Abstract
All proteinprotein interaction (PPI) predictors require the determination of an operational decision threshold when differentiating positive PPIs from negatives. Historically, a single global threshold, typically optimized via crossvalidation testing, is applied to all protein pairs. However, we here use data visualization techniques to show that no single decision threshold is suitable for all protein pairs, given the inherent diversity of protein interaction profiles. The recent development of high throughput PPI predictors has enabled the comprehensive scoring of all possible proteinprotein pairs. This, in turn, has given rise to context, enabling us now to evaluate a PPI within the context of all possible predictions. Leveraging this context, we introduce a novel modeling framework called Reciprocal Perspective (RP), which estimates a localized threshold on a perprotein basis using several rank order metrics. By considering a putative PPI from the perspective of each of the proteins within the pair, RP rescores the predicted PPI and applies a cascaded Random Forest classifier leading to improvements in recall and precision. We here validate RP using two stateoftheart PPI predictors, the Proteinprotein Interaction Prediction Engine and the Scoring PRotein INTeractions methods, over five organisms: Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana, Caenorhabditis elegans, and Mus musculus. Results demonstrate the application of a post hoc RP rescoring layer significantly improves classification (pā<ā0.001) in all cases over all organisms and this new rescoring approach can apply to any PPI prediction method.
Similar content being viewed by others
Introduction
Elucidating the proteinprotein interaction (PPI) network of an organism is necessary to understand cellular function and study disease pathogenesis^{1}. Computational methods have been leveraged to rapidly estimate protein interaction networks. Given advances in compute power and more efficient prediction algorithms, we are now able to estimate comprehensive interactomes (i.e. all proteins in a proteome predicted against all others) for several species^{2,3}. A number of paradigms have emerged in the field of PPI prediction including sequencebased^{3,4}, structurebased^{5}, evolutionbased^{6}, ontologybased^{7}, and networkbased methods^{8}, each with varying degrees of success and compatibility^{9}.
Historically, a broad range of machine learning algorithms have been applied to various facets of PPI prediction. Guo et al. demonstrated that Support Vector Machines (SVMs) used with autocovariance can be successfully applied to sequencebased PPI prediction tasks^{10}. Hamp and Rost expanded upon this work with the incorporation of evolutionary profiles to generate profilekernel SVMs, demonstrating further improvements to PPI classification performance^{11}. Neural networks with varying model architectures have also been successfully leveraged and most recently, Sun et al. have demonstrated that stacked denoising autoencoders (an artificial neural network which infers a function to construct hidden structures from unlabeled data) can achieve similar successes to predict PPIs^{12}. The sites of a protein which mediate PPIs have also been predicted algorithmically^{13} and using Random Forest ensemble models leveraging features extracted from the physiochemical properties of protein structures^{14}. More recently, Wang et al. used a Rotation Forest ensemble approach leveraging multiple sequence alignments which was found to be successful in the largescale identification of PPIs in several species^{15}. Overall, the field of PPI prediction has been highly active in the last decade, with new methods proposed each year as recently reviewed in Kotlyar et al.^{16}. While the field of PPI prediction is methodologically diverse, irrespective of the paradigm, learning algorithm, and scale of the number of predictions, the field has certain fundamental commonalities.
All of these methods examine the query protein pair and output a score denoting the predicted likelihood that the pair will physically interact. Despite the methodological differences between each paradigm, common to each is the intrinsic need to apply a decision threshold to the score that distinguishes the set of highconfidence predicted PPIs, potentially warranting experimental validation, from the set of protein pairs that are unlikely to physically interact. Establishing the expected number of PPIs for any given protein is an openly debated question, which is further complicated given that a protein can exhibit contextspecific binding patterns^{17}. While some proteins can exhibit promiscuous binding behaviours, as in the case of hub proteins, others are highly specific with few binding partners^{18}. The selection of an appropriate decision threshold remains an open question and directly influences the performance of a PPI predictor.
High Throughput Predictions Give Rise to Context
Historically, PPI prediction tasks have been limited to modest subsets of the complete interactome enabling the elucidation of localized subnetworks or the identification of an interspersion of isolated PPIs relative to the complete interactome. This limitation is due to the algorithmic timecomplexity of most PPI predictors, particularly those examining protein structure. Given that the number of putative PPIs grows as the square of number of proteins (i.e. the triangular number), the computational time for a given PPI using a given predictor is critical. For example, the human proteome contains over 20,000 proteins representing over 200 million potential interactions. A method predicting one interaction per second would require over 6.3 years to examine all pairs and produce the complete human interactome. This has prompted research groups to develop optimised predictors and leverage high performance computing. Only recently have these highthroughput predictors afforded us the capability to scale predictions and consider the comprehensive set of all possible interactions^{2,3}. This has given rise to context: the ability to appraise a given PPI prediction relative to all possible interactions. While highthroughput methods have now enabled the study of a given PPI within the context of all protein pairs, the interpretation of these results is critical to appropriately evaluate the PPI predictor.
Traditionally, crossvalidation experiments are used to evaluate the performance of a trained predictor: a random subsample of all interactions are retained, the remaining data are used to train a model, and the subsample is then evaluated. ReceiverĀ Operating Characteristic (ROC) curves are widely used to compare the performance between models and are leveraged to select an operating threshold that balances sensitivity and specificity. The area under the ROC curve (AUC) is often used to summarize a modelās performance across all possible decision thresholds, although the value of such a summary statistic is questionable, particularly in the case of highly imbalanced problems such as PPI prediction. Increasingly, the suitability of ROC curves and the AUC metric is being reconsidered in various fields^{19,20,21}, and prevalencecorrected PrecisionRecall Curves (PRCs) have been adopted as the new standard^{19}.
Once a decision threshold is selected, it is applied globally to all predictions and is used as a binary discriminator: predicted PPIs scoring above the threshold are considered positives, warranting further investigation, whereas those below are considered negatives. Tuning this threshold to less conservative levels threatens to introduce a large number of false positives, thereby reducing the utility of the classifier.
