The human JAK/STAT pathway is well detailed and fully annotated protein-protein interaction network is available from the Kyoto Encyclopedia of Genes and Genomes (KEGG) (http://www.genome.jp/kegg/).8 KEGG pathway is a collection that includes well-ordered pathways mined from textbooks, literature, other databases and expert knowledge.9–11 We extracted the JAK/STAT pathway from Kyoto Encyclopedia of Genes and Genomes (KEGG, hsa04630). The pathway was downloaded as KGML files. In the next a mathematical graph representation of the pathway was done. In the graph representation, a numbered vertex represents each protein and interactions between the proteins are represented by edges. The adjacency list was generated with the software R. The KEGG pathways have directional components as well. We view a network as a directed graph and note the number of edges and the minimum size of a vertex cover of the underlying undirected graph (a vertex cover in a graph is a set of vertices such that given any edge at least one of its vertex belongs to that set; for example for the graph G with V(G)={a,b,c,d} and E(G)={ab,ac,ad} both {a} and {b, c ,d} are vertex covers but {b, c} is not a vertex cover). For each network if one deletes a set of vertices then all the edges that have at least one vertex in that set also deleted and we are left with a smaller network. The considered network has 155 nodes, 868 edges and minimum size of a vertex cover is 83. We know that certain vertices (serially numbered from 59 to 99) are network "entry" points of this network (through which signals enter the network from environment). Each of the medications and viruses we experiment with acts by deleting some nodes of this network. Now as directed edges in this network imply "flow of signals", if after deleting some nodes it turns our that there are some nodes where no signal is entering, we delete that node as long as it is not an entry point; as this implies that it will not be part of our biological process anymore. Now deletion of such nodes may further create some nodes where no signals enter and we delete them too (as long as they are not entry point nodes). We continue this way until no more such nodes are left. And for each case we observe the number of edges and minimum size of a vertex cover. For doing this we use R programming software. We first calculated the size of the original unperturbed network. Then the effects of the following drugs (respective targets), and their combinations, commonly used in RA were tested: methotrexate (STAT 1 (hsa6772) and STAT 5 (hsa6776)), prednisolone (interleukin 2 receptor subunit alpha (has 3559), JAK3 (hsa3718)), rituximab (STAT3 (hsa6774)), tocilizumab (interleukin-6 receptor (hsa3570)), tofacitinib (JAK1 (hsa3716), hsa3718) and baricitinib (hsa3716, JAK2 (hsa3717)).12–14 Following viral systems were also tested for their ability to evade the immune system through interference with the JAK/STAT pathway: Measles: interferon alpha receptor 1 (hsa3454), hsa6772; Influenza A: hsa3454, hsa6774; hsa3454, hsa6772, interferon gamma receptors 1 and 2 (hsa3459, hsa3460); West Nile virus (WNV), Japanese B virus (JBV) and Yellow Fever virus (YFV): hsa6772; dengue virus: hsa6772, STAT2 (has 6773); respiratory syncytial virus (RSV): Tyk2 (hsa7297), CREB binding protein (hsa1387), hsa6772, hsa6773; Kaposi’s sarcoma virus (KSV): hsa3716, hsa7297, hsa6773; Hepatitis B and C virus (HBV and HCV): hsa3716, hsa7297, hsa6772); cytomegalovirus (CMV): hsa6772, interferon regulatory factor 9 (hsa10379); Hendra and Nipah virus (HV and NV): hsa6772, hsa6773; Coronavirus: hsa3454, hsa6772, hsa6773.15

In addition to calculation of network sizes in these perturbed networks, we also accessed the treatment responses of the above-mentioned drugs in RA in terms of the American College of Rheumatology 20 (ACR 20) response.16–25

The treatment responses (ACR20 numerical values) were correlated with the size invariants of the networks. The median sizes of the networks were compared between the viruses, which cause acute infections (acute: measles, influenza A, WNV, JBV, YFV, dengue virus, CMV, HV, NV, RSV, EBV, coronavirus; chronic: KSV, HBV, HCV).