin size in the MI calculation, for the size of the spectral window, for the used cutoffs of the spectral depth.E. coli proteome and proteomes from organisms distantly related to E. coli. Regarding the reviewer’s specific concerns:We agree with the reviewer’s assessment. As our workflow is mostly statistical, several parameters and thresholds needed to be instantiated to conduct our analysis. However, whenever possible, we derived these parameters in a data-driven manner or performed some sensitivity analysis to show the robustness of the chosen parameter. In addition, once these parameters were set, no additional parameter tuning – i.e. the same set of parameter was used for motility and non-motility systems as well analysis of the – ‘For the number of singular values considered’:We considered the top 3000 singular values because singular values beyond this point were not significantly enriched for biological information compared to our random model. We have edited the text to reflect this point (line 116-117).“Beyond component 3000, the MI shared between protein spectral correlations and PPIs rapidly converged to the estimation of background MI.”– ‘for the bin size in the MI calculation’:Estimating the information content from a sample is practically difficult because we do not have access to the complete underlying distribution. This creates a tradeoff between a high-resolution bin size, capturing all entries of the distribution, and a low resolution bin size ensuring that all bins have more than one entry. We selected the bin width of 0.25 because it seemed to provide a balance. While we have not performed a formal sensitivity analysis on this parameter choice, we point out the following: (1) we did not adjust the bin size on a case-by-case basis and (2) the quantitative value of the MI estimate is not relevant to our conclusions, but rather the relative distribution of MI across the SVD spectrum. It is therefore unlikely that the choice of bin size will have a significant impact on our main findings.– ‘for the size of the spectral window’:The choice for size of the spectral window was not arbitrary. Rather, we performed a comprehensive analysis to find an optimal point that balanced resolution and signal detection, as described in Figure 4—figure supplement 1A-D. Importantly, once we decided on this window size, no further adjustment was made to this parameter. We have edited the text to clarify this point (lines 134-137).“Third, we removed spurious spectral correlations by developing a model of statistical significance. The model defined an optimal spectral window of 100 components for computing spectral correlations as well as a threshold for what constitutes ‘statistically significant’ spectral correlations .”– ‘for the used cutoffs of the spectral depth’:The depicted cutoffs for spectral depth were chosen to reflect areas of the SVD spectrum we found to be enriched for different types of biological information: 50 for the center of the shallowest 100-component spectral window, 300 for a window enriched for indirect PPI information, and 1000 for a window enriched for direct PPI information. We have edited the text to clarify this point (lines 163-166).“To depict the structure of spectral depths across all pairs of proteins, we thresholded spectral depth at three different levels: 50, 300, and 1000. These thresholds were chosen to reflect areas of the SVD spectrum found to be enriched for different types of biological information per Figure 3C.”Together with the somewhat anecdotal results (concentration mostly on motility), this gives the impression that the biological system and parameters are hand selected to show nicely interpretable results.In response to the reviewer’s point, we note a few important aspects:First, our statement that biological information is spread across the SVD spectrum  was based on a comprehensive interrogation of multiple different databases containing the same type of information: GO and STRING for indirect interactions, the PDB, ECOCYC and Coev+ for direct interactions. Our rationale behind using several databases was to ensure that our results were not specific to a single database or a single type of data.E. coli K12. Our motivation for pursuing these analyses was to ensure that our hierarchical networks were not a result of ‘overfitting’ to specifically directed motility in E. coli K12 using FliC as a query.Second, while we concentrated on motility to show that we could create a hierarchical protein interaction graph, we also presented several supplemental figures demonstrating that our results are robust across (i) query protein, (ii) organism, and (iii) specific pathway. In particular, Figure 6—figure supplement 4 illustrates that our approach defines a relevant hierarchical decomposition of amino acid metabolism in Pseudomonas aeruginosa, an organism unrelated to E. coli K12, within the context of a different type of motility thereby highlighting the generality of our approach.Third, we tested the predictive potential of our approach by conducting an experiment testing whether uncharacterized proteins could be characterized using our hierarchical models . These experiments were performed in ’ (lines 272-274):Finally, the last section of our paper addresses using spectral correlations to infer protein interactions across a diversity of sequenced bacteria. Using several types of analyses, we demonstrate that our approach for inferring interactions at different biological scales produces predictions that are superior to those of current methods. Our motivation behind performing this analysis was to enable interrogation of pathways and organisms that are not