Tree inference with varifold distances

TL;DR

This paper introduces a novel method using varifold distances to infer differentiation trees from single-cell sequencing data, effectively capturing cellular progression and reconstructing dynamic developmental processes.

Contribution

It proposes a new approach that leverages varifold distances between gene expression trajectories to accurately approximate shortest-path distances in differentiation trees.

Findings

Varifold distances effectively approximate tree shortest-paths.

Method successfully reconstructs differentiation trees from sequencing data.

Approach integrates gene expression and RNA velocity information.

Abstract

In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a process, we are interested in the problem of ordering the cells according to their progression in the process. This is known as trajectory inference. If the process is differentiation, this amounts to reconstructing the corresponding differentiation tree. One way of doing this in practice is to estimate the shortest-path distance between nodes based on cell similarities observed in sequencing data. Recent sequencing techniques make it possible to measure two types of data: gene expression levels, and RNA velocity, a vector that predicts changes in gene expression. The data then consist of a discrete vector field on a (subset of a) Euclidean space of dimension equal to the number of genes under consideration. By integrating this velocity field, we trace the evolution of gene expression levels in each single cell from some initial stage to its current stage. Eventually, we assume that we have a faithful embedding of the differentiation tree in a Euclidean space, but which we only observe through the curves representing the paths from the root to the nodes. Using varifold distances between such curves, we define a similarity measure between nodes which we prove approximates the shortest-path distance in a tree that is isomorphic to the target tree.