Debiasing Sinkhorn divergence in optimal transport of cellular dynamics

Abstract

Single-cell RNA-seq analysis characterizes developmental mechanisms of cellular differentiation, lineage determination, and reprogramming with differential conditioning of the microenvironment. In this article, the underlying dynamics are formulated via optimal transport with algorithms that calculate the transition probability of the state of cell dynamics over time. The algorithmic biases of optimal transport (OT) due to entropic regularization are balanced by Sinkhorn divergence, which normally de-biases the regularized transport by centering them. In the case of reprogramming mouse embryonic fibroblasts [1] with dense time points, Sinkhorn divergence is shown to improve the trajectories of targeted cell fates depending on the specific cell types. When the time points are filtered out with sparser 9 and 5 time points, some cell phenotypes show better outcomes from strong entropic regularization. For 9 time points with 2 days interval, Sinkhorn divergence shows a clear advantage with broad bandwith of optimal entropic regularization. For these derived time points, when the cell population is scaled down from n = 8000 to n = 2000, there comes no benefit from Sinkhorn divergence for some specific cell types. In the case of stratifying morphogenesis of the epidermis [2], the sparsity of time points makes it not significant to prescribe Sinkhorn divergence in the accuracy of transporting to the expected cell fates. Overall, whether to prescribe Sinkhorn divergence for the accurate prediction of lineages of single cells depends on temporal sparsity.