Earth Mover’s Distance (EMD): A True Metric for Comparing Biomarker Expression Levels in Cell Populations

Abstract

Changes in the frequencies of cell subsets that (co)express characteristic biomarkers, or levels of the biomarkers on the subsets, are widely used as indices of drug response, disease prognosis, stem cell reconstitution, etc. However, although the currently available computational “gating” tools accurately reveal subset frequencies and marker expression levels, they fail to enable statistically reliable judgements as to whether these frequencies and expression levels differ significantly between/among subject groups. Here we introduce flow cytometry data analysis pipeline which includes the Earth Mover’s Distance (EMD) metric as solution to this problem. Well known as an informative quantitative measure of differences between distributions, we present three exemplary studies showing that EMD 1) reveals clinically-relevant shifts in two markers on blood basophils responding to an offending allergen; 2) shows that ablative tumor radiation induces significant changes in the murine colon cancer tumor microenvironment; and, 3) ranks immunological differences in mouse peritoneal cavity cells harvested from three genetically distinct mouse strains.

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“…Similarly, the distance between the reference center and each individual test profile was also calculated using the EMD. The obtained two groups of EMD distances were then used as input to PBE for conducting a statistical test between the two groups to establish (in) equivalence between the test and reference 33,34,35 .…”

Single-Cell Signalling Analysis of Heterocellular Organoids

“…Following cell-type and cell-state identification, we next sought to construct cell-type specific PTM signalling networks in small intestinal organoids. To investigate whether stem, Paneth, enteroendocrine, tuft, goblet cells, and enterocytes employ different PTM signalling networks, we combined Earth Mover's Distance (EMD) (19,20) and Density Resampled Estimation of Mutual Information (DREMI) (21) to build quantitative cell-type specific signalling networks from single-cell organoid PTM data ( Fig. 2b and Supplementary Fig.…”

Soft X-Ray Imaging of Cellular Carbon and Nitrogen Distributions in Heterocystous Cyanobacteria

“…The earth mover's distance (EMD) is a measure of the distance between two probability distributions, and the EMD-based similarity analysis can be used as an effective tool in pattern recognition (Rubner et al, 2000;Corrales-Guerrero et al, 2015), as already applied in several biological studies (Bernas et al, 2006;Eyiyurekli et al, 2008;Corrales-Guerrero et al, 2015;Orlova et al, 2016). Here, we used the EMD to quantify the dissimilarity of the histograms between heterocysts and vegetative cells (see "Materials and Methods").…”