Topological data analysis of pattern formation of human induced pluripotent stem cell colonies

Abstract

Understanding the multicellular organization of stem cells is vital for determining the mechanisms that coordinate cell fate decision-making during differentiation; these mechanisms range from neighbor-to-neighbor communication to tissue-level biochemical gradients. Current methods for quantifying multicellular patterning tend to capture the spatial properties of cell colonies at a fixed scale and typically rely on human annotation. We present a computational pipeline that utilizes topological data analysis to generate quantitative, multiscale descriptors which capture the shape of data extracted from 2D multichannel microscopy images. By applying our pipeline to certain stem cell colonies, we detected subtle differences in patterning that reflect distinct spatial organization associated with loss of pluripotency. These results yield insight into putative directed cellular organization and morphogen-mediated, neighbor-to-neighbor signaling. Because of its broad applicability to immunofluorescence microscopy images, our pipeline is well-positioned to serve as a general-purpose tool for the quantitative study of multicellular pattern formation.

Keywords: Cell pattern formation; Microscopy images; Persistence landscapes; Pluripotent stem cells; Topological data analysis.

Fig. 1

Our pipeline extracts topological descriptors from microscopy images of multicellular colonies. (a) An input microscopy image of cells with a nucleus signal in blue and two other signals: red (R) and green (G) (scale bar, ). This image is processed through the segmentation module of our pipeline to identify cell locations and associate a signal intensity to each cell. (b) A discretized version of the microscopy image in which cells are represented as points in the Euclidean plane and categorized into one of four cell types based on signal intensities by the cell type identification module. For the upper right patch, points in each cell type are shown. In general, there will be cell types identified for n signals based on signal intensity. (c) The points of a single cell type () in the patch. (d) The corresponding Voronoi diagram, a partition of the patch into regions enclosing a portion of the plane that is closest to each point. (e) A step in the Delaunay filtration for the top right part of the Voronoi diagram, built by connecting neighboring points with line segments and triangles using a proximity radius r. (f) Four stages in the Delaunay filtration of the patch, an increasing sequence of simplicial complexes, with the three most persistent enclosed empty regions shown at the radius r (in pixels) at which they appear, colored in blue, green, and purple, where we have listed the colors in order of decreasing persistence. (g) The resulting persistence diagram, a topological summary that encodes the radii at which holes appear and disappear, with points corresponding to the most persistent enclosed empty regions highlighted in the same blue, green, and purple colors. (h) The corresponding persistence landscape, a decreasing sequence of piecewise-linear functions, can be combined with statistical and machine learning tools. This is the primary output of the TDA module in our pipeline. For simplicity, the axis is labeled ‘Radius’ and the axis is labeled ‘Persistence’. Note that the blue, green, and purple points in the persistence diagram map to points of the same color in the persistence landscape.

Fig. 2

Artificial induction of exogenous GATA6-HA occurs within the context of endogenous GATA6 expression. (a) Gene circuit for chemical induction of GATA6-HA expression. The pan-GATA6 antibody can detect both induced GATA6-HA and endogenous GATA6 (i.e. the total amount of GATA6), whereas the HA antibody can only detect induced GATA6-HA (i.e. a subset produced via induction of the total amount of GATA6). (b) Representative immunofluorescence images of NANOG and pan-GATA6 or HA at 0 and 25 ng/ml Dox concentrations (scale bar, ). Using Volocity, we applied the gamma changes (gamma of 1.5) after brightness enhancement on all stitched large images used in the figure for better contrast for representation (see Methods). (c) Quantification of segmented images by each channel from (b). Green (NANOG) and red (pan-GATA6 or HA) fluorescent intensities are normalized to the corresponding nuclear Hoechst value in blue. The threshold for the signal in the green channel is given by the green dotted line, and the red dotted line indicates the threshold for the signal in the red channel. The four cell types based on these thresholds are given by the labels , , , and of the corresponding quadrant.

Fig. 3

Comparison of average persistence landscapes across various Dox concentrations for cell type in the HA group. As Dox concentration increases, the average persistence landscape gets taller and narrower.

Fig. 4

We performed support vector regression on (a) persistence landscape vectors and (b) cell count vectors extracted from patches; we then averaged the Dox concentration predictions of each image’s patches. The image predictions of each Dox treatment group are spread horizontally for better visualization, and the outliers are marked with gray points. The Dox concentration predictions of 5 ng/ml, 15 ng/ml, and 25 ng/ml images are close to their actual values and well separated from one another when using persistence landscape vectors (a, top). When using cell count vectors (b, bottom) the results are broadly similar – there is no overlap between the predictions in the second and third quartiles (the boxes in the box and whisker plots) for the 5 ng/ml, 15 ng/ml, and 25 ng/ml images. However, in contrast to the persistence landscape predictions, the cell count predictions in the fourth quartile for the 5 ng/ml images overlap with those in the first quartile for 15 ng/ml images (the whiskers in the box and whisker plots) and the predictions in the fourth quartile for the 15 ng/ml images overlap with those in the first quartile for 25 ng/ml images. The Dox concentration predictions of 0 ng/ml images are not well distinguished from 5 ng/ml images in both cases.

Fig. 5

Comparison between pattern formations in the pan-GATA6 and HA groups for cell type with 25 ng/ml Dox concentration. (a) Average persistence landscapes of the pan-GATA6 and HA groups and their difference. The gray vertical line splits the difference plot into two parts showing distinct types of dissimilarities between the cell differentiation patterns. (b) The TDA pipeline applied to a representative patch of the pan-GATA6 group, and (c) a representative patch of the HA group. For each patch, its persistence diagram, persistence landscape, and most persistent cycles are shown. In the persistence diagrams, the gray line indicates the persistence threshold of 20 and the red line marks the threshold of 5. There are 2 points above the gray line in the pan-GATA6 patch and 3 points in the HA patch; the corresponding representative cycles of these points are shown in the rightmost column. Note that the green cycle lies within the region enclosed by the blue cycle in the HA patch.

Fig. 6

The topological structures of the pan-GATA6 and HA populations are statistically different according to our results. This difference may be due to cellular organization and intracellular and/or intercellular communication in response to morphogen gradients. (a) Immunofluorescence images of co-stained pan-GATA6 and HA antibodies at 25 ng/ml Dox concentration (scale bar, ). The greater presence of cycles in the HA group which are more persistent suggests that cells whose differentiation is synthetically induced may be in close proximity due to chemotaxis or mitosis; we show illustrations of these mechanisms on the right (b and c). (b) We propose that morphogen-mediated signaling driven by heterogeneity in endogenous GATA6 levels could give rise to less persistent holes in the pan-GATA6 group. (c) An alternate hypothesis is that cell division alone allows HA^highNANOG^low cells to stay close to one another.