Computational methods to predict protein–protein interaction (PPI) typically segregate into sequence-based ‘bottom-up’ methods that infer properties from the characteristics of the individual protein sequences, or global ‘top-down’ methods that infer properties from the pattern of already known PPIs in the species of interest. However, a way to incorporate top-down insights into sequence-based bottom-up PPI prediction methods has been elusive. We thus introduce Topsy-Turvy, a method that newly synthesizes both views in a sequence-based, multi-scale, deep-learning model for PPI prediction. While Topsy-Turvy makes predictions using only sequence data, during the training phase it takes a transfer-learning approach by incorporating patterns from both global and molecular-level views of protein interaction. In a cross-species context, we show it achieves state-of-the-art performance, offering the ability to perform genome-scale, interpretable PPI prediction for non-model organisms with no existing experimental PPI data. In species with available experimental PPI data, we further present a Topsy-Turvy hybrid (TT-Hybrid) model which integrates Topsy-Turvy with a purely network-based model for link prediction that provides information about species-specific network rewiring. TT-Hybrid makes accurate predictions for both well- and sparsely-characterized proteins, outperforming both its constituent components as well as other state-of-the-art PPI prediction methods. Furthermore, running Topsy-Turvy and TT-Hybrid screens is feasible for whole genomes, and thus these methods scale to settings where other methods (e.g. AlphaFold-Multimer) might be infeasible. The generalizability, accuracy and genome-level scalability of Topsy-Turvy and TT-Hybrid unlocks a more comprehensive map of protein interaction and organization in both model and non-model organisms.https://topsyturvy.csail.mit.edu.Bioinformatics online. We focus on the problem of predicting PPIs from sequence data without the computational expense of multiple sequence alignments, thus enabling genome-scale predictions. Classically, the physical protein–protein interaction (PPI) prediction problem has been studied in two settings: one, where we only have access to each protein’s amino acid sequence and must determine from the sequence data alone if the two proteins bind e.g. .Our previous work introduced D-SCRIPT  and sequence-based (bottom-up) approaches to PPI prediction in the training phase of our sequence-based predictor. Topsy-Turvy introduces a multi-objective training framework that takes a pair of protein sequences as input, with the supervision provided by both experimentally determined PPIs (in the same manner as D-SCRIPT), as well as with global topological measures of protein pair compatibility. Importantly, it only requires protein sequences as inputs when making predictions—network information is used only during training. Since the trained Topsy-Turvy model makes predictions using just sequence data, it is particularly valuable in non-model organisms where almost no PPI data is available  we devise a hybrid model, TT-Hybrid, that is able to take advantage of species-specific network data. TT-Hybrid embodies a principled approach to combining the Topsy-Turvy sequence scores with GLIDE  whereas the D-SCRIPT algorithm showed that informative features generated by a protein language model enable transfer learning of the structural basis of interaction, we show that we can likewise transfer global patterns of PPI organization by integrating a topological compatibility score into the loss function. (ii) We approach the synthesis of bottom-up and top-down approaches as a multi-objective training problem that balances between structural and topological considerations when predicting PPIs. Except for the recent work of could also be predicted using global methods. We show that TT-Hybrid’s principled synthesis of the scores from the network-based GLIDE method  , 2021; nTo make top-down, network-based predictions of PPIs in a species, we use GLIDE , anotherGLIDE incorporates both local and global metrics into a single score in such a way that each metric is leveraged in the region of the network where it is most accurate. We use Common Weighted Normalized (CWN) as our local metric, and the inverse of the Diffusion State Distance  is a candidate protein pair and α and β as suggested by u term will be used.Following Topsy-Turvy retains the protein language model feature generation and convolutional neural net architecture of D-SCRIPT, with changes made to the training approach and loss function. To synthesize this model with link-based prediction, we introduce the additional task of predicting GLIDE scores between proteins, formulating it as an extra loss term in the objective. The entire model is then trained end-to-end.GLIDEL represents the loss when predicting GLIDE estimates and pg = 0, the function reduces to the original D-SCRIPT loss). To compute GLIDEL, we first generate GLIDE scores for every negative training example by computing the component p, q), the loss GLIDEL is defined asy is Topsy-Turvy’s predicted score for the protein pair . tg and then applying the standard BCE loss. For convenience, we define tg in terms of a percentile cutoff on the distribution of GLIDE scores  and do not follow a convenient closed form.In formulating The addition of the GLIDE loss term to the model training accounts for the observation that the original D-SCRIPT loss measures only pairwise interaction, and is unaware of global network structure. Since the GLIDE score of a protein pair takes into account local and global network properties, the GLIDE component of the loss should incorporate network-wide information into the predictions. Specifically, since D-SCRIPT prioritizes precision and is more likely to miss true interacting pairs than GLIDE, the absence of strong structural evidence of interaction could be supplemented by strong network evidence.p, q) being:During inference, Topsy-Turvy requires only protein sequences as input. When making predictions in a species where some PPI data is also available, predictions from pre-trained Topsy-Turvy (trained on data from another species) can be combined with GLIDE predictions informed by the target species’ PPI network. We note that these GLIDE scores are distinct from those corresponding to the training species; the latter were used only during training. To take advantage of the PPI network in the target species when available, we designed TT-Hybrid that can be applied on query protein-pairs where both GLIDE and Topsy-Turvy scores are available. We note that this requires both proteins of the queried pair to be present in the target species’ PPI network; otherwise, only Topsy-Turvy can be used. TT-Hybrid computes a weighted sum of Topsy-Turvy and GLIDE predictions for a query protein-pair, with the score for a protein pair . These pairs were labeled positive; negatively labeled pairs corresponded to random pairs of proteins from the subnetwork. The ratio of negative to positive examples was set to 10:1 to account for the inherent class imbalance in PPI data (see Section 3.2 for discussion). To avoid bias arising from data leakage, we also required that none of the examples occur in the original training data for Topsy-Turvy. We computed GLIDE and Topsy-Turvy scores for each protein pair, these methods having previously been trained on the rest of human PPI data. We then fitted a logistic regression model that sought to predict the label of a protein pair using its GLIDE and Topsy-Turvy score. The TT-Hybrid calibration weight pg (the relative weight of GLIDE versus binary cross-entropy loss) and tg (the binarization threshold for GLIDE scores) play a crucial role in Topsy-Turvy and we sought to estimate them from cross-validation runs on the human PPI dataset. We note that all Topsy-Turvy and TT-Hybrid results presented in this article are from models trained on human data but evaluated on out-of-sample, non-human data. To perform the hyperparameter search, we did cross-validation runs on the entire human PPI network, since GLIDE scores computed on smaller subnetworks might not be representative of the full network’s characteristics. Due to the computational expense of such runs, however, we modified the standard grid-search approach. Initial, small scale explorations suggested tg = 90 to be a promising choice. We first performed a grid search on pg, fixing tg to 90. This yielded tg, with pg fixed to this choice. The second search indicated The hyperparameters d choice  and we tt choice , and we d = 100, a hidden dimension of h = 50, a convolutional filter with width l = 9. Furthermore, we used We implemented Topsy-Turvy in PyTorch 1.2.0 and trained with a NVIDIA Tesla V100 with 32 GB of memory. Embeddings from the pre-trained Bepler and Berger model were produced by concatenating the final values of the output and all hidden layers. Apart from these pre-trained embeddings, Topsy-Turvy was trained end-to-end and did not use pre-trained D-SCRIPT model weights. However, we used the same hyperparameters as in is available and GLIDE would be applicable directly. We find that while GLIDE is broadly informative about the species-specific network rewiring, better performance can be achieved by TT-Hybrid, a combination of Topsy-Turvy and GLIDE.We start by presenting a comparative assessment of GLIDE and node2vec for PPI link prediction; the results of this analysis motivated our choice of GLIDE as the network-theoretic component of the Topsy-Turvy model. We next evaluate the cross-species generalizability of Topsy-Turvy, showing how incorporating network data during training results in superior performance in other species, using only sequence data for prediction. We note that in the typical cross-species setting, purely network-based methods like GLIDE are not applicable since they can only make predictions for pairs where both proteins exist in the training PPI network and hence cannot be applied to out-of-sample proteins. We therefore evaluated Topsy-Turvy against methods that require only sequence-based inputs (like D-SCRIPT), assessing if co-supervising Topsy-Turvy with topological information allows it to learn aspects of protein interaction that carry across species. As we show, it does, and in subsequent analyses we investigate various aspects of the comparison more deeply, also addressing the issue of ascertainment bias in the evaluation network. Lastly, we study how to best apply Topsy-Turvy in instances where PPI data Drosophila BioGRID network consisting of 3093 nodes and 25 427 edges. A certain fraction p. The dimension of the node2vec embedding was set to 300, i.e. approximately 10% of the node count . S.S. was supported by the National Science Foundation Graduate Research Fellowship [1745302].Conflict of Interest: none declared.btac258_Supplementary_DataClick here for additional data file.


