For many complex diseases, an earlier and more reliable diagnosis is considered a key prerequisite for developing more effective therapies to prevent or delay disease progression. Classical statistical learning approaches for specimen classification using omics data, however, often cannot provide diagnostic models with sufficient accuracy and robustness for heterogeneous diseases like cancers or neurodegenerative disorders. In recent years, new approaches for building multivariate biomarker models on omics data have been proposed, which exploit prior biological knowledge from molecular networks and cellular pathways to address these limitations. This survey provides an overview of these recent developments and compares pathway- and network-based specimen classification approaches in terms of their utility for improving model robustness, accuracy and biological interpretability. Different routes to translate omics-based multifactorial biomarker models into clinical diagnostic tests are discussed, and a previous study is presented as example. In spite of the remarkable advances in biomedicine over recent decades, for a wide range of common, systemic and chronic diseases, precise molecular markers for early diagnosis are not yet available. In particular, for some of the most prevalent neurologic disorders  are commonly assessed. Although these approaches have advantages in terms of simplicity and costs, for complex and heterogeneous diseases, single-molecule biomarkers tend to provide insufficient accuracy and robustness across different patient cohorts . BuildiIn recent years, new bioinformatics approaches have therefore been proposed, which involve the integration of prior biological knowledge from cellular pathways and molecular networks into the model-building procedure. These approaches make use of prior observations, according to which, differences in pathway activity between diverse biological conditions tend to be more stable than differences in individual gene activity , and disHere, a review of recent network- and pathway-based statistical learning approaches for high-throughput omics data set analysis is provided, including a critical discussion of limitations and the added value of different methodologies for improving model robustness, accuracy and biological interpretability. Because not all diseases are characterized by aberrant molecular signatures, the application focus is on diagnostic approaches for diseases with complex molecular manifestations. First, methods using information from public cellular pathway definitions will be discussed, then approaches exploiting prior knowledge from genome-scale molecular networks. Next, common limitations of pathway- and network-guided predictive modeling are pointed out, as well as shortcomings related to the biospecimen origin, processing and storage and possible techniques to address or alleviate limitations in data analysis. Finally, the potential for translating omics-derived multivariate sample classification models into chip-based diagnostic devices is discussed, and a previous success story is presented.Cellular pathway definitions from manually curated databases, including KEGG , BioCartThese methods mainly differ in terms of their pathway activity scoring approach  and the prediction method used . et al. , where fiy(x) is the conditional probability density function of gene i under phenotype y), and then uses these ratios for a weighted combination of expression levels into a summarized pathway activity fingerprint aj (aj = Σin LLRi (xij)), assuming independent contributions of the LLRs for different member genes. The authors compared their approach on two breast cancer data sets against gene-level predictors, the mean/median pathway summarization, the SVD- and CORG-based techniques described above, and their method achieved the highest predictive performance in both within-data set cross-validation experiments and one out of two cross-data set prediction experiments (the mean summarization scored higher in one case).A first probabilistic method to infer pathway activity from omics data was developed by u et al. . It estiet al. [While the techniques discussed above mostly summarize pathway activity via (weighted) averages or dimension reduction approaches, it was noted that disease-associated pathway alterations may affect the variance of expression levels in pathways more strongly than the mean. Generally, variance patterns in disease-related omics data can reflect inter-patient variation (e.g. differences in the etiology or disease stage) or intra-patient fluctuations , and the study of both of these sources of variation may be important to improve the understanding of the disease. Glaab et al.  thereforet al. . Rule-baet al. .et al. [A further strategy to improve classifier robustness is to use discretized pathway activity scores or counting statistics, e.g. Svenson et al.  presenteCellular pathway diagrams do not only capture information on the functional relatedness of biomolecules involved in a pathway, but also on the network topology of regulatory or molecular interactions that link them together.et al. [Efroni et al.  presenteet al. [Pathway topology information is also exploited in the approach by Vaske et al. , who conet al. [Apart from considering the topology of molecular interactions within a pathway, studying alterations in all the downstream targets of pathway members (i.e. including targets not belonging to the pathway) may provide an additional source of information to further improve pathway activity scoring. Breslin et al.  presenteet al. [Finally, although all approaches considered so far use pathway-level sample classification as a replacement for gene-level classification, these are not exclusive options. Kim et al.  proposedet al. , which aIn summary, a wide range of pathway activity inference methods and machine learning approaches are available, which can be combined effectively for pathway-based diagnostic classification of biological samples. While pathway-based prediction does not necessarily provide superior predictive performance in within-data set cross-validation experiments, improved robustness and accuracy was observed consistently in cross-study prediction tasks.Although manually curated pathways have many benefits for the biological interpretation of large-scale omics data, in living cells, metabolic and signaling pathways are not isolated but interconnected within large and complex molecular and regulatory networks. These networks often include several genes, proteins or metabolites that are not annotated for any pathway and therefore ignored by pathway-based analysis methods. Consequently, to identify disease-associated modules of interconnected biomolecules in a more unbiased manner (i.e. without restricting the search space to biomolecules with known pathway annotations), network-based analysis methods have been introduced. While pathway-based approaches for biomarker modeling may have advantages in terms of model interpretability, the search space exploration in network-based biomarker discovery is not restricted by subjectively defined pathway boundaries, and the genome-scale molecular networks used as input typically cover significantly larger numbers of biomolecules than all combined pathways. Nevertheless, similar to subjectively defined pathways, networks assembled from public data sources suffer from various limitations, e.g. missing molecular interactions and lack of tissue-specific annotations, and these issues have to be addressed by dedicated methods (see section on ‘limitations and possible solution strategies’ below). In the following, two main types of network-based modeling approaches will be discussed: First, two-step sequential approaches, which score the activity in molecular subnetworks and afterward use these activities for predictive machine learning; and secondly, one-step network analysis approaches, which exploit network topology information directly within the predictive model building.Network activity over multiple interconnected biomolecules can be summarized and scored using similar averaging or dimension reduction approaches as in pathway activity scoring methods. However, in contrast to the straightforward use of predefined pathway definitions, first a molecular or regulatory network has to be assembled or reconstructed, using either public molecular interaction databases or applying network inference methods to omics data  networks. Ma et al. [Instead of constructing new regulatory networks, discriminative disease-associated network alterations can also be identified by computationally mapping omics data onto a et al.  developea et al. , reestima et al.  for detaet al. focuses on improving the disease-association scores for individual genes, Chuang et al. [Lee et al. [While the approach by Ma g et al.  presentee et al. ). After et al. [insilico representation of a PPI network, they determined proteins with large numbers of biochemical interaction partners , and computed their relative expression compared with each of these interacting partners. They then determined for which hubs the relative expression differed significantly between long-term survivors and patients who died from the disease, and applied a clustering approach to assign a probability of poor prognosis to new patient samples (the specific method used is known as ‘affinity propagation clustering’ in the literature). The approach was evaluated using 5-fold cross-validation, providing accuracy, sensitivity and specificity estimates that compared favorably with the reported results for commercially available genomic breast cancer diagnostics.As an intermediate solution between focusing on individual biomolecules and entire network modules, Taylor et al.  proposedet al. [Instead of considering topological properties of individual nodes in a molecular network, information from a network graph can also be extracted via algorithms for finding sub-graphs, which stand out in terms of their high density of molecular interactions (using approaches referred to as ‘community identification’ or ‘graph clustering’ methods in the literature). Petrochilos et al.  proposedet al. [Apart from averaging molecular activities over network neighborhoods or using community identification methods, signal processing techniques may provide a further means to glean useful information from a network for predictive model building, as shown in an approach by Rapaport et al. . They maIn contrast to the network analysis approaches considered so far, which apply network feature extraction and predictive machine learning analysis in separate steps, more recently, one-step network-based feature selection approaches have been proposed, integrating the attribute selection directly into the predictive model building. Most of these approaches formulate the model building task as an optimization problem formulation, in which the objective function for classification or regression is extended by a penalty term promoting the selection of grouped features in a molecular network .et al. [et al. discarded censored observations and about 20 000 variables that could not be assigned to corresponding nodes in the molecular interaction network (see section on ‘limitations’ below). Yang et al. [Li et al.  proposedet al. . As possg et al.  suggesteg et al. . In expeet al. [However, with non-convex penalties, finding global optimal solutions is often not feasible and even identifying good local optima may require high computational effort. Lorbert et al. , 48 propet al. introduced a new instance of PEN, which penalizes differences between the ‘absolute’ values of weights of interlinked features in a network graph. The motivation behind this approach, termed GenePEN, is that the magnitude of a weight in a linear model reflects the predictive value of the corresponding variable, so that the weights for irrelevant features are driven to zero by the penalty. By ensuring the