currently well studied. This motivation is emphasized in the first paragraph of the section ‘Using spectral correlations to predict proteome-wide functional and physical interaction networks“Microbiome science has taught us that diverse bacteria affect human and environmental health. Therefore, there is a critical need to expand our knowledge of biology more broadly beyond the few well-studied model organisms.”We would like to reemphasize that, while there are several parameters that had to be chosen, at no point in the manuscript did we adjust our parameters to optimize the results for a specific database, organism, or pathway. In addition, we deliberately challenged our methods by predicting results across diverse databases, organisms, and pathways to ensure that our parameter choices were robust and generalizable.I sincerely hope this is not the case, but if the authors would, e.g., show the tree generated by changing spectral depth from largest to smallest values, the different levels of organisation could become more evident (in case well-separated levels exist).E. coli K12 .We thank the reviewer for this suggestion. We find that changing spectral depth from largest to smallest thresholds reveals a continuum of organization. To make the above point clear, we have added a new supplemental figure showing spectral depths 225, 500, and 750 for directed motility in 3. In some cases, it is hard to understand if the results are significant. If one considers Figure 1E, even a uniform MI distribution would have a similar shape as the blue curves, since the cumulative would be linear, and represented with a log-scale of the spectral position.‘Calculation of MI cumulative distribution functions (cdfs) shown in Figure 3C'). The specific MI for a uniform distribution would be expected to be zero thereby giving a distinct CDF curve compared to those in Figure 3C. To further clarify the question of significance, we have created a new Figure 3 where panels A and B highlight the non-random nature of the MI between protein spectral correlations and whether two proteins physically interact. We have included text to clarify this point (lines 112-116):We thank the reviewer for this insightful question. We agree that the cumulative distribution function for a uniform MI distribution might have a similar shape. However, we clarify that the curves in Figure 1E  are the cumulative ‘specific’ MI, that is the cumulative difference between the MI produced by the data and that produced by a randomized matrix . Even SVD components 2996 through 3000 harboring 0.025% data-variance contain non-random biological information reflecting direct PPIs .”4. In some places, results imposed by the analysis are presented as astonishing findings. The most evident case is the hierarchical structure when changing spectral depth. Since spectral depth is defined as the depth where correlations are for the first time non-significant, the edge set of the graphs at higher spectral depth is necessarily proper subsets of those at lower spectral depth, and thus connected components are proper subsets, too. If all statistically significant correlations in each spectral window would have been taken into account, edges between proteins might disappear at some depth, and reappear at a deeper one, making the network potentially non-hierarchical.The reviewer brings up a very good point: our approach does not consider spectral correlations that are significant deeper than the spectral depth of correlation. Our approach to only consider the spectral depth of correlation was to enforce a hierarchy: our definition of spectral depth is predicated on the pair of proteins being significantly spectrally correlated at all windows shallower than the spectral depth. Our intention in making this choice was to see whether we could extract a hierarchy of interactions from the SVD spectrum through a defined process, not whether the SVD spectrum naturally provides a hierarchy of interactions. We highlight this point in two separate places in the text: lines (127-129) and lines (380-387):“Given the results shown in Figure 3, we hypothesized that by relating deep and shallow SVD components, we could create a statistical representation of emergence—the integration of local scales of protein interactions into global scales reflecting collective biological functions.”“Understanding the origins of complex biological functions requires defining hierarchical relationships describing how protein interactions integrate to create scales of biological organization. While the use of SVD is fundamental to our method, SVD itself does not define hierarchical relationships; SVD defines orthogonal components of variance ordered according to the amount of variance explained. Two results of our study were key for being able to use the SVD spectrum to produce hierarchical models. First, different components contain information regarding different biological scales. Second, the information in different components could be related by tracking the persistence of spectral correlations across components .”6. Heavy but somewhat random statements like "Understanding the molecular basis of a phenotype requires (i) defining interactions that create units of collective function at different biological scales and (ii) relating these scales to create a hierarchical model of emergent phenotype." should be avoided.We thank the reviewer for this comment. We have edited the manuscript to remove several such statements, with particular care given transitions from one section to another. These changes can be viewed in the document comparing the previously submitted version with the current resubmission.