Small proteins, encoded by small open reading frames, are only beginning to emerge with the current advancement of omics technology and bioinformatics. There is increasing evidence that small proteins play roles in diverse critical biological functions, such as adjusting cellular metabolism, regulating other protein activities, controlling cell cycles, and affecting disease physiology. In prokaryotes such as bacteria, the small proteins are largely unexplored for their sequence space and functional groups. For most bacterial species from a natural community, the sample cannot be easily isolated or cultured, and the bacterial peptides must be better characterized in a metagenomic manner. The bacterial peptides identified from metagenomic samples can not only enrich the pool of small proteins but can also reveal the community-specific microbe ecology information from a small protein perspective. In this study, metaBP  has been developed as a comprehensive toolkit to explore the small protein universe from metagenomic samples. It takes raw sequencing reads as input, performs protein-level meta-assembly, and computes bacterial peptide homolog groups with sample-specific mutations. The metaBP also integrates general protein annotation tools as well as our small protein-specific machine learning module metaBP-ML to construct a full landscape for bacterial peptides. The metaBP-ML shows advantages for discovering functions of bacterial peptides in a microbial community and increases the yields of annotations by up to five folds. The metaBP toolkit demonstrates its novelty in adopting the protein-level assembly to discover small proteins, integrating protein-clustering tool in a new and flexible environment of RBiotools, and presenting the first-time small protein landscape by metaBP-ML. Taken together, metaBP (and metaBP-ML) can profile functional bacterial peptides from metagenomic samples with potential diverse mutations, in order to depict a unique landscape of small proteins from a microbial community. Small proteins or peptides, translated from short open reading frames, largely exist in biological systems in both eukaryotes  and prokBacterial peptides are much harder to decompose and they annotate in a natural community. While detecting and testing a small gene can be difficult in a single organism, microbiome at community level brings additional challenges in the data complexity and sparsity for small protein detection, classification, and function annotation. Metagenomics from short gun sequencing provides information from the community-specific population to gene functions, but there haven’t been many previous efforts specifically focusing on the role of bacterial peptides from a natural community. The lack of detection power and poor analytical resolution indicate the limitation from both the computation and experiment. First, the peptides detection from mass spectrometry needs abundant input materials and suffers from large search spaces in an unbiased and untargeted scenario. It usually requires a confident database from reference genomes or from metagenomes. Poor annotation of small genes in reference genomes is also an obstacle of the direct detection from mass spectrometry. Even by combining multiple types of omics data, the false positives can still be high in small bacterial peptides detection . Second,In order to address the limitations from the nucleotide-level metagenomic assembly and the current shortages of small protein annotation from microbe communities, metaBP  has been developed as a comprehensive and user-friendly toolkit to explore the small protein universe in a more thorough and detailed way. The metaBP applies protein-level assembly from the metagenomic sequencing data to maximize the protein recovery and search from the open reading frames . The metThe metaBP is an integrated and automated toolkit for identifying and annotating small proteins from the metagenomic sequencing data. MetaBP’s implementation consists of three major modules , and five main procedures : proteinThe input data for metaBP is the raw sequencing reads (paired-end short gun sequencing) in a FASTQ format. The output data consists of mainly three parts of the information, protein clusters with mutations, small protein annotations, and a protein copy number table from annotations, which will be demonstrated in this study. For the purpose of this study, only the small protein analysis is mentioned and emphasized. In fact, the metaBP toolkit can also identify the entire proteome wide space of open reading frames, other than just small proteins.The raw FASTQ files used in this study are downloaded from NCBI SRA by the sra-toolkit. The sample IDs and general sequencing information are summarized in the supplementary table , with diRaw sequencing reads in FASTQ files are pre-processed by BBTools . The preThe assembled protein sequences are used in the clustering process. Linclust is one of the most recent protein clustering techniques that can approach both the good accuracy and linear time complexity . The metThe protein clustering by Linclust has two purposes: one is to remove the redundancy from proteins and protein fragments, and the other is to group protein families by homology for mutations. The protein sequences generated from the PLASS example dataset are duplicated to test the effects of truncated sequences. Each protein is truncated up to 50% of the total length from either beginning or end of the sequence, mixed with their intact versions, and then they are clustered by Linclust at different settings. When the default parameter for Linclust is applied, the sequences truncated to 90% of the original length can still be clustered with its full-length version, but sequences truncated to 80% of the length cannot be clustered well. When using the customized setting in Linclust and setting the coverage rate to 50%, most of the truncated protein can still be clustered with the original full-length protein . For smaThe strategy to isolate small proteins from metagenomics data is as follows. First, sequences with longer than 100 amino acids are separated. Second, short sequences clustered with long sequences are removed so that the protein fragments can be minimized in the final output. Third, in this study, only protein clusters with four or more protein members are considered as confident protein families. This means that the same small protein should occur at least four times in a single sample. In addition, only protein clusters with a large size can display a meaningful sequence diversity. On average, after these criteria are applied to the datasets, less than 5% from the metagenomics data are small bacteria peptides, which is consistent with the study from MAGs (metagenome-assembled genomes) or contigs .The database for small protein sequences (not more than 100 amino acids) is constructed from the sequence files in the FASTA format downloaded from the Uniprot  . In totaAs a transformer-based machine learning model inspired from natural language processing, ESM  is used After the database is constructed with vectorized small protein sequences, small proteins from metagenomic samples must be processed in the same ESM model . Each ofThe final protein annotation strategy based on the ten nearest neighbors is heuristic. First, rule of thumb is used if there is a most frequent annotation in the neighborhood. Second, if there is no difference between annotation frequencies, the top annotation is always picked. Third, if useful annotation cannot be extracted from the top ten neighbors, the protein will be left as unannotated.6 to represent the copy numbers per million proteins.In this study, the enzyme commission (EC) number and the taxonomy information will be provided in the small protein annotation. For simplicity of this research, protein copy numbers are used to quantify the abundance of every annotation so that different samples are compared. The protein copy numbers are added together from different clusters with the same annotation. The protein copy numbers can be normalized by the total number of small protein copies in the data set. The normalized protein copy number  for a certain annotation A is calculated with the following formula, where The metaBP is applied on various metagenomic data sets, including sixteen mice gut samples , one hump-value correction, none of the EC numbers are significant in the high-fat diet mice anymore. So, the EC numbers displayed in the heatmap are simply ranked by its original p-value (less than 5%). It is noticeable that the quantification pattern of these EC numbers from the human gut sample is more like the mice gut samples compared with the other samples. Human saliva samples do not have good yield of small proteins compared to the other samples.The analysis from mice samples shows interesting enzyme activities. In order to compare EC numbers across samples, only those ECs existing in all the samples are used in this analysis. First, the normalized counts of every EC number from mice samples are tested by ANOVA and the top ten important EC functions enriched in the high-fat diet of 12-week-old mice are presented in the heatmap . The comIn this study, 29 of the known short proteins derived from bacteria are searched from the metaBP output and only four of those are discovered in our samples . The UniBesides the search for the known 29 small genes, sixteen mice gut samples are used to systematically compare the annotation outcomes from eggNOG and metaBP-ML for small protein families. As known that not many small proteins have clear enzyme activities, EC number annotation overall has lower yields compared with the taxonomy (organism group) annotation, no matter by eggNOG or metaBP-ML.For the EC number annotation, metaBP-ML can annotate almost five times more proteins than eggNOG . Both meFor taxonomy annotation, metaBP-ML can annotate almost twice of the proteins than eggNOG . In ordeAs mentioned above, the entire small protein database composed of 3 million of short sequences are transformed into a 1,280-dimension vector space. In order to visualize the landscape within two dimensions, principal components analysis is performed, and the first two principal dimensions are shown in a dot plot . The colTo explore several interesting clusters identified in the mice gut samples, we pull out the protein cluster sequences from metaBP results and conduct further analyses. The clusters shown in this section are from the 12-week-old mice with a high-fat diet. One of the known small genes, senS, is widely discovered in the mice gut samples, and its sequence diversity is shown after the sequence alignment . The senAnother interesting cluster is from catalase EC1.11.1.6. The alignment of the sequences shows very few possible mutations are detected in the high-fat diet mice . The strThe metaBP adopts protein level assembly by PLASS, and therefore it is not constraint by the requirement of long contigs or high-quality MAGs from the nucleotide level assembly. As we know, low-abundant rare species may overall constitute a large amount of the sequencing reads in the complex metagenomic samples but may not yield long contigs. When the sequencing depth is low, more than half of the data could be wasted as unassembled sequencing reads. But for small proteins this fragmented sequencing data should already provide sufficient information for both the sequence and function. The metaBP together with metaBP-ML provide users with a complete toolkit to explore small proteins in natural metagenomic samples. For potential extension, the metaBP-ML does allow users to build their application specific models for protein annotation. In addition to metaBP-ML, we still provide eggNOG in the package to annotate proteins alternatively. In terms of the running time, eggNOG is more efficient with their pre-built reference database. The metaBP-ML is relatively taking more time when annotating proteins through vectorization and nearest neighbors. But due to our constructed small protein database, metaBP-ML can be very specific to identify and annotate small proteins. With the integration of both the tools, the metaBP can be used in various kinds of metagenomic data and annotate arbitrary protein classes.However, there are still concerns and limitations from the current version of metaBP. Clusters with singletons at this moment are not used for the downstream analysis in the current metaBP. We assume that only re-occurred sequences within the same cluster can indicate the reliability of small proteins and their mutations. Generally, high quality metagenomic data should be sufficient in the sequence depth. However, in many unexpected cases, metagenomic dataset can be sparse, and the clusters with lower number of protein members can also be informative for small proteins. Computationally, there has not been a perfect strategy to balance the false positives and false negatives without knowing the ground truth in the real data sets. But with the metaBP, we can at least provide a short list for the experimental detection through mass spectrometry and biochemical analysis.The metaBP quantify the annotated features using the normalized protein copy numbers. Due to the protein level assembly, the protein copy numbers are the most straightforward quantification obtained from the data set. Although metaBP can recover more annotations than eggNOG, the quantification may not be sufficient to statistically recover significant features when comparing the samples. One future direction is to improve the resolution of the quantification using the original sequencing reads. The metaBP also displays the protein diversity by homologous protein clustering, but the current metaBP cannot quantify the confidence level of each amino acid mutation. So, the current metaBP is only for the discovery of the potential sequence diversity in a protein family, not for the strict quantification of mutation occurrence.This study proposes a new and comprehensive toolkit, metaBP (and metaBP-ML), to discover and annotate the community specific bacterial (microbe derived) peptides from the metagenomic samples. It is built upon a new idea of direct protein level assembly and one of the current protein clustering tools, as well as machine learning based approaches. The exploration of the small protein landscape and the analyses of peptides annotation demonstrate the efficacy of this work and the value of machine learning.