Related Work and Previous Approaches to Local Threshold Determination
In PPI prediction tasks, a quantitative score can be assigned to a given protein pair of interest, say proteins x_{i} and y_{j} in pair P_{ij}. Researchers studying protein x_{i} would typically consider the set of sorted scores for all pairs \({P}_{in},\forall \,n\) and investigate the topranking PPIs through experimental validation. However, the arbitrary selection of the topk ranking interactors for a given protein fails to impart any confidence in the resulting PPIs. The choice of the value of k is arbitrary since no single value of k can be optimal for all proteins. Furthermore, when considering the interaction P_{ij}, this topk ranking approach only considers the scores of pairs involving x_{i}, but not all pairs involving y_{j}. That is, they are only leveraging half of the available context.
A widely used algorithm that does examine both partners within a putative relationship is the Reciprocal Best Hit method to identify putative orthologs. Here, two genes in different genomes are considered to be orthologs if and only if they find each other to be the topscoring BLAST hit in the other genome^{22}. Reciprocal Best Hit is an example of the most conservative application of a local threshold, where kā=ā1. While useful for determining an orthologous relationship between the two genes that are typically expected to have a single ortholog in other species, our situation differs as proteins are expected to participate in several PPIs (i.e. \(k\ge 1\)); therefore, a more suitable approach is required.
A similar challenge arises in the control of false discovery rates (FDRs) in applications such as genomics where high dimensional genotyping arrays are used to evaluate millions of variants (e.g. single nucleotide polymorphisms) for correlation with phenotype or experimental condition. The established method for controlling against multiple testing has been to adjust familywise error rates (FWERs) such as using the HolmBonferroni method^{23}. The control of FWERs has been considered too conservative and severely compromises statistical power resulting in many true loci of small effect being missed^{24}. Recently local FDRs (LFDRs) have been proposed and are defined as the probability of a test result being false given the exact value of the test statistic^{25}. The LFDR correction, through reranking of test statistic value, has been demonstrated to eliminate biases of the former nonlocal FDR (NFDR) estimators^{24,26}. Our application is similarly motivated, though differs in that we consider the paired relationships between two elements and leverage the context of a given protein relative to all others.
The networkbased analysis of PPI networks contextualizes proteins using undirected connected graphs, often with a scalefree topology and hierarchal modularity^{27}. The importance of a PPI is determined by considering topological features, path distances, and centrality measures of a given protein relative to the neighbours in its vicinity (e.g. khop distance). While useful for post hoc evaluation of cluster density, cliques, and protein complex prediction^{28}, these approaches are notoriously plagued with false positives^{29}. Networkbased PPI prediction methods will attribute scores based on these quantitative metrics and often incorporate external information to reweight their score such as protein localization, coexpression, and literaturecurated data.
In essence, various methods have taken into account localized decision thresholds, paired comparison, PPI context, and rankorder metrics, however no one modality has leveraged these in combination and proposed a unified method to determine localized decision thresholds for predicted PPIs based on their interactome context. Again, such analysis has only recently become possible with the development of efficient highthroughput methods capable of assessing all possible protein pairs.
The Challenge with Selecting Decision Thresholds
A central problem to PPI prediction is the wide variance observed in the number of actual interactions of each protein (the degree from networkbased terminology). This is further complicated when considering protein binding site characteristics, where some proteins exhibit highly specific interaction profiles, while others have a tendency towards promiscuity due to large (and at times, overlapping) binding sites^{30,31} wherein the same polypeptide will participate in several interactions. Furthermore, the subset of proteins known to exhibit promiscuity, given their high affinity binding sites, tend to have an increased probability to develop new connections over time relative to proteins exhibiting modest binding affinities^{32}. These hub proteins have the tendency to interact with considerably larger number of proteins and often have physiochemical sites (structured or unstructured) enriched with intrinsic disorder enabling an aboveaverage propensity to interact with other proteins^{33,34,35}.
PPI predictors trained with known interactions involving promiscuous proteins risk developing a bias towards these windows, thereby producing an inflated predicted score for such proteins relative to others. While useful for the identification of hub proteins, resulting PPI models risk having an overrepresentation of these windows and an underrepresentation of their highly specific counterparts. Given that true PPIs are rare and PPI predictors tend to overpredict interactions for some proteins while underpredicting for others, we aim to quantify this behaviour and incorporate it into the decision function. True interactions are rare among all possible pairs and predictors exhibiting a bias towards certain proteins is problematic. For example, should a PPI predictor, when applied to a given protein A, produce a large number of highscoring targets, one naturally questions the validity of each score and would favor a conservative decision threshold, D_{A}. Conversely, when applied to protein B and only a small number of highscoring targets are observed, even if these few are low relative to the stringent decision threshold D_{A}, one might be inclined to pursue these few predictions further.
FigureĀ 1 illustrates this phenomenon with a OnetoAll Score Curve using seven example proteins from the Saccharomyces cerevisiae predicted interactome^{36}, where PIPE was used to predict all scores between the yeast proteome and seven diverse yeast proteins. These OnetoAll Score Curves depict the rank order distribution (i.e. the sorted descending ordering of scores) of a single protein. When plotted together, these curves illustrate the comprehensive set of predicted scores for one protein, enabling researchers to interpret each distribution relative to other proteins and compared to the globally defined decision threshold (Fig.Ā 1, in grey). An obvious question arises for a protein such as the UPF0479 Membrane Protein (in pink): if no PPIs score above the defined global threshold, how might we determine the number of interactions to consider? Tuning the global threshold to a lower point threatens to introduce an exorbitant number of lowerconfidence PPIs with a protein such as the Nuclear polyadenylated RNAbinding protein (in orange). Here we propose a method to define a local threshold on a perprotein basis which addresses these challenges and more appropriately defines what constitutes a positively and negatively predicted PPI. Beyond the definition of a localized perprotein threshold, a PPI can be further contextualized through paired comparison.
