  Cytometry experiments yield high-dimensional point cloud data that is
difficult to interpret manually. Boolean gating techniques coupled with
comparisons of relative abundances of cellular subsets is the current standard
for cytometry data analysis. However, this approach is unable to capture more
subtle topological features hidden in data, especially if those features are
further masked by data transforms or significant batch effects or
donor-to-donor variations in clinical data. Analysis of publicly available
cytometry data describing non-na\"ive CD8+ T cells in COVID-19 patients and
healthy controls shows that systematic structural differences exist between
single cell protein expressions in COVID-19 patients and healthy controls. We
identify proteins of interest by a decision-tree based classifier, sample
points randomly and compute persistence diagrams from these sampled points. The
resulting persistence diagrams identify regions in cytometry datasets of
varying density and identify protruded structures such as `elbows'. We compute
Wasserstein distances between these persistence diagrams for random pairs of
healthy controls and COVID-19 patients and find that systematic structural
differences exist between COVID-19 patients and healthy controls in the
expression data for T-bet, Eomes, and Ki-67. Further analysis shows that
expression of T-bet and Eomes are significantly downregulated in COVID-19
patient non-na\"ive CD8+ T cells compared to healthy controls. This
counter-intuitive finding may indicate that canonical effector CD8+ T cells are
less prevalent in COVID-19 patients than healthy controls. This method is
applicable to any cytometry dataset for discovering novel insights through
topological data analysis which may be difficult to ascertain otherwise with a
standard gating strategy or existing bioinformatic tools.