convexity of the penalty function, global optimal solutions can be identified efficiently with existing optimization frameworks. When evaluating GenePEN on simulated data and real-word microarray data sets, in comparison with other classification methods using feature grouping, the method provided similar predictive power and gene selections, sharing significantly more connections within a molecular interaction network. Visualization of the corresponding subnetworks enabled a biological interpretation of disease-affected network regions, which were enriched in known disease-related genes obtained from literature mining.More recently, Vlassis Overall, network-based sample classification methods provide a new means to analyze complex omics data sets, allowing researchers to identify coherent molecular network alterations under different biological conditions. Identifying such network-level patterns in omics data for diseases with complex molecular manifestations can shed new light on the molecular mechanisms of the disease and facilitate the development of robust multifactorial biomarker signatures.In contrast to single-molecule-based biomarker modeling, a network-level approach has the potential to capture diverse facets of a heterogenic disease reflected via alteration patterns in different network regions. In comparison with pathway-based machine learning approaches, methods using genome-scaled networks as prior knowledge may produce models that are more difficult to interpret biologically, but which can identify a much wider range of alterations in cellular processes . Finally, network- and pathway-based classification approaches share the main benefit of improving model robustness in cross-study analyses as compared with using individual biomolecules as features. Among these new higher-level biomarker signatures, network-based signatures accounting for molecular activities over larger and algorithm-derived network regions may often provide more robust multifactorial markers than signatures for smaller pathways, which are typically defined subjectively, possibly overlooking relevant functionally related molecules in the surrounding network. However, the model robustness will also depend on other factors, e.g. the occurrence of protein complexes in the studied pathway/network  and the reliability and completeness of the specific network or pathway data source used (see limitations discussed in the following section).While pathway- and network-based analyses of omics data can enrich the biological interpretation of complex molecular alteration patterns and facilitate robust biomarker modeling, users should also be aware of common limitations behind these methods and possibilities to address them.Although detailed functional annotations have been collected for a large portion of genes in humans and common model organisms, many identified genes still lack any functional assignment. Consequently, a significant portion of genes and proteins analyzed via current high-throughput measurement techniques can often not be assigned to any pathway or molecular network for systems-level analyses. Similarly, several gene regulatory interactions and PPIs are still unknown, and experimental techniques to identify molecular interactions may also generate false-positive results . Thus, pA further limitation of current pathway databases and assembled molecular networks is that tissue- and cell-type specificity of molecular interactions and protein functions is typically not considered in these data resources. This can be particularly problematic when studying diseases showing selective vulnerability for specific tissues or cell types, e.g. as found in many neurodegenerative disorders . SimilarTo account for the varying reliability of public biochemical interaction data when assembling a molecular network, various approaches to determine confidence scores have been proposed . One of A frequently encountered difficulty in pathway analyses is also the conversion of the information content of public pathway diagrams into adequate data structures for computational investigations. Pathway structures usually contain more complex layers of information than gene–gene networks, e.g. meta-nodes representing protein complexes or gene families, and catalysis reactions represented by edges pointing to edges. Dedicated computational approaches are therefore required to convert pathway diagrams into uniform network representations, e.g. using biology-driven rules as in the R/Bioconductor software package ‘graphite’ .Apart from this conversion task, building tissue-specific pathway/network representations or assigning probabilities for tissue specificity to the biological interactions in an existing network is a further challenging problem because interactions are rarely confirmed experimentally in multiple specific tissues. Most bioinformatics approaches for assigning tissue specificity scores to protein interactions use publicly available gene or protein expression data from large-scale tissue profiling studies , 64, e.gWhile changes in the mean or variance of the overall molecular activity in pathways can provide robust biomarkers for some diseases, pathways may also contain forks, and only one of their branches or stems may be affected in a pathological condition. Approaches focusing on changes in the overall pathway activity may therefore fail in detecting significant alterations affecting only one pathway branch. Although network analysis methods identifying altered subnetworks may be helpful in this situation , ideally, available knowledge on distinct pathway branches or outstanding regions in a complex pathway architecture should be exploited directly, e.g. by partitioning a pathway into corresponding ‘subpathways’ and separately analyzing their molecular alterations using existing pathway-level bioinformatics tools.invitro and invivo perturbation experiments rather than from high-throughput data analysis, even when using high-quality time-series data with large sample sizes and dedicated statistics for identifying cause–effect relationships  of a disease. Apart from philosophical disagreements on how causation should be defined , the disity test ). Prior ity test . Bill Shity test . These aImproving incomplete pathways and networks by identifying missing molecular interactions is arguably one of the most challenging problems in this domain. Pathway definitions are typically created in a subjective manner because no universal predefined criteria for determining pathway membership and boundaries are available, and the curators of the corresponding databases are required to make judgments on the relevance of potential pathway members. These subjective definitions may be prejudiced and erroneous, and even networks assembled automatically from public databases may contain biases, e.g. resulting from prior subjective decisions on which putative PPIs are of sufficient interest for experimental validation. Moreover, in diseases the pathway topology may change, and generic pathway databases have recently been complemented by dedicated pathway maps for specific human disorders, e.g. AlzPathway  for Alzhinvitro disease models, and the success may strongly depend on whether reliable prior pathway knowledge is available.Moreover, dedicated bioinformatics techniques have been developed to identify ‘network rewiring’ events, e.g. broken chains or new interactions changing the pathway/network topology, which remain undetected by conventional pathway analyses. Instead of assuming that molecules close to each other in a network undergo similar changes in a disease, these approaches identify alterations in the correlations between the activities of these molecules as signatures for potential pathological changes in network topology . Howeverab initio discovery of pathways within genetic or molecular networks have been proposed [in silico prediction approaches are however still bound to provide limited reliability, and only high-confidence biochemical interactions should be included in networks for omics data analysis.To support relevant manual pathway curation efforts, computational approaches for proposed , as wellproposed . Moreoveproposed , e.g. thproposed . For proin silico analyses.Finally, to reduce the influence of false-positive predictions on network analyses, molecular interactions should not only be prefiltered by confidence when assembling the network, but also weighted by confidence to apply analysis techniques exploiting these weights to score the reliability of identified network alterations. In subsequent biological validation experiments, investigators can then focus on verifying only the most reliable network alteration patterns derived from the High-throughput omics measurement techniques are typically not designed for diagnostic applications, but for broad systems-level analyses, hypothesis generation and the construction of first tentative machine learning models for sample classification. Such tentative models require subsequent refinement and validation using more sensitive and reproducible measurement techniques to evaluate their potential for diagnostic applications. For example, a sample classification model built and cross-validated using microarray gene expression data, with an embedded feature selection to choose only the most informative genes as predictors, can be validated using more accurate quantitative reverse transcription polymerase chain reaction (qRT-PCR) measurements for the subset of chosen genes.Importantly, to avoid wrong conclusions in the evaluation of diagnostic classification models, adequate statistical methods have to be chosen to assess a model’s overall predictive performance , its calibration/reliability  and its discriminative ability  . Owing tFor the study design, initial power calculations are required to ensure that sufficient sample sizes are available for all statistical assessments . This alin vitro diagnostic test devices. These tests can be developed and validated either through review by the Food and Drug Administration (FDA) or through validation and performance by a specific laboratory certified according to Clinical Laboratory Improvement Amendments (CLIA) [Importantly, clinical validation does not only necessitate significantly larger sample sizes than most research studies, but also independent replication tests on data from other patient cohorts, the clear specification of the biological rationale behind the method and a demonstration of its clinical utility. In contrast to the regulatory framework for drugs, there are multiple pathways for the translation of omics-based tests into validated s (CLIA) .Because using established medical product development pipelines as in pharmaceutical companies is not common practice in academia, for many biomedical research institutions an early collaboration with an experienced industrial partner is often advisable. Although currently no unique and widely recognized standard process for translating omics research findings into clinical diagnostics is available, common recommendations by widely recognized health organizations can be followed. In particular, a committee by the US Institute of Medicine has conducted a study on omics-based clinical test development and proposed a generic process for the development and evaluation of these tests as a recommended guideline . A correInterestingly, the authors of the guideline highlight that a frequent shortcoming of omics-based tests is the lack of a biological rationale behind the test—while single-molecule markers are often known to play a role in the disease, multifactorial omics models obtained from machine learning are often more difficult to interpret and involve a greater risk of overfitting. New pathway- and network-based modeling techniques as discussed in this review could therefore help to address some of these shortcomings and provide more interpretable and robust models as opposed to classical ‘black box’ machine learning models.In the following stage of the clinical development process, the locked-down test is evaluated for clinical utility via one of the following approaches: (i) A prospective–retrospective study using archived specimens from previous clinical trials, (ii) a prospective clinical trial in which the test (a) directs patient management, or (b) does not direct patient management . The comA variety of multifactorial, omics-based biomarker models have been translated successfully into diagnostic tests in recent years, in particular, in the field of cancer sub-type stratification. A prominent example is the Oncotype DX test to assess a woman’s risk of recurrence of early-stage, estrogen-receptor-positive breast cancer and the likelihood of benefitting from chemotherapy after surgery. This test measures the activity of 21 genes in tumor samples and then determines a recurrence score number between 0 and 100 (higher scores reflect greater risk of recurrence within 10 years). As opposed to other diagnostic tests using frozen samples, the Oncotype DX assay uses tumor tissue samples that are chemically preserved and sealed in paraffin wax .This work was supported by the


