Approximate Bayesian Computation for Inferring Waddington Landscapes from Single Cell Data

Single cell technologies allow us to gain insights into cellular processes at unprecedented resolution. In stem cell and developmental biology snapshot data allows us to characterise how the transcriptional state of cells changes between successive cell types. Here we show how approximate Bayesian computation (ABC) can be employed to calibrate mathematical models against single cell data. In our simulation study we demonstrate the pivotal role of the adequate choice of distance measures appropriate for single cell data. We show that for good distance measures, notably optimal transport distances, we can infer parameters for mathematical models from simulated single cell data. We show that the ABC posteriors can be used to characterise parameter sensitivity and identify dependencies between different parameters, and to infer representations of the Waddington or epigenetic landscape, which forms a popular and interpretable representation of the developmental dynamics. In summary, these results pave the way for fitting mechanistic models of stem cell differentiation to single cell data.