library(knitcitations) library(bibtex) allbib = read.bibtex("sigiwu.bib")
The recent PNAS paper of Wu and
colleagues
(r citet(allbib[["Wu2016"]])
)
demonstrates the use of
cluster analysis of spatially organized
data to identify gene expression signatures
for regions of the cell-fate map of D. melanogaster.
We have repackaged some of their data and code
to demonstrate the key ideas.
For developmental stages 4-6 of Drosophila (1.3-2h
after egg deposit at 25C) a classic cell-fate map
has been published (r citet(allbib[["Hartenstein1985"]])
).
library(png) library(grid) im = readPNG("map1.png") grid.raster(im)
The image for "opa" in developmental stages 4-5 (1.3-3.0h after egg deposit)
im = readPNG("bdgpOPA.png") grid.raster(im)
library(drosmap) data(expressionPatterns) data(uniqueGenes) dim(expressionPatterns[,uniqueGenes]) data(template) dim(template) args(imageBatchDisplay)
imageBatchDisplay(expressionPatterns[, "opa", drop=FALSE], nrow=1, ncol=1, template=template[,-1])
imageBatchDisplay(expressionPatterns[, uniqueGenes[1:25]], nrow=5, ncol=5, template=template[,-1])
The expression patterns in the matrix $X$ with rows corresponding to positions in the blastocyst ellipse and column corresponding to genes are re-expressed via $X \approx DA$, where all entries in $D$ and $A$ are nonnegative. Matrix $D$ is referred to as basis, and matrix $A$ holds 'mixture coefficients'. We'll accept the statement that a rank 21 basis is adequate.
library(NMF) uex = expressionPatterns[,uniqueGenes] mm = nmf(data.matrix(uex), rank=21) mm
The rows of the basis matrix can be clustered to exhibit its structure.
basismap(mm)
These can be projected back into the blastocyst image space. The 21 principal patterns are then
imageBatchDisplay(basis(mm), nrow=5, ncol=5, template=template[,-1])
bibliography() #style="markdown")
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