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

Cells use signaling pathways to sense and respond to their environments. The transforming growth factor-ß (TGF-ß) pathway produces context-specific responses. Here, we combined modeling and experimental analysis to study the dependence of the output of the TGF-ß pathway on the abundance of signaling molecules in the pathway. We showed that the TGF-ß pathway processes the variation of TGF-ß 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-ß 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-ß 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.

Machine learning unveils RNA polymerase II binding as a predictor for SMAD2-dependent transcription dynamics in response to Actvin signalling.

The transforming growth factor-ß (TGF-ß) superfamily, including Nodal and Activin, plays a critical role in various cellular processes. Understanding the intricate regulation and gene expression dynamics of TGF-ß signalling is of interest due to its diverse biological roles. A machine learning approach is used to predict gene expression patterns induced by Activin using features, such as histone modifications, RNA polymerase II binding, SMAD2-binding, and mRNA half-life. RNA sequencing and ChIP sequencing datasets were analysed and differentially expressed SMAD2-binding genes were identified. These genes were classified into activated and repressed categories based on their expression patterns. The predictive power of different features and combinations was evaluated using logistic regression models and their performances were assessed. Results showed that RNA polymerase II binding was the most informative feature for predicting the expression patterns of SMAD2-binding genes. The authors provide insights into the interplay between transcriptional regulation and Activin signalling and offers a computational framework for predicting gene expression patterns in response to cell signalling.