Automated high-dimensional flow cytometric data analysis

Abstract

Flow cytometric analysis allows rapid single cell interrogation of surface and intracellular determinants by measuring fluorescence intensity of fluorophore-conjugated reagents. The availability of new platforms, allowing detection of increasing numbers of cell surface markers, has challenged the traditional technique of identifying cell populations by manual gating and resulted in a growing need for the development of automated, high-dimensional analytical methods. We present a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation. We demonstrate its ability to detect rare populations, to model robustly in the presence of outliers and skew, and to perform the critical task of matching cell populations across samples that enables downstream analysis. This advance will facilitate the application of flow cytometry to new, complex biological and clinical problems.

Fig. 1.

Enhanced fit using skew distribution with FLAME. (A) Expression of HLA-DQ and CD95 in a lymphoblastic cell line: A representative sample from 194 cell lines is plotted with hue intensity representing data density. The data contours, in white, show a single unimodal asymmetric population of cells. The mode estimated by skew-t modeling (cyan dot) coincides with the highest percentile contour. (B) Gaussian mixture modeling (MCLUST) yields 2 distinct subpopulations. The true (cyan dot) and estimated (center of cross) modes do not coincide. (C) FLAME fits a single skew t distribution capturing the asymmetry in 1(a) and correctly estimating the mode.

Fig. 2.

Automated discovery of a rare subset of regulatory T cells with FLAME. (A) 3-dimensional projection (for markers CD4, CD25, Foxp3) of the stained PBMCs. FLAME's 4-variate modeling yielded 19 clusters as optimal. Cluster 5 (orange) has high expression of CD4 and CD25, rendering it the best candidate to represent the regulatory T cell population. (B) Clusters' expression profiles as a heat map of the 4 markers, FSC and SSC. Lower CD4 and high FSC and SSC in cluster 2 suggest activated T cells rather than regulatory T cells. (C) Subclustering of cluster 5 yields an optimal model of 9 subpopulations. Subcluster 9 (purple) matches the CD4⁺DR⁺CD25^brightFoxp3⁺ of regulatory T cells. Subclusters 1–8 are in green. (D) The heat map shows that subcluster 9 has the highest expression levels of DR, CD25 and Foxp3, and is 0.81% of live PBMCs, consistent with an expected frequency of ∼1%.

Fig. 3.

Mixture modeling of prephosphorylation and postphosphorylation T cell populations. (A and B) FLAME modeling of (A) pre- and (B) postphosphorylation data for a representative subject. The data are fit with 4-variate t mixtures projected into 3 dimensions, ZAP70 is not shown. Three-dimensional abstractions of the (A) pre- and (B) postphosphorylation clusters are shown in yellow and purple respectively. Black dots mark the cluster modes. (C) The results are superimposed, and the view is rotated to emphasize the differences in the SLP76 dimension that occur with stimulation. A green arrow indicates the increase in SLP76 phosphorylation of the naïve and memory CD4⁺ T cell populations and in the CD4⁻CD45RA^intermediate population.