Reciprocal Perspective
We introduce a novel concept in the application of interactomewide analyses of proteinprotein interaction networks: Reciprocal Perspective (RP), which jointly considers an interaction from the perspective of each partner to determine a new assessment of the interaction. Intuitively, when two elements interact, that interaction may have differing implications from each elementās respective perspective. Therefore, the relationship can be characterized from the two perspectives separately, taking into account the context relevant to each element. We define perspective as the set of relationships of one element with all others. Applied to PPI predictions, the āelementsā correspond to proteins and the ārelationshipsā are PPIs. Simply put, when considering a putative interaction between elements A and B (AB), one can examine AB in the context of all of Aās putative interactions (A*) and also in the context of all of Bās putative interactions (*B). Here, we formalize these concepts into a generalized method termed RPPPI (Reciprocal Perspective for PPI prediction) and demonstrate its ability to improve the classification accuracy of two stateoftheart PPI predictors using a cascaded Random Forest classifier.
Methods
Inspired by the visualization of the rank order distribution of PPIs for selected proteins (Fig.Ā 1), we seek to develop a method to determine the optimal local threshold for each protein. Noting that, while the average magnitude of each curve varies, these distributions share a characteristic Scurve shape, with a high scoring region, a baseline region, and a low scoring region (the latter is sometimes missing, thereby forming an Lcurve shape). We first seek to determine a robust procedure to estimate this baseline, with the ultimate goal of differentiating the high scoring region. To examine a predicted PPI in the context of the baseline level, a number of PPI rescoring metrics are introduced as functions of the estimated baseline. Finally, reciprocal perspective is applied to develop a number of reciprocal rank order metrics to characterise a given PPI. These new PPI reranking metrics are validated using two stateoftheart PPI predictors over five organisms: Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana, Caenorhabditis elegans, and Mus musculus.
Modeling the Curve
The generation of the set of comprehensive PPI predictions using the two stateoftheart methods for each of the five organisms is described in the Evaluation Design section and their results were used here. An examination of several onetoall PPI score curves reveals a characteristic āSāĀ or āLāshaped curve with a certain number of higherscoring PPIs relative to a large baseline. Due to the inherent class imbalance in PPI prediction tasks, true interactions are rare. We therefore assume that the baseline region corresponds to the typical score assigned to a noninteracting protein pair involving the query protein. The baseline level thus provides a proxy for estimating the degree of bias that the predictor has for the query protein; as described above, some proteins will universally produce higher prediction scores than others. We therefore seek to estimate this baseline level and identify those putative interactions residing significantly above this baseline score.
To differentiate between highscoring PPI and baseline, we seek to identify the knee of these curves. A continuous smooth curve is therefore fit to the onetoall score curves and the maximum value of the second derivative of the fitted curve represents the knee. Given the variability of the shapes of the curves we do not assume a specific distribution and use the nonparametric Locally Weighted Regression (LOESS) method to fit loworder polynomials (degreeā=ā2) to local windows of scores to produce a piecewise continuous curve^{37}. LOESS curve fitting is parameterized by the span parameter, Ī±, which determines the proportion of points considered in a window and controls the degree of smoothing. Parameter tuning was accomplished by varying Ī± over the [0.05, 0.75] range and observing the quality of curve fit over a stratified sample of 1% of proteins. The space of onetoall score curves was stratified and visualized by first sorting all curves by their maximum score and then plotting a surface over all curves in a third dimension in increments of 100 proteins. We could therefore qualitatively appraise the fit of the curve with a given Ī± over the space of all onetoall curve shapes by randomly selecting a representative from each increment, accounting for 1% of the complete dataset (repeated for each method and organism dataset). A preliminary coarsegrained analysis restricted our range to the [0.05, 0.20] range, wherein a finegrained analysis varying Ī± by 0.01 was used to select the final value. Repeating the stratified sampling procedure, a value of Ī±ā=ā0.10 was selected as it provided qualitatively the best fit and generalized across both methods and for distributions across the five organism datasets. Fig.Ā 2 illustrates an example of the LOESS curve fit to the onetoall scores for protein YJL124C and the corresponding first and second derivative curves based on the original fit. The piecewise linear characteristic of Fig.Ā 2A depicts the rapid rate of decline of the rank order values followed by the gradual decline beyond the knee of the curve. The maximum value in the second derivative curve (Fig.Ā 2C) corresponds to the point of greatest upwards concavity in the original plot; we establish this as the knee and the starting point of the baseline (Fig.Ā 2A; arrow). Having established this knee for each protein we wish to restate each putative interactorās score with respect to this baseline. To that end, we defined several quantitative metrics.
Notation
We define our metrics using set theory. We first define the set of proteins for a given organism a as \(A=\{{x}_{1},{x}_{2},\ldots ,{x}_{n}\}\). Organism a is said to have a proteome of size n. Similarly, organism b has a set of proteins defined as \(B=\{{y}_{1},{y}_{2},\ldots ,{y}_{m}\}\) and a proteome of size m. We define \({x}_{i}{y}_{j}\mathrm{\ \ }{x}_{i}\in A,{y}_{j}\in B,i\in \mathrm{\{1,}\,\mathrm{2,}\ldots ,n\},j\in \mathrm{\{1,}\,\mathrm{2,}\ldots ,m\}\) as a predicted binary PPI with symmetric relation: \(\forall \,x,y\in C(xRy\iff yRx)\) where C is the set of all possible interactions between organisms a and b:
and R represents the binary proteinprotein interactions relation over the set C.
In the case where we consider intraspecies interactions (i.e. organism a is also organism b), we satisfy \(\forall \,z[z\in A\leftrightarrow z\in B]\). Furthermore, we define the score and rank order for a given interaction, x_{i}y_{j}. The score of a given PPI, \({x}_{i}{y}_{j}\sim {y}_{j}{x}_{i}\), is defined as \({s}_{{x}_{i}{y}_{j}}={s}_{{y}_{j}{x}_{i}}\) and these values are used to sort the respective sets. The ordered set of interactions involving protein x_{i} is defined as the totally ordered set \(X=\{{x}_{i}{y}_{k},\ldots ,{x}_{i}{y}_{l}\mathrm{\}\ \ }k,l\in \mathrm{\{1,}\,\mathrm{2,}\ldots ,m\}\) and the set involving protein y_{j} is similarly defined as \(Y=\{{y}_{j}{x}_{u},\ldots ,{y}_{j}{x}_{v}\mathrm{\}\ \ }u,v\in \mathrm{\{1,}\,\mathrm{2,}\ldots ,n\}\). We, therefore, define the rank order for x_{i}y_{j} as \({r}_{{x}_{i}{y}_{j}}\), the ordinal rank of x_{i}y_{j} in X, and \({r}_{{y}_{j}{x}_{i}}\) as the ordinal rank of y_{j}x_{i} in Y and say that \({r}_{{x}_{i}{y}_{j}}\) and \({r}_{{y}_{j}{x}_{i}}\) are reciprocal rank order (RRO) values.