Using a neural network to predict how green fluorescent proteins respond to genetic mutations illuminates properties that could help design new proteins. Related research article Gonzalez Somermeyer L, Fleiss A, Mishin AS, Bozhanova NG, Igolkina AA, Meiler J, Alaball Pujol M-E, Putintseva EV, Sarkisyan KS, Kondrashov FA. 2022. Heterogeneity of the GFP fitness landscape and data-driven protein design. eLife11:e75842. doi: 10.7554/eLife.75842.Protein engineering is a growing area of research in which scientists use a variety of methods to design new proteins that can perform certain functions. For instance, enzymes that can biodegrade plastics, materials inspired by spider silk, or antibodies to neutralize viruses .In the past, protein engineering has commonly relied on directed evolution, a laboratory procedure that mimics natural selection. This involves randomly mutating the genetic sequence of a naturally occurring protein to create multiple variants with slightly different amino acids. Various selection pressures are then applied to identify the ‘fittest’ variants that best carry out the desired role . AlternaNow, in eLife, Fyodor A Kondrashov (from the Institute of Science and Technology Austria and the Okinawa Institute of Science and Technology Graduate University) and colleagues – including Louisa Gonzalez Somermeyer as first author – have combined elements of both approaches to engineer new variants of naturally occurring green fluorescent proteins GFP; . First, Using this machine learning approach, Gonzalez Somermeyer et al. were able to design fluorescent proteins that differed from their closest natural relative by as many as 48 mutations. This is remarkable because in most protein mutagenesis experiments it only takes a few mutations before the function of the protein deteriorates. Evolution, on the other hand, can generate functional variants that differ by hundreds of mutations through a process of trial and error, which is akin to walking along a narrow ridge of high fitness one mutational step at a time. The neural network, however, appears to have jumped straight to a distant peak of high fitness . So, howTo answer this, Gonzalez Somermeyer et al. experimented with three GFP proteins that originated from evolutionarily distant species. They found that machine learning was better at generating functional variants of cgreGFP than its two homologues, amacGFP and ppluGFP2 . This allowed the team to look for properties within each protein’s genetic sequence and fitness landscape which correlated with its machine learning performance.Analysis of the fitness landscape revealed that the homologues differed in the number of mutations they could tolerate: it took on average three to four mutations until the fluorescence of cgreGFP and avGFP deteriorated, but seven to eight mutations were needed to compromise the function of amacGFP and ppluGFP2. The proteins also differed in their general sturdiness: ppluGFP2 was stable when exposed to high temperatures, whereas the structure of cgreGFP was more sensitive to changes in temperature.Finally, Gonzalez Somermeyer et al. found that the increased mutational sensitivity of avGFP and cgreGFP (and to a lesser degree ppluGFP2) was due to negative epistasis – that is, when an individual mutation is well tolerated, but has a negative effect on the protein’s function when combined with other mutations . The redIn order to generate functional variants, the network needs an opportunity to learn which properties of the fitness landscape are relevant from the data provided. The findings of Gonzalez Somermeyer et al. suggest that to predict a protein’s function, the algorithm only requires data on the effects of single-site mutations and low-order epistasis . This is good news for the protein engineering field as it suggests that prior knowledge of high-order interactions between large sets of mutations is not needed for protein design. Furthermore, it explains why the neural network is better at generating new variants of cgreGFP, which has a sharp fitness peak and high prevalence of epistasis.In sum, these experiments provide a successful case study in protein engineering. An interesting extension would be to analyse the three-dimensional structures of the variants using AlphaFold, an algorithm which can predict a protein’s structure based on its amino acid sequence . This wo


Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state. The topomer search model suggests that proteins “search” for their native state through an ensemble of possible conformations and that folding rate is determined by the ability of the protein to reach the topology of its native state2. This model emphasizes the importance of the 3-dimensional structure  of the native state. It is natural therefore to hypothesize that the more complex a native state is, the slower its conformation will be attained, and thus, slower the folding rate of the protein. In this manuscript, we use rigorous tools from topology to characterize the complexity of the native state (in the absence of knots), and examine the role of topology and geometry on protein folding rates.Proteins attain a specific conformation in space, called the native state, in order to perform their biological function. The process by which a protein attains its native state is called protein folding. Even though the mechanisms of protein folding remain largely unknown, it is possible to measure how fast a protein folds, the protein folding rate. Protein folding rates span many orders of magnitude22. One of the simplest characterizations of the native state is the number of sequence distant contacts, which is the number of sequence distant amino acids which are close in 3-space3. This quantity has shown one of the best correlations with experimental folding rates, suggesting that it captures something relevant to protein folding. Many studies have further explored this idea, showing that, in some cases, the N- to C- termini coupling is a major determinant of the protein folding rate23. However, it has been difficult to create a model of protein folding based on the number of sequence distant contacts alone. The number of contacts may in fact be a proxy for a more meaningful characteristic of a 3-dimensional conformation of a protein9.Many measures have been used to characterize the tertiary structure of the native state and its effect in protein folding24. Most efforts that aim at applying rigorous notions of topology to proteins, focus on identifying knots in proteins34. Proteins, however are not closed curves; by ignoring the chemical details and simply representing a protein by its CA atoms, the native state of a protein can be seen as an open ended polygonal curve in 3-space. Previous efforts to define knotting in proteins have relied on approximating the protein by a knot 40. This method was very successful and revealed that many proteins contain knots or slipknots , but it also showed that knotted or slipknotted proteins comprise less than 30. Using this method, the rest of the proteins, are all assigned a trivial topological characterization. However, the native states of the remaining proteins are not identical and their folding rates, even when comparing single domain two-state proteins, differ over many orders of magnitude. It is therefore necessary to find new ways to characterize the tertiary structure of proteins that bridge the notion of topological complexity continuously from unknotted to knotted states. A measure of complexity which does not require an artificial closure of the proteins to measure protein complexity is the Gauss linking integral. When applied over a protein or an arc of a protein, it gives the Writhe or the Average Crossing Number. It can also be used to study the linking between parts of a protein. These measures have shown strong correlation with protein folding rate and support the hypothesis that a more geometrically/topologically complex native structure leads to a lower folding rate43. However, the Writhe and the ACN are significantly affected by the local geometry of the protein and are not strong measures of topological complexity.A rigorous framework to define conformational complexity of curves is given in knot theory, which focuses on studying simple closed curves in 3-space (knots). Topological invariants are functions defined on closed curves which can classify them in different knot types44. We show that the second Vassiliev measure can be applied to proteins without artificial closure of the chains to quantify topological complexity (including knotting). It takes a non-trivial value for most proteins and reflects various subtle degrees of topological complexity, varying continuously from trivial to knotted topology. In contrast to the Writhe and ACN, this tool is not affected by secondary structure elements. We apply the Writhe, the Average Crossing Number (ACN) and the second Vassiliev measure to a set of two-state proteins  and a set of multi-state proteins (known to have well populated intermediates). Our results show that these measures capture different characteristics of the tertiary structure of the native state and that the folding rate depends both on the geometry and the topology of the native state, even for proteins without knots or slipknots.To decouple geometry from topology of proteins and capture topological effects in both knotted and unknotted proteins, with or without slipknots, we propose a new measure of the protein complexity; the second Vassiliev measure17. More precisely, single domain protein without disulfide bonds or covalently bound ligands were considered. For the multistate kinetics, the rate constants of the rate-limiting transition were considered, if the latter was not attributed solely to cis-trans proline isomerization. In addition, the experimental temperature was in the range, or could be reliably extrapolated, to 25C. Each protein was represented as a polygonal curve by connecting the consecutive alpha carbon atoms, CA atoms, with a line segment. The coordinates of the CA atoms were obtained from the Protein Data Bank (PDB)45.In this Section, we analyze the geometry and topology of a data set of two-state and multi-state proteins whose folding rates were reported inWr, and the Average Crossing Number, ACN, are derived from the Gauss linking integral and are very sensitive on the local geometry of proteins. The second Vassiliev measure, we denote 9, but it is difficult to decouple the role of topology from the role of geometry or the role of secondary structure elements.The Writhe, we denote To detect the effect of topology in protein folding, we propose using a stronger measure of topological complexity, the second Vassiliev measure, mentclass2pt{minimWr and ACN are measures of entanglement complexity of the protein, including secondary structure element effects. These can have different values on the same protein. Examples of unknotted proteins with similar ACN and Writhe values but different Both entclass1pt{minimaIn “30, while other studies show that 32% of proteins contain an “entangled motif” 46. Here we provide a simple measure of topological complexity that applies to practically all proteins to characterize their topological complexity.We analyze a set of proteins with no knots and no slipknots. Such proteins have been “invisible” by the common mathematical methods to characterize protein conformations. However, we find that 95.4% of the proteins analyzed in this study have non-zero value for the second Vassiliev measure. Putting this result in the context of previous studies, we note that by using the knot fingerprint method and the HOMFLYPT polynomial, it has been shown that less than 2% of proteins in the PDB contain a knotWe apply the second Vassiliev measure, as well as the Writhe and ACN on a set of multi-state and two-state proteins. We stress that these measures capture different conformational information. Figure 9. At a closer inspection, we see that the folding rate decreases with more negative Writhe values. This was also observed in9. This further corroborates the result that the Writhe captures some aspects of handedness related to folding rates, as well as secondary structure elements. In particular, we know that helices contribute a positive value of Writhe. In an effort to decouple the local secondary structure effect from the topology of the protein using the Writhe, the Writhe of the primitive path was introduced in9 and it was shown that the folding rate correlates better with the latter. Note that previous results have also showed a different impact on folding rate of local versus global properties of the protein47.Figure Figure The second Vassiliev Measure , the role of the topology of the 3-dimensional conformation of the entire protein in protein folding remains unclear. A reason why the role of topology in protein folding is elusive is that topological complexity has traditionally been associated with the presence of knots, but proteins with no knots or slipknots can have very different folding rates. In this manuscript, we rigorously show that folding rates depend on the mathematical topology of the native state, even for unknotted proteins. This is done using the second Vassiliev measure, a new measure of topological complexity of proteins that can characterize the topology of protein conformations continuously from trivial to knotted state. Our data show a moderate to strong correlation of the logarithm of the experimental folding rate with the second Vassiliev measure of the native state with lower folding rates associated to greater second Vassiliev measure.We also report the ACN and Writhe values for the proteins analyzed, which are measures of conformational complexity more sensitive on the local geometry of a protein. The ACN and the Writhe are affected by the secondary structure elements, with helical proteins giving higher values. The Writhe in particular can capture some aspects of handedness as well, since right-handed turns and helices contribute a positive value, while left-handed turns contribute a negative value. Even though these characteristics may be important in understanding folding mechanisms, they can hinder our understanding of the role of the global topology of the native state in protein folding. 