We used established databases in standard ways to systematically characterize gene ontologies, pathways and functional linkages in the large set of genes now associated with autism spectrum disorders (ASDs). These conditions are particularly challenging—they lack clear pathognomonic biological markers, they involve great heterogeneity across multiple levels —and yet everyone with this diagnosis meets the same defining behavioral criteria. Using the human gene list from Simons Foundation Autism Research Initiative (SFARI) we performed gene set enrichment analysis with the Kyoto Encyclopedia of Genes and Genomes (KEGG) Pathway Database, and then derived a pathway network from pathway-pathway functional interactions again in reference to KEGG. Through identifying the GO (Gene Ontology) groups in which SFARI genes were enriched, mapping the coherence between pathways and GO groups, and ranking the relative strengths of representation of pathway network components, we 1) identified 10 disease-associated and 30 function-associated pathways 2) revealed calcium signaling pathway and neuroactive ligand-receptor interaction as the most enriched, statistically significant pathways from the enrichment analysis, 3) showed calcium signaling pathways and MAPK signaling pathway to be interactive hubs with other pathways and also to be involved with pervasively present biological processes, 4) found convergent indications that the process “calcium-PRC (protein kinase C)-Ras-Raf-MAPK/ERK” is likely a major contributor to ASD pathophysiology, and 5) noted that perturbations associated with KEGG’s category of environmental information processing were common. These findings support the idea that ASD-associated genes may contribute not only to core features of ASD themselves but also to vulnerability to other chronic and systemic problems potentially including cancer, metabolic conditions and heart diseases. ASDs may thus arise, or emerge, from underlying vulnerabilities related to pleiotropic genes associated with pervasively important molecular mechanisms, vulnerability to environmental input and multiple systemic co-morbidities. While there remains controversy regarding the relative contributions of artifact and true increase to the rising prevalence of ASDs, there is no question that these spectrum conditions have major human, public health and economic impacts. They also pose major challenges to research, since while ASDs are defined by social impairments, communication difficulties, and restricted, repetitive, and stereotyped patterns of behavior, there are no pathognomonic biological features universally present in people meeting the behavior-level diagnostic criteria, and many other biological features have been identified in subgroups both in the brain and systemically whose contributions to the development and ongoing characteristics of ASDs are not clearly understood.As of December 2014, the SFARI Gene-Human Gene Module recorded 667 human genes implicated as relevant to ASDs. These genes are widely expressed and are involved in a variety of biological activities. To make full biological sense of this large number and diversity of genes, it is important both to consider the full range of their biological activities, and to identify processes with higher likelihood of substantial relevance to ASDs.In this study we chose to consider the accumulated set of genes as a whole, and to utilize established databases and analytical processes to seek patterns and connections within this large aggregate. To do this we expanded the framework from just genes to also include the contexts, reactions and processes in which they participate. We used enrichment analysis to identify 1) pathways in which ASD-associated genes were over-represented, 2) biological features for which ASD-associated genes were particularly present, and 3) overlaps and convergences amongst the several types of analyses that we performed. Future studies may add more nuances to the analyses we report, including addressing biases that may be present at various stages of the process ranging at least from gene discovery to database construction. For the present study we did not introduce any biases from favoring certain types of biological processes or domains over others, and we did not utilize any weighting systems, as we could not locate any established or fully developed weighting methods that could do justice to all the different varieties of ASDs, considering the marked heterogeneity this diagnosis encompasses. We aimed simply to let the data speak through the patterns and relationships that emerged from performing standard analyses, regardless of whether the resultant findings were consistent with areas of predominant focus in the existing literature. To our knowledge the aggregate of genes associated with ASD, along with their functions, contexts and pathway networks, have not previously been analyzed in this manner.The networks in which cellular processes often function, which involve sets of gene products acting in concert, can be mapped as pathways. Since there are many overlaps among pathways, identifying convergent molecular pathways in which multiple candidate genes are involved has been discussed for years , as thisIn this study we developed an ASD pathway network and performed a systematic analysis of the network. With this approach we aimed to expand our understanding to include not only genes but also the function of gene products, as well as the networking of reactions and interactions. In thus generating a coordinated presentation whose depictions take account of gene-pathway coherence, pathway-pathway interactions, and disease-disease relationships, our objective was to provide a framework and clues for further investigations.https://gene.sfari.org/autdb/HG_Home.do, http://www.broadinstitute.org/gsea/msigdb/index.jsp). We applied the “Compute Overlaps” tool from MSigDB website, under “Investigate gene sets” category, which uses the hypergeometric distribution to examine how SFARI genes and other gene sets may overlap. Gene symbol was used as gene identifier to import the gene set. MSigDB is a collection of annotated gene sets for use with Gene Set Enrichment Analysis (GSEA) software . Th. Th13]. Although it is intriguing and surprising that the most represented disease pathway / collection in our ASD pathway network is cancer pathways, other methodologies have identified multifunctional genes associated with both cancer and nervous system development or disease –16. The The single most interactive pathway in the ASD Pathway Network, MAPK signaling pathway , has a diverse range of relationships to functions and diseases. It is involved in a variety of fundamental cellular processes such as proliferation, differentiation, migration, stress response, and apoptosis ,17. It iIt is worth considering what the biological overlap might be between ASD and cancer, specifically given the involvement of MAPK signaling. We would suggest that metabolism might bridge this apparently large gap. Our chain of reasoning here includes the following considerations: 1) MAPK signaling plays an important role in metabolism: it responds to changes in the extracellular or intracellular milieu that often affect the metabolism of the cell; in this regard, altered MAPK signaling has been associated with metabolic syndrome . 2) In oThe enrichment analysis of SFARI genes showed the calcium signaling pathway to be the most enriched, statistically significant pathway. This is consistent with the results from recent ASD studies that used genome-wide association studies (GWAS) data for enrichment analysis ,31. GWASCACNA1C gene was found to be associated with Timothy syndrome (a syndromic autism) in 2004 [2+  participates in the majority of the enriched pathways/collections, and 4) ASD-associated genes in the calcium signaling pathway are highly involved in the network.It was not surprising to see that the calcium signaling pathway emerged from these analyses as important for ASDs. Ever since mutation of the  in 2004 , neuroge in 2004 . The impIt was unexpected to derive a number of cardiomyopathy pathways from ASD genes . After lHow might the neural and cardiac phenomena mechanistically overlap in ASDs? Common vulnerability to calcium signaling abnormalities are a potential link. Calcium signaling has a wide range of important physiological roles including learning and memory, cellular motility, muscle contraction, etc. . In the CACNA1s and PRKCB. CACNA1s genes encode a group of proteins functioning in voltage-sensitive calcium channels, which mediate the entry of calcium ions into excitable cells , and thereafter initiate a variety of calcium-dependent processes, including muscle contraction, hormone or neurotransmitter release, gene expression, cell motility, cell division, and cell death [PRKCB has been reported to be involved in many different cellular functions, which associate with tumorigenesis [CACNA1s and PRKCB are reported to be involved in both cancer development and metabolism-related issues.The common ASD genes in the MAPK and calcium signaling pathways are ll death . The proigenesis , insulinigenesis  and diabigenesis , as welligenesis  and retiigenesis . We thusRAF1, which is also an ASD-associated gene, is additionally associated with dilated cardiomyopathy [That our integrated findings point to the process “calcium-PKC-Ras-Raf-MAPK/ERK” suggests the possibility that disturbances of this process involving the overlapping genes may contribute to ASDs. Notably, the mutation of myopathy  and hypemyopathy , whose tmyopathy ,47 and imyopathy ,48. Takemyopathy –27.Based upon the above analyses of pathway-gene relationships, we developed a visualization linking across the different categorical groups using the results as well as the methods from each analysis . Based ohttp://www.genome.jp/kegg/pathway.html#environmental, or go to KEGG, click on “KEGG PATHWAY”, and find the category “Environmental Information Processing” listed as number 3 under “Pathway Maps”) to which calcium and MAPK signaling pathways and many of our other enriched pathways belong. EIP means the procedures that cells utilize to react to environmental information and conduct consequent signal transductions. For example, the calcium signaling, MAPK signaling and receptor activities we have been discussing constantly react to signal molecules and changes in the environment outside of cells, with processing of that information leading to a series of reactions including activities inside the nucleus such as gene transcription  of the pathways/collections in our ASD pathway network. Whether or not this is a “bias,” it still remains germane to gain further knowledge regarding how these pathways may contribute to ASD mechanisms.In the end the best protection against bias is to acknowledge its possible sources and to present our data modestly with the aim of contributing to further inquiry.In summary, based upon our analyses the MAPK signaling and calcium signaling pathways, particularly the overlapping process “calcium-PKC-Ras-Raf-MAPK/ERK” were found to be strongly associated with ASDs. Both pathways play a central role in a large range of biological processes, whose activities, when abnormal, may compromise biological output and contribute not only to features of ASD themselves but also to a range of other vulnerabilities. It seems quite possible that ASDs may well to a significant extent arise, or emerge, from vulnerabilities related to a set of pleiotropic genes that are also associated with multiple co-morbid systemic issues and that also overlap with other conditions.The results generated by our emphasis upon gene function leads us to reflect that part of the genetic contributions to ASD pathogenesis may arise from functional disturbances of the processes in which these genes are involved, with such disturbances potentially originating from a variety of reactions and processes changing gene and pathway function, since it is the ensemble of these factors that in the end shapes the phenotype.Our intention is to give “the lay of the land” within the terms of some of the best resources presently available, and at their current state of development—and not claim discovery of any absolute final truths—we chose to “let the data speak for itself” and offer it up to the community of researchers as one step in a much larger and more collective research enterprise. If our results point any researcher toward a fruitful line of inquiry that might otherwise not have been considered, we will consider that our efforts were well rewarded.S1 Table(XLS)Click here for additional data file.S2 TableThe enrichment analyses data for KEGG and GO  groups were shown in four separate sheets labeled as "KEGG", "BP", "CC", and "MF". Each data sheet contains two parts: the one above is a table of the enriched gene sets, and the one below is the gene set overlap matrix.(XLS)Click here for additional data file.S3 Table(XLS)Click here for additional data file.