Taking into account the knee of the curve as the baseline threshold obtained from the second derivative of the continuous curve using LOESS, denoted Ļ, we obtain useful definitions specific to each protein, namely \({s}_{{x}_{\tau }}\) as the score corresponding to \(max(\frac{{d}^{2}({s}_{x})}{{x}^{2}})\) and \({r}_{{x}_{\tau }}\) as its ordinal rank value. In the partner protein, we similarly define \({s}_{{y}_{\tau }}\) and \({r}_{{y}_{\tau }}\). A predicted PPI can then be compared relative to these baselines in a number of ways, resulting in various metrics to define the score of a putative PPI relative to the baseline level. Here, we use a binary value \({\beta }_{{x}_{i}{y}_{j}}\in \mathrm{\{0,}\,\mathrm{1\}}\) to denote whether \({s}_{{x}_{i}{y}_{j}}\) resides above or below \({s}_{{x}_{\tau }}\), the binary variable \({\beta }_{{y}_{j}{x}_{i}}\in \mathrm{\{0,}\,\mathrm{1\}}\) to denote whether \({s}_{{y}_{j}{x}_{i}}\) resides above or below \({s}_{{y}_{\tau }}\), and a binary variable \({\gamma }_{{x}_{i}{y}_{j}}\sim {\gamma }_{{y}_{j}{x}_{i}}\in \mathrm{\{0,}\,\mathrm{1\}}\) to denote whether \({s}_{{x}_{i}{y}_{j}}={s}_{{y}_{j}{x}_{i}}\) resides above or below the global threshold. Furthermore, the respective folddifferences from the baseline are defined:
From the estimated baseline of a given proteinās perspective, we obtain the following five metrics, which we summarize in TableĀ 1: RankXY, RankLocalCutoffX, ScoreLocalCutoffX, InteractionXYAboveLocalX, FoldDifferenceFromLocalX. Considering that each putative PPI has two perspectives, we obtain an additional five metrics from the reciprocal perspective: RankYX, RankLocalCutoffY, ScoreLocalCutoffY, InteractionYXAboveLocalY, FoldDifferenceFromLocalY. Furthermore, these can be utilized to derive metrics characterizing each PPI and jointly accounting for the context of the putative PPI within each proteinās respective perspective.
Reciprocal Perspective Notation
For a given protein within a pair, a set of metrics can be determined to rescore the predicted PPI relative to all other PPIs involving that protein, taking into account its estimated baseline. However, this examines the PPI from only a single perspective. RP examines a putative PPI in the context of both proteins in the pair. By jointly considering these reciprocal perspectives, RP may be applied as a postprocessing step to the raw predicted scores to augment the predicted outcomes by supplying additional context to previously generated scores and produce the final output classification. Having defined new metrics in the context of a proteinās perspective, we now define those which combine information from each perspective. In its simplest form, the NaĆÆve Reciprocal Rank Order (NaRRO) value is the product of the rank order values, inversed to cast into the \([\frac{1}{nm},\,\mathrm{1]}\) range.
This representation doesnāt account for the proteome size and the potentially imbalanced number of predictions when comparing predicted values from different species. To account for interspecies predictions where each organism has a differently sized proteome (such as predicting PPIs between host and pathogen), we must normalize the NaRRO value to avoid artificially inflated values from smaller proteomes. To correctly normalize scores for interspecies interactions we define the Adjusted Reciprocal Rank Order (ARRO); we normalize each rank order value with the respective proteome size:
This corrects any biases due to differently sized dataset in interspecies predictions. ARRO values are positive float values in the range \(\mathrm{[1,}\,nm]\).
Finally, for the case of intraspecies predictions (i.e. Aā=āB), we simplify the ARRO notation to define the Normalized Reciprocal Rank Order (NoRRO) which normalizes each RRO value by dividing by the proteome size, where p is the proteome size, pā=ānā=ām.
This metric is generally appropriate only for intraspecies predictions and is useful to compare scores across different species. The NoRRO values are positive float values in the range \([\frac{p}{nm},p]\). A special case arises when considering the NoRRO metric in the context of interspecies predictions, where organisms with differently sized proteomes would require the selection of either as normalization factor. Exploration of this use case is deferred to future study and beyond the scope of this current work. These 15 new metrics (10 proteinspecific; five derived from RP) are summarized in TableĀ 1 and are each amenable to the analysis of the PPI prediction results of any PPI predictor over any organism, or combination thereof.
Evaluation Design
We validated our method using the comprehensive set of predicted scores from two stateoftheart PPI prediction methods and on five organisms: H. sapiens, S. cerevisiae, A. thaliana, C. elegans, and M. musculus. The PPI predictions methods were selected since they are uniquely amenable to the comprehensive prediction of interactomes: the Proteinprotein Interaction Prediction Engine (PIPE)^{2,4,13} and the Scoring PRotein INTeractions (SPRINT)^{3} algorithms. PIPE has successfully been used in the comprehensive prediction of a number of intra and interspecies interactomes since its release in 2006 including H. sapiens, S. cerevisiae, Human Immunodeficiency Virus, the Zika Virus, Plasmodium falciparum, and Glycine max^{2,4,38,39}. Leveraging pairs of known interacting proteins, the PIPE algorithm identifies subsequence regions of similarity (termed āwindowsā) and uses these windows to determine whether or not pairs of unknown PPIs are likely to interact. High frequency windows present challenges as they may artificially inflate predicted scores for those proteins that contain them. Efforts to normalize variable frequency windows have previously been proposed, most notably with the introduction of the SimilarityWeighted (SW) scoring metric used in PIPE3, which normalizes the PIPEScore for a given window by the frequency of that window throughout the training dataset. The SW score is a positive, float value which captures the likelihood of interaction between any two proteins. We consider this as the original score in the RP method.
