Liebig's law of the minimum in the TGF-β/SMAD pathway

Cells use signaling pathways to sense and respond to their environments. The transforming growth factor-{beta} (TGF-{beta}) pathway produces context-specific responses. Here, we combined modeling and experimental analysis to study the dependence of the output of the TGF-{beta} pathway on the abundance of signaling molecules in the pathway. We showed that the TGF-{beta} pathway processes the variation of TGF-{beta} receptor abundance using Liebigs law of the minimum, meaning that the output-modifying factor is the signaling protein that is most limited, to determine signaling responses across cell types and in single cells. We found that the abundance of either the type I (TGFBR1) or type II (TGFBR2) TGF-{beta} receptor determined the responses of cancer cell lines, such that the receptor with relatively low abundance dictates the response. Furthermore, nuclear SMAD2 signaling correlated with the abundance of TGF-{beta} receptor in single cells depending on the relative expression levels of TGFBR1 and TGFBR2. A similar control principle could govern the heterogeneity of signaling responses in other signaling pathways. One-sentence summaryHeterogeneous TGF-{beta} signaling responses are dictated by the low abundance TGF-{beta} receptor in different cell types and in single cells, resembling Liebigs law of the minimum.