In this report we describe a novel graphically oriented method for pathway modeling and a software package that allows for both modeling and visualization of biological networks in a user-friendly format. The Visinets mathematical approach is based on causal mapping (CMAP) that has been fully integrated with graphical interface. Such integration allows for fully graphical and interactive process of modeling, from building the network to simulation of the finished model. To test the performance of Visinets software we have applied it to: a) create executable EGFR-MAPK pathway model using an intuitive graphical way of modeling based on biological data, and b) translate existing ordinary differential equation (ODE) based insulin signaling model into CMAP formalism and compare the results. Our testing fully confirmed the potential of the CMAP method for broad application for pathway modeling and visualization and, additionally, showed significant advantage in computational efficiency. Furthermore, we showed that Visinets web-based graphical platform, along with standardized method of pathway analysis, may offer a novel and attractive alternative for dynamic simulation in real time for broader use in biomedical research. Since Visinets uses graphical elements with mathematical formulas hidden from the users, we believe that this tool may be particularly suited for those who are new to pathway modeling and without the in-depth modeling skills often required when using other software packages. We postulate that there is a broad and still unmet need to process, analyze/model and interpret biological information at the early stage of data acquisition and analysis. Combined with a user-friendly format that is accessible to an average health professional and scientist not trained in mathematics/statistics and programming, such tools may lower the barrier to entry for researchers who can be empowered to analyze their conceptual models and thus provide a potential boost for discovery process in biomedicine.One of the persistent challenges in today’s biomedical research is the development of easy to use modeling software tools for biological networks, which would be widely accessible for bench scientists. There are a number of advanced software packages for pathway display, analysis and simulation, including: Cytoscape, Ingenuity, CellDesigner, KEGG, SymBiology in Matlab, just to name a few. These tools are primarily used by trained modelers and are not suited for biologists who do not have rigorous training in mathematics and computation, thus leaving the most numerous group of scientists without adequate computational biology tools to aid their bench work. Many of these tools also lack features that would enable interactive and dynamic ways for pathway visualization and simulation. Others employ Ordinary Differential Equations (ODE) as their mathematical method of modeling. This approach is more complex to use and larger ODE models (above 130 nodes) are more difficult to build and manage, and may also require dedicated computational facilities. These shortcomings further underscore the need for the development of novel and more accessible tools for bench scientists. Such tools, if available, would greatly accelerate the discovery process by: i) introducing bench scientists to modeling of biological systems in an interactive graphical way; ii) allowing for hypothesis testing at the early stage in the laboratory; iii) providing dynamic visualization of data in the context of signaling pathways; iv) enabling visualization of perturbations within the pathways by observing changes in pathway graphical display in an interactive and dynamic way; v) facilitating de novo” model of EGFR and Erk1/2 signaling with manual parameter adjustment and; b) translated existing model of insulin signaling in diabetes from published ODE model [In this report we describe our attempt to create such a software tool based on a standardized approach using causal mapping (CMAP). In this approach, first introduced in 2006 , all eleall the components of the system of interest, along with all interactions between them, with an underlying aim to replace mathematical descriptions with graphical equivalents. While it requires simplification and generalization of the mathematical framework, it provides the power of graphical user-computer interaction particularly for users without rigorous training in mathematics of physics and chemistry. The basic idea of the causal mapping is to graphically represent A causal map is a graph in which the components (concepts) are the nodes (species) and causal influences are the edges. The behavior of each species Cj(t) is described by the following basic CMAP equations for a network of N nodes:Cj(t)) can assume any value between 0 and Cjmax (≤1) and are variables; they could represent species concentration and/or combination of concentration and activity. The weights  are constant during simulations. The absolute values of the weights are also normalized and limited to the same interval . Each influence may be assigned positive or negative value (activation or inhibition) and carry positive or negative numerical value depicted in green or red, respectively (Cj(t)) value assigned zero, e.g. they are not active unless activated by another species (cause). The right side of Eq  contains two factors. Ʌj restricts the species to the 0–1 scaled interval. The causal function fj includes all influences from the system , as depicted in Cj(t). Parameter α in Eq  , to increase the species responsiveness to change in input.The species (ectively . Multiplα in Eq   determinThe front-end (GUI) and back-end of the Visinets software was developed using the Google Development Kit and Dart. Visinets uses Google's Big Table database to store all of the data that the software will create including: experimental data, models, graph visualizations, user information and analytics, references and other data. Visinets also employs Google's App Engine to host the application and APIs through multiple RESTful APIs that allow the front-end client to access, modify, and search data on the database. In addition, we use Amazon's Elastic Compute Cloud (ec2) (written in C/C++) to power the simulations. The web-based implementation ensures platform-free execution throughout all the available devices, from PC to tablets and smart phones.Visinets graphical interface employs HTML5 technology to ensure cross-platform compatibility and takes advantage of its features: the Canvas to draw hardware accelerated pathway maps and graphs; application cache and local storage to use the software when not connected to the internet; and file-reader and drag and drop API's to efficiently use local files. Users may use Visinets in two modes: a) Build/Modify mode, where the user can construct the pathway using graphical means and manually apply initial values for parameters, and perform simulations; and b) Parameter Search mode, where user can perform global parameter search using user-selected rules.Build/Modify mode, users can take full advantage of the graphical environment and draw all components of the biological network in a causally linked manner, using both positive and negative influences (arrows/connectors). Three or four species that form a specific reaction module may be used to build signaling pathway in a more automated way. Larger network blocks, representing multiple biochemical reactions, can be selected, moved around and/or copied and pasted into new pathway files. Left side pull-out menus provide the list of all species and influences and pop-up menus for each species and influence allowing to visually inspect and edit parameters, initial conditions and graphical appearance. Several graphical features have been developed for easier workflow and more attractive visualization of signal transduction throughout the network; a) clone function to allow multiple copies of the same species to be associated with different parts of the network and thus avoiding the dense network of intersecting connections throughout the working area; b) dynamic changing of the thickness of the influence connector (arrow) in proportion to the corresponding signal intensity; and c) dynamic changing of the transparency of species that is inversely proportional to the C value (activity/concentration). Each network can be shown in Basic View with essential connections only showing the causality and direction of signal transduction, which is recommended for simulations and visualization and in Full View with all influences shown, recommended for model building, editing and/or parameter adjustments.  and a list of executable signaling pathways with embedded parameter datasets (fully user-adjustable), including those described in this report (http://www.visinets.com/pathway/list))In ini, and weights) automatically. The rules currently available in Visinets include Increase, Decrease, Transient up, Transient down, and Oscillations and may be set for any species. Once initiated, the search will stop at the first randomly generated set of parameters that satisfy the chosen rules and results can be viewed using the Plot function. If the result is not satisfactory the user can repeat the search for a new set of parameters or continue with manual adjustments.In Parameter Search mode the user can apply a set of rules (criteria) to search for parameters  . The netProtein phosphatase PTP1B binds to EGFR through Grb2 adaptor protein to terminate EGFR signaling and protein phosphatase MKP2 terminates the Erk1/2 signaling. The pathway illustrates Erk1/2 feedback negative regulation of several species, including Mek1/2, Raf1 (c-Raf), Receptor-Shc-Grb2-Sos1 (RSGS) complex and tyrosine phosphorylated receptor (RP). The delayed Ser/Thr phosphorylation of EGFR by Erk1/2 remains more controversial and may be indirect. Feedback phosphorylation-inhibited species do accumulate and are named iRShGS, iR, iRaf and iMek and may be subject for dephosphorylation and recycling, or for internalization and degradation (not included in this model). Erk1/2 activity itself is terminated by protein phosphatase MKP (DUSP4). The criteria used to re-construct the core network behavior were the transient phosphorylation (activation) for RP, RSGS, Rafpp and Erkpp, generated by EGFR and several negative feedbacks of Erk1, PTP1B and MKP activities. This behavior, including relative time delay, recapitulates some of the typical regulation that is common for EGFR and MAPK pathways –6 Fig 6Fig 6.α parameter was left at default value of 1.2 for all but RafPP and ErkPP, in which case it was set at 4 to enhance its responsiveness to input and induce a more pronounced”switch-like” behavior. The sum of these adjustments produced RafPP responding to EGF levels in a concentration dependent manner. However, the less responsive way of ErkPP may be due to incomplete negative regulation of activated Erk1/2 represented in our scheme.The manual parameter selection strategy applied for this model involved three guiding principles, each helped by the visual analysis of signal propagation throughout the network during execution of simulation; a) slow reaction  following fast reaction will cause the relative accumulation of the reaction intermediate; a) having only same type of inputs (“activation” or “inhibition”) can cause only corresponding monotonic change; b) to obtain “transient” (non-monotonic) response there should be at least two inputs but of different type; c) several rounds of adjustments were applied to find each weight value in the most sensitive range defined as a smallest weight adjustment made to cause the largest change in activity, and d) final execution of simulation with visual determination of node transparency  to identify potential remaining signaling roadblocks or diversions. These adjustments did not need to be exhaustive, in the above case the criteria were satisfied within 2 hours of manual weight parameter manipulations. The To further test the performance of Visinets, and to directly compare our approach to ODE method, we used an existing ODE model of insulin signaling in normal and type 2 diabetes (T2D) cells [To obtain parameter sets for the simulation of Insulin pathway in normal and pathological states and to compare the ODE and CMAP simulations directly, we exported CMAP code from Visinets and run parameter search and simulations in Matlab . The transient phosphorylation of Insulin Receptor and IRS1 were used as search rules and the search was conducted in a step-wise manner:Export the model from Visinets (File/Export Model) to create a programing code for further simulations.Generate the 1 million random sets of weights (corresponding to rate constants in the ODE model) so that max(W)/min(W) = 1000 and α-s (0.5–3) and the values were evenly distributed in these ranges.Run simulation for each weight set until steady state was achieved with the initial values for the species shown in the IR(T2D) = 0.55* IR;GLUT4(T2D) = 0.5* GLUT4;Diabetes (T2D) = 0.15* Diabetes;After