Peptides are prevalent in biology, mediating as many as 40% of protein-protein interactions, and involved in other cellular functions such as transport and signaling. Their ability to bind with high specificity make them promising therapeutical agents with intermediate properties between small molecules and large biologics. Beyond their biological role, peptides can be programmed to self-assembly, and they are already being used for functions as diverse as oligonuclotide delivery, tissue regeneration or as drugs. However, the transient nature of their interactions has limited the number of structures and knowledge of binding affinities available–and their flexible nature has limited the success of computational pipelines that predict the structures and affinities of these molecules. Fortunately, recent advances in experimental and computational pipelines are creating new opportunities for this field. We are starting to see promising predictions of complex structures, thermodynamic and kinetic properties. We believe in the following years this will lead to robust rational peptide design pipelines with success similar to those applied for small molecule drug discovery. Computational modeling is routinely used in the early stages of the drug discovery process to identify molecules that might bind with high affinity to a particular protein receptor. Three key aspects that contribute to the success of computational tools are: 1) the availability of small molecule virtual libraries , 2) thePeptides are flexible molecules that can bind specifically to receptors even in the absence of pockets–targets that were once deemed undruggable by small molecule drugs . Our celn, where n is the length of the peptide) to thousands of sequences. But, dealing with peptide flexibility reduces the efficiency of both docking tools and scoring functions to predict accurate structures  (https://github.com/aqlaboratory/openfold) of these technologies. However, these are all focused on the structure prediction. What will we need to predict binding affinities or binding mechanisms? Approaches such as the one presented for MHC are only possible when enough existing data on binding affinities is known and are thus not directly transferable to all systems. Similar to the Protein Structure Initiative   and traiitiative , will thitiative ) lead toitiative  and CASPitiative  have spuitiative .Machine learning has already shown promising results for predicting peptide-protein interactions despite being trained for a different task–training for peptide binding will require increasing our structural and energetic understanding of these interactions. However, the transient nature of peptide-protein interactions has made it challenging to accumulate large datasets, both in terms of structures and binding free energies. Both are needed to develop computational software that predicts high affinity peptide binders . Two advd) but also the specificity of the binding region.The protein data bank  has an oin vivo and in vitro which are summarized in position binding motifs (PBMs) and compiled in databases such as TRANSFAC(d), and fast dissociation rates  and kinetic properties  , efficient sampling strategies, and computational cost . At thisnd koff) .With an increasing number of methods that capture thermodynamics, the question is whether or not they will become computationally feasible and routine to match the success of FEP calculations in small molecules. These types of methods could address some of the limitations that are prevalent in small chemical changes (single point mutations) and explicitly account for posttranslational modifications . FurtherRecent protein design work is already leveraging machine learning to hallucinate novel folds based on the idealized version of proteins learnt by the algorithms . FurtherPeptides have programmable self-assembly properties, while maintaining the ability to incorporate functional motifs recognized by other macromolecules. Fortunately, due to these properties, peptides are increasingly used for biomaterial design applications  . DespiteThe recent Sars-COV2 pandemic highlighted the need to account for post translational modifications (PTM). Yet, as modelers we are often faced with the challenge of knowing which and where these modifications occur, lack of parameters or datasets (machine learning) to model these modifications. This issue becomes accentuated for the transient interactions of interest in peptide-protein interactions. However, the community has shown a fast response and adaptation to model these systems. We believe going forward the community will collect more data on such PTM that will improve modeling efforts. For example, many of the peptide-protein experimental binding affinity assays already incorporate the ability to introduce such PTMs —and compWe are excited by the role that recent advances in a variety of areas can have in the field of peptide-protein structure and affinity prediction. Peptides can be of interest as single molecule therapeutics or as programmable molecules that aggregate to specific patterns creating scaffolds . In bothA particular field of interest where we see methods expanding their presence is in material bioengineering . Here, pThe rapid pace of advances in AI, coupled with increased computational power, access to larger and more curated databases and improvements in other computational modeling pipelines is changing many aspects of structural biology pipelines. We believe this presents an opportunity to advance our understanding of systems involving peptide molecules, where advances both experimental and computational have faced the challenges of working with such flexible molecules. Peptides already have multiple applications ranging from drugs, to nanodevices, or tissue regeneration to name a few. Developing robust computational pipelines to design and control the properties of these molecules will allow a rapid increase in the number of applications and uses of these molecules.