50 and the topological complexity of a protein is expected to increase with its size. For this reason, we also report the normalized values of ACN, Wr and 51. For 2-state proteins, the folding rate shows a strong correlation with ACN than with 53. Note that the multi-state proteins attain higher The size of the proteins is a parameter already known to impact the protein folding rate10. However, in addition to correlation, it is important to establish causation. Our results show that the topology and geometry of the native state, as it is captured by rigorous and well understood mathematical tools from knot theory, should be accounted in a model of protein folding that is applicable to all proteins, with or without knots and slipknots.It is possible that many of the proposed measures together could provide better correlations with protein folding rateIn this Section, we give the definitions of the mathematical measures used to characterize the 3-dimensional conformation of proteins.54:The Writhe of a curve in 3-space is defined as the Gauss linking integral over the curveWr, is the double integral over l:For an oriented curve The Writhe measures how much the chain turns around itself. Taking into account the orientation of the curve (from start to end-point), given a projection of the curve, one can add up the number of crossings, with signs according to orientation and the convention shown in Fig. By taking the absolute value of the integrand, we obtain the Average Crossing Number. Namely,ACN, is the double integral over l:For an oriented curve The ACN is a positive real number that measures the average sum of crossings (without signs) over all possible projection directions.55. The Writhe and the ACN are continuous functions of the chain coordinates  for both closed and open curves.Both Writhe and ACN can be computed exactly, avoiding numerical integration, using the algorithm described in44 and is defined as follows:The second Vassiliev measure of open curves in 3-space was introduced inl with parametrization For an oriented curve The second Vassiliev measure of an open curve in 3-space is equal to the average of the algebraic sum of “alternating pairs” of crossings over all projection directions. Namely, for any given projection of the curve, an alternating pair of crossings, For closed curves, the second Vassiliev measure is a second Vassiliev invariant of knots and it is an integer topological invariant that can distinguish several knot types. For proteins, the second Vassiliev measure is a real number that is a continuous function of the chain coordinates in 3-space, and, if the protein ties a knot, it tends to the topological invariant of the knot. We note that the term “topology” in mathematics may be elusive for open curves in 3-space. It would be more accurate to use another term, such as “potential topology” for such curves. However, in this manuscript, we will use the term topological complexity, for all proteins, when Since d in Eq. . For opeSupplementary Figures.


In this study, we presented an AISID method extending AlphaFold-Multimer’s success in structure prediction towards identifying specific protein interactions with an optimized AISIDscore. The method was tested to identify the binding proteins in 18 human TNFSF (Tumor Necrosis Factor superfamily) members for each of 27 human TNFRSF (TNF receptor superfamily) members. For each TNFRSF member, we ranked the AISIDscore among the 18 TNFSF members. The correct pairing resulted in the highest AISIDscore for 13 out of 24 TNFRSF members which have known interactions with TNFSF members. Out of the 33 correct pairing between TNFSF and TNFRSF members, 28 pairs could be found in the top five (including 25 pairs in the top three) seats in the AISIDscore ranking. Surprisingly, the specific interactions between TNFSF10  and its decoy receptors DcR1 and DcR2 gave the highest AISIDscore in the list, while the structures of DcR1 and DcR2 are unknown. The data strongly suggests that AlphaFold-Multimer might be a useful computational screening tool to find novel specific protein bindings. This AISID method may have broad applications in protein biochemistry, extending the application of AlphaFold far beyond structure predictions. Over the last several decades, various algorithms have been developed to model unknown structures based on the information deposited at the Protein Data Bank (PDB). The AphaFold2 is an Artificial Intelligent (AI) program that utilizes deep learning to perform protein structure prediction , which dWhile precise atomic structures of protein complexes could provide insight of the detailed static interactions, identifying novel specific protein interactions may have a broader interest in protein characterizations. To identify the possible binding partner for a bait protein from a long list of protein candidates, it would be very helpful that a computational screening method can quickly predict binding potentials and prioritize the candidates for further biochemical assays. Such a method could revolutionize the protein characterization process. In this study, we presented an AI-based protein interaction screening and identification (AISID) method extending AlphaFold-Multimer’s success in structure prediction towards identifying specific protein interactions.To predict a heterodimer protein complex structure, the AlphaFold-Multimer generates 25 (by default) complex structure models with a model confidence value for assessing the quality of each model. We derive a metric score (denoted as AISIDscore hereafter) from the model confidence values, and the AISIDscore is optimized for assessing binding potentials between the protein pairs. We hypothesize that the AISIDscore can serve as a quality indicator to evaluate the binding potential between the protein pair. In the computational screening, a bait protein and a panel of protein ligand candidates can be input into the AlphaFold-Multimer for calculations. A higher AISIDscore might indicate the higher likelihood of specific binding between the bait and the protein ligand.To test our method, 27 human TNFRSF members and 18 human TNFSF members were utilized. In all, 24 TNFRSF members out of the 27 can specifically bind at least one of the 18 TNFSF members as documented by the Uniprot database . The speD of ~1nM. DcR1 and DcR2 do not interact with other TNFSF members [D of ~5 nM [It is of great interest to examine the ability of AISID for specific interactions between proteins with unknown structures. The TNFRSF members TNFRSF10C and TNFRSF10D (TRAIL DcR1 and TRAIL DcR2) can interact specifically with their ligand TNFSF10 (TRAIL), while their structural information is missing. Surprisingly, the pairing between the DcR1 and DcR2 and their ligand TRAIL gave the highest AISIDscore in the list A,B. Bioc members ,19. In aof ~5 nM . TherefoAs a positive control, we took advantage of a nanobody that can specifically bind TNFα . The proIt is worth noting that a relatively high sequence homology exists in TNFRSF and TNFSF family members. For example, the TNFα and TRAIL share ~25% sequence identity and ~60% sequence similarity. Our data indicate that the AISID method can reveal the specific interactions even among the highly homologous TNFSF family members. It is highly likely that the AISID may greatly speed up the screening for unknown specific protein bindings by prioritizing a long list of potential binding partners. The AISID-guided biochemical assay may follow to confirm the bindings.Many protein interactions are mediated by intrinsic disordered proteins (IDP). Some IDPs have been showed to undergo a disorder-to-order transition upon recognizing their physiological partners . Trying The detailed atomic structure of predicted complex model is not the focus of AISID screening. It is structure-blind, and no other prior biological information, except only a pair of protein sequences, are needed for calculating the AISIDscore. Users will not need to examine the accuracy of the model complex structures, which makes the method user-friendly for people working in wet lab.The presented AISID method may have significant biological impact in general biochemistry and cell biology. To characterize a protein with unknown functions, it is important to identify its binding partners. Using the traditional methods such as a yeast two hybrid system has been shown to be problematic and time-consuming. The AISID method may provide a fast alternative to identify the possible binding partner for a bait protein from a long list of protein candidates. Our method offers an AISIDscore which quantitatively measures the likelihood for a particular protein-protein interaction. The data showed that the AISIDscore was accurate in revealing specific protein interactions even among highly homologous proteins. Such a method may revolutionize how protein interactions are characterized.https://github.com/deepmind/alphafold, accessed on 18 March 2022) recently released by DeepMind which extends the AlphaFold2 to multiple chains during both training and inference with native support for multiple-chain featurization and symmetry handling, surpassing those of inference-only modifications to the AlphaFold2.In this presented AISID method for specific protein bindings screening, the AlphaFold-Multimer  was usedWhen used in complex structure prediction, the AlphaFold-Multimer generates a merit index, the model confidence, defined as a weighted combination of ipTM and pTM:Here, ‘avp’ is the averaged percentage pLDDT  score ofThe sequence of the bait protein to be investigated, and each sequence from the list of candidate proteins to be screened, are used to create a composite sequence file as input to the AlphaFold-Multimer for heterodimer complex structure predictions. As computing time of a prediction job heavily depends on the size of sequence, the list of composite sequence files is sorted by the number of amino acid residues from small to large. The sorting helps optimize the project production cycle (not the machine time of a prediction job), especially when carrying out a large screening project on a server with limited computing nodes and/or the candidate proteins are quite different in sizes. Batch jobs with inputs from the sorted list of composite sequence files are submitted through a load-balanced scheduler to the computer server running the AlphaFold-Multimer. Each of the composite sequence file will instruct the AlphaFold-Multimer to generate 25 (by default) predicted heterodimer complex structure models. The AISIDscore is then derived for the pair from harvesting and analyzing the outputs. Upon the finish of the screening project, a list of AISIDsocres will be generated, each for one bait-ligand pair.For proof of concept, we picked 29 bait proteins including 27 human TNFRSF (tumor necrosis factor receptor superfamily) member proteins, a TNFα nanobody as positive control, and protein Hsp40 Hdj1 as negative control. The 18 human TNFSF (tumor necrosis factor superfamily) member proteins are used as the ligand proteins to be screened. Human TNFRSF and TNFSF are two of the well-studied protein superfamilies with many known specific bindings, which is good for methods validation and evaluation. The AISID screening focuses on finding the potential specific binding proteins, not the detailed atomic structure of the predicted complex models. The sequences of bait and ligand proteins are the only inputs to the AlphaFold-Multimer for calculating the the AISIDscores. No other prior biological information is needed. For routine uses, one simply needs to examine the AISIDscore in search for the potential specific binding protein(s). The workflow diagram of a typical screening project is summarized in In our test sets, 27 human TNFRSF members and 18 human TNFSF members were utilized. The specific interactions between TNFRSF members and TNFSF members have been extensively studied. Relatively high sequence homologues exist among TNFRSF members and TNFSF member, while each TNFRSF member can specifically bind TNFSF members to initiate distinct signaling pathways. The interaction network constituted by TNFRSF and TNFSF members provide us with an excellent database to investigate the AISID method for revealing specific protein bindings. We reason that this small but very well-informed database may be ideal for testing our method. Our results showed that out of the 33 correct pairings between TNFRSF and TNFSF members, 25 pairs can be found in the top three seats of the AISIDscore rankings .The data in this study strongly suggest that the AISID method has the capability to identify novel protein interactions. It may greatly speed up the screening for unknown specific protein bindings by prioritizing a long list of potential binding partners. The AISID method may have broad applications for protein characterizations in protein biochemistry, extending the application of the AlphaFold far beyond structure predictions.