achieving the steady states values for all species, we used those as initial conditions to run the simulation in the presence of insulin (insulin = 1) and tested for two rules: transient response for measuredIRp = IRp+IRip and measuredIRS1p = IRS1p + IRS1p307 for both normal and T2D conditions. Representative simulations qualitatively confirming the finding from the original ODE model are shown in Using obtained parameters sets that satisfy the above rules, we found those that belong to both normal and T2D ensembles and saved them for further analysis.We ran these sets to satisfy observations presented in It is also important to note that to achieve pathway behavior as described in the original paper , the VisWe have compared computational efficiency of simulations with CMAP and ODE approaches by running simulations of 3 different biological pathways: Insulin signaling in the Normal state as described above, EGFR signaling pathway as described by Kholodenko & co-authors , and EGFThe underlying mathematical approach in Visinets ) is a modeling method that allows for the integration of diverse data into a single model of networks organized in causally linked relationships. Initially applied to model of cortical contraction , 9, CMAPCMAP permits the investigation of system’s dynamics, with all its elements connected in a biologically and causally meaningful way  and is tolerant to knowledge gaps, discrepancies and uncertainties. Since this standardized method for pathway modeling can easily be executed within the user-friendly graphical interface, it allows for an intuitive and non-technical network analysis for bench biologists, geneticists and health professionals. Although other standardized mathematical approaches have been proposed , 11, theTo evaluate the “ease of use” and simulation performance, and potentially broader user appeal in biomedical research, we have successfully re-created the behavior of EGFR and MAPK pathway by employing manual selection of weight parameter for each reaction. Such method may also be used for refining pathway behavior after initial automated parameter search. Though in some cases the manual method may seem tedious, the process of weight  adjustments itself may provide the user with an intuitive way for better understanding of pathway dynamics, relationships between different sections of the networks, and mechanistic relationships such as positive and negative feedback loops. In fact, this more intuitive manual way of model refinement and associated benefit of learning pathway dynamics may better help the user to discern between similar network topologies and settings and find the most optimal network circuitry for further experimentation and analysis. As such Visinet’s dynamic computational models can be considered a means of conceptual model verification, by which models generated by researchers from the understanding of their research field can be verified computationally and the outcomes simulated, and thus the behavioral consequences of the researcher’s proposed topology/hypothesis can be evaluated in an easy to follow graphical way . This waThe direct comparison of insulin ODE and CMAP models provides strong evidence that both approaches give very similar outcomes. Furthermore, direct comparison of computational efficiency for 3 independent models show the clear advantage for CMAP approach for use in simulations of biological pathways on desktop computers. The insulin signaling pathway, studied in more detail above, is also an example of using an existing ODE model and importing it into Visinets. If such model is available, the translation into Visinets may be relatively straightforward and allows the user to generate simulations and dynamic pathway illustrations within the extensive graphical capabilities of Visinets. Furthermore, user may import and then modify, add or delete species (nodes) or influences (edges) or even combine smaller models into larger one within the Visinets platform. The software module of ODE model import function into Visinets is being currently developed. In a reverse process, if necessary, the Visinets model/network can also be exported into more capable software packages where more extensive parameter search and parameter space study using qualitative rules could be performed. Importantly, Visinets will continue to extend the range of statistical tools and graphical features in Visinets modeling software, thus potentially alleviating the need for further analysis in other software packages.Due to its graphical capabilities, the usefulness of Visinets may be extended beyond modeling of signaling pathways, and into dynamic visualization of other biological processes. Thus, the modeling capability of Visinets, in combination with attractive visualization, may offer a unique way for the integrated graphical analysis of different biological scenarios and also use it for presentation purposes.In this version Visinets may be a particularly useful tool for semi-quantitative analysis of pathway models that are larger than 50–100 nodes, a large size considered for computationally more demanding ODE models. With the zoom function currently in place, Visinets graphical working space can practically accommodate pathway models larger than 300 nodes.https://github.com/paulspychala/CMAPdart under open source MIT license.The code for Visinets CMAP modeling engine has been deposited for free use at http://www.visinets.com/pathway/list.EGFR signaling complex with MAPK and PTP1B feedback inhibition. This pathway model has parameter dataset embedded in the pathway and is listed in Featured Pathways at http://www.visinets.com/pathway/list.Insulin signaling in Diabetes. This pathway model has parameter datasets embedded in the pathway and is listed in Featured Pathways at http://www.visinets.com/index.htm with full user documentation (User Guide and Help) and a list of executable signaling pathways with embedded parameter datasets (fully user-adjustable), including those described in this report (http://www.visinets.com/pathway/list).Visinets software is freely available to general public as an online resource at


We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach. The low costs of sequencing and other high-throughput technologies have made available large amounts of data to address molecular biology problems. However, often this means thousands of measurements, for example on gene expression, are assayed for a much smaller number of samples. The imbalance complicates the identification of genes that generalize to new samples and in finding a collection of genes that suggest a theme for interpreting the data. Pathway and network-based approaches have proven their worth in these situations. They force solutions onto known biology and they produce more robust predictors. In this manuscript, we describe a new formulation of statistical learning approaches that naturally incorporates gene-gene relationships, like those found in gene network databases. The theory we present helps unify and codify an explicit formulation for gene pathway-informed machine-learning that should have wide reach. A natural extension beyond immediate adjacency is the diffusion kernel . The kers HotNet . If D isany positive semi-definite measure of dissimilarity between pairs of features. For example, we may be interested in grouping features together according to some predetermined factor and defining P in such a way as to penalize selection of feature pairs that do not belong to the same group. This is closely related to group LASSO [While most of our attention has been given to gene interaction networks, we reiterate that GELnets are more general and can accommodate up LASSO , where tai are the sample weights, and dj, P encode domain-specific information regarding feature importance and association. Note that we will generally use i to iterate over the samples and j to iterate over the features.We discuss how to solve wk at a time, while keeping the values of wj fixed for all j ≠ k[glmnet[LIBLINEAR[We solve the problem in all j ≠ k. The coo k[glmnet and LIBLLIBLINEAR. Their pLIBLINEAR.i, made by the model when feature k is excluded. Our goal is to find the value of wk that minimizes the remaining residual. We solve the subproblemwk and setting it equal to zero:For notational convenience, we define wk:S = sgn(v)(|v| − γ)+ is the soft-threshold operator that “snaps” values within γ of zero to be exactly zero [λ1 is not zero. The reason for this speedup is the fact that a wk that was previously “snapped” to be exactly zero will remain at zero, unless its absolute value exceeds λ1dk. When wk is zero, it makes no contribution to partial fits j ≠ k. Thus, if the value of wk remains at zero, no updates to λ1 will therefore lead to both sparser solutions and faster convergence times.This results in the following update rule for tly zero . The sofb:Similar to the weight updates above, we can differentiate the objective with respect to the bias term. The derivative is given byNote that this is a simple weighted average of the residuals.λ1 meta-parameter. Specifically, by initializing all wk to zero and b to λ1 to any value higher thanwk will remain at zero and no updates will be made.Using Eqs  and 8),,8), we cϵ. We make the code available as an R package gelnet.The training procedure cycles through all the coordinates and the bias term until the desired stopping criterion is reached. In our experiments, we used both the number of iterations and the difference in the objective value between updates as the convergence criteria. For the latter, we terminated training whenever that difference fell below a certain threshold Many other loss functions can be reduced to regression. In P. As we show below, GELnets are able to correctly utilize such prior information to achieve better accuracy.We begin with experiments on synthetic data to investigate a key question: under what circumstances does the prior information about the gene regulatory network help prediction performance? To answer this question, we generate synthetic data from predefined gene-gene relationships and then compare the performance of classical elastic nets to GELnets, where the gene interactions are provided to the latter via the penalty matrix A has an entry of 1 if two nodes share an edge in the graph and an entry of 0 otherwise. We begin the experiment by using A to generate the “true” weight vector w. The goal of w is to simulate a signaling pathway, whose activity contributes to the phenotypic observations. The prediction task then aims to uncover this pathway from the observable data. To simulate a signaling pathway, we select a connected subcomponent of our scale-free graph via a random walk. The walk is terminated when 10% of the nodes are selected. The feature weights wj are set to 1 for j in the selected set and to 0 for all other nodes.For synthetic data experiments, we consider a randomly-generated scale-free graph. The associated adjacency matrix X ∼ N, where we consider two scenarios for specifying the covariance matrix S. In the first scenario, a random covariance matrix is used. This creates a decoupling between the simulated expression data X and the simulated signaling pathway w, modeling the negative control case in which the observable data has no relationship to the gene regulatory network. The second scenario assumes that the feature covariance structure is dictated by the graph adjacency matrix A. A Gaussian Graphical Model (GGM) is used, with S selected such that S−1 closely approximates A[X and w that models a biological scenario, where the observable phenotype is driven by a small number of genomic correlates belonging to the same signaling pathway, while the rest of the simulated transcriptome is expressed according to the regulatory relationships encoded by A.We simulate gene expression data from a multivariate normal distribution: ximates A. The GGMy = wTX. Note that because the data dimensionality vastly exceeds the number of samples, the problem of reconstructing the signaling pathway w from gene expression X and phenotypic observations y is under-determined.To simulate a typical high-dimensional low-sample scenario found in biological applications, we made use of a 5000-by-5000 adjacency matrix and generated 50 samples for each of the two scenarios above. The observable phenotypic response in all cases was computed as X,y) defines a regression problem, to which we apply the classical Elastic Nets and the GELnets, comparing the two regularization schemes. We provide additional information about feature-feature relationships to GELnets through the penalty matrix P, as in dj are left at 1.0. To evaluate how performance is affected by prior knowledge in the form of feature-feature relationships, we consider two distinct choices for P. The first choice encapsulates the true information via the normalized Laplacian of the graph adjacency matrix A. For the second choice of P, we investigate the effect of providing the “wrong” information to the