Meta-analysis of Caenorhabditis elegans single-cell developmental data reveals multi-frequency oscillation in gene activation

Abstract

Motivation: The advent of in vivo automated techniques for single-cell lineaging, sequencing and analysis of gene expression has begun to dramatically increase our understanding of organismal development. We applied novel meta-analysis and visualization techniques to the EPIC single-cell-resolution developmental gene expression dataset for Caenorhabditis elegans from Bao, Murray, Waterston et al. to gain insights into regulatory mechanisms governing the timing of development.

Results: Our meta-analysis of the EPIC dataset revealed that a simple linear combination of the expression levels of the developmental genes is strongly correlated with the developmental age of the organism, irrespective of the cell division rate of different cell lineages. We uncovered a pattern of collective sinusoidal oscillation in gene activation, in multiple dominant frequencies and in multiple orthogonal axes of gene expression, pointing to the existence of a coordinated, multi-frequency global timing mechanism. We developed a novel method based on Fisher's Discriminant Analysis to identify gene expression weightings that maximally separate traits of interest, and found that remarkably, simple linear gene expression weightings are capable of producing sinusoidal oscillations of any frequency and phase, adding to the growing body of evidence that oscillatory mechanisms likely play an important role in the timing of development. We cross-linked EPIC with gene ontology and anatomy ontology terms, employing Fisher's Discriminant Analysis methods to identify previously unknown positive and negative genetic contributions to developmental processes and cell phenotypes. This meta-analysis demonstrates new evidence for direct linear and/or sinusoidal mechanisms regulating the timing of development. We uncovered a number of previously unknown positive and negative correlations between developmental genes and developmental processes or cell phenotypes. Our results highlight both the continued relevance of the EPIC technique, and the value of meta-analysis of previously published results. The presented analysis and visualization techniques are broadly applicable across developmental and systems biology.

Availability and implementation: Analysis software available upon request.

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Projection of binarized gene expression profiles onto the first three principal component axes. Each node represents a cell, and the edges between the nodes connect a cell with each of its two daughter cells. The color of each node indicates the division depth in the cell pedigree. (a) A perspective view of the first three principal components. (b) A top-down view of PC3 versus PC1, showing the curved path of the manifold relative to the first principal component axis

Fig. 2.

(a) The projection of gene expression onto the first 10 principal component axes, PC1–PC10, shown as 2D projections. (b) Larger views of PC3 versus PC1, PC6 versus PC1 and PC6 versus PC3, showing what appears to be sinusoidal oscillation of two different frequencies. Plotting PC6 against PC3 causes the cell pedigree to trace an α-shaped path as development proceeds

Fig. 3.

Identification of simple linear weightings of gene expression levels that can produce oscillations across a range of sinusoidal frequencies and phases. (a) A target sine wave is generated. (b) Cells are assigned to Class 0, at developmental times when the sine wave is positive, or Class 1, at times when the sine wave is negative. (c) FDA is used to maximally separate Class 0 from Class 1 in the vertical axis, minimizing intra-class variance and maximizing inter-class variance, producing a best-fit square wave approximation of the target sine wave. (d) The best-fit FDA results are plotted across a range of phases in the rows and frequencies in the columns, with phase wrapping vertically ($0\to \pi \to 0$), and with frequency increasing across the columns. (e) A heatmap of FDA weight given phase and frequency for each gene, with the largest negative weight for the gene in blue, and the largest positive weight for the gene in yellow

Fig. 4.

Separation of the E cell lineage (Class 1) from other cells in the cell pedigree (Class 0) using FDA. The horizontal axis indicates developmental time, and the vertical axis represents the linear projection onto the 1D vector ω that gives maximal inter-class variance and minimal intra-class variance. (Only a subset of cell labels is shown for legibility.) The resulting gene weights are strongly positive for genes primarily expressed in the E lineage, and strongly negative for genes primarily expressed in cells other than those in the E lineage

Fig. 5.

(a) The projection of gene expression onto the first principal component, PC1, versus b, the cell birth time (i.e. the cell onset time) in minutes. The plot is strongly linear from 100 to 200 min. (b) After solving the linear equation $\mathit{Ax}=\mathit{b}$, where A is the binarized gene expression matrix and b is the vector of cell birth times, this plot shows the best-fit linear estimator mapping birth time to gene expression