Through interviews with domain experts, we identified four common tasks that require an understanding of the ReactionFlow, a visual analytics application for pathway analysis that emphasizes the structural and causal relationships amongst proteins, complexes, and biochemical reactions within a given pathway. To support the identified causality analysis tasks, user interactions allow an analyst to filter, cluster, and select pathway components across linked views. Animation is used to highlight the flow of activity through a pathway.We introduce ReactionFlow by providing our application to two domain experts who have significant experience with biomolecular pathways, after which we conducted a series of in-depth interviews focused on each of the four causality analysis tasks. Their feedback leads us to believe that our techniques could be useful to researchers who must be able to understand and analyze the complex nature of biological pathways. ReactionFlow is available at https://github.com/CreativeCodingLab/ReactionFlow.We evaluated  Understanding complicated networks of interactions and chemical components is essential to solving contemporary problems in modern biology, especially in domains such as cancer and systems research . PathwayResearchers who work with pathway data are confronted with a number of challenges ,6. Pathwcausality analysis tasks, in which an investigation of how upstream and downstream participants of biochemical reactions may lead to new understanding of the nature of the pathway. The four tasks, described in more detail later in the paper, include:We worked closely over a period of six months with four computational and molecular biologists to identify and prioritize visualization tasks that were important to the biological community. The experts include: a bioinformatician working at a major cancer research lab ; a graduate student with a background in both biology and computer science; and two professors in a molecular biology department at a large public university, each running their own research lab. Our in-depth interviews with these experts led us to identify four important tasks that were not currently well-supported in existing visualization tools for pathway analysis. These four tasks each involve reasoning about the causal relationships between proteins and biochemical reactions within a pathway. We refer to these as T1 Visualizing the downstream consequences of perturbing a protein or protein complex;T2 Finding the shortest path between two proteins;T3 Detecting feedback loops within the pathway;T4 Identifying common downstream elements from two or more proteins.ReactionFlow, visually separates the inputs and outputs of biochemical reactions within a pathway, and emphasizes the relationships between reactions. Visual separation of input and output participants helps reveal highly connected proteins and complexes which may be of particular importance to understanding the nature of a pathway. Perhaps the most useful aspect of ReactionFlow involves the representation of causality within the pathway, highlighting casual relationships between reactions. We use animation as a means to clearly demonstrate the causal relationships in the pathway.Working with the domain experts led us to design and implement a novel, interactive representation of biological pathways that emphasizes the causality within the pathway, focusing on the biochemical reactions as the "backbone" of the pathway, and highlighting the flow of input and output participants of these reactions through various visual encodings, including animation. Our tool, To augment the visual representation of the pathway with a "reaction-centric" view, we enable a variety of user interactions that make it easier to search through proteins, complexes, or reactions , to organize the layout so that reactions are clustered via a topological ordering algorithm or so that edge-crossings are minimized, and to control the animation speed of the flow of activity through the pathway from a selected starting point.ReactionFlow was an iterative process that relied on feedback from the four domain experts at various stages of the design and implementation. Many of the ideas that were included were first suggested by one of the domain experts, or emerged organically through these conversations with them. The contributions of this paper are centered around the ReactionFlow application and the tasks they enable:The process of developing  - We identify four tasks related to understanding causal relationships within a pathway; - We introduce a novel visualization to enable causality analysis tasks; - We make use of animation to highlight the flow of activity through a pathway; - We include mechanisms to search, filter, and order pathways to more effectively present relevant data; - We evaluate the effectiveness of our approach through interviews with domain experts.The visualization of biological pathways is challenging due to the complex nature of pathway data, as indicated in the previous section. Given this complexity, publications in molecular biology frequently present biological pathways with human-generated figures. Human creators have the flexibility to arrange visual elements in ways that make representations human readable, and this can allow authors to efficiently encode large volumes of complex information. The human-generated nature of these diagrams allows this complex information to be encoded through clear spatial layouts, organizing the pathway in a meaningful way.This hand-made approach has been replicated digitally in public databases available online, such as the Kyoto Encyclopedia of Genes and Genomes  as well Several tools exist which automatically produce interactive pathway visualizations from structured pathway data, rather than relying on layouts generated by hand. The visualizations produced by these tools mimic the style and visual encoding of human-generated figures in an attempt to to communicate complex network information efficiently. As the layout is computed algorithmically, it is easily updated with new data without requiring extra human effort as networks increase in size. Prominent examples of this approach include Cytoscape , ChiBe , and VANIn addition, ChiBe allows the user to search for proteins of interest, to find relevant pathways, to interactively trace paths between entities, and to identify common regulators or targets of proteins. Finally, experimental data, such as gene expression data or disease association data, can be overlaid on these networks and encoded through color . These fHowever, complexity remains a significant challenge for these applications, particularly with respect to the critical task of viewing causality in a pathway. Pathway visualizations show causal direction through directed edges from one event to another, allowing researchers to address questions about what lies downstream of one protein or reaction in a pathway. To see these causal relationships, researchers must trace paths beginning at some starting point and following directed edges through the pathway, but as the number of steps or branches in a pathway increases this task becomes cognitively challenging.In addition, since these tools mimic the style of pathway diagrams, they do not abstract away details to capture higher-order patterns. For instance, researchers may want to use pathway diagrams to understand the importance of a particular protein in a pathway in order to find suitable targets for drug design. However, critical proteins in a pathway may appear in more than one place in the visualization, perhaps because they are involved in several reactions. To see this, the researcher must either scan visually or use a search tool to find all instances of a protein. Multiple instances of one protein are not immediately evident from the representation, and can be difficult to find through exploration.ReactionFlow. Jigsaw uses a table-style approach to represent entities of one specific type; related entities that are of different types are connected by links. However, there are basic differences due to specific aspects of pathway datasets. For example, proteins or biomolecules may participate in biochemical reactions directly or they may first bind together in a complex hierarchy before participating. The main visual component of our application can be thought of as a hybrid representation that uses features of network and table layouts.Other tools also make use of alternative approaches to representing networks, such as the transition graphs introduced by Pretorius and van Wijk , or the ReactionFlow, which provides scalable views of pathway data that reduce complexity while retaining important pathway information relevant for causality analysis tasks. All example biological pathways can be found in the Reactome Pathway Database and are encoded using the BioPAX format. ReactionFlow was created over the course of six months via an iterative development cycle in which we made changes or added features based mainly on the feedback from the four domain experts.In this section, we describe details about our application, ReactionFlow displaying several biochemical reactions, in this case using the ERK activation pathway. Within this view - which resembles a parallel coordinates layout - input proteins are listed on the left, and output proteins are listed on the right. Input proteins may directly participate in a reaction (shown with green links) or they may form complexes with other proteins (shown with green links) before participating in a reaction (shown with blue links). Complexes are displayed either as blue diamonds or as blue triangles. Triangles represent complexes that only appear as inputs or outputs, while diamonds represent complexes that act as both inputs and outputs within the pathway. Larger triangles/diamonds indicate complexes containing more proteins. In the pathway shown in Figure Figure ReactionFlow highlights all biochemical reactions that it participates in.When a reaction is selected via a mouse click, a textual description is displayed, along with the names of all the proteins that participate in this reaction. Figure ReactionFlow also includes a search box to filter reactions. As users type a phrase into the search box, reactions and participants that include the typed phrase in their description are highlighted. Typing the word "dissociation", for example, highlights the reactions that dissociate complexes into proteins. A user can also select words from a list of the top 20 most common words that are found in the descriptions of biochemical reactions  in the pathway. For example, the ERK1 protein effects the entire ERK1 pathway while ERT2 is only involved in two reactions. Figure ReactionFlow also provides a tool that