GELnets, by using the normalized Laplacian of another graph adjacency matrix A′. This matrix A′ is constructed by randomly permuting the columns  of A; such a permutation operator maintains the overall structure of the graph, while scrambling the individual feature-feature relationships.The simulated data  or via a GGM (GGM), and the suffix denotes whether the normalized Laplacian is computed over the true adjacency matrix (+) or the permuted one (−). We introduced two ways to generate the data matrix The performance was evaluated in a leave-pair-out cross-validation (LPOCV) setting, due to its tendency to yield less bias in performance estimation . We focuw and its estimate the reconstruction error, measured as y and the predictions the root mean squared error (RMSE), L as Z is the set of nodes associated with the non-zero feature weights in the model.and dispersion, measured using the normalized Laplacian w is unknown, and the reconstruction error is therefore not directly observable. RMSE is a standard performance metric for regression problems, capturing the deviation between predicted and observed response.The first performance measure captures how accurately we are able to recover the original signaling pathway that gave rise to the observable phenotypic response. Note that in real applications, the true weight vector Z is completely disconnected, the corresponding normalized Laplacian is the identity matrix and dispersion is equal to 1. Conversely, for every edge that appears between the nodes in Z, the corresponding off-diagonal entry in the normalized Laplacian will be negative, resulting in a lower dispersion value. This is a positive control, because GELnet regularization directly minimizes dispersion in its L2-norm term. Consequently, we expect dispersion to always be lower in the GELnet models, compared to their Elastic Net counterparts.Dispersion measures the degree to which features found to be predictive are near one another in network space. The metric we use arises directly from the L2-norm regularization term and acts as a positive control. Specifically, when the set of nodes marginalized estimate. Specifically, we iterate λ2 over { 10,000, 1,000, 100, 10, 1 } for both regularization schemes. For the Elastic Nets, we also iterate λ1 over λ1 off λ1 for the GELnet models were specified such that the number of non-zero feature weights equaled the corresponding Elastic Net models to allow for a fair comparison. Based on our preliminary experiments with parameter tuning, we found that such a grid covers a wide range of models.To address the question of meta-parameter selection, we average performance measures across a grid of meta-parameter values to obtain a given a particular training set?”. This is important as we are not claiming that GELnet regularization is universally better than classical Elastic Nets, nor should we expect it to be. Besides the “No Free Lunch” considerations [whether GELnet pathway-based regularization is better, but under what conditions does it boost performance. Answering this question will help us properly utilize prior biological information to gain novel insight in bioinformatics applications.As discussed in the literature, marginalized performance estimates are useful for method comparison , 39. Noterations , we expeX and the signaling network w. The GELnets are able to more accurately recover the simulated signaling pathway w when the information about true feature-feature relationships is provided (GGM+ case), and the inverse is true when the GELnets are given the scrambled relationship information (GGM- case). The latter is explained by GELnets selecting features in close proximity on the scrambled network, which is unlikely to contain the connected subcomponent encoded by w.As a positive control, we note that all GELnet solutions have lower dispersion than the corresponding Elastic Net models, when evaluated on the network provided to the GELnets. This indicates that the feature-feature penalties are working as intended. Surprisingly, GELnet regularization consistently led to better RMSE, regardless of whether the method was given the true or the scrambled network. We speculated that this was due to the effect of the false network sharing some neighbors and paths as the true network. To test this idea, GELnet-based models were retrained with increasingly scrambled information about true feature-feature relationships. To compose a partially-scrambled network, we randomly permuted a fraction of rows  in the graph adjacency matrix, before using the graph’s Laplacian to train a GELnet model. We refer to this fraction as the “Scramble Factor” and present the results from 100 runs of the experiment in We also consider the performance of the two regularization methods on data generated with a random covariance matrix, with results presented in When viewed together, these synthetic data results allow us to reason about the relevance of prior information to the application of a given dataset. Specifically, by training a model regularized with the GELnet, we are not only able to extract pathway-aligned features, but to also estimate how well those pathways represent the underlying biological mechanism that gave rise to the observed phenotype. We do this by comparing the performance to a model regularized by the classical Elastic Nets.SGL. Because SGL requires a collection of pathways rather a single graph, we apply community-based clustering (R package igraph) to split up the synthetic network before providing it to SGL. In w (lower reconstruction error), suggesting that SGL overfits the data in this situation. A similar trend with dispersion and reconstruction error can be observed in the Rand+/- scenarios  . SGL takcenarios , except I − D, as described in the Methods section) as an alternative penalty matrix for the GGM+/- scenarios. We also evaluated the use of a diffusion kernel , where GI50 is the amount of compound needed to inhibit cell growth by 50%. For every drug, we trained two linear regression models, one regularized by an Elastic Net and another by a GELnet. We used the same grid of values for the λ1 and λ2 meta-parameters as in the synthetic data experiments, and provided all GELnet models with an interaction network from Pathway Commons (http://www.pathwaycommons.org/) [The dataset by Heiser, ement of ) is compns.org/) , reducinλ1 and λ2 meta-parameters.et al.[p-values greater than 0.05). We note that while we expected BIBW2992 to be specific to the HER2 subtype, the sensitivity spectrum across the cell lines does indeed seem to sensitize additional lines w/o the amplification.Many of the drugs used in breast cancer were developed to target specific subtypes that have clear expression signatures . We indicate drugs whose sensitivity profiles correlate significantly with breast cancer subtypes  with diWhile we observe the most consistent improvement in RMSE for both BIBW2992 and 5-FdUR, the GELnet models for BIBW2992 also yield the largest reduction in dispersion over Elastic Nets. A large improvement in both performance metrics suggests that BIBW2992 falls into what we called the GGM+ scenario in our synthetic data experiments: the expression data and the mechanism of resistance are both captured by the network that is provided to GELnets. We further tested this intuition by training 30 GELnet models for BIBW2992 sensitivity using randomly scrambled versions of the PathwayCommons network. BIBW2992  is an inhibitor of kinases from the epidermal growth factor receptor family, specifically EGFR and ERBB2 (Her2). It acts by covalently binding to and irreversibly blocking the receptors, thereby shutting down the signaling networks whose deregulation is commonly known to be implicated in epithelial cancer growth and proliferation . Consequλ1 and λ2 meta-parameter values. The models are sorted by their improvement in RMSE over the Elastic Net equivalents. For each model, we show the feature weights for 30 genes that had the highest median rank across all meta-parameter values, where the ranking was according to the absolute values of the weights.A signaling) from these overexpressed receptors. In support of this observation, the overexpression of FGFR2 has been previously observed in cells resistant to Lapatinib, another Her2 inhibitor [et al. speculated that FGFR2-targeted therapy may provide a promising salvage strategy after Lapatinib failure [As expected, higher expression of the HER2 gene is correlated with higher sensitivity to BIBW2992. This is demonstrated by the relatively high negative model weights of ERBB2 and GRB7, a positional neighbor of ERBB2 on the chromosome and often co-amplified and co-expressed. Furthermore, a positive model weight for FGFR2 and GABRA3 suggests that cells resistant to BIBW2992 may be responding to alternative stimuli . For each principal component, we constructed two GELnet models. The first model used the Laplacian of PathwayCommons as its penalty matrix, as in the previous experiments. For the second model, we set the penalty matrix as P = I − D, where D is the diffusion kernel of PathwayCommons and I is the identity matrix. Our intuition is that, by capturing indirect gene connectivity, the diffusion kernel will produce models that more tightly cluster on the corresponding interaction network. The empirical results presented in λ1 and λ2 meta-parameters.We downloaded the data from the Synapse TCGA_Pancancer repository Click here for additional data file.S1 Text(PDF)Click here for additional data file.S1 FigPlotted are 30 trials of the same experiment. The x- and y-axes in every plot correspond to Elastic Nets and GELnets, respectively. The top three plots show the scenario where the GELnets were provided the true feature-feature relationships, while the bottom three plots correspond to the scrambled network case. Lower values are better for all three performance metrics, and the points are colored in red whenever the performance metrics are lower in the GELnet models, and blue otherwise.(TIFF)Click here for additional data file.S2 FigRed curve corresponds to the case where GELnets were provided with the true network used to generate the data. Blue curve depicts the case where the permuted network was provided instead.(TIFF)Click here for additional data file.S3 FigThe heatmap presents median-centered mRNA expression for 15 genes with the largest absolute weights in the corresponding model. The weights are displayed in the left barplot, while the model score for each sample is presented at the top. The samples are sorted by the signature score, and the true labels are shown in the colored bar labeled “Resistance”.(TIFF)Click here for additional data file.S4 FigThe heatmap presents median-centered mRNA expression for 15 genes with the largest absolute weights in the corresponding model. The weights are displayed in the left barplot, while the model score for each sample is presented at the top. The samples are sorted by the signature score, and the true labels are shown in the colored bar labeled “Resistance”.(TIFF)Click here for additional data file.S5 FigAs in (TIFF)Click here for additional data file.S6 FigPresented are results from 100 runs, where reconstruction error (left column), RMSE (center column) and dispersion (right column) are plotted against the fraction of edges reordered in the true network before the network was provided to GELnets. The red and blue points correspond to Elastic Net and GELnet models, respectively. The bottom row presents % improvement over Elastic Nets.(TIFF)Click here for additional data file.S7 FigPlotted are 30 trials of the same experiment. The x- and y-axes in every plot correspond to Sparse Group LASSO and GELnets, respectively. The top three plots show the scenario where both regularization methods were provided the true feature-feature relationships, while the bottom three plots correspond to the scrambled network case. Lower values are better for all three performance metrics, and the points are colored in red whenever the performance metrics are lower in the GELnet models, and blue otherwise.(TIF)Click here for additional data file.S8 FigThe interpretation of the Figure is similar to that of (TIF)Click here for additional data file.S9 FigThe black curves present the distribution of values over 30 random scrambles of the PathwayCommons network. The performance of GELnets with the original, unscrambled network are shown in red.(TIF)Click here for additional data file.S10 FigPlotted are 30 trials of the same experiment. The x- and y-axes in every plot correspond to the Laplacian and diffusion penalty matrices, respectively. The top three plots show the scenario where the GELnet was provided with the true feature-feature relationships, while the bottom three plots correspond to the scrambled network case. Lower values are better for all three performance metrics, and the points are colored in red whenever the performance metrics are lower in the diffusion penalty models, and blue otherwise.(TIF)Click here for additional data file.


