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Learning developmental landscapes with optimal transport/A tutorial on optimal transport

Geoffrey Schiebinger
Broad Institute, MIT Statistics
Learning developmental landscapes from single-cell gene expression with optimal transport

Abstract:  Understanding the molecular programs that guide cellular differentiation during development is a major goal of modern biology. Here, we introduce an approach, WADDINGTON-OT, based on the mathematics of optimal transport, for inferring developmental landscapes, probabilistic cellular fates and dynamic trajectories from large-scale single-cell RNA-seq (scRNA-seq) data collected along a time course. We demonstrate the power of WADDINGTON-OT by applying the approach to study 65,781 scRNA-seq profiles collected at 10 time points over 16 days during reprogramming of fibroblasts to iPSCs. We construct a high-resolution map of reprogramming that rediscovers known features; uncovers new alternative cell fates including neural- and placental-like cells; predicts the origin and fate of any cell class; highlights senescent-like cells that may support reprogramming through paracrine signaling; and implicates regulatory models in particular trajectories. Of these findings, we highlight Obox6, which we experimentally show enhances reprogramming efficiency. Our approach provides a general framework for investigating cellular differentiation.

Lénaïc Chizat
ENS Paris Mathematics
Primer: A tutorial on optimal transport

Abstract:  The optimal transport (OT) problem is often described as that of finding the most efficient way of moving a pile of dirt from one configuration to another. Once stated formally, OT provides extremely useful tools for comparing, interpolating and processing objects such as distributions of mass, probability measures, histograms or densities. This talk is an up-to-date tutorial on a selection of topics in OT. In the first part, I will give an intuitive description of OT, its behavior and basic properties. I will also explain a useful extension of the theory to deal with unnormalized distributions of mass. In the second part, I will introduce state-of-the-art numerical methods for solving OT related problems, namely scaling algorithms based on entropic regularization.