highlights the shortest path between two proteins in terms of the number of reactions between an input and an output. When users select an input protein, say, for example, cRaf, ReactionFlow displays numbers in front of output proteins that indicate the minimum number of reactions - the number of biochemical "hops" from cRaf - that are needed to generate each output protein from the selected starting point. The color of the links in this view indicate whether steps involve proteins directly (red links) or proteins within a complex (green links). The path from a selected protein to other downstream proteins can also be animated.Figure ReactionFlow to detect feedback loops within a pathway. This makes it easier to identify where cyclical processes are occurring, and thus where perturbations in the network influence both downstream and upstream events. Figure We can also use An important task for understanding the effects of pathways involves finding common downstream elements that may participate in biochemical reactions. For instance, understanding the functionality of pathways through understanding downstream elements is an active area of cancer research -24. In sReactionFlow provides a "common downstream" function that highlights all reactions that are "downstream" of two or more input participants. Figure ReactionFlow is to simplify the visual representation of a pathway, especially to aid in the causality analysis tasks described above, visual clutter can still be an issue, especially in larger pathways containing many proteins and reactions. ReactionFlow thus provides various methods to mitigate the visual clutter. For instance, edge crossings can be reduced by reordering reactions and participants, as in Figure Although an aim of NGF signaling via TRKA from the plasma membrane pathway containing over a hundred biochemical reactions. Figure In the next example, we use a larger pathway, ReactionFlow to other popular tools. Cytoscape features advanced layout algorithms that can minimize edge crossings. Nonetheless, even a medium-sized pathway network, such as HIV life cycle which contains 206 proteins and molecules, 184 complexes, connected via 112 biochemical reactions, demonstrates visual clutter due to link crossing. ChiBE 2 avoids the issue of edge crossing by introducing duplicates of proteins if necessary. However, this makes it more difficult to keep track of reactions involving a selected protein or protein complex . Another problem with node duplication is that for a set of n proteins there may be, at least potentially, up to 2n complexes, greatly increasing the scale of the network. Figures ReactionFlow pushes proteins and complexes participating into the same reactions together, Figures Regarding the issue of clutter, we compare ReactionFlow shown in Figure The right panel of Figures Reaction-Flow when visualizing the early phrase of HIV life cycle. In this figure, we compare our application (in the lower panel) to VANTED (in the top panel). Notice that VANTED displays all biochemical reactions, proteins, and complex participants in the same network. In ReactionFlow, we separate input/output proteins and complexes to both sides and reserve the middle section to present causality between reactions in the pathway. This helps ReactionFlow to scale more effectively when representing larger networks.Although we show all edges connecting reactions to input/output proteins and complexes for the comparison to other existing tools, this is not the main interface of our visualization. Instead, a view where only causal arcs connecting biochemical reactions are displayed is the starting point of our pathway analysis. The input/output participants are only displayed on demand for selective biochemical reactions. Therefore, the original tasks are still viable on a system of large size, such as examples in Figures As depicted, both tools successfully reveal the linear nature in the first part of the network (the longest path contains 30 hops). The main difference of two tools is how they display parts of the pathway that contain cycles. A close-up of this sub-network is displayed to the right of each visualization for comparison. Since our revised topological ordering algorithm attempts to push the downstream arcs to the right of the reactions, every arc on the left potentially creates a feedback loop. In this example, we can easily detect the feedback loops associated with these arcs; the same information is not as easy to discern in VANTED without further analysis. Following the recommendation given in a user study conducted by Holten and van Wijk , our useReactionFlow is implemented in Java and built on top of Processing framework. It is cross-platform, with a minimum requirement of Java 7. ReactionFlow uses Paxtools  helps capture some of that, which can be lost in some network layouts. Once you figure out what's going on this tool seems more intuitive." When pressed on how an interactive layout could better support the ordering in hand-drawn diagrams, he replied: "You can't completely avoid the complexity - it's inherent. But it's good to get different views that give you some more information from a different perspective."One of the experts commented explicitly on the unusual layout, mentioning that he was used to seeing pathways organized as node-link diagrams and saying that "the difficulties in this layout could be with the understanding the flow from left to right, but the animation helps you see how the pathway is organized." After the initial interview, this expert wrote us further comments about the animation: "Animating the flow of biochemical reactions is very useful for understanding causality in the network. Flexible control of that animation is essential, because networks have very different levels of complexity, so some can be viewed quickly, but others must be slowly stepped through." We also asked the experts to comment on the specific tasks. In response to a question for feedback on Task 1, one expert compared our visualization positively to the "gold-standard" of hand-drawn diagrams: "I like hand-drawn diagrams because there is an order... and [Regarding Task 2, one expert found out implementation a bit confusing, even after explanations of how it worked. Based on his evaluation, we plan to clarify the visual encoding in a future version of the application. The other expert didn't have trouble understanding the task, but told us that it didn't correspond to his interpretation of what it meant to find the shortest path: "I'd like to be able to click on two proteins and see the shortest path between them." In our current implementation, the user clicks on a single protein, and all downstream components are highlighted, with a number appearing to indicate how many "hops" away it is from the selected protein. The expert thought that provided too much information and was perhaps too similar to Task 1.Both experts found Task 3 straightforward and easily to understand, and both commented on the importance of identifying feedback loops across multiple pathways, a feature we plan to include in later versions. Regarding Task 4, both experts remarked that it was useful to see which biochemical reactions are "common downstream" components from multiple proteins. One expert told us that one main component of his research was precisely related to this task, which was difficult to visualize in other tools without extensive manual curation: "Sometimes I am interested in understanding how multiple upstream input signals are integrated to drive cellular responses." The other expert also described the usefulness of Task 4: "Families of related proteins are common in human biology. These proteins often share many reactions, but differ in a few key reactions. A view that highlights these commonalities and differences is very useful to parse out these subtleties."ReactionFlow which they found to be either effective or ineffective. Both appreciated the grouping of reactions using the topological ordering. One expert noted "it helps to organize the reactions into modules for cleaner layout and visualization." The other also told us: "A key use for pathway representations is to quickly grasp causality. The topological ordering helps a great deal in this by clustering groups of closely related reactions."We also asked the experts to point out any other features of Both experts noted that they thought that node-link diagrams, though imperfect in many ways, nonetheless were a more familiar representation for pathways and wondered if that would make it difficult for our tool to be adopted by other biologists. Again, they also both suggested as an obvious next step that we make it possible to load in multiple pathways and moreover then be able to easily remove the elements that were not relevant to them, so as not to overwhelm the visualization with too much information. One expert was initially confused about the use of arcs to indicate relationships in the search terms, since it seemed to clash with the main use of the arcs to illustrate causality between biochemical reactions.Despite these concerns, both experts were highly positive about the ability to observe and reason about the causality within a pathway. One of the experts also repeatedly expressed his appreciation that our tool emphasized the biochemical reactions within the pathway, since that was a main interest in his own research, and since other visualizations he had used sometimes made it difficult to see only the reactions.ReactionFlow presents an alternative visual representation of biological pathways, not found in other visualization tools. Our visualization enables a series of novel tasks related to finding patterns within a pathway and to the analysis of causal mechanisms involving proteins and biochemical reactions. Enabling these tasks is potentially very useful to biologists and cancer researchers, as it provides with a means to more deeply understand aspects of biological pathways, such as the downstream connections related to a specific protein complex, or quickly identifying feedback loops.Our interviews with domain experts show that our visualization techniques, and especially our ability to represent causality in different ways, have the potential to be useful to the larger community of researchers investigating biological pathways. Although we are encouraged by the positive feedback, we have already identified areas for future investigation. For instance, although this paper focuses largely on an alternative representation to a node-link diagram, we believe that it may be possible to present our visualization techniques alongside (instead of in replacement of) a node-link diagram. Although one advantage of our representations is that they are less cluttered than node-link representations, we plan to further investigate the scalability of our system and to explore other ways of interactively compressing or expanding parts of the pathway as needed, something that may prove important for very large pathways containing more than a few dozen reactions. Finally, as suggested by the interviews with domain experts, we plan to explore ways of visualizing multiple pathways simultaneously. A future aim is to enable biologists to understand not just the functionality of a single pathways, but also to help clarify how each pathway functions within a forest of pathways.The authors declare that they have no competing interests.TND, PM, JA, and AGF conceived of the interactive visualization technique and its application to biological pathways. JA provided insight into the datasets used during the development of the technique and TND, PM, JA, and AGF investigated related work. TND and AGF determined the causality analysis tasks through interviews with domain experts. TND designed and implemented all aspects of the prototype visualization tool and provided the comparison to existing tools. TND, PM, JA, and AGF drafted, read, and approved the final manuscript.


