A low-dimensional transcriptional code enables decoding of BMP/TGFβ signaling from single-cell transcriptomes

Cells interpret complex extracellular environments through signaling pathways that compress diverse ligand inputs into a limited set of intracellular mediators. How this information is encoded in transcriptional responses, and whether it can be decoded to infer the original signaling environment, remains unclear. Here, we systematically map BMP/TGF{beta} transcriptional responses using single-cell RNA sequencing across 48 ligand-concentration conditions, generating a multi-ligand dose-response atlas. We find that, for each ligand, transcriptional responses collapse onto a one-dimensional, highly coordinated program in which concentration modulates response amplitude without altering gene identity. Across ligands, we find a small number of distinct, ligand-dependent transcriptional programs. We leverage this structured encoding to define a quantitative perception score that captures pathway activity at single-cell resolution. Finally, we train a machine learning model to decode extracellular ligand concentrations from single-cell transcriptomes. The model further generalizes to in vivo intestinal epithelium, where it reconstructs the spatial BMP gradient profile. Together, these results reveal a low-dimensional transcriptional code in BMP/TGF{beta} signaling that constrains cellular responses and enables quantitative inference of extracellular signaling environments from gene expression.