Evidence of probabilistic behaviour in protein interaction networks

The probability of edge existence due to node degree: a baseline for network-based predictions

Important tasks in biomedical discovery such as predicting gene functions, gene-disease associations, and drug repurposing opportunities are often framed as network edge prediction. The number of edges connecting to a node, termed degree, can vary greatly across nodes in real biomedical networks, and the distribution of degrees varies between networks. If degree strongly influences edge prediction, then imbalance or bias in the distribution of degrees could lead to nonspecific or misleading predictions. We introduce a network permutation framework to quantify the effects of node degree on edge prediction. Our framework decomposes performance into the proportions attributable to degree and the network's specific connections using network permutation to generate features that depend only on degree. We discover that performance attributable to factors other than degree is often only a small portion of overall performance. Researchers seeking to predict new or missing edges in biological networks should use our permutation approach to obtain a baseline for performance that may be nonspecific because of degree. We released our methods as an open-source Python package (https://github.com/hetio/xswap/).

The probability of edge existence due to node degree: a baseline for network-based predictions

Important tasks in biomedical discovery such as predicting gene functions, gene-disease associations, and drug repurposing opportunities are often framed as network edge prediction. The number of edges connecting to a node, termed degree, can vary greatly across nodes in real biomedical networks, and the distribution of degrees varies between networks. If degree strongly influences edge prediction, then imbalance or bias in the distribution of degrees could lead to nonspecific or misleading predictions. We introduce a network permutation framework to quantify the effects of node degree on edge prediction. Our framework decomposes performance into the proportions attributable to degree and the network's specific connections. We discover that performance attributable to factors other than degree is often only a small portion of overall performance. Degree's predictive performance diminishes when the networks used for training and testing-despite measuring the same biological relationships-were generated using distinct techniques and hence have large differences in degree distribution. We introduce the permutation-derived edge prior as the probability that an edge exists based only on degree. The edge prior shows excellent discrimination and calibration for 20 biomedical networks (16 bipartite, 3 undirected, 1 directed), with AUROCs frequently exceeding 0.85. Researchers seeking to predict new or missing edges in biological networks should use the edge prior as a baseline to identify the fraction of performance that is nonspecific because of degree. We released our methods as an open-source Python package (https://github.com/hetio/xswap/).

Systems biology approaches for discovering biomarkers for traumatic brain injury

The rate of traumatic brain injury (TBI) in service members with wartime injuries has risen rapidly in recent years, and complex, variable links have emerged between TBI and long-term neurological disorders. The multifactorial nature of TBI secondary cellular response has confounded attempts to find cellular biomarkers for its diagnosis and prognosis or for guiding therapy for brain injury. One possibility is to apply emerging systems biology strategies to holistically probe and analyze the complex interweaving molecular pathways and networks that mediate the secondary cellular response through computational models that integrate these diverse data sets. Here, we review available systems biology strategies, databases, and tools. In addition, we describe opportunities for applying this methodology to existing TBI data sets to identify new biomarker candidates and gain insights about the underlying molecular mechanisms of TBI response. As an exemplar, we apply network and pathway analysis to a manually compiled list of 32 protein biomarker candidates from the literature, recover known TBI-related mechanisms, and generate hypothetical new biomarker candidates.

Bias tradeoffs in the creation and analysis of protein-protein interaction networks

Networks constructed from aggregated protein-protein interaction data are commonplace in biology. But the studies these data are derived from were conducted with their own hypotheses and foci. Focusing on data from budding yeast present in BioGRID, we determine that many of the downstream signals present in network data are significantly impacted by biases in the original data. We determine the degree to which selection bias in favor of biologically interesting bait proteins goes down with study size, while we also find that promiscuity in prey contributes more substantially in larger studies. We analyze interaction studies over time with respect to data in the Gene Ontology and find that reproducibly observed interactions are less likely to favor multifunctional proteins. We find that strong alignment between co-expression and protein-protein interaction data occurs only for extreme co-expression values, and use this data to suggest candidates for targets likely to reveal novel biology in follow-up studies.

BIOLOGICAL SIGNIFICANCE

Protein-protein interaction data finds particularly heavy use in the interpretation of disease-causal variants. In principle, network data allows researchers to find novel commonalities among candidate genes. In this study, we detail several of the most salient biases contributing to aggregated protein-protein interaction databases. We find strong evidence for the role of selection and laboratory biases. Many of these effects contribute to the commonalities researchers find for disease genes. In order for characterization of disease genes and their interactions to not simply be an artifact of researcher preference, it is imperative to identify data biases explicitly. Based on this, we also suggest ways to move forward in producing candidates less influenced by prior knowledge. This article is part of a Special Issue entitled: Can Proteomics Fill the Gap Between Genomics and Phenotypes?