Q-method to discern whether changed pathway response is caused by mechanistic rewiring of pathways due to evolution. The main innovation is a cumulative pathway interaction heterogeneity statistic accounting for rewiring-specific effects on the rate of change of each molecular variable across conditions. The Q-method remarkably outperformed differential-correlation based approaches on data from diverse biological processes. Strikingly, it also worked well in differentiating rewired chaotic systems, whose dynamics are notoriously difficult to predict. Applying the Q-method on transcriptome data of four yeasts, we show that pathway interaction heterogeneity for known metabolic and signaling pathways is indeed a predictor of interspecies genetic rewiring due to unbalanced TATA box-containing genes among the yeasts. The demonstrated effectiveness of the Q-method paves the way to understanding network evolution at the resolution of functional biological pathways.Changes in response of a biological pathway could be a consequence of either pathway rewiring, changed input, or a combination of both. Most pathway analysis methods are not designed for mechanistic rewiring such as regulatory element variations. This limits our understanding of biological pathway evolution. Here we present a  Modular and hierarchical orderings of molecules in a cell give rise to the biochemical mechanisms underlying functionally distinct biological pathways. Chemical reactions and physical interactions among these molecules govern observed pathway response. We call genetic or epigenetic modifications to the connections among molecules mechanistic rewiring. Both mechanistic rewiring and changed upstream input, though two fundamentally different causes, can elicit divergent pathway responses. Under the overarching goal to understand how evolution may have rewired a biological pathway, we aimed at discerning whether a changed pathway response is likely a result of mechanistic modifications within the pathway or changed upstream input to the pathway. Although other studies linked rewired gene interactions, e.g., TATA box variation, to gene expression variability among related speciesDue to its cumulative nature, pathway analysis is more effective for interpretation of biological functions than single-gene approaches at modest effect and sample sizes. Most pathway analysis methods, e.g., GSEAAvailable pathway topology databases4ScorePAGEQ-method to meet three of them. Specifically, we address the third challenge, the annotation challenge: “missing condition- and cell-specific information” by adapting an annotated pathway topology to context-specific data, instead of using the topology exactly, to allow pathway rewiring. Our main design consideration overcomes methodological challenge 2 “inability to model and analyze dynamic response,” by adopting nonlinear dynamical system models (DSMs). Responding to methodological challenge 3 “inability to model effects of an external stimuli,” we distinguish whether observed dynamic changes are caused by external stimuli or intrinsic pathway rewiring.After reviewing 33 pathway analysis methods, Khatri et alQ-method discerns mechanistically rewired pathways by comparative dynamical system modeling. We consider a DSM to be conserved if it has the same parameters or coefficients with the original model but the variables in the DSM are not required to have the same initial values. On the other hand, a rewired or differential DSM must have different parameters from the original model, regardless of the initial values for model variables. Given a super-pathway topology, we partially reconstruct the active interactions in this pathway. All active interactions constitute one homogeneous and two heterogeneous DSMs for a pathway under two conditions. If the heterogeneous models are significantly supported by observed data, the pathway is declared to undergo a mechanistic rewiring, or differential; otherwise, it is conserved. In this paper, we reserve the word differential for mechanistic differences and use the word divergent for dynamical response differences. Using 12 modes from the BioModels databaseQ-method detected pathway rewiring more effectively than GSCA in most cases. Chaotic dynamical systems are increasingly recognized in molecular biology14Q-method successfully differentiated rewired Lotka-Volterra predator-prey models. Using interspecies yeast transcriptomes, the Q-method predicted rewired pathways consistent with TATA box disparity, painting rewired mechanisms among four yeast species. When the rate of change for biological quantities can be reliably estimated, our results suggest broad applicability of the Q-method for detecting pathway rewiring in dynamic biological networks at the mechanistic level.The Q-method tests whether a pathway is mechanistically rewired across two conditions or species, as summarized in D1 and D2 under each of two conditions. Partial pathway reconstruction is first performed to infer active interactions in the super-pathway topology. This partial reconstruction step can be done using many network inference methods and here we use dynamical system modeling to capture rate of change information. It is partial because only those inferred active interactions constitute one homogeneous and two heterogeneous DSMs for a pathway under two conditions. The two heterogeneous DSMs can be used to determine rewired interaction strength or topology across conditions by statistically meaningful differences in model parameters. Three Q-statistics and their statistical significance are calculated to characterize pathway interaction homogeneity , heterogeneity , and total interaction strength . By pathway interaction heterogeneity/homogeneity, we measure the cumulative difference/similarity in the manner that pathway elements interact across conditions or species. By total interaction strength, we measure the overall dynamical activity of a pathway. For example, a pathway already reaching a steady state in all experimental conditions will have a low total interaction strength. The overall null hypothesis is that the pathway is not rewired across conditions. Statistical significance of the Q-statistics determines, as the output, whether changed pathway response can be explained by mechanistically rewired DSMs under each condition. The Q-method software is freely available to non-commercial organizations at http://www.cs.nmsu.edu/~joemsong/software/Q-method.The p variables, each representing the abundance of a molecule. Let ix(t) be the value of variable i at time t. Let iy(t) be its rate of change. Let t. Let i. i asβ0 is a constant, l, q1 and q2, and s, and sh is the value of variable s producing half target occupation, i.e. when sx(t) = sh, the term if is the functional part of the model. For clarity purpose, we omitted the subscript i for all coefficients, or parameters, though they are indeed child specific.We represent pathway mechanisms by DSMs. The key advantage of DSM is its ability to track rate of change in a dynamical system. It is widely used in mathematical biology but disproportionally under-explored for pathway analysis. With rate-of-change information, we are theoretically equipped to distinguish the causes for observed differences in dynamics between biological systems. Each node on a pathway is mapped to a variable in a DSM. Via a system of additive nonlinear ordinary differential equations (ODEs), a DSM quantifies the rate of change for each child variable as a function of its parent variables. Each ODE uses a linear combination of linear, quadratic, and sigmoidal terms as functions of parent variables. Linear terms delineate the simplest possible interactions; quadratic terms can capture combinatorial effects; and sigmoidal terms approximate transcription activation kineticsβ0 from the pooled data. Pooled data are obtained by combining the data sets from all conditions.We partially reconstruct four pathway DSMs and compute residuals using the given super-pathway topology as a superset of all possible interactions. Partial refers to the fact that a reconstructed DSM contains only a subset of active interactions from the super-pathway topology. Directed-graph representations of pathways can be extracted from Kyoto Encyclopedia of Genes and Genomes (KEGG)F-test method to reconstruct the first three pathway DSMs by estimating the parameters in the DSMs (t), derivative i, the number of time points sampled n1 occurring non-uniformly over time at T(1) = {kt|k = 1, ¼, n1}, observed data x(1)(kt) at kt, and estimated derivative D2 for condition 2, including x(2)(t), n2, T(2), x(2)(kt), and We use the term P(1) ism(1)(i) parameters for variable i. The model complexity, or number of parameters, of P(1) is RSS) for variable i isP(1) and P(2) heterogeneous models because their parameters are optimized for each condition.We first obtain two heterogeneous pathway models for each condition. By comparative dynamical system modelingP(1) and P(2), we get the pooled pathway DSM:i, estimated using the pooled data, has m(i) parameters. We call P the homogeneous model as it fits to data under both conditions. The model has complexity RSS for variable iNovelty of our pathway analysis builds on two additional models, a homogeneous model and a pooled null model, to be used to examine pathway homogeneity and also as a reference for pathway heterogeneity. With pooled data iy(kt) for variable i over pooled sample in m0(i) = 1. The model complexity of P0 is thus RSS for variable iWe write the pooled null model of the pathway byRSS's defined, we backtrack to give the criterion used to reconstruct the pathway models. To capture total interaction strength for both conditions for variable i, we use the F-statistictu(i) = m(1)(i) + m(2)(i) − m0(i) and tv(i) = n1 + n2 − (m(1)(i) + m(2)(i)) are the numerator and denominator degrees of freedom. The parent variables involved in p-value of tF(i).With all RSS's for comparative pathway analysis. In contrast to full network reconstruction without pathway topology, partial pathway reconstruction is efficient with a greatly reduced search space of interactions spanned only by sub-graphs of the given super-pathway topology. As