Delineating feedback activity in the MAPK and AKT pathways using feedback-enabled Inference of Signaling Activity

An important aspect of cellular signaling networks is the existence of feedback mechanisms. However, due to the complexity of signaling networks, as well as the presence of multiple interrelated feedback events, it can be difficult to identify which signaling routes are active in any particular context. We have previously shown that Inference of Signaling Activity (ISA) can be a useful method to study steady-state oncogenic signaling across different cell lines and inhibitor treatments. However, ISA did not explicitly include feedback signaling events. Incorporating feedback will increase the complexity and computational cost of the model, and more data is likely to be needed to infer feedback activities. Here, we developed feedback-ISA (f-ISA), an extension of the ISA modeling approach which incorporates feedback signaling events. It also includes integrated batch correction in order to fit the models to multiple, independent datasets simultaneously. We find that the identifiability of feedback activities can be counter-intuitive, which shows the importance of analyzing the full, joint uncertainty in model parameters. By iteratively adapting the model and including multiple datasets, including both steady state and intervention data, we constructed a model that can explain a large part of the phosphorylation levels of several signaling molecules in the MAPK and AKT pathways, across many breast cancer cell lines and across various conditions. The resulting model delineates which routes in the signaling network are likely to be active in each cell line and condition, given all of the data. Additionally, such models can indicate whether datasets agree with each other, and identify which parts of the data cannot be explained, thereby highlighting gaps in the current knowledge. We conclude that this modeling approach can be useful to quantitatively understand how complex cellular signaling networks behave across different cell lines and conditions.