Clinical diagnosis of acute infectious diseases during the early stages of infection is critical to administering the appropriate treatment to improve the disease outcome. We present a data driven analysis of the human cellular response to respiratory viruses including influenza, respiratory syncytia virus, and human rhinovirus, and compared this with the response to the bacterial endotoxin, Lipopolysaccharides (LPS). Using an anomaly detection framework we identified pathways that clearly distinguish between asymptomatic and symptomatic patients infected with the four different respiratory viruses and that accurately diagnosed patients exposed to a bacterial infection. Connectivity pathway analysis comparing the viral and bacterial diagnostic signatures identified host cellular pathways that were unique to patients exposed to LPS endotoxin indicating this type of analysis could be used to identify host biomarkers that can differentiate clinical etiologies of acute infection. We applied the Multivariate State Estimation Technique (MSET) on two human influenza (H1N1 and H3N2) gene expression data sets to define host networks perturbed in the asymptomatic phase of infection. Our analysis identified pathways in the respiratory virus diagnostic signature as prognostic biomarkers that triggered prior to clinical presentation of acute symptoms. These early warning pathways correctly predicted that almost half of the subjects would become symptomatic in less than forty hours post-infection and that three of the 18 subjects would become symptomatic after only 8 hours. These results provide a proof-of-concept for utility of anomaly detection algorithms to classify host pathway signatures that can identify presymptomatic signatures of acute diseases and differentiate between etiologies of infection. On a global scale, acute respiratory infections cause a significant proportion of human co-morbidities and account for 4.25 million deaths annually. The development of clinical diagnostic tools to distinguish between acute viral and bacterial respiratory infections is critical to improve patient care and limit the overuse of antibiotics in the medical community. The identification of prognostic respiratory virus biomarkers provides an early warning system that is capable of predicting which subjects will become symptomatic to expand our medical diagnostic capabilities and treatment options for acute infectious diseases. The host response to acute infection may be viewed as a deterministic signaling network responsible for maintaining the health of the host organism. We identify pathway signatures that reflect the very earliest perturbations in the host response to acute infection. These pathways provide a monitor the health state of the host using anomaly detection to quantify and predict health outcomes to pathogens. Upon infection, human pathogens  induce a complex cascade of host responses that have evolved to detect the pathogen and minimize the disease severity . This muEarly diagnosis of an acute infection is critical to quickly select the appropriate medical intervention for optimum patient care and improve the overall disease outcome. While most clinical diagnostic assays rely on pathogen detection, advances in technologies  to measure the host response to infection provide a wealth of data that can be exploited to improve infectious disease diagnostics . DespiteIn order to enhance information that may be obtained by the analysis of single genes, pathway-based analysis has become increasingly popular as an approach to elucidate the underlying biological processes under investigation , 14. InsIn this study we investigate the human cellular response to infection by treating the changes in gene expression as a problem in anomaly detection. Healthy individuals are assumed to be in a homeostatic state with immune systems that are expressing nominally while individuals who are becoming sick possess a cascade of pathways that reflect the systematic response to a specific invading pathogen. Our goal was to elucidate pathway-based signatures that may aid in diagnosis as well as early prognosis of acute infection. We employed a pathway-based implementation of the Multivariate State Estimation Technique (MSET), a method for detecting anomalies where the nominal data possesses substantial nonlinear structure in temporally evolving systems –21. ThisWe evaluated the anomaly detection approach using temporal gene expression data sets to identify early host functional pathways associated with acute respiratory infections in humans. Acute respiratory disease is a common diagnosis in clinical settings and a major cause of mortality worldwide . The higIn order to test and validate the methodology, we explore MSET for biological early warning using data generated by a mathematical model of the immune system’s response to infection as well as gene expression data sets arising in influenza and endotoxin experiments.There are only a limited number of gene expression data sets that measure the human immune system’s response to infection. Generally they have low temporal resolution, e.g., samples every 8 hours, but detailed gene coverage that allows us to perform a pathway based modeling approach. Real data sets also typically have a small number of subjects , 5, 23. In what follows, we first use the numerical simulation data to test MSET’s effectiveness for the detection and prognosis of sepsis. We then proceed with a more realistic proof of concept concerning the ability to use pathway analysis coupled with failure prediction algorithms for early warning of a biological disease.P, activated phagocytes (neutrophils) N, tissue damage D, and anti-inflammatory mediators CA. This model consists of four ordinary differential equations:R = f(knnN + knpP + kndD), and To illustrate the performance of the early warning algorithm on a large dataset, we use a mathematical model to simulate the immune system’s response to infection. The model  describeH):  =  for CA > 0, 2) Aseptic (S0):  =  for N, D, CA > 0, and 3) Septic (S1):  =  for all components positive.The system characterizes the time evolution of these four variables, which we view metaphorically as proxies for gene expression. The model admits three final states under certain parameter choices  The symptomatic data sets S0 and S1 serve as test data to evaluate the model. An example simulation of a patient is shown in Rt in the MSET model grows quickly indicating early that this subject is becoming symptomatic. We observe this residual growing before 10 hours have elapsed indicating that the patient will become septic. After 20 hours the pathogen is brought under control by the immune response but the damage continues to increase. We emphasize that this model does not incorporate a therapy that would presumably be administered after the early prognosis. S0 and 6.3 hours for S1, the most severe outcome, i.e., septic death.For MSET analysis, the healthy data set denoted by S0 and S1. The time of peak expression levels for each variable is shown for purposes of comparison. It is interesting to observe that the MSET model outperforms any model based on the use of a single variable using the time to peak expression. Despite the early occurrence of damage shown in S0 but has high standard deviation; it’s performance degrades for S1 to over 20 hours. In summary, when compared with the model variables in The statistical measures of prognosis time, mean and standard deviation are shown in t = 0 in the sense that the initial condition information alone contains enough information to predict final outcome. However, in general it is not possible to establish these basins of attraction for higher dimensional systems, or in the presence of noise establishing a need for alternative methods for early warning such as the one advocated here.To underscore this point, we note that for this particular dynamical systems model for sepsis it is possible to numerically partition the space of initial conditions into basins of attraction that indicate the final state based solely on the initial condition without error. Hence, for this given model we can do optimal early warning trivially at Next we apply the anomaly detection algorithm MSET to identify host cellular signaling pathways associated with the human immune response to infection by respiratory viruses. As proof of concept, we interrogated four publicly available gene expression data sets obtained from peripheral blood samples of human subjects experimentally infected with 4 different respiratory viruses, including 2 influenza virus strains: influenza viruses , HRV and RSV . In eachfor each of the 511 functional pathways used in our analysis. Each pathway model is a mapping of the identity that serves to detect any deviation from nominal, or healthy, gene expression levels for each subject whose samples are evolving in time. We expect healthy pathway expression levels will evolve into those distinctly characteristic of symptomatic and asymptomatic individuals and the analysis will classify the differentially expressed pathways in the context of host signaling networks. The analysis was performed on each dataset and ranked pathways identified in all 4 datasets were used for downstream analysis to identify robust early host signature biomarkers for respiratory virus infections.We constructed an anomaly detection model using MSET Based on the average predictive accuracy score for each pathway, there were 16 top host pathways associated with symptomatic human subjects that met the 0.7 probability cutoff across all acute respiratory infection datasets . Note thThe top pathways based on diagnosis accuracy were further analyzed to identify the host signaling networks in humans predicted to deviate first from the asymptomatic or healthy state as a result of acute respiratory virus infection . Of centThe top host signaling pathway, lysosome, is a cellular network involved with immune sensing of non-self or foreign entities in the host and is utilized by respiratory viruses to infect cells. The inflammatory bowel disease (IBD) pathway is reported in the other analyses was identified as a potential early biomarker and contains genes that influence immune system dysregulation of the mucosa, early TLR signaling, T-cell differentiation, and pro-inflammatory macrophage responses. The influenza A and TLR receptor pathways encompass gene sets that regulate host viral sensing and the antiviral response to acute respiratory virus infection in humans. The intestinal immune network for IgA production pathway plays a role in host-microbe interaction making it a natural site for the first detection of infection . The topThe performance of these pathways as early warning mechanisms for human subjects exposed to the H1N1 or the H3N2 influenza virus strain is shown in . The cumIt is interesting to further examine the explicit time-dependent behavior of the pathway models more closely. We applied the toll like receptor anomaly detection model to determine the prognosis for both an asymptomatic subject (A) and a symptomatic subject (B). The toll like receptor pathway did not detect an anomaly for the subject who remains asymptomatic while, in contrast, this pathway shows a clear anomaly for the symptomatic subject some forty hours after infection . We measIn order to detect host pathway anomalies associated with an endotoxin or bacterial infection we analyzed host response data sets that studied the acute inflammatory and immune response to understand the mechanism of LPS response over time between the endotoxin-treated and control groups , 34. By n = 13) and respiratory virus pathway signatures (n = 16). Affiliation networks demonstrated that the viral and bacterial pathways are connected and the majority of pathways share a subset of genes with at least one other pathway  [H1N1 dataset includes 9 subjects who developed symptoms and 6 subjects classified as asymptomatic.H3N2: The H3N2 microarray experiment consists of 17 human subjects inoculated with influenza A (A/Wisconsin/67/2005) [H3N2 dataset has 9 symptomatic and 6 asymptomatic subjects.HRV: The HRV microarray experiment consists of 20 human subjects inoculated with Rhinovirus (HRV) serotype 39 [HRV dataset includes 10 subjects who developed symptoms and 10 subjects classified as asymptomatic.otype 39 . The HRVRSV: The RSV microarray experiment consists of 20 human subjects inoculated with respiratory syncytial virus (RSV) serotype A [RSV dataset includes 8 subjects who developed symptoms and 11 subjects classified as asymptomatic.rotype A . One subhttp://people.ee.duke.edu/~lcarin/reproduce.html. We investigate an endotoxin lipopolysaccharide (LPS) microarray experiment that included 8 human subjects [h and at 2, 4, 6, 9, and 24 h afterward. The LPS dataset consists of 4 subjects who were administered endotoxin and 4 who were administered a placebo. The LPS dataset is also publicly available at: http://www.gluegrant.org/pubsupport/Nature_1.For both H1N1 and H3N2, the actual time points are -5, 0, 5, 12, 21.5, 29, 36, 45.5, 53, 60, 69.5, 77, 84, 93.5, 101, 108 hours. For HRV, peripheral blood was taken at baseline, then at 4 hour intervals for the first 24 hours, then 6 hour intervals for the next 24 hours, then 8 hour intervals for the next 24 hours, and then 24 hour intervals for the remaining 3 days of the study. 