CTLA4 receptor is an immune checkpoint involved in the downregulation of T cells. Polymorphisms in this gene have been found to be associated with different diseases like rheumatoid arthritis, autosomal dominant immune dysregulation syndrome, juvenile idiopathic arthritis and autoimmune Addison's disease. Therefore, the identification of polymorphisms that have an effect on the structure and function of CTLA4 gene is important. Here we identified the most damaging missense or non-synonymous SNPs (nsSNPs) that might be crucial for the structure and function of CTLA4 using different bioinformatics tools. These in silico tools included SIFT, PROVEAN, PhD-SNP, PolyPhen-2 followed by MutPred2, I-Mutant 2.0 and ConSurf. The protein structures were predicted using Phyre2 and I-TASSER, while the gene–gene interactions were predicted by GeneMANIA and STRING. Our study identified three damaging missense SNPs rs1553657429, rs1559591863 and rs778534474 in coding region of CTLA4 gene. Among these SNPs the rs1553657429 showed a loss of potential phosphorylation site and was found to be highly conserved. The prediction of gene–gene interaction showed the interaction of CTlA4 with other genes and its importance in different pathways. This investigation of damaging nsSNPs can be considered in future while studying CTLA4 related diseases and can be of great importance in precision medicine.The  Non-synonymous SNP (nsSNPs) /missense SNPs residing in the coding region are very crucial and accounts for residual change which may have neutral or deleterious effect on protein3. These variations may account for some damaging effects i.e. protein structure destabilization, aberrant gene regulation4, alteration in protein hydrophobicity, proteins charge disturbance, change in protein geometry5, dynamics, translation, protein–protein interactions7 and loss of protein integrity8.The human genome possesses various types of variation, but the amplest among these variations are single nucleotide polymorphisms (SNPs). There are roughly about 3–10 million SNPs which comprises almost 1% of the whole genome11. Analysis of PTPN22 identified missense mutation (R620W), which shows association with different autoimmune diseases including diabetes type 112. Another study indicates missense mutation (Y402H) in CFH, increased the macular degeneration susceptibility13.Missense mutations are responsible for almost 50% of the entire DNA mutations, associated with genetic diseases including inflammatory and autoimmune diseases either as causative or susceptibility factorsABCA1 polymorphism revealed association with familial hypoalphalipoproteinemia and tangier disease14. Another study investigated the association of CYP27B1 polymorphism with vitamin D deficiency15. Similarly, various other studies have used insilico tools to establish the role of nsSNPs in other human diseases such as mental disorders16 congenital cataracts17, rheumatoid arthritis18, steroid resistant nephrotic Syndrome19 and breast cancer20.A significant number of studies have used insilico tools to predict the structural and functional impact of nsSNPs on different proteins. For instance, a study on CTLA4 has not been conducted before. Human CTLA4 is a receptor protein that belongs to immunoglobulin superfamily and is mainly expressed on activated T-cells. It functions as a negative regulator of T cells and competes with CD28 for binding with B7-1(CD-80) and B7-2 (CD-86) ligand present on the surface of Antigen Presenting Cells (APCs). It directly inhibits the T cells mediated immune response and blocks CD28 signaling which further leads to inhibition of T cells interaction with APCs22. The non-synonymous mutations in CTLA4 gene might disturb its interaction with its ligands and can lead to autoimmune diseases and cancer. Therefore, studying the effect of nsSNPs on its structure and function is crucial for establishing its role in different diseases.The computational analysis of damaging nsSNPs of CTLA4. CTLA4 (Cytotoxic T-lymphocyte-associated protein 4) also called CD152, encoded by CTLA4 gene in human located at chromosome 2q33.2. It is a 223 amino acids long protein which belong to immunoglobulin family, having three exons encoding V like domain, hydrophobic putative transmembrane and putative cytoplasmic domain24. CTLA4 act as an immune checkpoint, and downregulate T lymphocytes after CD80 or 86 attachment with it, evident from CTLA4 deficient mouse25, and can lead to elevated level of blast cells and their infiltration to heart, lung, and pancreas tissue26. Different studies proposed association of CTLA4 with rheumatoid arthritis (RA)27, autosomal dominant immune dysregulation syndrome28, juvenile idiopathic arthritis29 autoimmune Addison's disease (AAD)30 and Breast cancer31. Therefore, it is vital to analyze the potential damaging effect of nsSNPs on CTLA4. The most deleterious nsSNPs in CTLA4 and their functional consequences have been predicted in this work by means of various in silico tools. The 3D model of wild type and its mutants have also been anticipated and the comparison is carried out to explore the diversion between wild and mutants resulting from nsSNPs. This is the first computational analysis of the CTLA4 which predicts the deleterious effect of potential nsSNPs on structure, stability, protein–protein interaction and post translational modification of this protein using different publicly available computational tools. In future this study might be helpful for studying CTLA4 associated diseases.The current study investigates the structural and functional influence of nsSNPs on CTLA4 gene. Out of total SNPs, 945 were in intronic region, 111 were missense, 71 were found to be synonymous, 36 located in 5’UTR, while 294 were present in 3’UTR region and the remaining SNPs were . Only the missense or nsSNPs were selected for further in silico analysis. The detailed information of all nsSNPs is given in Table The dbSNP provided a total of 1835 SNPs in All the nsSNPs obtained were subjected to four different computational tools to investigate their effect on the structure and function of CTLA4 protein. The different tools used were SIFT, PROVEAN, PolyPhen-2, and PhD‐SNP. A TI (Tolerance Index) threshold of 0.05 was taken for SIFT and the results having values less than the threshold were considered to be affected. SIFT identified 33 nsSNPs to be affected. For PROVEAN a value of − 2.5 cut off was considered as threshold and the nsSNPs having score below this value were considered deleterious. PROVEAN filtered a total of 23 nsSNPs to be deleterious. PhD‐SNP resulted in 38 SNPs to be diseased. The nsSNPs that were found damaging by all the three tools were further submitted to PolyPhen-2. Out of total SNPs submitted to above mentioned tools, 8 were found to be damaging by all the tools and were shortlisted for further analysis. The results of all the computational tools are summarized in Table All the shortlisted 8 damaging nsSNPs were submitted to MutPred for predicting the impact of nsSNPs on CTLA4 protein structure and function. The probability scores of nsSNPs are given in the Table The function of a protein is associated with its stability that’s why it is important to identify the change in stability of protein due to nsSNPs. Mutant 2.0 predicted to what extent the damaging nsSNPs alter the stability of CTLA4 protein. The nsSNPs were submitted one by one and RI and DDG values were obtained. It was predicted that all of the damaging nsSNPs decrease the stability of CTLA4 protein except P137L. Three of the most damaging nsSNPs having highest RI values  may be involved in causing greater damage to CTLA4 protein stability. The prediction of changes in stability of CTLA4 are given in Table The damaging nsSNPs located in a highly conserved region can have more effect on protein structure and function as compared to damaging nsSNPs that are present in a region that is less conserved. The conservation profiles of CTLA4 amino acids were analyzed by ConSurf. The results provided by ConSurf are given in Fig. CTLA4 and 8 of its mutants were predicted by Phyre2. The Phyre2 results were incomplete as it predicted structure for only 118 amino acids (53% Coverage) out of 223 total amino acids. The wild type CTLA4 and the mutants were then submitted to I-TASSER which is a more advance and reliable modeling tool. It predicted 5 models for CTLA4 protein and each of its mutant. The models with the highest C value were selected for further analysis. The protein models were also subjected to three different protein structure validation tools . For wild type CTLA4 the ERRAT calculated the overall quality factor as 57.672 whereas ProSA Web and MolProbity predicted − 3.49 Z-Score and 3.816 MolProbity score respectively which suggests that the protein structure was of good quality. The finalized 3 mutant models were also validated with the above-mentioned tools and the results showed Z-Score, overall quality factor and MolProbity Score for P137L , G146L  and P209R  respectively. The protein structures were further refined with Galaxy Web. The predicted protein models were then compared using TM-Align to obtain TM-scores and RMSD values. The TM-score gives information about topological similarities between two proteins and RMSD values shows the average distance between backbone atoms of wild type and mutant proteins. The mutant with high RMSD value indicates greater deviation from its wild type. The mutant model for P137L (rs1553657429), P209R (rs778534474), G146L (rs1559591863), and P138T (rs1553657430) showed highest variation with RMSD values of 4.18, 3.73, 3.65, and 3.61 respectively. N145S and T147A showed RMSD values of 3.33 and 3.32 while R70W and G118R showed the lowest values of 3.0 and 2.49. Table The 3D structures of wild type The results of Post translational modifications (PTMs) sites predicted by using different tools are discussed below.CTLA4, GPS‐MSP 3.0 was used, and no methylation sites were predicted.For the prediction of potential methylated sites in CTLA4 predicted by ModPred and NetPhos 3.1 are mentioned in Table The phosphorylated sites in Potential glycosylated sites were found by N-Glyde and NetOGlyc4.0. N-Glyde predicted 2 sites 113 and 145 with scores 0.732072 and 0.9271713 respectively, to be N glycosylated while NetOGlyc4.0 predicted no site to be glycosylated. N-Glyde also predicted that mutant N145S and T147A showed loss of N-glycosylation at position 145. The results are given in Table UbPred predicted 3 residues in CTLA4 capable of ubiquitination while BDM-PUB predicted 5 residues to get ubiquitinated and mutant R70W showed loss of ubiquitination at position 65. None of these ubiquitylation sites predicted were at deleterious SNPs regions. The results obtained from BDM-PUB and UbPred are given in Table CTLA4 with other genes inside the cell GeneMANIA and STRING were used. Results obtained from STRING are given in Table CTLA4 with CD80, CD86, AP2M1, JAK2, STAT5A, STAT5B, PTPN11 and FYN. The genes that were predicted to be co-expressed with CTLA4 are CD5, CXCL9, GPR132, CD200, CTSZ, JAK2 and FYN. In pathways it showed relation with