Monotone and near-monotone network structure (part II)

We next describe recent work on monotone input/output systems (“MIOS” from now on). Monotone i/o systems originated in the analysis of mitogen-activated protein kinase cascades and other cell signaling networks, but later proved useful in the study of a broad variety of other biological models. Their surprising breath of applicability notwithstanding, of course MIOS constitute a restricted class of models, especially when seen in the context of large biochemical networks. Indeed, the original motivation for introducing MIOS, in the 2003 paper [1], was to study an existing non-monotone model of negative feedback in MAPK cascades. The key breakthrough was the realization that this example, and, as it turned out, many others, can be profitably studied by decompositions into MIOS. In other words, a non-monotone system is viewed as an interconnection of monotone subsystems. Based on the architecture of the interconnections between the subsystems (“network structure”), one deduces properties of the original, non-monotone, system. (Later work, starting with [2], showed that even monotone systems can be usefully studied through this decomposition-based approach.)