14 time points were found in the original data set without actual time provided. For RSV, peripheral blood was taken at baseline, then at 8 hour intervals for the initial 120 hours, and then 24 hours for the remaining 2 days of the study. 21 time points were found in the original data set without actual time provided. A summary of the number of data samples associated with data set is provided in subjects , 34. TheA collection of 511 pathways were used for the actual analysis of the gene expression data sets. These pathways map the multivariate interactions between genes associated with biological processes, such as metabolism, signal processing, and human diseases, based on biological knowledge. The pathways included in our analysis are comprised ofwww.genome.jp/kegg),294 KEGG pathways (www.biocarta.com).217 BioCarta pathways  subjects is used for training a model function f(x(t)) where the pathway evolving in time may be viewed as a nonlinear curve observed over T time unitsn is the number of genes in the pathway. One approach to anomaly detection is the construction of the mapping of the identity, i.e.,x(t) that are considered to be nominal. When this relationship fails to be true then we conclude that there is a novelty in the data and that the system for which the model was constructed has changed. At this point we refer to the model as being in alarm.Our hypothesis is that the immune system behaves There are a number of approaches for constructing mappings of the identity for a given data set, see  for a geThe MSET model of a system is constructed from a historic sample of nominal data. In the current application this data will be the gene expression levels of healthy individuals. Since we are interested in understanding the immunological response we have organized the gene expression data by pathways. In this setting an MSET early warning system will be constructed for each pathway. Each of these MSET pathway models can now be used to monitor the temporally evolving system and identify departures from nominal state behavior.χ2) test on the residuals as a means to identify alarm points. As the results indicate, we found this test to be very effective for detecting anomalies, but there is no theoretical basis to claim it is the optimal approach. Statistically significant outliers in the model residual are then used to indicate anomalous system behavior.Each model maps the given state of the system to a new state. If the system is operating in a nominal manner, the output of this mapping is effectively the same as the input to within some error tolerance. However, if the system’s operating characteristics have changed then the output of this mapping will no longer satisfy this property, i.e., the output of the MSET mapping will now deviate from the input by more than the allowed tolerance. It is standard practice with MSET to use the Sequential Probability Ratio Test (SPRT) to detect system alarms, i.e., critical deviations where the model is deemed to no longer apply to the system. In our application there are not enough data points (in time) to implement this approach so we implement a chi-square  is a p-dimensional vector measurement of a healthy state at time ti. The value p is the number of genes in the given pathway and will vary amongst pathways. The value M is the total number of healthy data states available for building the model. The expression levels of the p genes in a given pathway encode a component of the subject’s biological state. Thus the vector x(ti) consisting of the measurements of the p genes expression levels reflect the biological state of that pathway at time ti.As shown in yobs, are mapped by MSET to model estimated states yest. As described below, if yobs ≈ yest then we conclude that the system is operating under nominal conditions.Each MSET pathway model is effectively a monitoring system that detects deviations in the gene expression patterns from the ideal healthy state. New measurements of gene expression levels, denoted by D as [DT ⊗ D is called a similarity matrix.The MSET mapping used to detect novelty is based on the construction of similarity operator in terms of the memory matrix D as –18:yests encodes the similarity Xi)( and Yj) random multivariate variable. For an observed state that is not similar to the columns of D, i.e., it contains some significant novelty, the residual is larger and the assumption that it is governed by an i.i.d. normal distribution no longer holds.The residual Tobs, the estimates Test are calculated using the memory matrix D by RT = Tobs − Test are then obtained by RT represent the deviation of the system under test from its healthy operating condition D and are called actual residuals.For all observations from the test data i.e., anomalous observations which are deviating from the normal data variability. Here, the standard outlier detection method, chi-square (χ2) test, is applied to detect the anomalous observations.The outliers describe the abnormal data behavior, nominal data, i.e., data that is assumed to be taken from subjects whose immune system is not responding to an infection. We partition each data set into subsets of size m and n, associated with either symptomatic and asymptomatic subjects, respectively. Further, the data are measured at the discrete time points labeled {t1, t2, ⋯, tM}. The data is divided into two groups, one for training the models of size nh, and one for testing the models, as shown in t = −5) is used to train the models. The memory matrix Dk defined in kth pathway is constructed from the microarray data from the nh healthy subjects selected at random and thus has size pk × nh. Given there are n − nh healthy test subjects and m symptomatic test subjects not in the training data set, the test data matrix for the kth pathway Tk has size pk × (m + n − nh).For each data set we construct a model based on using a subset of Using this notation the algorithm can now be summarized in five basic steps:k consisting of pk genes is assembled from the available microarray data for each of the k = 1,…,511 pathways under consideration. The data matrices Dk and Tk are created by these pk gene expression levels that constitute pathway pk.Pathway RTk are calculated using Dk and Tk and the MSET mapping.The test residuals μk and standard deviation σk for RTk are obtained to perform the χ2 test with pk degrees of freedom.The mean Tk, the χ2 values are calculated over the time course {t1, t2, ⋯, tM}. These are used to perform anomaly detection. If an anomaly is detected we refer to the time of detection as the diagnosis time. A P-value of 0.005 is used as a cutoff between normal and anomalous observations. We refer to the the χ2 value as the irregular score.For each subject in The performances for the selected pathway, the classification accuracy and the average diagnosis time are computed.Affiliation network and overlap analysis of genes represented within the viral and bacterial-specific biological pathways were generated using the R platform (v3.1.3). Graph adjacency evaluation and network visualization was done using the Bioconductor package ‘igraph’ (v0.7.1) . NetworkAdvances in host gene expression technologies have provided a wealth of data on the host response to infectious diseases. The large data sets generated by microarray and RNA sequencing (RNA-Seq) requires analytical tools that utilize new algorithms that can exploit the information to derive biologically meaningful results. The current challenge is applying an analytical tool or mathematical model to identify the critical host genes or gene networks in an unbiased manner to develop targeted clinical diagnostic assays and host-derived therapeutics against pathogenic microorganisms. Host pathway analysis incorporates the functional linkage between gene sets to rapidly derived host gene signatures associated with an acute infection. We utilized MSET, a well-known approach in the anomaly detection field, to analyze acute respiratory virus and endotoxin gene expression datasets from exposed human subjects. Our dynamical systems based MSET analysis incorporated the temporal dynamics of the host pathways, i.e. the changes in host response to infection overtime, to identify early host pathway biomarkers associated with acute infection.There are only a limited number of gene expression data sets publicly available that measure the human cellular response to acute infection. Generally they have low temporal resolution, e.g., samples every 12-24 hours, but detailed gene coverage that allows us to perform a pathway based modeling approach. Clinical data sets with temporal sampling also typically have a small number of subjects , 23. In Our results suggest that the anomaly detection framework can be used effectively to objectively identify key functional pathways or biomarkers that play a fundamental role in discriminating biological states such as symptomatic versus asymptomatic. The analysis provided a ranking of the most accurate diagnostic host pathways associated with respiratory virus infection or endotoxin exposure. From these we identified the pathways with superior prognostic properties in the sense that they alarm, i.e., display novelty first following infection with a virus or bacteria. The top ranked respiratory virus pathways across all 4 viral datasets  reveal an overall host signal generally associated with the intestinal mucosa and homeostasis of the gut epithelium. Respiratory viruses are known to cause gastrointestinal symptoms that are associated with direct infection of the intestinal epithelial cells and through modulation of the intestinal microbiome . One stuEarly differential diagnosis between bacterial and viral respiratory infections would greatly enhance the treatment of acute respiratory infectious diseases. In this study, we defined pre-symptomatic or early warning pathway signatures for both data sets and found these pathogen-specific biomarkers could distinguish between a patient infected with a bacteria (12 pathways) vs. a virus (8 pathways) within 24 hours post exposure. The pre-symptomatic 8 pathway respiratory virus signature contains host-signaling networks involved with the innate antiviral sensing, inflammation, and mucosal integrity. These functional pathways are consistent with other studies predicting host biomarkers for respiratory diseases . The preBased on the results obtained here, we feel further evaluation of the anomaly detection approach for pathway analysis is warranted. We plan to further validate our results using other algorithms for discovering novelties in temporally evolving biomarkers, as well as supervised approaches for classification. By applying various anomaly detection approaches to human gene expression data sets with temporal sampling, we can define unique host gene classifiers that can distinguish between symptomatic (infected) and asymtomatic (uninfected) subjects. This will also permit additional elucidation of the complex processes of the host cellular response to infection, such as host signaling networks or functional pathways to diagnosis patients infected with different pathogenic etiologies . As human data sets in response to acute infectious diseases becomes more readily accessible mathematical algorithms may be employed to identify host gene signatures that can predict infections in presymptomatic patients and distinguish between closely related viruses (SARS vs. MERS) and/or at the virus strain level (Influenza H1N1 vs. H3N2) that present similar disease manifestations. Rapid host-derived gene panels that represent pathogen-specific biomarkers could be developed to complement PCR-based assay panels that target pathogen genomes for more accurate clinical diagnostics of acute infectious diseases.


