Supplementary Data: Designing signaling environments to modulate neural progenitor cell differentiation with regulatory network models

During development, progenitors integrate external signaling cues to control differentiation. How combinatorial signal inputs modulate fate decisions and the underlying molecular information processing logic remains elusive. In this study, using single-cell mRNA-seq and regulatory network reconstruction, we identify an additive signal integration rule in mouse neural progenitor cells (NPCs) where the probability of neuronal versus glial cell fate choice is quantitatively regulated log-linearly by the input of EGF/FGF2, BMP4, and Wnt signaling. By profiling the developing mouse brain and NPCs cultured in different media and 40 combinatorial signaling conditions, we show that NPCs extracted from mouse embryos lost neurogenic potential during cell culture and collapsed into glial states, and that combinatorial signal inputs can restore the neuronal population following a simple log-linear model. We build regulatory network models by D-SPIN that quantitatively capture cell state distribution shifts induced by signal combinations and identify circuit structures and candidate regulators underlying the neuronal-glial fate switch, such as Olig1, Neurod1, and Hes1. Circuit models suggest that the log linearity emerges through high transcriptional heterogeneity. The models further predict an early bipotent state expressing regulators of both fates together, and we verify the bipotent state in single-cell profiling. Our work demonstrates that single-cell profiling combined with D-SPIN network reconstruction can elucidate regulatory nodes that control cell fate selection to facilitate building mechanistic models, and identifies a design principle of noise-driven additive regulation in the logarithm cell-fate probability space, providing a new strategy for population-level stem cell control.