CD86, PTPN11, CD80, FOXP3, CD28, PTPN7, PTPN6, and NFATC2. Co-localization was found with STAT5B, CD86, FYN, STAT5A, PLA2G2D, CD28, GPR132, CD4 CXCL9, CTSZ, PTPN6 and NFATC2. The proteins that were predicted to share domain with CTLA4 are CD28, CD80 and CD86. Predictions made by GeneMania and STRING are given in Figs. For the prediction of interaction of The function of a protein is determined by the tertiary structure and therefore any modification in the amino acid sequence of that protein can have the potential to change the structure of protein and lead to disease. Bioinformatics analysis gives us the opportunity to predict the structural and functional effects of single nucleotide polymorphisms on a protein using different tools and algorithms. However, the sophistication of these algorithms is completely dependent on raw experimental data. The inauthentic and inaccurate raw data can lead to incorrect downstream structural and functional analysis. Therefore, it is suggested to use multiple tools and draw a consensus by comparing the results obtained from these tools. Furthermore, the bioinformatics results should be validated in the laboratory through different in-vitro and in-vivo experiments.CTLA4 polymorphism with various diseases. The association of CTLA4 polymorphism has been established with various autoimmune diseases like rheumatoid arthritis33, type 1 diabetes35, and multiple sclerosis37 and also different cancers such as breast cancer39, colorectal cancer41, lung cancer43, and cervical cancer45.Different studies have investigated the role of CTLA4 revealed that rs606231422 at position R70W and rs1553657429 at position P137L were found highly conserved and exposed while rs1553657430 and rs1466152724 at positions P138T and T147A respectively were found to be highly conserved and buried. The rest of the SNPs were only found buried or exposed and not very conserved. The mutation in buried resides of protein can affect the structural integrity of the protein whereas the polymorphism in exposed resides may alter the protein function46. The structure of CTLA4 and its mutants were predicted via I-TASSER. The nsSNPs directly influence the structure and hence function of a protein therefore, the effect of nsSNPs on structure of CTLA4 was assessed47. It was observed that the predicted mutant structures of CTLA4 have significantly distinguished RMSD values than the wild type and may compromise the structural integrity of the protein47.In the present study a total of 1835 SNPs were obtained from dbSNP out of which 111 non-synonymous or missense SNPs were subjected to different in silico tools including SIFT, PROVEAN, Polyphen2, and PhD‐SNP. These in silico tools predicted 8 SNPs to be damaging while other were found to be neutral. The damaging SNPs were subjected to further computational analysis to investigate their effect on protein structure and function. All these SNPs decreased protein stability as predicted by Mutant 22.0 except P137L. The amino acids that are directly involved in biological processes tend to be more conserved and thus changes in these amino acids will significantly affect the function of protein . The conservation analysis for 48. Similarly, N-Glyde showed that mutant N145S and T147A resulted in loss of N-glycosylation at position 145 which is the site of another most damaging SNP that’s why a loss of glycosylation at position 145 is important.For PTMs predictions of our protein different in silico tools were used. Phosphorylation is an important PTM which can activate or deactivate a protein by changing its structural conformation. The NetPhos result showed that mutant P137L and P138T have lost a phosphorylation site at position 40 and T147A lost a phosphorylation site at position 147 and gained phosphorylation site at position 150. As T147 is one of the most damaging nsSNP predicted in this study and was also found to be highly conserved and buried, that’s why a loss of phosphorylation at this site can be very significant for protein structure and function. The mutations that leads to the abolishing of a phosphorylation site can cause a direct deleterious effect on proteinThe gene–gene interaction was performed to identify the interacting partners of CTLA4 protein. The mutation analysis performed in the present study is important in this regard as mutation especially in ligand binding domains and motifs can disrupt the interaction of CTLA4 with its interacting proteins such as CD80, and CD86 which can lead to various disease conditions.50.The domain analysis of the CTLA4 protein was performed to check the location of the predicted mutations in different domains of CTLA4. It was found that two of the predicted mutations  were found to be in Immunoglobulin V-set domain, while the third mutation site (P209R) was in cytoplasmic domain. The mutations in the Immunoglobulin V-set domain can alter the binding affinity of CTLA4 with CD80 and CD80 that are involve in the negative regulation of T-cells whereas, the polymorphism lied in the cytoplasmic domain may affect the binding of multiple proteins i.e., PI3K, lipid kinase phosphatidylinositol 3-kinase (PI3K), the phosphatases SH2 domain containing protein tyrosine phosphatases (SHP-2), the serine threonine phosphatase PP2A and clathrin adaptor proteins activator protein1 (AP-1) and AP-2 may results in cancer developmentCTLA4 identified in the current study are unique and their association with human diseases have not been assessed in wet lab experiments. It is evident from this insilico analysis that these nsSNPs have resulted in lower stability of CTLA4 protein in comparison with their wild type protein. Moreover, the mutant proteins deviated in structure and showed loss of potential PTMs sites. It has been established that CTLA4 is a negative regulator of T cells and inhibit immune responses by interacting with CD80 and CD8622. The proper interaction of CTLA4 with its ligand is very crucial for its immune inhibitory function. Analysis of mutations especially in the ligand binding domain of CTLA4 protein can disrupt its interaction with ligands which can lead to various autoimmune diseases and also cancer.The three nsSNPs in CTLA4 which can potentially disrupt ligand-receptor interactions. However, further in-vitro and in-vivo studies are required to investigate and establish the role of these nsSNPs in different diseases. Moreover, Molecular Dynamics (MD) simulation analysis of the proteins predicted is required to study the stability and structural flexibility of predicted wild-type and mutant proteins in dynamic environment.The current study predicted high-risk SNPs in A schematic flowchart of complete methodology is given in Fig. https://www.ncbi.nlm.nih.gov/snp/)  database was used to retrieve all the SNPs of CTLA4 gene. The identification number (rsIDs) of nsSNPs were obtained from NCBI and protein sequence of CTLA4 in FASTA format was retrieved from UniProt (https://www.uniprot.org) Only the missense or non-synonymous SNPs (nsSNPs) were selected for further in silico study.The NCBI dbSNP 52, and PhD‐SNP (Predictor of human Deleterious SNP)53. The damaging nsSNPs found by these in silico tools were then submitted to PolyPhen2 (Polymorphism Phenotyping 2)54. The protein sequence in FASTA format and details of amino acids substitutions were used as input data for PolyPhen2.After retrieving the nsSNPs and protein sequence, the functionally damaging nsSNPs were predicted using different in silico tools including, SIFT (Sorting Intolerant From Tolerant)55. It is a web application which predicts the pathogenicity of amino acid change in a protein. The sequence of CTLA4 protein was submitted in FASTA format to MutPred 2 along with the information of amino acid substitutions. The p- value less than 0.05 (p < 0.05) was taken as “Confident” and less than 0.01 (p < 0.01) as “Very Confident”.To analyze the structural and functional effect of nsSNPs on CTLA4 protein, MutPred2 was usedCTLA4 gene was submitted at 25 °C with pH = 7.0. It gives result in the form of RI (Reliability index) with the values ranging from 0 to 10 (0 showing lowest and 10 showing highest reliability)56.To study the influence of all the damaging nsSNPs on the stability of CTLA4 protein, I‐Mutant 2.0 was used. It is an online tool based on support vector machines (SVM) which predicts the extent to which a mutation affects a protein stability. The protein sequence of 57. FASTA sequence of CTLA4 was submitted as input option. The nsNSPs that were identified as highly conserved were further analyzed.ConSurf server was used for the prediction of the effect of nsSNPs on amino acids that are evolutionary conserved in CTLA4. ConSurf predicts the conserved amino acids in each protein by analyzing phylogenetic relation among homologous sequences using an empirical Bayesian inference and gives conservation scores ranging from 1 to 958. The wild type CTLA4 and selected mutant proteins were then submitted to I-TASSER59 for remodeling. The I-TASSER predicted top five protein structures for wild type and all the mutants using fold recognition or threading approach. Among the top 5 predicted models the best models were selected for further study. After that the wild type and all the mutant models were compared using an online structure alignment tool called TM-Align which provides TM scores (Template Modelling score) and RMSD (root‐mean‐square deviation) values. The values of TM score ranges from 0 to 1, and 1 means the two proteins are perfectly matching. The higher RMSD means high structure variations between mutant and wild‐type and vice versa60. Three mutants with high RMSD values were selected and further analyzed using Chimera V1.1461.The 3D models for native and mutant  CTLA4 gene were predicted using Phyre2 . It is an online tool which predicts 3D models for protein based on principles of homology modeling62. For the prediction of phosphorylation at serine, threonine and tyrosine sites in CTLA4, ModPred63 and NetPhos3.1 was used. For NetPhos 3.1 the threshold was set to 0.5 and the amino acids having values higher than the threshold were predicted to be phosphorylated64. The potential glycosylation sites in CTLA4 were predicted by NetOglyc4.065 and N-Glyde. For N-Glyde the residues with prediction score higher than 0.6 were predicted to have glycosylation potential66. BDM‐PUB, and UbPred were used for predicting Ubiquitylation sites in CTLA4. UbPred showed lysine residues having ubiquitylation potential with score equal to or higher than the threshold (0.62)67. For BDM-PUB balanced cut-off was selected68.Post translational modifications (PTMs) are very important for the structure, folding and proper function of proteins. Potential PTMs sites in CTLA4 protein and the gain/loss of PTMs sites in all the mutants due to nsSNPS were identified using several in silico tools. The sites where methylation occur in CTLA4 protein were predicted using GPS‐MSP69. STRING uses its database of 24′584′628 proteins from 5′090 organisms and predicts protein protein–protein interaction networks either through direct or indirect association among proteins70. The terms CTLA4 and Homo sapiens were searched as input options for both the tools.A protein interacts with many other proteins inside the cell and this interaction is important for the function and regulation of protein. The functional interaction of CTLA4 with other proteins inside the cells was predicted using GeneMANIA and STRING (accessed: 16 June 2020). The GeneMANIA use different parameters including genetic and protein interaction, co-expression, co-localization, pathways and protein domain similarities to predicts the interaction of input gene with many other genesCTLA4 gene. They may have a major role in diseases associated with CTLA4 gene as they are involved in decreasing the stability of protein and loss of potential phosphorylation site. The mutants possessing these nsSNPs showed deviation in structure from wild type CTLA4 protein. These nsSNPs can be significance for therapeutic strategies and personalized medicine and can be used for further experimental investigations to study the role of these nsSNPs in pathogenesis of related diseases.This study identified 3 major high risk nsSNPs, rs1553657429 (P137L), rs1559591863 (G146L), rs778534474 (P209R) within the coding region of Supplementary Information.