Pathway analysis is a common approach to gain insight from biological experiments. Signaling-pathway impact analysis (SPIA) is one such method and combines both the classical enrichment analysis and the actual perturbation on a given pathway. Because this method focuses on a single pathway, its resolution generally is not very high because the differentially expressed genes may be enriched in a local region of the pathway. In the present work, to identify cancer-related pathways, we incorporated a recent subpathway analysis method into the SPIA method to form the “sub-SPIA method.” The original subpathway analysis uses the k-clique structure to define a subpathway. However, it is not sufficiently flexible to capture subpathways with complex structure and usually results in many overlapping subpathways. We therefore propose using the minimal-spanning-tree structure to find a subpathway. We apply this approach to colorectal cancer and lung cancer datasets, and our results show that sub-SPIA can identify many significant pathways associated with each specific cancer that other methods miss. Based on the entire pathway network in the Kyoto Encyclopedia of Genes and Genomes, we find that the pathways identified by sub-SPIA not only have the largest average degree, but also are more closely connected than those identified by other methods. This result suggests that the abnormality signal propagating through them might be responsible for the specific cancer or disease. However, using such information to better understand the underlying biological phenomena remains a challenge. Pathway analysis has become a popular approach for gaining insight into the underlying biology of differentially expressed genes (DEGs) and proteins. The evolution of knowledge-driven pathway analysis can be divided into four generations. The first-generation analysis method is called the overrepresentation approach (ORA)  and compet al.  proposedet al. –12. Subpet al. , the cliet al. , and Patet al. . These aet al. [In the present work, we combine the approaches of subpathway analysis and SPIA, which we call sub-SPIA, to identify biologically meaningful signaling pathways. One key problem in subpathway analysis is how to define a subpathway. Li et al.  used theWe applied the sub-SPIA method to the colorectal cancer (CRC) and lung cancer datasets, and our results demonstrate that the proposed method can identify more disease-related pathways than SPIA, DEgraph, Clipper, and Pathiways. Furthermore, we find that most of the pathways identified by sub-SPIA have a high degree and are tightly connected within the entire pathway network. This result reveals that diseases  may result from the synergic interactions of a group of related pathways.PG(FDR) which combine the enrichment and perturbation p-values (see definition in the method section), were computed from the nominal p-values by using the R function “p.adjust.” We present herein the significantly enriched pathways by applying sub-SPIA and SPIA to CRC and lung cancer datasets. The significant pathways that were also identified by DEgraph, Clipper, and Pathiways and are given in Tables There are 137 signaling pathways in KEGG. To deduce pathway significance, we used a significance threshold of 1% on the p-values corrected for false discovery rate (FDR). For both sub-SPIA and SPIA, the FDR-adjusted p-values PG are listed in focal adhesion, pathways in cancer, PPAR signaling pathway, and ECM-receptor interaction. Previous studies show that some common pathways are highly associated with various cancers, including CRC and lung cancer, such as focal adhesion , 17, pat and the p53 signaling pathway , 34. Sub-SPIA identified all of these pathways, whereas SPIA only identified three of them. However, some pathways are not likely to be relevant to CRC, such as the pathways for Huntington’s disease, Alzheimer's disease, and Parkinson’s disease [Sub-SPIA identified 18 potential pathways associated with CRC, while SPIA identified only 8 pathways. These pathways and their corresponding regulation of actin cytoskeleton pathway plays a key role in the progression of CRC [Concerning the significant pathways identified by sub-SPIA but not by SPIA, existing evidence indicates that they may be associated with CRC. The dysregulation of the n of CRC , 19; thicomplement and coagulation cascades pathway involves 14 DEGs and also plays a key role in the progression of CRC. For example, in a comparison of radiosensitive and radio-resistant lines of CRC cells, the result of five lines of CRC cells shows that 30 up-regulated genes were identified as being involved in DNA damage response pathways, immune response pathways, and the complement and coagulation cascades pathway [The  pathway , 36.notch signaling pathway was observed in colorectal and other forms of cancer [The deregulation of the f cancer . NOTCH if cancer . A recenf cancer  indicatePseudomonas aeruginosa and Staphylococcus aureus, and which modulates inflammation through its antiprotease activity. A delicate relationship between proteases and antiproteases is central in determining how inflammation develops during colitis. Proteases damage tissues during inflammation whereas protease inhibitors minimize tissue damage and facilitate healing. In a microarray study of human colonic biopsies, patients with ulcerative colitis expressed 30-fold more elafin mRNA than healthy controls, which indirectly indicates that the Staphylococcus aureus infection pathway is associated with CRC [Elafin is a protease inhibitor with antibacterial effects against bacteria such as with CRC .T cell receptor signaling pathway is responsible for impaired immune responsiveness of T cells in cancer patients. In such patients, the TCR-β gene in lymphocytes is less expressed in colon cancer, renal cell carcinoma, melanoma, and cervical cancer, which has important clinical implications for monitoring the patient immune status during therapy [The  therapy .ErbB signaling modules include the phosphatidylinositol 3-kinase/Akt pathway, the Ras/Raf/MEK/ERK1/2 pathway, and the phospholipase C pathway. Several malignancies are associated with the mutation or increased expression of members of the ErbB family, including lung, breast, and stomach cancer [et al. found that receptor tyrosine kinase (RTK) members ErbB2, ErbB3, and c-Met were indeed differentially overexpressed in samples from CRC patients, leading to constitutive activation of RTK signaling pathways. By using the ErbB2-specific inhibitor Lapatinib and the c-Met-specific inhibitor PHA-665752, they further demonstrated that this constitutive activation of RTK signaling is necessary to the survival of CRC cells [The human epidermal growth factor receptor family contains four members that belong to the ErbB lineage of proteins (ErbB1-4)–45 42–4–442–45. RC cells .mycobacterium tuberculosis (MTB) is the second leading cause of death from an infectious disease [tuberculosis pathway plays an important role in them and thus is identified by sub-SPIA as being significant in CRC.As of 2008, CRC is the third most commonly diagnosed cancer in males and the second in females . Worldwi disease . Signifi disease . AlthougPG are listed in ECM-receptor interaction, cell cycle, and focal adhesion. Qiu et al. found that DEGs may promote metastasis of lung cancer cells through complicated networks, including pathways in cancer, focal adhesion , 52, reg. These pathways are also identified by sub-SPIA, whereas SPIA only identifies five of them with P<0.06.Sub-SPIA identified 19 potential pathways associated with lung cancer, whereas SPIA only identified 5 pathways see . These pcell-cycle pathways have been frequently observed in a variety of human malignancies, including lung cancer [CCND1 and STK15, and tumor-suppressor genes, such as p53, p21, and p27, are commonly associated with increased cell proliferation, defective apoptosis, elevated cancer risk, and poor survival rates [Gene anomalies in g cancer –58. Dysfal rates , 59.NF-κB signaling may be a critical target for enhancing the efficacy of CDDP against NSCLC. Wang et al. [Constitutive activation of NF-κB was detected in non-small-cell lung carcinoma (NSCLC) and was implicated in imparting resistance to CDDP , 61. Theg et al.  found thet al. [fanconi anemia pathway in NSCLC. They demonstrated that inactivation of the FANC-BRCA pathway is relatively common in solid tumors and may be related to tobacco and alcohol exposure and to the survival of these patients.By using methylation-specific PCR, Marsit et al.  found thvascular smooth muscle contraction and the focal adhesion pathways may play key roles in the initiation and development of NSCLC. Fang et al. [Aberrant activities of the g et al.  demonstrtuberculosis (TB) is a clinical problem whose diagnosis and treatment presents a challenge [salmonella pneumonia, or lung abscess, Cohen et al. noted that thirteen of them (36%) had prior abnormalities of the lung or pleura. From among these thirteen, seven had lung malignancies [salmonella pathogens, it is possible that the tuberculosis pathway plays an important role in them and thus is identified by sub-SPIA.The comorbidity of lung cancer and pulmonary hallenge . In a regnancies . AlthougWnt signaling and MAPK signaling, are common driving forces during carcinogenesis [According to the KEGG pathway hsa05200 , the signals from the outside pathways, such as ogenesis . The subWnt signaling pathway has a canonical Wnt/β-catenin cascade and two non-canonical pathways named the Wnt/Planar cell-polarity (Wnt/PCP) pathway and the Wnt/Ca2+ pathway. Sub-SPIA identified that both the canonical Wnt/β-catenin cascade and the Wnt/Planar cell-polarity (Wnt/PCP) pathways are significantly enriched with DEGs relating with CRC and lung cancer. Figs Wnt signaling pathway with the differentially expressed genes highlighted on the two datasets. The identified subpathways are circled by the red dashed lines for ns = 4 and the blue dashed lines for ns = 2. β-catenin was observed highly expressed in the CRC patients. According to the identified Wnt/β-catenin cascade, the upstream signal of Wnt triggers the activation of gene Frizzled and Dv1, and the downregulation of the inhibitor GSK-3β by Dv1 activates the expression of β-catenin. Genes belonging to the Wnt/PCP pathway, such as JNK are known to be up-regulated in cancer [Wnt signaling activation is consistent with the regulation flows.The n cancer . Based ons = 4. We see that, not only do the number of DEGs differ for the two datasets, but also