The impact of multifunctional genes on "guilt by association" analysis

Many previous studies have shown that by using variants of "guilt-by-association", gene function predictions can be made with very high statistical confidence. In these studies, it is assumed that the "associations" in the data (e.g., protein interaction partners) of a gene are necessary in establishing "guilt". In this paper we show that multifunctionality, rather than association, is a primary driver of gene function prediction. We first show that knowledge of the degree of multifunctionality alone can produce astonishingly strong performance when used as a predictor of gene function. We then demonstrate how multifunctionality is encoded in gene interaction data (such as protein interactions and coexpression networks) and how this can feed forward into gene function prediction algorithms. We find that high-quality gene function predictions can be made using data that possesses no information on which gene interacts with which. By examining a wide range of networks from mouse, human and yeast, as well as multiple prediction methods and evaluation metrics, we provide evidence that this problem is pervasive and does not reflect the failings of any particular algorithm or data type. We propose computational controls that can be used to provide more meaningful control when estimating gene function prediction performance. We suggest that this source of bias due to multifunctionality is important to control for, with widespread implications for the interpretation of genomics studies.

Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure

We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.

The modern RNP world of eukaryotes

Eukaryote gene expression is mediated by a cascade of RNA functions that regulate, process, store, transport, and translate RNA transcripts. The RNA network that promotes this cascade depends on a large cohort of proteins that partner RNAs; thus, the modern RNA world of eukaryotes is really a ribonucleoprotein (RNP) world. Features of this "RNP infrastructure" can be related to the high cytosolic density of macromolecules and the large size of eukaryote cells. Because of the densely packed cytosol or nucleoplasm (with its severe restriction on diffusion of macromolecules), partitioning of the eukaryote cell into functionally specialized compartments is essential for efficiency. This necessitates the association of RNA and protein into large RNP complexes including ribosomes and spliceosomes. This is well illustrated by the ubiquitous spliceosome for which most components are conserved throughout eukaryotes and which interacts with other RNP-based machineries. The complexes involved in gene processing in modern eukaryotes have broad phylogenetic distributions suggesting that the common ancestor of extant eukaryotes had a fully evolved RNP network. Thus, the eukaryote genome may be uniquely informative about the transition from an earlier RNA genome world to the modern DNA genome world.

Influence of protein abundance on high-throughput protein-protein interaction detection

Experimental protein-protein interaction (PPI) networks are increasingly being exploited in diverse ways for biological discovery. Accordingly, it is vital to discern their underlying natures by identifying and classifying the various types of deterministic (specific) and probabilistic (nonspecific) interactions detected. To this end, we have analyzed PPI networks determined using a range of high-throughput experimental techniques with the aim of systematically quantifying any biases that arise from the varying cellular abundances of the proteins. We confirm that PPI networks determined using affinity purification methods for yeast and Escherichia coli incorporate a correlation between protein degree, or number of interactions, and cellular abundance. The observed correlations are small but statistically significant and occur in both unprocessed (raw) and processed (high-confidence) data sets. In contrast, the yeast two-hybrid system yields networks that contain no such relationship. While previously commented based on mRNA abundance, our more extensive analysis based on protein abundance confirms a systematic difference between PPI networks determined from the two technologies. We additionally demonstrate that the centrality-lethality rule, which implies that higher-degree proteins are more likely to be essential, may be misleading, as protein abundance measurements identify essential proteins to be more prevalent than nonessential proteins. In fact, we generally find that when there is a degree/abundance correlation, the degree distributions of nonessential and essential proteins are also disparate. Conversely, when there is no degree/abundance correlation, the degree distributions of nonessential and essential proteins are not different. However, we show that essentiality manifests itself as a biological property in all of the yeast PPI networks investigated here via enrichments of interactions between essential proteins. These findings provide valuable insights into the underlying natures of the various high-throughput technologies utilized to detect PPIs and should lead to more effective strategies for the inference and analysis of high-quality PPI data sets.

Probing the extent of randomness in protein interaction networks

Protein-protein interaction (PPI) networks are commonly explored for the identification of distinctive biological traits, such as pathways, modules, and functional motifs. In this respect, understanding the underlying network structure is vital to assess the significance of any discovered features. We recently demonstrated that PPI networks show degree-weighted behavior, whereby the probability of interaction between two proteins is generally proportional to the product of their numbers of interacting partners or degrees. It was surmised that degree-weighted behavior is a characteristic of randomness. We expand upon these findings by developing a random, degree-weighted, network model and show that eight PPI networks determined from single high-throughput (HT) experiments have global and local properties that are consistent with this model. The apparent random connectivity in HT PPI networks is counter-intuitive with respect to their observed degree distributions; however, we resolve this discrepancy by introducing a non-network-based model for the evolution of protein degrees or "binding affinities." This mechanism is based on duplication and random mutation, for which the degree distribution converges to a steady state that is identical to one obtained by averaging over the eight HT PPI networks. The results imply that the degrees and connectivities incorporated in HT PPI networks are characteristic of unbiased interactions between proteins that have varying individual binding affinities. These findings corroborate the observation that curated and high-confidence PPI networks are distinct from HT PPI networks and not consistent with a random connectivity. These results provide an avenue to discern indiscriminate organizations in biological networks and suggest caution in the analysis of curated and high-confidence networks.