s at least one significant-enrichment subpathway. Map DEGs to 946128-88-7 graphs of pathways We downloaded the signaling pathways from KEGG. These are directed graphs based on biochemical-reaction information in the KGML file. The KEGG database PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/19747383 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. We applied the graphite package to reconstruct the gene network from the pathway. Next, the DEGs were mapped to the gene network. Locate subpathways by DEGs 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: we define a node set S = and add a randomly selected signature node to it. if the shortest path between a signature nodes u2S and v= S is less than ns + 1 ns+1, then we add the non-signature nodes in their shortest path and node v to S. We repeat step until no other signature 11 / 19 Sub-SPIA The statistical significance of subpathways 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 PNDE = P captures the significance of the given subpathway Pi by an over-representation analysis of the number of DE genes observed on the pathway.H0 stands for the null 12 / 19 Sub-SPIA Fig 4. An example of the MST. A sub gene network extracted from Fig 1B for ns = 2. The converted undirected weighted graph. The resulted MST. doi:10.1371/journal.pone.0132813.g004 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 PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/19749456 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: t p1 r1 X x0 ! mt nx ! m n ! x The second probability PPERT is calculated based on the amount of perturbation measured in each pathway. A gene perturbation factor is defined as: PFgi DEgi n X j1 bij: PFgj Nds gj where the term E represents the signed normalized measured expression change of the gene gi. 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. The absolute value of ij quantifies the strength of the interaction between genes gi and gj. Other detailed information can be referred in Ref.. 13 / 19 Sub-SPIA The global probability value 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 hyp