The SPRINT algorithm is also a sequencebased PPI predictor amenable to the comprehensive prediction of all possible PPIs. It distinguishes itself from similar predictors by using a multiple spacedseed encoding to prune away high frequency elements that occur too often to be involved in PPIs, and then returns a score indicative of the probability to interaction^{3}. It has been compared to several stateoftheart methods including PIPE2, as in^{40}. For H. sapiens, the SPRINT method has been postulated to outperform the PIPE2 algorithm, suggesting it is comparable with the stateoftheart^{3}. This work used the PIPE3 (i.e. MPPIPE) model which was previously successful in generating the first comprehensive H. sapiens interactome^{2}. An explicit comparison of the SPRINT and PIPE3 methods is beyond the scope of this work and here the two are used as independent methods capable of generating predicted scores for any given PPI, and therefore are amenable to analysis using RP.
PPI predictions for five different organisms were used to validate the RP method. To generate the comprehensive set of interactions, the high quality PPI datasets to train and evaluate each method were obtained using the Positome framework^{41}. Specifically, the āconservativeā dataset, as defined in^{41} was acquired for each organism except for the C. elegans where the āpermissiveā dataset was used following the recommendations of^{41} for organisms where the conservative dataset is excessively stringent resulting in very few training samples. This framework preprocesses the data and ensures a consistent definition of a PPI and provides the corresponding protein sequences data for all proteins present in the dataset. The training data for each of the five organisms is summarized in TableĀ 2. The comprehensive prediction (i.e. āalltoallā) was obtained using the respective default parameters for each of the PIPE and SPRINT prediction methods for each organism.
With the alltoall datasets computed for each organism over each method, the global threshold was determined for each model and for each organism. The leaveoneout crossvalidation (LOOCV) method will remove a known interaction from the positive training dataset, build a model on the remaining, and then predict that removed interaction. It is considered the computational equivalent of wetlab experimental validation of a PPI and useful in estimating the global decision threshold of a given predictor. Given the large class imbalance, it is crucial to select a decision threshold which minimizes the number of false positives. For both methods, the specificity was set as 99.95% and the corresponding decision threshold was chosen as in^{2,42}.
The RP method was then used to compute the defined metrics for each PPI and a feature matrix was generated. To evaluate the improvement provided by the RP postprocessing method, the set of positive PPIs and an equivalently sized subsample of negative PPIs (sampled without replacement) was created to train and evaluate a Random Forest classification model. We used the scikitlearn Python library default parameters where tree depth was unbounded and feature selection occurred over the root of the number of features. We selected a forest size of tā=ā100 trees in favor of the default tā=ā10 since a finergrained classification confidence and numerical precision could be obtained from the t number of trees. We opt to arbitrarily select these hyperparameters as we cannot expect that there exists a singular set of Random Forest hyperparameters which will uniquely lead to the best increase in performance over all methods and all organisms. Moreover, using the same set of hyperparameters in our Random Forest models enables us to appropriately compare the results between the two principal conditions (RPEnhanced vs. Original) for a single dataset, as well as observe consistent improvement in predictive performance across all methods and organisms. The feature space with respect to t and PRCAUC was explored and summarized in Supplementary FigureĀ S1, available online.
We selected this machine learning method given that they have been demonstrated to be robust against overfitting, relatively simple to tune, and generally outperform standard classifiers^{43}. Each model was produced using a fivefold crossvalidation to further avoid overfitting the data. The feature subsets types (āRankā, āScoreā, āFoldā) of the postprocessed RP features, from TableĀ 1 were tested in combination to delineate their contribution to the discrimination of the positive and negative class. We refrained from further tuning the hyperparameters so as to consistently evaluate each test condition. These results were plotted on prevalencecorrected precisionrecall curves. Since the class imbalance in our test data is not necessarily reflective of the actual degree of imbalance expected when the classifier is applied to a complete genome, we use the prevalencecorrected precision defined as:
where TP is the estimated true positive rate of the classifier, FP is the estimated false positive rate of the classifier, r is the expected ratio of negative to positive samples in the realworld data, Sn is the estimated sensitivity, and Sp is the estimated specificity of the classifier. The precision is interpreted as the portion of positively predicted PPIs that are actually true interactions whereas the recall is interpreted as the proportion of positives that were correctly classified as true. Here we use a value of 100 for r representing a 1:100 class imbalance, as estimated and used in^{40,42}. Finally, to quantify the statistical difference between the nonRP and RPenhanced conditions we used bootstrap testing over 1,000 iterations and summarize the resulting PRC and ROC curves using the area under the curve metrics: PRCAUC, ROCAUC.
Data availability
The data that support the findings of this study are available from BioGrid (known PPIs) and UniProt (protein sequences).
Results and Discussion
Throughout the history of PPI prediction, and in general applications of machine learning, the question of selecting an appropriate decision threshold Ļ has been a source of much debate. Applications with balanced and equivalently valued classes can simply select the point which jointly maximizes the sensitivity and specificity of an ROC curve (i.e. the threshold \({\tau }^{\ast }\) nearest to [0, 1] of the ROC curve). As the class imbalance varies and the relative cost of a FP versus a FN changes, the selection of a decision threshold becomes increasingly critical. The arbitrary selection of Ļ^{*} threatens to flood the prediction results with Type I errors (assuming a class imbalance pos:neg where \(pos\ll neg\)). To account for this, the tradeoff between sensitivity and specificity can be adjusted such that the specificity is valued much more (i.e. reduction of the false positive rate) at the expense of the true positive rate. As a result, we have an increased confidence in the predicted positives (high precision), however this comes at the cost of missing a majority proportion of actual positives (high number of Type II errors).
