Statistical approaches and software for clustering islet cell functional heterogeneity

Abstract

Worldwide efforts are underway to replace or repair lost or dysfunctional pancreatic β-cells to cure diabetes. However, it is unclear what the final product of these efforts should be, as β-cells are thought to be heterogeneous. To enable the analysis of β-cell heterogeneity in an unbiased and quantitative way, we developed model-free and model-based statistical clustering approaches, and created new software called TraceCluster. Using an example data set, we illustrate the utility of these approaches by clustering dynamic intracellular Ca(2+) responses to high glucose in ∼300 simultaneously imaged single islet cells. Using feature extraction from the Ca(2+) traces on this reference data set, we identified 2 distinct populations of cells with β-like responses to glucose. To the best of our knowledge, this report represents the first unbiased cluster-based analysis of human β-cell functional heterogeneity of simultaneous recordings. We hope that the approaches and tools described here will be helpful for those studying heterogeneity in primary islet cells, as well as excitable cells derived from embryonic stem cells or induced pluripotent cells.

Keywords: calcium signals; insulin; oscillations.

Figure 1.

Cell composition of intact islets and dispersed islet cells of test sample. (A) Representative immunofluorescence staining of insulin, glucagon, and Pdx1 in intact islets from the donor. DNA counterstaining employed DAPI. The percentage of β-cells and α-cells (out of the major endocrine population i.e., β-cells or α-cells) is shown. Intact islets from this preparation contained attached non-endocrine cells; insulin positive cells were 37.3% of all cells and glucagon-positive cells were 23.7% of all cells. (B) Cultures of dispersed islet cells (including all endocrine and non-endocrine cells labeled with DAPI) contained 48.2% cells that stained robustly for insulin.

Figure 2.

Ca²⁺ traces and exploratory data analysis. (A) Raw Ca²⁺ traces from Fura-2 stained islet cells showing the timed glucose perturbations and KCl depolarisation. (B) Cells were imaged in three microscopy fields (Supplementary Fig. 1). Shown are the five top ranked MDS dimensions of the raw Ca²⁺ traces based on large mean silhouette width between the fields (details provided in Supplementary Information). Cells are colored red, dark gray or light gray to reflect the three different microscopy fields. We noticed that the cluster of cells circled in yellow enriched for cells of one field due to inhomogeneous dispersion, but more importantly that these cells showed a distinct Ca²⁺ trace pattern irrespective of field. The traces are shown for these cells which are mostly/only responding during KCl depolarisation.

Figure 3.

Hierarchical clustering of Ca²⁺ trace features and cells. The heatmap shown is reproduced from the provided software app (Supplementary Software), where users are able to select similar behaving cells and visualize their traces. In the heatmap, columns are clustered Ca²⁺ trace features while rows are clustered cells. Example traces from the software are also provided, where the first column of traces are cells from the top black box in the heatmap and the second column of traces are from the bottom black box. These are representative cells for the 2 β-like subtypes observed: oscillators and non-oscillators. The correlations between the features are provided in Supplementary Figure 3.

Figure 4.

Model-based clustering of high glucose response and oscillations. All scatter-plots are of the same two features, though colored according to suggested clusters for drift-corrected (top row) and raw (bottom row) versions of the data. Gaussian mixture model BICs suggest optimal clustering of 3 major cell sub-types: non-responders (blue), oscillating responders (red) and non-oscillating responders (green). Drift-corrected BIC for four clusters was similar to that for three clusters, it did not suggest the same clustering pattern as the raw data. Three clusters therefore robustly describe the cell sub-type number. The drift-corrected 3-cluster plot highlighted is provided in the Trace Cluster software app (Supplementary Software), where users can upload their own data for analysis.