pathway conditions and cellular contexts are often not encoded in a database, partial reconstruction tailors a pathway to observed data. This strategy is effective when a pathway topology is inclusive of interactions known to occur in some molecular contexts but not necessarily all active in the current experiment. Although the pathway DSMs share a subgraph topology, an interaction or edge in the subgraph can be considered deleted in a condition if the DSM parameter corresponding to that interaction approaches zero under the condition.In summary, partial pathway reconstruction produces four DSM models with P(1) and P(2) may differ numerically due to noisy observations even when the underlying systems are identical. Direct numerical comparison of the two models would lead to high false-positive rates for differential pathways. Instead, using the four pathway models and their residuals, we develop a statistically reliable framework to evaluate pathway homogeneity and heterogeneity across conditions.Changed pathway response can be caused by various modifications to biological mechanisms. Mutations in promoter sequences, the presence or absence of enhancer or silencer regions, mutations in general transcription factors, chromatin remodeling, or changes in upstream promoter regions of genes may all alter dynamics of regulatory pathways. Parameters in heterogeneous pathway models P over the pooled null model P0. We compute the overall homogeneous homRSS of P, indicating its absolute goodness-of-fit to the data, by adding the individual RSS's for each variableP(1) and P(2) over a single pooled model P. We measure the overall heterogeneous hetRSS of P(1) and P(2), also indicating their absolute goodness-of-fit to the data, bynullRSS of the pooled null model P0Homogeneity is the improvement of homogeneous model RSS indicates model goodness-of-fit, it is unfair to compare them directly because of unequal model complexity. Instead, we compute their RSS differences normalized by degrees of freedom as in an F-test. To capture pathway interaction heterogeneity across conditions, we measure the normalized difference between homRSS and hetRSS bydu = m(1) + m(2) − m and dv = n1 + n2 − (m(1) + m(2)) are the numerator and denominator de grees of freedom. A high dQ value for pathway interaction heterogeneity provides strong evidence for a pathway to have been rewired across experimental conditions.Although an nullRSS and homRSS bycu = m − m0 and cv = n1 + n2 − m are the numerator and denominator degrees of freedom. A high cQ value for pathway interaction homogeneity suggests that a pathway has a consistent wiring behavior across conditions.To capture pathway interaction homogeneity across conditions, we measure the normalized difference between nullRSS and hetRSS bytu = m(1) + m(2) − m0 and tv = n1 + n2 − (m(1) + m(2)) are the numerator and denominator degrees of freedom. A high tQ value for overall pathway involvement suggests strong interaction patterns are observed for the pathway regardless of conserved or differential.To capture total pathway strength for both conditions, we measure the normalized difference between cQ, heterogeneity dQ, and total strength tQ mathematically constrain each other. From their definitions in Eqs (14), (15), and (16), we obtainpathway interaction decomposition rule, extending the decomposition rule for a single interaction across conditionsPathway homogeneity F-test as in regression analysis, cQ, dQ, and tQ follow asymptotic F-distributions with their respective numerator and denominator degrees of freedom under the null hypothesesp-values cp, dp, and tp are statistical significance of pathway homogeneity, heterogeneity, and total interaction strength.Based on statistical significance of observed pathway homogeneity and heterogeneity, we decide whether a pathway is conserved or differential. Under standard normality assumptions for the dQ and cQ. We randomly sample nodes in the entire system to form new pathways and permute their conditions. The permuted dp and cp of the originally observed dQ and cQ are determined by the fraction of permutations with To address the potential violation of the normality assumption for the residuals, dependent nodes in a pathway, or evaluation of multiple pathways, we use a permutation test to adjust statistical significance of α-level, i.e., dp ≤ α, the pathway is differential regardless of homogeneity; the pathway is conserved if homogeneity is significant at cp ≤ α and the heterogeneity is insignificant (dp > α); otherwise, there is insufficient evidence to declare a differential or conserved pathway across conditions.Finally, if pathway heterogeneity is significant at a given type I error Q-method, we simulated data from 12 curated dynamic models  of 100, 20, 10, or 0 dB. The time courses were generated by solving ODEs in each model using R package deSolveWe generated ground truth of conserved and differential models from original models in BioModels databaseQ-method decides if they are from a pair of conserved (negative) or differential (positive) models based on dp and α. The decision is compared with the ground truth to tabulate the numbers of false positives and true positives at different α-levels to produce a receiver operating characteristic (ROC) curve.Given a pair of time courses and model (pathway) topology, the Q-method on differentiating a rewired cell division cycle modelQ-method on time course data simulated from 100 conserved and 100 rewired versions of this model, we plot the ROC curves  model of predator-prey systems that can exhibit chaotic behavior with certain parameters. The LV model is defined byx1, x2, and x3 are variables and β1 to β9 are model parameters. The LV model, originated from modeling biochemical reactions, has been widely used to model competitive relationships in ecology and also economics. Its dynamics can exhibit point attractors, limited cycles, and chaos, depending on the parameter choices. From the original model, we also created conserved and differential models as ground truth and then simulated data from all models with noise added. To understand the Q-method and GSCA on the simulated data, we obtain ROC curves at four noise levels in Q-method/GSCA, and the output is a decision dp-value/divergence index evaluating strength of rewiring. It is somehow unexpected that GSCA performed well at a low noise level (SNR = 100 dB), suggesting comparison of chaotic systems is approachable. Nonetheless, the Q-method demonstrated an enormous advantage at both low and intermediate noise levels. Therefore, this example establishes the possibility to distinguish mechanistically changed chaotic systems.Applying both the Q-method to prioritize rewiring of 68 known KEGG pathways in yeast and reveal a consistent association between pathway interaction heterogeneity and TATA box disparity—a form of pathway rewiring. This thus offers a connection between mechanistic rewiring and observed divergent dynamics among the yeasts at a pathway scale.Although network rewiring is expected among related yeast species because they are mechanistically different biological systems, we hypothesize that the various functional pathways in them are not rewired to the same extent. We thus apply the S. cerevisiae, S. paradoxus, S. mikatae, and S. kudriavzevil) in response to five environmental stresses including DNA damage, heat shock, oxidative stress, carbon source switch, and nitrogen starvation. Using this data set (Gene Expression Omnibus accession number GSE3406), we examined 68 metabolic and signaling pathways from KEGGDivergence in expression of single genes has been at least partially explained by the presence of TATA box in the promoter region of the genesdQ-statistics are normalized to The obtained P = 1.09 × 10−23  with low TATA box disparity (40%) yet between S. paradoxus and S. kudriavzevii the normalized heterogeneity was high (7.54) with 100% TATA box disparity. By hierarchical clustering, a tree is obtained based on the pathway heterogeneity between pairs of the four yeast species  of a target molecule by a regulator molecule that is most often characterized in established mathematical models of molecular interactions. Description of such control is typically given in the language of differential equations. In signal transduction models, the rate at which a protein is phosphorylated is mediated by the corresponding kinaseQ-method can overcome the inadequacies of differential-correlation-based pathway rewiring detection approaches. The nearly zero AUC under the ROC curves of GSCA in some cases, e.g., BIOMD0000000005 (Q-method overcomes all these issues by detecting potentially nonlinear patterns utilizing both the rate of change and the trajectory pattern.We have thus demonstrated that 00000005  and BIOM00000005  to S4 ap00000005 . This laQ-method depends on the availability of time course data and accurate estimation of the rate of change. Although not all experimental design offers such opportunities to study pathway rewiring, high-resolution temporal sampling technologies are being rapidly developed to study vaccine responseQ-method as the topology can be alternatively obtained using various network inference approaches. The BioModels testing data set used in our study covered a broad spectrum of biological processes including cell cycle, circadian clock, glycolysis, metabolic oscillation, and calcium oscillation. We also tested and compared methods on a chaotic Lotka-Volterra predator-prey system. The corresponding benchmark results supported the effectiveness of the Q-method. It is informative to point out that most examples we tested exhibited large dynamic ranges, a necessary condition to track how mechanistically-rewired pathways may differentially respond to external stimuli. When no such wide dynamic ranges are recorded with the observed data, it is possible that a rewiring decision could be unreliably made, by either the Q-method or other methods based on rate-of-change variations. Under sufficient data conditions, by discerning whether a pathway has been mechanistically rewired, the Q-method can eliminate many pathways with divergent responses only as a consequence of pathway input, instead of