This conservative approach has been demonstrated to be successful in the elucidation of novel PPIs when predicting across the entire interactome of various organisms^{2,4,42}; however, the visualization of predicted scores relative to that globally applied decision threshold provides insight into the distribution of the scores of a given PPI in the context of each participating protein relative to all others within the proteome. Most notably, we observe that the definition of a single conservative and globally applied decision threshold appears to be appropriate for a subset of proteins and inappropriate for others (Fig.Ā 1). These onetoall curves characterize the distribution of predictions for a given protein against all others within the proteome. Having a totally rankordered distribution, one can immediately appraise a number of important properties such as the values, size, and range of both the highest scoring PPIs and the baseline, as well as the location of the knee of the curve. Investigating the distribution of scores across all interacting proteins, we observe some proteins with a disproportionately large number of retained interactions (where putative PPI scores are above the global threshold). These might occur for two reasons: biologically, the protein windows have a high binding affinity, or computationally, the PPI predictor overestimates the predictions. The converse is also likely, wherein certain proteins exhibit having very few, or no predicted PPIs score above the global decision threshold when interpreting the OnetoAll curve. Realizing that a large number of predicted PPIs on this OnetoAll curve score highly relative to the other predicted PPIs despite falling below the global decision threshold prompted the formulation of hypotheses that those putative PPIs might comprise a proportion of false negatives. This opens the opportunity to appraise a given protein in the context of the interactome, something that has only recently become possible with the ability to generate comprehensive interactomes.
Generating a score for all possible protein pairs is a computationally demanding process. Historically, only targeted subsets of protein pairs were considered and therefore did not face scalability challenges. The size of the comprehensive set of all intraspecies predictions is the triangular number of the size of the proteome, \(\frac{n(n+\mathrm{1)}}{2}\); the number of required predictions grows in O(n^{2}) necessitating predictors capable of producing predictions on the order of the fraction of a second. With the advent of such predictors and the availability of cloud computing resources, such interactomes are available and give rise to context: the ability to appraise a given interaction in relation to all others. This enables the opportunity to estimate the baseline on a perprotein basis and derive quantitative metrics of a given PPI in relation to all others and inspired the development of the RP framework.
Global to Local: A Single Global Decision Threshold is Inappropriate
Leveraging visualization techniques, we observe considerable variation in the distribution of comprehensive predictions between the onetoall curves of various proteins (Fig.Ā 1). This is not unexpected, given the variation of binding affinities exhibited by different proteins. However, relative to the globally defined decision threshold delineating those PPIs considered as positively interacting from the negatives, we observe the simultaneous over and underrepresentation of different proteins. Whereas proteins with high affinity windows will have the tendency to āpull upā the decision threshold, proteins with highly specific windows will be excluded from the set of positively interacting PPIs. We note that these proteins exhibit a rare few PPIs scoring higher than the others on the OnetoAll curve, providing evidence for their putative interaction despite falling below the global decision threshold. To address this, the definition of a localized threshold on a perprotein basis is required. Furthermore, generating the comprehensive set of predictions guarantees that every protein can be consistently evaluated in relation to all compliments and vice versa, motivating the development of methods leveraging these reciprocal perspectives.
Reciprocal Perspective Significantly Improves Classification Accuracy
To evaluate the improvement of the postprocessing RP layer, we examine the contribution of each feature type and summarize the classification performance enhancement when utilizing RPEnhanced contextbased features. FigureĀ 3 depicts the PRC curves of the cascaded Random Forest predictions results applying SPRINT to yeast and PIPE to human. We depict the predictions with curves illustrating the independent contribution of each feature type subset from TableĀ 1. As can be clearly seen in these figures, the joint use of the original score and context, denoted RPEnhanced, provides a consistent boost in recall over a wide range of precision values. We note that Rank and Fold types alone perform worse than the Original score, whereas Score type features perform better than the Original for SPRINT on Yeast. The Rank and Fold types only become useful when combined with the Original score. Finally, the RPEnhanced combination of the Original score with all three RP metric types leads to the best overall performance. While each feature subset combined with the Original score exhibits a considerable increase in performance, it is the joint use of the Original prediction score in combination with all three proposed RP context features which substantially improves the classification performance.
To test for statistical significance of the difference between the nonRP and RPEnhanced classification performance bootstrap testing was performed. A distribution of PRCAUC and ROCAUC summary statistics were formed by repeatedly (nā=ā1,000) sampling random subsets of PPIs, performing the crossvalidation training and testing, and evaluating the resulting classification performance. Considering the null hypothesis, (H_{0}: no significant difference in summary statistics between nonRP and RPEnhanced) we computed pvalues using Welchās unequal variances ttest (to account for unequal variance in the resulting distributions) and found the observed differences in AUC to be significant at the p < 0.001 level, for all cases. These results are summarized in TableĀ 3. Further improvement in predictive performance can be expected by individually tuning the Random Forest model for each dataset. Preliminary evidence for this is summarized in Supplementary FigureĀ S1 (available online) which explores the feature landscape with respect to the Random Forest tree number parameter, t. In combination, these findings support the claim that the incorporation of context to derive postprocessed features from the comprehensive predicted output can help further improve the classification results and these improvements promise to apply to any PPI predictor capable of generating these compressive predictions.
Reciprocal Perspective Properties
The RP framework has been defined in such a way that it is amenable to any weighted complete graph problem. PPI predictions are an example of an undirected graph problem, however, the framework is extensible to directed graph problems. A directed graph problem can easily be converted into an undirected graph problem by averaging the values of the directed edges (e.g. score AāāāB is the averaged value of the score for AāāāB and BāāāA). Due to the sensitivity of machine learning methods to the directionality of the inputs, we investigated the symmetry property of the RP method to account for the arbitrary selection of the paired ordering (choosing AB vs. BA). To quantify the difference of swapping the directionality of the paired relationships we ran permutation tests (nā=ā1,000) comparing the two directionalities across the four conditions (both organisms and methods) computing the percent difference over the same summary statistics ROCAUC and PRCAUC, in addition to the F1 Measure, and Test Accuracy. Across all conditions and metrics, the largest percent difference observed was 0.55% with an average of 0.33%. From these experiments, we conclude that the magnitude of these differences are negligible. However to eliminate them in future applications of RP, we consider combining the complimentary metrics into a single averaged value thereby guaranteeing the symmetry of the method.
