A fundamental unanswered biological question with biomedical and industrial relevance is how cells integrate external information from multiple biochemical pathways to enter and exit quiescence in response to stress. Non-destructive measurements of single-cell protein expression in yeast cells have revealed that signaling in quiescence-related biochemical pathways can be highly heterogeneous across genetically identical cell populations as they transition into dormancy, even though they are treated with the exact same stress type and timing. Mathematical modeling has produced remarkable insights into the protein interaction networks that govern the yeast cell cycle and quiescence, however, predicting the transition from proliferation into quiescence at the single-cell level remains unclear under most physiological scenarios. The goal of this project is to develop a mathematical model that recapitulates the heterogeneity in proliferation/quiescence transitions of yeast cells in response to multiple quiescence-promoting stimuli. To accomplish this goal, this project will couple the development of novel scientific machine learning methods, chemical and environmental perturbation experiments, and single-cell protein expression measurements in live yeast cells. This research will address the mathematical challenges of learning and validating mathematical models from heterogeneous high-dimensional time series data to answer significant questions about how signaling pathways govern cell fate and differentiation. The project’s findings will be applicable to quiescence-related phenomena such as chemotherapy-resistant quiescent cancer cells, stem cells that exit quiescence for wound healing, and developmental processes that rely on the ubiquitous stress signaling pathways that will be studied. Research findings will be communicated to the scientific community through conference workshops and minisymposia, and to the general public through the creation of new K-12 outreach exhibits.<br/><br/>The proposed work will develop a data-driven mathematical framework to mechanistically explain inter-cellular variability during proliferation-quiescence transitions. Specifically, new deep learning tools will be developed to directly learn differential equation models from multivariate protein expression data collected from individual yeast cells undergoing quiescence in response to a diverse range of biologically relevant stressors. These research efforts will involve the integration of recurrent neural networks, multi-task learning, and novel regularization methods that enable deep learning models to simultaneously learn differential equations from thousands of single-cell replicates of protein expression time series data. Sensitivity analysis methods will be developed in conjunction with these new deep learning tools to enable optimization within a vast space of stress combinations and timing, thereby generating quantitative predictions about which experimental perturbations have the greatest effect on inter-cellular phenotype variability. The application of the new framework to non-destructive single-cell data arising from state-of-the-art experimental setups will shed new light on how coordinated cell division, stress, and metabolic signaling pathways produce intercellular variability in protein expression and quiescence phenotypes observed across species. In addition, this project will provide interdisciplinary training to graduate and undergraduate students, and develop open-source code for application to biological data sets involving perturbation experiments with multivariate time series data.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.