rewiring. In order to determine what biological variations may have caused the rewiring, one will need to investigate additional information regarding the rewired pathway. This can include sequences of the involved proteins or transcripts and their methylation profiles or histone modification data. For example, when both genome sequences and gene expression are provided for the species being compared for rewiring, we can associate TATA box sequence presence/absence for each gene with its calculated interaction heterogeneity based on expression levels. In this manner, we can establish a model where TATA box disparity is a model parameter to predict interaction heterogeneity or rewiring. This will eventually lead to testable hypotheses on the biological causes for rewiring. We thus evaluated how detected pathway rewiring as a phenotypical change could be indicative of the underlying genotypical modifications among four yeast species. Based on gene expression data demonstrating large dynamic ranges collected in these yeasts subjected to five stress conditions, we found a strong positive correlation between pathway interaction heterogeneity and TATA box disparity. This confirms the power of Q-method to discover pathway rewiring indeed explainable by genotypical variations in biological systems.The usefulness of Q-method has addressed three challenges called forth by Khatri et alQ-method. Most importantly, the Q-method predicted rewired pathways by their interaction heterogeneity across yeast species. The correlation between pathway heterogeneity and TATA box disparity suggests a potential effect-cause relationship linked by the inferred pathway rewiring. The Q-method is readily extendable to multiple conditions with the number of heterogeneous models equal to the number of conditions. The principle that we have established to compare ODE models is highly innovative. Although we have illustrated the Q-method using an additive nonlinear DSM, the same principle is immediately generalizable to other forms of ODE models. As time course experimental design, genome sequences, and epigenome markers become increasingly available, we expect that the Q-method will link observed changed dynamics to various causative genetic and even epigenetic factors at the pathway level pointing to evolved biological functions.The Supplementary Information


Identifying subtypes of complex diseases such as cancer is the very first step toward developing highly customized therapeutics on such diseases, as their origins significantly vary even with similar physiological characteristics. There have been many studies to recognize subtypes of various cancer based on genomic signatures, and most of them rely on approaches based on the signatures or features developed from individual genes. However, the idea of network-driven activities of biological functions has gained a lot of interests, as more evidence is found that biological systems can show highly diverse activity patterns because genes can interact differentially across specific molecular contexts.In this study, we proposed an in-silico method to quantify pathway activities with a resolution of genetic interactions for individual samples, and developed a method to compute the discrepancy between samples based on the quantified pathway activities.By using the proposed discrepancy measure between sample pathway activities in clustering melanoma gene expression data, we identified two potential subtypes of melanoma with distinguished pathway activities, where the two groups of patients showed significantly different survival patterns. We also investigated selected pathways with distinguished activity patterns between the two groups, and the result suggests hypotheses on the mechanisms driving the two potential subtypes.By using the proposed approach of modeling pathway activities with a resolution of genetic interactions, potential novel subtypes of disease were proposed with accompanying hypotheses on subtype-specific genetic interaction information. Since the emergence of high throughput genomic profiling techniques, genomic profile data became a primary source of information in recognizing the various statuses of complex diseases. Cancer is one of such complex diseases, where even tumors from the same tissue locations can have strikingly diverse molecular mechanisms for their origins. Such high heterogeneity in cancer is one of the main obstacles in treatment, as different driving mechanisms may require different therapeutic approaches to repair their abnormality. For this reason, identifying subtypes of cancer with different functional mechanisms is very important for improving their successful diagnosis and treatment.One of the popular approaches to recognizing the subtypes of cancer is clustering the gene expression data of patient samples , as eIn order to overcome such limitation, utilizing known pathway information together with the expression data can be a promising approach. Considering that a joint probability distribution of a set of variables can give a comprehensive picture of its pattern, an ideal approach is modeling the joint probability distribution that describes the combinatorial gene expression levels within a pathway. However, this approach is not practical due to the complexity of the model to represent the joint probability distribution, and the lack of available data to infer such complex models with sufficient reliability. Hence, most of the methods to utilize pathway information focus on specific features of pathways rather than considering the complete joint probability distributions. Characterizing individual samples with pathway information and applying it to clustering achieved limited success, while there is a recent study that proposed a method called PARADIGM , which iIn this study, a method was proposed to compute the dissimilarity between two gene expression samples based on features that represent pathway activity patterns. Unlike conventional methods, our proposed method converts a gene-level matrix  to a pathway-level matrix, where each cell in the matrix represents a pathway activity pattern for a sample. We applied the proposed sample dissimilarity measure to clustering of cancer samples, where the RNA-Seq data of 267 melanoma patients from The Cancer Genome Atlas (TCGA) was clustered based on their pathway activities. Two patient groups of potential subtypes were identified with clear difference in their survival patterns, where they were associated with different stages of melanoma. Investigation on selected pathway activity patterns across two patient groups suggested hypotheses on different functional mechanisms driving two potential subtypes.A sample pathway activity vector (PAV), which represents the comprehensive picture of all pathway activities of a single sample, is represented as a collection of pathway activities for all pathways for the sample. A pathway activity vector distance (PAVd) is proposed as a discrepancy measure between two sample pathway activity vectors, which represents the dissimilarity between the two samples from the perspective of pathways. As PAVd is a distance metric (this will be discussed in the following subsections), arbitrary clustering methods and cluster validation indexes can be used for clustering and quality evaluation. Details of this formulation will be given in the following subsections.Our approach is based on an assumption that the activity pattern of a pathway for a sample can be represented with the probability distribution of the genetic network likelihoods from the pathway, which is computed from the given gene expression data. pathway activity distribution Pr of a pathway PAi for a sample sj is computed from the following steps:We compute the activity of a pathway for a sample by approximating the probability distribution of genetic networks from the pathway. Specifically, the Step 1) Consider PAi as a discrete random variable that has a finite set of N genetic network structures g1, g2, …, gN as its possible values.Step 2) Compute the likelihood Lk = P(gk|sj) for each genetic network gk for sample sj. The collection of likelihoods  for N genetic network structures constitutes the pathway activity distribution Pr of pathway PAi for a sample sj.Compared to the idea of computing a single scalar-valued activity for a pathway, our approach of computing the pathway activity as a probability distribution is a generalized version of such idea. From this generalization of considering multiple genetic networks, it is expected to achieve more reliable measurement of pathway activities than the idea of computing a single scalar-valued activity.PAi, sj), we utilize existing knowledge base on pathways and gene regulatory interactions. Instead of enumerating all possible genetic network structures for PAi, a selected list of candidate genetic networks are considered in reference with a knowledge base of choice, to compute Pr. The list of candidate networks will include one genetic network of normal status, where we assume that a normally acting pathway has all known genetic interactions functioning. From this normal network with all known genetic interactions, we assume that eliminating an interaction can represent a disturbed status of the pathway. This assumption is based on an idea that disruption of a pathway by external variables  can be represented with silencing certain genetic interactions within the pathway. As a result, a normal network and disturbed networks with one silenced interaction are considered as possible values of PAi. The schematic outline of this approach is illustrated in Fig. In computing the pathway activity distribution Pr(Lk = P(gk|sj) for each genetic network gk for sample sj, we model a genetic network with a Bayesian network structure assuming discrete random variables as its nodes. The computation of likelihood is done using the Bayesian Dirichlet equivalence uniform (BDeu) scoring method [To compute the likelihood g method . HoweverD represents the collection of all samples. Even though we use the Bayesian network model assuming discrete random variables, our formulation is independent of model choices. Thus other network and random variable