The NaRRO, NoRRO, and ARRO features defined here were all similarly distributed, though differed in scale as a result of their respective normalization factors. This work limited the scope to intraspecies predictions for which the NaRRO metric is most appropriate since we do not compare values between organisms. We however, emphasize the utility of the ARRO and NoRRO metrics for interspecies predictions and the comparison of PPI predictions between organisms. Future work will investigate their individual contribution to these prediction tasks and to support interpretation of results by experimentalists looking to curate a set of putative PPIs for experimental validation.
Interpretability of PPI Results by Experimentalists
The current RP framework is a datadriven approach to leverage the context provided by jointly considering facets of the pairwise PPI relationships. Following the transition from static to interactive graphs to enable additional exploration of empirical data^{44}, the production of fully interactive visual depictions of these PPI results, as illustrated in the onetoall curves, promise to facilitate exploration and interpretation when communicating results with experimentalists. For example, demonstrating that two underrepresented proteins find themselves to be the highest scoring complimentary proteins in their respective perspectives, despite falling below the global threshold, would provide increased confidence in further investigating their putative interaction. Similarly, should they both find themselves in their respective baselines this would reinforce the likelihood that they are noninteractors. Future work will look to develop a visualization framework incorporating RP to serve as an intuitive interface for experimentalist to explore prediction results.
Future Work
Applicable to any weighted complete graph problem exhibiting class imbalance, the RP framework can be applied to fields other than PPI prediction. A large number of multiclass multilabel problems can be modeled as complete bipartite graph problems, such as protein function prediction or disease prediction from electronic health records in a patient population. In each, RP could be leveraged to augment the predicted outcomes. Since the paired comparison of elements is prevalent in a wide breadth of fields, including social network analysis^{45} and twomarket structures in economics^{46}, we anticipate the utility of the RP framework in numerous applications.
Conclusion
In this work, we suggest revising the assumption that a single global threshold can be appropriately defined across the proteome due to the inherent diversity of protein interaction profiles. In leveraging visualization techniques, we propose that the recent development of PPI predictors capable of generating the comprehensive set of putative interactions has given rise to context, enabling us now to evaluate a putative PPI within the context of all possible predictions. Leveraging this context, we introduce a novel modeling framework called Reciprocal Perspective, which estimates a localized threshold on a perprotein basis using several rank order metrics. We demonstrate that it significantly improves classification performance (ROCAUC, PRCAUC; p < 0.001) using two stateoftheart PPI predictors, PIPE and SPRINT, over five organisms: H. sapiens, S. cerevisiae, A. thaliana, C. elegans, and M. musculus.
References
Braun, P. & Gingras, A.C. History of proteināprotein interactions: From eggwhite to complex networks. Proteomics 12, 1478ā1498 (2012).
Schoenrock, A., Dehne, F., Green, J. R., Golshani, A. & Pitre, S. Mppipe: a massively parallel proteinprotein interaction prediction engine. In Proceedings of the international conference on Supercomputing, 327ā337 (ACM, 2011).
Li, Y. & Ilie, L. Sprint: ultrafast proteinprotein interaction prediction of the entire human interactome. BMC bioinformatics 18, 485 (2017).
Pitre, S. et al. Pipe: a proteinprotein interaction prediction engine based on the reoccurring short polypeptide sequences between known interacting protein pairs. BMC bioinformatics 7, 365 (2006).
Zhang, Q. C., Petrey, D., Garzon, J. I., Deng, L. & Honig, B. Preppi: a structureinformed database of proteināprotein interactions. Nucleic acids research 41, D828āD833 (2012).
Li, Z.W., You, Z.H., Chen, X., Gui, J. & Nie, R. Highly accurate prediction of proteinprotein interactions via incorporating evolutionary information and physicochemical characteristics. International journal of molecular sciences 17, 1396 (2016).
Luo, X., AlMubaid, H. & Bettayeb, S. Ontology based semantic similarity for protein interactions. In Proceedings of BICOB2013 Intāl Conf on Bioinformatics and Computational Biology (2013).
Wu, J. et al. Integrated network analysis platform for proteinprotein interactions. Nature methods 6, 75 (2009).
Dick, K. & Green, J. Comparison of sequenceand structurebased proteinprotein interaction sites. In Student Conference (ISC), 2016 IEEE EMBS International, 1ā4 (IEEE, 2016).
Guo, Y., Yu, L., Wen, Z. & Li, M. Using support vector machine combined with auto covariance to predict proteināprotein interactions from protein sequences. Nucleic acids research 36, 3025ā3030 (2008).
Hamp, T. & Rost, B. Evolutionary profiles improve proteināprotein interaction prediction from sequence. Bioinformatics 31, 1945ā1950 (2015).
Sun, T., Zhou, B., Lai, L. & Pei, J. Sequencebased prediction of protein protein interaction using a deeplearning algorithm. BMC bioinformatics 18, 277 (2017).
AmosBinks, A. et al. Binding site prediction for proteinprotein interactions and novel motif discovery using reoccurring polypeptide sequences. BMC bioinformatics 12, 225 (2011).
Hou, Q., De Geest, P. F., Vranken, W. F., Heringa, J. & Feenstra, K. A. Seeing the trees through the forest: sequencebased homoand heteromeric proteinprotein interaction sites prediction using random forest. Bioinformatics 33, 1479ā1487 (2017).
Wang, L. et al. An ensemble approach for largescale identification of proteinprotein interactions using the alignments of multiple sequences. Oncotarget 8, 5149 (2017).
Kotlyar, M., Rossos, A. E. & Jurisica, I. Prediction of ProteinProtein Interactions. Current Protocols in Bioinformatics 60(8), 2.1ā8.2.14, https://doi.org/10.1002/cpbi.38 (2017).
Atkins, W. M. Biological messiness vs. biological genius: mechanistic aspects and roles of protein promiscuity. The Journal of steroid biochemistry and molecular biology 151, 3ā11 (2015).
Schreiber, G. & Keating, A. E. Protein binding specificity versus promiscuity. Current opinion in structural biology 21, 50ā61 (2011).
Saito, T. & Rehmsmeier, M. The precisionrecall plot is more informative than the roc plot when evaluating binary classifiers on imbalanced datasets. PloS one 10, e0118432 (2015).
JimĆ©nezValverde, A. Insights into the area under the receiver operating characteristic curve (auc) as a discrimination measure in species distribution modelling. Global Ecology and Biogeography 21, 498ā507 (2012).
