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A problem ubiquitous in almost all scientific areas is escape from a metastable state, or relaxation from one stationary distribution to a new one 1 . More than a century of studies lead to celebrated theoretical and computational developments such as the transition state theory and reactive flux formulation. Modern transition path sampling and transition path theory focus on an ensemble of trajectories that connect the initial and final states in a state space 2, 3 . However, it is generally unfeasible to experimentally observe these trajectories in multiple dimensions and compare to theoretical results. Here we report and analyze single cell trajectories of human A549 cells undergoing TGF-β induced epithelial-to-mesenchymal transition (EMT) in a combined morphology and protein texture space obtained through time lapse imaging. From the trajectories we identify parallel reaction paths with corresponding reaction coordinates and quasi-potentials. Studying cell phenotypic transition dynamics will provide testing grounds for nonequilibrium reaction rate theories.

Understanding how gene expression in single cells progress over time is vital for revealing the mechanisms governing cell fate transitions. RNA velocity, which infers immediate changes in gene expression by comparing levels of new (unspliced) versus mature (spliced) transcripts (La Manno et al. 2018), represents an important advance to these efforts. A key question remaining is whether it is possible to predict the most probable cell state backward or forward over arbitrary time-scales. To this end, we introduce an inclusive model (termed Dynamo ) capable of predicting cell states over extended time periods, that incorporates promoter state switching, transcription, splicing, translation and RNA/protein degradation by taking advantage of scRNA-seq and the co-assay of transcriptome and proteome. We also implement scSLAM-seq by extending SLAM-seq to plate-based scRNA-seq (Hendriks et al. 2018; Erhard et al. 2019; Cao, Zhou, et al. 2019) and augment the model by explicitly incorporating the metabolic labelling of nascent RNA. We show that through careful design of labelling experiments and an efficient mathematical framework, the entire kinetic behavior of a cell from this model can be robustly and accurately inferred. Aided by the improved framework, we show that it is possible to reconstruct the transcriptomic vector field from sparse and noisy vector samples generated by single cell experiments. The reconstructed vector field further enables global mapping of potential landscapes that reflects the relative stability of a given cell state, and the minimal transition time and most probable paths between any cell states in the state space. This work thus foreshadows the possibility of predicting long-term trajectories of cells during a dynamic process instead of short time velocity estimates. Our methods are implemented as an open source tool, dynamo ( https://github.com/aristoteleo/dynamo-release ).