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-β (TGF-β) pathway produces context-specific responses. Here, we combined modeling and experimental analysis to study the dependence of the output of the TGF-β pathway on the abundance of signaling molecules in the pathway. We showed that the TGF-β pathway processes the variation of TGF-β receptor abundance using Liebig's 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-β 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-β 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.