models can be also used as long as the likelihood of a network structure can be computed based on the model of preference.where PAV of sample sj for a set of A pathways PA is defined with a vector of pathway activity distributions as follows:The sample pathway activity vector A pathways and S samples, the pathway activity distribution matrix R is defined as a A × S matrix, where a cell R corresponds to a pathway activity distribution Pr of a pathway PAi for a sample sj. In other words, R is a collection of column vectors PAV for S samples.For R is a scalar-valued vector with each pathway activity represented with a scalar value, conventional distance measures (such as Euclidean distance) assuming ordinary scalar-valued vectors can be used to evaluate the discrepancy between two samples. In our approach of representing the pathway activity with a discrete probability distribution Pr, the representation of sample pathway activity PAV of a sample sj for a set of A pathways is a vector of probability distributions as shown in Eq.  is a probability distribution rather than a scalar value, a new method is necessary to compute the distance between two vectors of probability distributions PAV and PAV from two samples sl and sm.If a column vector in a pathway activity distribution matrix n in Eq. . As eachpathway activity vector distance (PAVd) to compute the distance between two vectors of discrete probability distributions PAV and PAV, which is defined as follows:We designed a new distance measure JS is the Jensen-Shannon divergence. The Jensen-Shannon divergence is a symmetrized version of the Kullback-Leibler divergence, and a popular method of measuring the similarity between two probability distributions. Note that PAVd is a metric, as it satisfies the four required properties – non-negativity, identity of indiscernibles, symmetry and triangle inequality.where Corollary 1.PAVd satisfies a property, the non-negativity.Proof. The Jensen-Shannon divergence JS of two probability distributions is a non-negative value.Corollary 2.PAVd satisfies a property, the identify of indiscernibles.Proof. PAVd || PAV) is a sum of non-negative values from Eq.  || PAV) = 0 requires JS(Pr(PAi | sl) || Pr(PAi | sm)) to be 0 for all i. As the square root of the Jensen-Shannon divergence is a metric [JS(Pr(PAi | sl) || Pr(PAi | sm)) = 0 if and only if Pr(PAi | sl) = Pr(PAi | sm). If Pr(PAi | sl) = Pr(PAi | sm) for all i, then PAV = PAV.from Eq. . Thus, Pa metric , 11, JS, PAV and PAV. As the square root of the Jensen-Shannon divergence JS is a metric, the following is true for all i:Thus, the following is also true:Theorem 1.PAVd is a distance metric.Proof. From Corollary 1 to 4, PAVd satisfies the four properties of metric.PAVd with conventional clustering algorithms, we can group samples based on the sample pathway activities.By using this distance metric We collected 1932 filtered gene sets of canonical pathways, Gene Ontology (GO) biological process and molecular functions from MSigDB , where eR was built as a result. Using PAVd as a distance measure between sample pathway activity vectors that correspond to the columns of R, hierarchical clustering with complete linkage was applied to R to find groups of patients.We obtained the RNA-Seq data of 267 melanoma patients from TCGA. The normalized gene-level transcript counts were used for the analysis. The normalized counts of each gene were discretized into two values of 0 (not expressed) and 1 (expressed) using SIBER . A samplR of the TCGA melanoma RNA-seq data. After visual inspection, we identified two groups of patients, Group I and II. Based on the sample annotations regarding the stage of melanoma, we also computed what stages of melanoma cases are significantly enriched in each group of patients. Table p-value = 0.0362). In Stage I of melanoma, cancer has formed on skin, but tumor is not present in deep skin. Thus it represents relatively early stage of melanoma prognosis. Regarding Group II, there were 52 patients classified as Stage II among the 267 patients, and 24 of them were included in this group of patients . When melanoma is in Stage II, it indicates that the tumor is in deeper skin than Stage I, with possible ulceration. Thus this stage indicates a more progressed status of melanoma. The absolute numbers of Stage I patients and II patients in these two groups may not be high, but Group I represents patients with earlier stage of (or less aggressive) melanoma while Group II represents patients with relatively later stage of (or more aggressive) melanoma. This observation can be confirmed in the following subsection.Figure p-value = 0.0044), with much longer median survival length (4254 days) than the rest of the patients. Patients in Group II have relatively shorter survival  than the rest of the patients, but the main difference is with the patients in Group I  curves from the comparison are shown in Fig. p I Fig.  rather tp I Fig. . In compp I Fig. . This suRegulation of Cell-Cell Adhesion with one genetic interaction from Pathway Commons, and the second pathway was a DNA Fragmentation pathway with eight genetic interactions.We compared the pathway activity patterns between Group I and II, and two pathways with distinguished activity patterns were selected for further investigation. The first pathway was a GO gene set Regulation of Cell-Cell adhesion, Group) by averaging the likelihoods of considered genetic networks across the samples within the group. Figure Regulation of Cell-Cell adhesion pathway, where Group I patients have higher likelihood of “Normal” genetic network while Group II patients have higher likelihood for a network with a missing SIRPG – CD47 interaction. The Regulation of Cell-Cell adhesion pathway is involved in cell-cell adhesion biology, which is a mechanism to bind a cell to a surface, such as an extracellular matrix or another cell. CD47 is a ligand for the SIRP protein family, and SIRP-gamma can bind to CD47. As mentioned earlier, the tumors from the Group II patients are more advanced (or aggressive) melanoma, where cancer cells show more break-in through skin tissues. As can be seen in Fig. From each group, we computed the average pathway activity distribution Pr(DNA Fragment pathway between Group I and II. Figure DNA Fragmentation pathway, where Group I patients have higher likelihood of “Normal” genetic network. This suggests that the genetic interactions in the DNA Fragmentation pathway are better preserved in Group I patient tumors than the case of Group II, indicating Group II patients may have more abnormal activities of the DNA fragmentation mechanism. The DNA fragmentation pathway is one of the mechanisms that can be utilized during the immune response process, where immune cells send signals into target cells and cause apoptosis through the fragmentation of DNA in the target cells. From the pathway activity patterns in Fig. We also compared the average pathway activity patterns of the PAVd that can compute the discrepancy between two gene expression samples in the scope of activity patterns of entire pathways. The proposed method of sample pathway activity quantification and computing distances based on the quantified activities has several potential benefits, as active biological mechanisms from individual samples can be more easily interpreted than using individual gene-based approaches. Compared to previous pathway evaluation methods such as GSEA [PAV provides unique functional benefit of analyzing single-sample pathway activities with a resolution of genetic interactions (Table PAV still needs to be extended to incorporate multiple types of genomic data. By applying the proposed method to cluster gene expression data of melanoma patients, we identified two potential subtypes of melanoma with distinguished pathway activity patterns. The two identified groups of patients showed distinctive survival patterns, and we suggested two hypotheses on biological mechanisms that can distinguish and potentially drive the two subtypes. This was possible because of our novel formulation on pathway activity considering genetic interactions, and we believe that there are much more potential applications of this approach as all components of the analysis – pathways, genetic interactions and etc. – are defined based on probabilistic models and can be easily extended with additional features. The two identified patient groups from this study correlate with stages of the disease, but each group still includes patients with multiple different stages. This implies that disease-driving biological mechanisms can reside across different stages of disease progression, and the proposed method contributes to identify such mechanisms.We proposed a method to represent the complete pathway activity patterns of individual gene expression samples based on collected pathway information. By using each pathway activity as a feature rather than using individual genes, we formulated a distance measure  as GSEA  or PARADns Table , while PK missing interactions. We can also develop methods to quantitatively evaluate the abilities of pathways in discerning different clusters. As our formulation of the distance measure satisfies the properties of metric, we can incorporate the ideas of many conventional cluster validation indexes to evaluate the quality of clusters based on individual pathways. Lastly, we considered only gene expression data in our study, but integrating multiple types of genomic data in evaluation of pathway activity patterns and computing the effect of latent environment variables on pathways can be a promising direction to extend our current models.We are considering several directions for future studies. From our current study, we modeled the pathway activity patterns with a genetic network of normal status and genetic networks with only one missing interactions. Even though we showed a successful application of our formulation in this study, it will be definitely beneficial to consider genetic networks with more than one missing interactions, which leads to the generalization of the formulation with up to Not applicable.Not applicable.All the data used in this article were obtained from public sources as cited.