The accurate characterization of protein functions is critical to understanding life at the molecular level and has a huge impact on biomedicine and pharmaceuticals. Computationally predicting protein function has been studied in the past decades. Plagued by noise and errors in protein–protein interaction (PPI) networks, researchers have undertaken to focus on the fusion of multi-omics data in recent years. A data model that appropriately integrates network topologies with biological data and preserves their intrinsic characteristics is still a bottleneck and an aspirational goal for protein function prediction.In this paper, we propose the RWRT  method to accomplish protein function prediction by applying bi-random walks on the tensor. RWRT firstly constructs a functional similarity tensor by combining protein interaction networks with multi-omics data derived from domain annotation and protein complex information. After this, RWRT extends the bi-random walks algorithm from a two-dimensional matrix to the tensor for scoring functional similarity between proteins. Finally, RWRT filters out possible pretenders based on the concept of cohesiveness coefficient and annotates target proteins with functions of the remaining functional partners. Experimental results indicate that RWRT performs significantly better than the state-of-the-art methods and improves the area under the receiver-operating curve (AUROC) by no less than 18%.The functional similarity tensor offers us an alternative, in that it is a collection of networks sharing the same nodes; however, the edges belong to different categories or represent interactions of different nature. We demonstrate that the tensor-based random walk model can not only discover more partners with similar functions but also free from the constraints of errors in protein interaction networks effectively. We believe that the performance of function prediction depends greatly on whether we can extract and exploit proper functional similarity information on protein correlations.The online version contains supplementary material available at 10.1186/s12859-022-04747-2. As the major components of cells, proteins play important roles in almost all cell functions. Biological functions are not conducted by a single protein but by a group of interacting proteins with the same or similar functions. Accurate annotation of protein function is fundamental to understand life at the molecular level, which has far-reaching influences for biomedicine and pharmacy. Therefore, how to accurately determine functions of unknown proteins is the most challenging problem of the post-genomic era. Unfortunately, biological experiments have been unable to meet the need for functional annotation of the growing sequence data hampered by their high costs and inherent difficulties. To solve this dilemma, a number of computational methods have been put forward, which implement functional annotation by discovering interacting proteins with known functions in biological networks. High throughput techniques provided high-quality and large-scale protein–protein interaction data and resulted in the emergence of network-based method –3 to preGrAPFI [Domain Combination Similarity) [Domain combination Similarity in Context of Protein Complex) depending on the domain compositions of both proteins and complexes including them. Rehman et al. develop the FP  [Considering the diversity, systematicness and dynamics of protein functions, as well as the poor quality of PPI networks, a variety of approaches have been proposed to promote the prediction of protein function by incorporating multi-source biological information. The typical processing mode of these methods is to integrate and represent functionally associated attributes of proteins in the form of biological network, and then carry out annotation of functions of using diffusion algorithm , clusterGrAPFI , which rGrAPFI . In our GrAPFI , we haveGrAPFI  annotateilarity)  method. tential)  method ttential)  and INGAtential) , which itential)  find thatential)  instead tential) , which eRandom Walks with Restart on Tensor) method to infer protein function. The RWRT method not only improves its performance but also preserves the functional relevance between multi-omics data and their own attributes. We apply the RWRT to the yeast protein interaction network and combine it with multiple biological data, including protein complexes and domain information. Experimental results demonstrate that our proposed RWRT method outperforms six types of methods, including NC [GrAPFI [These methods attempt to improve quality of PPI networks by assigning different weights to the edges at different levels corresponding to multi-omics data. They classically aggregate multiple biological data into a composite and reliable network, which tends to eliminate the topologies and attribution of the individual protein interaction networks. Research and experimental results indicate that each type of biological data has its property or correlation and can play a different role in prediction of protein functions. The way of representing different types of data source in a system with a single type of link is no longer a magic cure-all for network science. In this context, the very pressing need for protein function prediction is to find a suitable data model. Intuitively, a proper data model describing function relevance in multi-omics data should satisfy two properties: it should not only be able to describe the hierarchy and heterogeneity of biological network, but also reflect the complex relationship between multi-omics data, and it should be supported by diversified solutions and rigorous theoretical system, which is conducive to generalization to other research fields. We formalize these two properties with a multidimensional tensor model integrating the topology of PPI networks with multiple biological data and develop the RWRT . However, neighbors with no functional similarity  in the constructed single network are picked out to characterize the protein YAL024C. Meanwhile, the weight of multiple biological data in constructing a unique network varies from species to species, and even from different data sets within the same species. We believe that aggregating multiple biological data into a single and unique network is not the wisest choice. Therefore, we introduce the tensor model to characterize the functional correlation between multi-omics data and PPI networks.Plagued by the small-world and scale-free characteristics of PPI networks, traditional short-path distance or Euclidean distance is not suitable for the measure of functional distances between proteins. As an alternative approach, random walk model provides us with a more refined way by using the flow of information through network connections as a means to establish relationships between nodes . A largeT is constructed. The similarity tensor preserves and reflects multiple relationships between proteins derived from multi-omics data. In the second stage, an iterative procedure calculates functional correlation score for protein pairs in the network. The iterative procedure is an extension of bi-random walks algorithm on the tensor model, which simulates a high-order Markov chain by means of two state transition tensors. In the third stage, scoring and sorting all functions of their “similar” partners (neighbors), target proteins are annotated by top K of these predicted functions. The flowchart for the RWRT approach is given in Fig. Our RWRT method is composed of three major stages. First, integrating the topology of PPI networks, protein domains, and protein complexes information, a functional similarity tensor n and m represents the number of proteins and types of connection between proteins, respectively. If there is a k-th type of interaction between two proteins i and j, then The success of functional genomics is involved in the rapid accumulation of diverse biological data about genes, proteins or other macromolecules . We havepi, pj with common interacting partners, their functional similarity is estimated as follows:pi and pj themselves and their direct neighbors, respectively.The first type of association is guided by the ‘Guilt by Association’ principle. Given two proteins pi and pj, let Di represents the set of distinct domain types in the neighbors of pi with itself included, and Dj is that of pj as well of its neighbors. DC denotes the set of distinct domain types contained by both neighbors of pi and neighbors of pj, while DT is the set of domain types in the whole PPI networks. Then domain content similarity between pi and pj is calculated using the following equations:Research shows that certain sets of domains are frequently found together and cooperate with each other to perform cellular functions . Based opi and pj is measured by the normalization processing of their domain content similarity, which is formally described as follows:Figure Ek and Vk denotes the set of physical interactions and proteins in the module Mk, respectively. After getting the score of benchmark functional modules using Eq.  denote the total functional similarity score between all other proteins inside the functional module and the protein pi, and let fs.out(pi) denote the total functional similarity score between all proteins outside the functional module and the protein pi. The cohesiveness coefficient of pi is then given byM is a set of partners that have same or similar functions as the target protein. Cohesiveness coefficient provides an efficient way to assess whether a functional module satisfies the properties of high cohesion and low coupling. A well-separated module consisted of many proteins with similar function has a high fsin and a low fsout. For a partner with similar functions to the target protein, its CC value is less than or equal to1/3 [FSP = {fsp1, fsp2, …, fspl}. Let F = {f1, f2, …, fm} be a list of