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The deluge of single-cell data obtained by sequencing, imaging and epigeneticmarkers has led to an increasingly detailed description of cell state. However,it remains challenging to identify how cells transition between differentstates, in part because data are typically limited to snapshots in time. Aprerequisite for inferring cell state transitions from such snapshots is todistinguish whether transitions are coupled to cell divisions. To address this,we present two minimal branching process models of cell division anddifferentiation in a well-mixed population. These models describe dynamicswhere differentiation and division are coupled or uncoupled. For each model, wederive analytic expressions for each subpopulation's mean and variance and forthe likelihood, allowing exact Bayesian parameter inference and model selectionin the idealised case of fully observed trajectories of differentiation anddivision events. In the case of snapshots, we present a sample path algorithmand use this to predict optimal temporal spacing of measurements forexperimental design. We then apply this methodology to an \textit{in vitro}dataset assaying the clonal growth of epiblast stem cells in culture conditionspromoting self-renewal or differentiation. Here, the larger number of cellstates necessitates approximate Bayesian computation. For both cultureconditions, our inference supports the model where cell state transitions arecoupled to division. For culture conditions promoting differentiation, ouranalysis indicates a possible shift in dynamics, with these processes becomingmore coupled over time.

Coupled differentiation and division of embryonic stem cells inferred from clonal snapshots