some DEGs exist that are highly expressed on the CRC dataset but lowly expressed on the lung dataset. this demonstrates that the Wnt signaling pathway may function differently in the CRC and lung cancer. For example, the downstream of the Wnt/PCP pathway which leads to the gene transcription in CRC is down-regulated whereas it is upregulated in lung cancer.Figs As mentioned in introduction, several subpathway analysis methods have been proposed to exploit the various functions of the pathway. For example, DEgraph  uses mulIt seems that, in comparison with sub-SPIA, the three methods mentioned above are very sensitive to the dataset. With a p-value of 0.01, Clipper, and DEgraph identified 13 and 21 significant pathways, respectively, from the CRC dataset. However, they identified many significant pathways with dubious biological meaning in the lung cancer dataset . Pathiways identified 10 significant pathways from the colorectal- cancer dataset but no significant pathways at all from the lung cancer data set. Therefore, in comparison, the proposed sub-SPIA generally performs more stably with both data sets.From Tables From the perspective of systems biology, the emergence and development of a cancer or disease may be due to abnormal changes in some related pathways instead of in individual pathways. Based on the connection between pathways, we construct the entire pathway network in the KEGG. To investigate the topological relationship of the significant pathways identified by each method in the entire pathway network, we extracted from The average clustering coefficient generally reflects the degree of the closeness of the identified pathways. For both datasets, the average clustering coefficient of pathways identified by sub-SPIA is about 0.38, which is the largest obtained of the five methods. Considering the relative sparseness of the entire pathway network, this indicates that the pathways identified by sub-SPIA are more closely related than those identified by other methods. In other words, they interact closely with each other to fulfill various biological functions.Epstein-Barr virus infection [To identify significant pathways, we combine the subpathway analysis and the SPIA in a method we call sub-SPIA. Compared with the original SPIA, sub-SPIA dramatically improves the resolution for identifying significant pathways because subpathway analysis focuses on a local region in a pathway. From Tables nfection , 69. HowWe also compared sub-SPIA with three other subpathway-analysis methods: DEgraph, Clipper, and Pathiways. Based on the number of the identified significant pathways, sub-SPIA is more stable than these three methods because they either find many dubious pathways or no significant pathways at all on the lung cancer dataset. Analyzing the relationship between the significant pathways identified by those methods further reveals that those identified by sub-SPIA not only play a more important role in the entire network but also are highly connected. Because most of these pathways are known to relate to various cancers, we may conclude that the abnormality signal propagating through them may be responsible for the specific cancer or disease.Finally, The MST structure overcomes the disadvantage of the k-clique method, which generally results in many overlapped subpathways. For example, in the pathways identified by sub-SPIA on the two datasets with p-values of 5%, most pathways contain just one significant subpathway whereas only seven pathways contain two to five subpathways . Additionally, the cross talk between pathways had been found to play an important role in cancer . The fleet al. [The first is the CRC dataset, which compares 12 CRC samples with 10 normal samples  by usinget al. , is a luA spanning tree is a subgraph that is a tree and connects all the vertices of the parent graph. Minimal-spanning trees (MSTs) have many applications in telecommunication and transportation-route design. As mentioned in the introduction, genes in a pathway are generally sparsely connected and the DEGs mapped in it may not be connected directly, so we search for a minimal-spanning tree that includes both the maximum number of signature nodes and the minimum number of non-signature nodes. This concept is more flexible than the k-clique concept for representing a subpathway. The Kruskal algorithm is one commonly used algorithm to find the minimal-spanning tree.https://github.com/eshinesimida/subpathway-analysis. The main steps to identify significantly enriched subpathways include (i) reconstruct the gene network from the signaling pathways, (ii) map the DEGs in the constructed gene network, and (iii) locate subpathways and evaluate their statistical and perturbation significance. In this work, a pathway confers significantly enriched pathways if and only if it contains at least one significant-enrichment subpathway.Sub-SPIA is implemented by using the statistical programming language R and can be freely downloaded from http://www.kegg.jp/kegg/xml/). The KEGG database provides one xml file for each pathway. In the KGML format, nodes in pathways often correspond to multiple gene products and compounds. Gene products can be divided into protein complexes and groups containing alternative members (gene families). We applied the graphite [We downloaded the signaling pathways from KEGG. These are directed graphs based on biochemical-reaction information in the KGML file  if the shortest path between a signature nodes u∈S and v∉S is less than ns + 1 (parameter ns is the maximum number of permitted non-signature nodes in the shortest path between two signature nodes)ns+1, then we add the non-signature nodes in their shortest path and node v to S. (iii) We repeat step (ii) until no other signature nodes can be added to S. (iv) If there exist some signature nodes in the pathway not included in the node set S, we repeat steps (i)–(iii) on them to find other node sets S′.DEGs within a pathway provide important signatures to locate subpathways associated with diseases of interest. Because DEGs in a subpathway are generally closely connected in the converted gene network, we first find all node sets in a pathway which include closely connected signature nodes. The main process is as follows: (i) we define a node set S = ku and kv are the number of signature nodes connected with nodes u and v. The Kruskal algorithm first sorts the edges in a graph according to their weight and then iteratively selects |S|-1 minimal-weighted edges that cannot form a loop with the previously selected edges at each step. After trimming these non-signature nodes in the leaves, we obtain the MST that includes the maximum number of signature nodes and the minimum number of non-signature nodes.Obviously, genes in the node set S forms a connected sub-gene-network. However, it may include some redundant non-signature nodes that are not necessarily needed to make the signature nodes form a connected subregion. According to the definition of the MST, these redundant non-signature nodes should locate in the leaves of MST. Therefore, we first use the Kruskal algorithm to find the MSTs and then remove these non-signature nodes in the leaves of MST. We convert the subgraph of nodes in set S into an undirected weighted graph. The weight w of an edge connecting two nodes u and v is defined asns. A smaller value of ns means that only those nodes meeting stricter distance similarities will be added to the corresponding subpathway, and the subpathways thus identified become smaller compared with what happens with larger values of ns. A smaller number of permitted non-signature nodes helps to increase the ratio of signature nodes in the located subpathway regions. In this paper, we use ns = 4 to search the minimal-spanning tree based on the DEGs.Flexibility can be introduced to this subpathway strategy by varying the parameter ns = 4, and Figs ns = 2. The subpathway circled by the red dashed lines in Figs In Figs ns = 2 and starting from signature node 16, we reach the node set S = {16,17,19,20,21,22,24}, which includes the two non-signature nodes 19 and 21. We now give a brief description of the MST by referring to the node set in PNDE = P(X≥Nde|H0) captures the significance of the given subpathway Pi by an over-representation analysis of the number of DE genes (NDE) observed on the pathway.H0 stands for the null hypothesis where random DEGs appear on a given subpathway. From a biological perspective, this would mean that the subpathway is not relevant to the condition under study. The value of PNDE represents the probability of obtaining a number of DEGs on the given subpathway that is at least as large as the observed number Nde. The probability PNDE is obtained by assuming that NDE follows a hypergeometric distribution. If the whole genome has a total of m genes of which t are involved in the pathway under investigation, and the set of genes submitted for analysis has a total of n genes of which r are involved in the same pathway, then the p-value can be calculated to evaluate enrichment significance for that pathway as follows:We used the hypergeometric test and abnormal perturbation to calculate the statistical significance of each subpathway. This process contains two types of evidence: the overrepresentation of DEGs and the abnormal perturbation in a given subpathway. The first probability PPERT is calculated based on the amount of perturbation measured in each pathway. A gene perturbation factor is defined as:E(gi) represents the signed normalized measured expression change of the gene gi (log fold-change if two conditions are compared). The second term in Equation is the sum of perturbation factors of the genes gj directly upstream of the target gene gi, normalized by the number of downstream genes of each such gene Nds(gj). The absolute value of βij quantifies the strength of the interaction between genes gi and gj. Other detailed information can be referred in Ref. [The second probability  in Ref. .PG, which tests whether the subpathway is significantly perturbed by the condition being studied, combines PNDE and PPERT to rank the pathways. When the null hypothesis is true, the probability of observing a pair of p-values whose product, ci = PNDE(i)*PPERT(i) is at least as low as that observed for a given pathway Pi isPG values can occur by chance. Therefore, we control the FDR of the subpathway 1% by applying the commonly used FDR algorithm [The global probability value lgorithm .S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.