distinct functions of proteins in FSP. We score and rank functions within F in descending order to annotate the target protein with top K of them. Given a function fi for the target protein pt, its ranking score is calculated by the following formula:fspk and the target protein pt, GO (fspk) is a set of functions belonging to fspk. In this paper, the parameter K was assigned as the number of functions of the protein within FSP, which had the highest functional similarity score to the target protein.Benefiting from the iteration on the constructed tensor, we are able to discover more partners with similar functions to target proteins, which are ignored by PPI networks. These partners as well as the target protein interact with each other to carry out biological functions within multiple functional modules. Intuitively, members within the same functional module are often more densely connected than those across functional modules . Unfortual to1/3  implies GrAPFI on two benchmark datasets from yeast, including DIP [To estimate the performance of RWRT for protein function prediction, we perform computational analysis on our method as well as other six competing algorithms, such as NC, Zhang, DCS, DSCP, PON and ding DIP  and BioGding DIP . The DIPding DIP . We primding DIP . The proding DIP , which iding DIP , which mFor a better understanding of the behaviour of the proposed RWRT method, we provide descriptive statistics on the two PPI networks and their corresponding functional similarity networks, which are represented by functional similarity matrixes in Eq. . Table 2To evaluate the effectiveness of RWRT and other six competing methods in protein function prediction, we apply cross validation to split proteins of PPI networks into the training set and the testing set using two strategies, which are leave-one-out cross validation and ten-fold cross validation. In one round of cross validation, the functions of each protein in the testing set are predicted according to the proteins in the training set. The validation process is repeated multiple times until each protein has an opportunity to become a member of the testing set. The final performances are evaluated by the average of all rounds. The process of function prediction using leave-one-out cross validation and ten-fold cross validation is described below.To measure quality of the predicted functions by each method, we use two assessment criteria: AUROC (area under the receiver-operating curve)  and averGrAPFI. The performance is averaged with only one protein into the testing set and rest of proteins used as the training set. We first evaluate the performance of RWRT and six competing methods on these target proteins by the average Precision, TPR (True Positive Rate), FPR  and F-Score. Table GrAPFI, respectively. For comprehensive performance comparison between RWRT and competing methods, we employ piecewise statistics of the predicted results according to functional size of target proteins. The results, shown in Figs. In our first set of evaluations, we apply leave-one-out cross validation to assess quality of the predicted functions predicted by RWRT, as well as other six competing methods: NC, Zhang, DCS, DSCP, PON and GrAPFI, respectively. As for the DIP dataset, the AUROC of RWRT increases by no less than 60% compared with other competing methods. Comparison results also reveal a phenomenon that the performance of these methods in the DIP dataset is significantly inferior to that of them on the BioGRID dataset. For NC, Zhang, DCS and DSCP, which mainly depend on neighbors, the gap is even more obvious. In our opinion, it is due to the fact that the DIP network is sparser than the BioGRID network. However, this does not appear to have much effect on the RWRT method. Experimental comparison results strongly prove the effectiveness and robustness of our method.To further investigate the performance of RWRT and six competing methods, we adopt the ROC curve, whose vertical and horizontal coordination are the values of TPR and FPR, respectively. Figure OM is the number of proteins that match at least one function, while FM is the number of proteins whose functions are fully matched and ZM is the number of proteins annotated by zero mismatching functions. PM is the number of proteins perfectly matching the known functions. In other words, a prediction has the same functions with the known functions matched with it. From Table OM) and number of fully matched proteins (FM) after NC, while ZM and PM of our method is far higher than NC’s. The low precision of the NC method is mainly limited by its unweighted strategy, which is similar to that of the GrAPFI and PON method. Researches show that if the weight of an interaction reflects its reliability, then the weighted interactions should better represent the actual interaction network than the initial binary ones. RWRT archives the biggest number of perfect matching proteins (PM) and number of zero mismatching proteins (ZM), which is due in large part to the constructed tensor model for the integration of multi-omics data. In addition, predicted functions of RWRT, NC, PON and GrAPFI are derived from multiple functional neighbors, while that of Zhang, DCS and DSCP only come from the most similar protein. Our statistics show that nearly 68 percent of proteins have partners whose functions completely overlap, and more than 70 percent of these have only one function. Proteins interact with each other to form functional modules or protein complexes and perform useful cellular functions. Although some redundancy may be of biological importance, functional modules overlapping keep within a certain extent. So, we believe that the strategy of annotating target proteins with the functions of multiple proteins is sensible, which is especially favorable to proteins with large functional sizes.To analyze why RWRT obtains superior performance for the prediction of protein function, we investigate full matching, perfect matching, etc. between the benchmark set and the predicted set by the seven approaches. Table To assess the relative importance of each type of biological information on protein function prediction, we try to remove these multi-omics data respectively and run our RWRT method. Ablation results of RWRT on the DIP and BioGRID dataset are shown in Table SN is summarized by three types of physical or functional association involved in constructing the functional similarity tensor T. For a pair of proteins pi and pj, the weight of edge  in SN is defined as:a + b < 1. t, t and t is calculated in Eqs.  is close to 1, but the precision is very low. This is largely due to the fact that almost all known proteins are picked out as candidates to annotate the target protein. Integrating multiple biological data into a credible single network can indeed improve network connectivity and effectively eliminate false negatives in PPI networks, which leads to an increase in recall. However, it also inevitably introduces a lot of noise and reduces the precision of prediction. So, any increase in recall is more than offset by the accompanying increase in false positives [In the RWRT method, we obtain a functional similarity network by performing iterative operations on the tensor model, which is formally described by Eq. . To veri b)*ti,j,$$\end{do in Eqs. , respectentclass1pt{minimaGrAPFI, Zhang, DCS and DSCP, respectively. On the DIP dataset, AUROC of RWRT increases by 110.79%, 559.46%, 241.54%, 322.87%, 103.87% and 61.80%, respectively, compared to the above six methods. All of these experimental results indicate that RWRT still outperforms other six competing methods using other validation.For comprehensive comparison between the novel method RWRT and the six other competing methods, we adopt the ten-fold cross validation to examine the stability of these methods on the training dataset. Proteins are randomly divided into ten subsets, a single subset is retained for the testing set, and the remaining nine subsets are used as the training set. The cross validation process is then repeated ten rounds, each of which uses different folds as the training and validation data. Ten results from the folds are then averaged to produce the final performance. We run functional annotation methods of RWRT as well as other six competing methods on the BioGRID and DIP network. Figure Accurate annotation of protein functions is still a big challenge for understanding life in the post-genomic era. In spite of the advances in computational methods for protein function prediction, it still fails to achieve satisfactory prediction accuracy plagued by the incompleteness and errors in the original PPI data. To overcome this problem, the integration of different types of biological data has become an important and popular strategy, which has led to the emergence of various interactions between proteins. Each type of biological data has its own property or correlation and can play a different role in prediction of protein functions. Inspired by it, we set up a multidimensional data model and describe it formally with the tensor. To get rid of constraints of the small-world and scale-free properties of PPI networks, we extend the bi-random walks algorithm to the tensor model. In this way, we can discover more potential proteins with similar functions to target proteins and improve the true positive rate of prediction. However, enlargement of the traversal range of similar functional neighbors will inevitably lead to the increase of noise. The NC method is a typical example to illustrate the fact. For this purpose, we run the functional module detection algorithm based on the concept of cohesiveness coefficient to filter out pretenders and reduce the false positive rate of prediction. We are of the opinion that there are both overlaps and differences in functional annotation between proteins. It is not appropriate to annotate a target protein with all the functions of the protein most similar to it.In this paper, we design a novel protein function prediction method named RWRT by applying a tensor-based bi-random walks model. The RWRT method constructs a functional similarity tensor depending on the original PPI network as well as multi-omics data firstly. And then, it extends the random walk with restart algorithm to the tensor by simulating a high-order Markov chain. After this phase, RWRT can discover more functional similarity partners ignored by original protein interactions data. However, it also inevitably introduces some spurious nodes. Therefore, a pretender-filtering procedure is applied to remove possible pretenders loosely connected to the target protein and finally generate predicted functions from the remaining functional partners. Experimental comparison results on two PPI networks indicate that RWRT performs significantly better than the state-of-the-art methods and the proposed model can provide more insights for future study in PPI networks.Additional file 1. Tensor-based random walk model. This file provides the derivation process of how to extend random walk model from two-dimensional matrix to the tensor model.