Halligan, S., Altman, D. G. & Mallett, S. Disadvantages of using the area under the receiver operating characteristic curve to assess imaging tests: a discussion and proposal for an alternative approach. European radiology 25, 932ā939 (2015).
MorenoHagelsieb, G. & Latimer, K. Choosing blast options for better detection of orthologs as reciprocal best hits. Bioinformatics 24, 319ā324 (2007).
Holm, S. A simple sequentially rejective multiple test procedure. Scandinavian journal of statistics 65ā70 (1979).
Mei, S., Karimnezhad, A., Forest, M., Bickel, D. R. & Greenwood, C. M. The performance of a new local false discovery rate method on tests of association between coronary artery disease (cad) and genomewide genetic variants. PloS one 12, e0185174 (2017).
Efron, B. Correlation and largescale simultaneous significance testing. Journal of the American Statistical Association 102, 93ā103 (2007).
Bickel, D. R. Correcting false discovery rates for their bias toward false positives, http://hdl.handle.net/10393/34277 (2016).
KoschĆ¼tzki, D. & Schreiber, F. Centrality analysis methods for biological networks and their application to gene regulatory networks. Gene regulation and systems biology 2, GRSBāS702 (2008).
Srihari, S. & Leong, H. W. A survey of computational methods for protein complex prediction from protein interaction networks. Journal of bioinformatics and computational biology 11, 1230002 (2013).
Orchard, S. et al. Protein interaction data curation: the international molecular exchange (imex) consortium. Nature methods 9, 345 (2012).
Krasowski, M. D., Reschly, E. J. & Ekins, S. Intrinsic disorder in nuclear hormone receptors. Journal of proteome research 7, 4359ā4372 (2008).
Wright, P. E. & Dyson, H. J. Intrinsically disordered proteins in cellular signalling and regulation. Nature reviews Molecular cell biology 16, 18 (2015).
Hsu, W.L. et al. Exploring the binding diversity of intrinsically disordered proteins involved in onetomany binding. Protein Science 22, 258ā273 (2013).
Higurashi, M., Ishida, T. & Kinoshita, K. Identification of transient hub proteins and the possible structural basis for their multiple interactions. Protein Science 17, 72ā78 (2008).
Manna, B., Bhattacharya, T., Kahali, B. & Ghosh, T. C. Evolutionary constraints on hub and nonhub proteins in human protein interaction network: insight from protein connectivity and intrinsic disorder. Gene 434, 50ā55 (2009).
Patil, A., Kinoshita, K. & Nakamura, H. Hub promiscuity in proteinprotein interaction networks. International journal of molecular sciences 11, 1930ā1943 (2010).
Pitre, S. et al. Global investigation of proteināprotein interactions in yeast saccharomyces cerevisiae using reoccurring short polypeptide sequences. Nucleic acids research 36, 4286ā4294 (2008).
Cleveland, W. S. & Devlin, S. J. Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American statistical association 83, 596ā610 (1988).
Kazmirchuk, T. et al. Designing antizika virus peptides derived from predicted humanzika virus proteinprotein interactions. Computational biology and chemistry 71, 180ā187 (2017).
Barnes, B. et al. Predicting novel proteinprotein interactions between the hiv1 virus and homo sapiens. In Student Conference (ISC), 2016 IEEE EMBS International, 1ā4 (IEEE, 2016).
Park, Y. Critical assessment of sequencebased proteinprotein interaction prediction methods that do not require homologous protein sequences. BMC bioinformatics 10, 419 (2009).
Dick, K., Dehne, F., Golshani, A. & Green, J. R. Positome: A method for improving proteinprotein interaction quality and prediction accuracy. In Computational Intelligence in Bioinformatics and Computational Biology (CIBCB), 2017 IEEE Conference on, 1ā8 (IEEE, 2017).
Pitre, S. et al. Short cooccurring polypeptide regions can predict global protein interaction maps. Scientific reports 2, 239 (2012).
FernĆ”ndezDelgado, M., Cernadas, E., Barro, S. & Amorim, D. Do we need hundreds of classifiers to solve real world classification problems. J. Mach. Learn. Res 15, 3133ā3181 (2014).
Weissgerber, T. L., Garovic, V. D., Savic, M., Winham, S. J. & Milic, N. M. From static to interactive: transforming data visualization to improve transparency. PLoS biology 14, e1002484 (2016).
Backstrom, L. & Kleinberg, J. Romantic partnerships and the dispersion of social ties: a network analysis of relationship status on facebook. In Proceedings of the 17th ACM conference on Computer supported cooperative work & social computing, 831ā841 (ACM, 2014).
GonzĆ”lezDaz, J., Hendrickx, R. & Lohmann, E. Paired comparisons analysis: an axiomatic approach to ranking methods. Social Choice and Welfare 42, 139ā169 (2014).
Acknowledgements
The authors would like to acknowledge funding support from the Natural Sciences and Engineering Research Council of Canada.
Author information
Authors and Affiliations
Contributions
K.D. and J.R.G. conceived of the study. K.D. prepared the datasets, ran the experiments, and drafted the manuscript. K.D. and J.R.G. revised and approve of the manuscript.
Corresponding authors
Ethics declarations
Competing Interests
The authors declare no competing interests.
Additional information
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the articleās Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the articleās Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dick, K., Green, J.R. Reciprocal Perspective for Improved ProteinProtein Interaction Prediction. Sci Rep 8, 11694 (2018). https://doi.org/10.1038/s41598018300441
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598018300441
This article is cited by

TRTCD: trust route prediction based on trusted community detection
Multimedia Tools and Applications (2023)

Struct2Graph: a graph attention network for structure based predictions of proteināprotein interactions
BMC Bioinformatics (2022)

Assessing sequencebased proteināprotein interaction predictors for use in therapeutic peptide engineering
Scientific Reports (2022)

Reciprocal perspective as a super learner improves drugtarget interaction prediction (MUSDTI)
Scientific Reports (2022)

PIPE4: Fast PPI Predictor for Comprehensive Inter and CrossSpecies Interactomes
Scientific Reports (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.