PROJECT SUMMARY Recent advances of experimental techniques allow quantitative and systems‐wide measurements of non‐ genetic heterogeneity of mammalian cells, which serves as a crucial factor for stem cell dynamics and differentiation potentials, as well as drug resistance of cancer cells. However, it remains challenging to understand many puzzling observations regarding this type of heterogeneity in terms of underlying gene regulatory networks. For example, progenitor cells restore their heterogeneity on timescales of days from subpopulation with extreme gene expression patterns, and these cells switch from plasticity‐enabling dynamics to robust commitment and pattern formation during differentiation; epithelial cells can be distributed in a stable continuum in the epithelial‐mesenchymal spectrum upon receiving signals in tumors. Existing theories provide very limited insights into these important dynamics and patterns. We propose to combine mathematical modeling, new methods of analyzing gene regulatory networks and gene expression data, and experiments in a motor neuron differentiation system, and systems involving epithelial‐mesenchymal transition to study transcriptional and post‐transcriptional mechanisms underlying non‐genetic heterogeneity in mammalian cells. We propose to test a novel theoretical framework of a diverging oscillator for controlling progenitor cell dynamics with both computational methods and experimental systems. We will rigorously formulate and test a new hypothesis of an oscillator‐to‐switch transition for motor neuron differentiation in the developing spinal cord. Stemming from our recent results on surprising post‐transcriptional mechanisms for multistability and oscillation, we will use novel algebraic approaches to establish the relationship between the number of microRNA bindings sites and biologically plausible cell states. We will test the roles of microRNA binding in epithelial cell plasticity experimentally. We will examine the roles of epithelial plasticity and microRNAs in dynamics of lung cancer cells. The success of the proposed study will provide a new theoretical basis and new methods for interpreting and understanding dynamical gene expression data on non‐genetic heterogeneity in mammalian cells. The theories and methods can used as a foundation to develop therapeutics for diseases related to development, tissue degeneration and cancer.