Data exploration, quality control and testing in single-cell qPCR-based gene expression experiments

Abstract

Motivation: Cell populations are never truly homogeneous; individual cells exist in biochemical states that define functional differences between them. New technology based on microfluidic arrays combined with multiplexed quantitative polymerase chain reactions now enables high-throughput single-cell gene expression measurement, allowing assessment of cellular heterogeneity. However, few analytic tools have been developed specifically for the statistical and analytical challenges of single-cell quantitative polymerase chain reactions data.

Results: We present a statistical framework for the exploration, quality control and analysis of single-cell gene expression data from microfluidic arrays. We assess accuracy and within-sample heterogeneity of single-cell expression and develop quality control criteria to filter unreliable cell measurements. We propose a statistical model accounting for the fact that genes at the single-cell level can be on (and a continuous expression measure is recorded) or dichotomously off (and the recorded expression is zero). Based on this model, we derive a combined likelihood ratio test for differential expression that incorporates both the discrete and continuous components. Using an experiment that examines treatment-specific changes in expression, we show that this combined test is more powerful than either the continuous or dichotomous component in isolation, or a t-test on the zero-inflated data. Although developed for measurements from a specific platform (Fluidigm), these tools are generalizable to other multi-parametric measures over large numbers of events.

Availability: All results presented here were obtained using the SingleCellAssay R package available on GitHub (http://github.com/RGLab/SingleCellAssay).

Fig. 1.

Histogram and theoretical (normal) distribution of for single-cell (left, light gray) and 100-cell experiments (right, dark gray). Genes FASLG, IFN- , BIRC3 and CD69 are depicted. The frequency expression of each gene in the single-cell experiments is printed above each histogram. The mean of the 100-cell and single-cell experiments is indicated by a thick black line along the x-axis

Fig. 2.

Concordance between 100 cell and , the in silico average of single-cell wells for datasets A, B and C. In the top row, wells with are included and treated as exact zeroes. In the middle row, they are excluded, resulting in a clear lack of concordance. In the final row, wells are filtered as per Section 2.3. Dark, thin lines show the initial location of a gene before filtering and connect to the location of the gene after filtering. In each panel, , the concordance correlation coefficient and , the average weighted squared deviation of expression measurements is printed. The dotted black line shows a loess fit through the data. In all cases, the expression values are transformed using a shifted log-transformation []. As such, a graphed value of zero corresponds to a zero expression value (i.e. )

Fig. 3.

Number of discoveries (genes units) versus FDR, by treatment, dataset A. The combined LRT is compared with a Bernoulli or normal-theory only LRT, as well as a t-test of the raw expression values ( scale), including zero measurements

Fig. 4.

of tests (genes units) versus frequencies of expression of the genes. The Bernoulli, normal-theory and combined LRTs are plotted. Asterisk indicates test is different from the combined test at 5% significance in a Wilcoxon signed-rank test

Fig. 5.

Heatmap of signed for selected genes (rows, see main text) and all 16 individuals (columns). The color above each column indicates the antigen stimulation applied to the cells; thus, individuals are randomly arranged in each antigen block. Red and purple are two different CMV antigen pools; yellow and orange are two different HIV antigen pools