Animating RNA velocity with moving arrows
Oct 15, 2021
In my previous blog post, I discussed how we can use animations to enhance our data visualizations and tell stories about our data. Here, I wanted to use animation to potentially further enhance the visualizations of cellular trajectories.
Recently, my lab published a method called VeloViz in Oxford Bioinformatics that integrates information regarding each cell’s predicted future transcriptional state inferred from RNA velocity analysis to create 2D and 3D embeddings of single cell transcriptomics data to visualize cellular trajectories. In our paper, we show how by taking into account the predicted future transcriptional states of cells from RNA velocity analysis, VeloViz can help visualize a more reliable representation of underlying cellular trajectories even when intermediate cell states may be missing. Following the VeloViz analysis tutorial for visualizing cellular trajectories, I obtained the 2D embedding of a pancreas endocrinogenesis dataset with missing intermediate cell states using UMAP and VeloViz.
I then changed a few lines of code in the show.velocity.on.embedding.cor() function of the velocyto.R package to allow me to represent each cell as a colored arrow (where color represents the cell’s cell-type in this case) going from its observed transcriptional state to its projected predicted future transcriptional state inferred from RNA velocity analysis. I then used the animation package to animate the arrows.
Perhaps some additional opacity tinkering, size of arrow heads, or other features could be helpful. Try it out for yourself and see what you think!
show.velocity.on.embedding.cor2 <- function (emb, vel, n = 100, cell.colors = NULL, corr.sigma = 0.05,
show.grid.flow = FALSE, grid.n = 20, grid.sd = NULL, min.grid.cell.mass = 1,
min.arrow.size = NULL, arrow.scale = 1, max.grid.arrow.length = NULL,
fixed.arrow.length = FALSE, plot.grid.points = FALSE, scale = "log",
nPcs = NA, arrow.lwd = 1, arrow.alpha = 0.5, xlab = "", ylab = "", n.cores = velocyto.R:::defaultNCores(),
do.par = T, show.cell = NULL, cell.border.alpha = 0.3, cc = NULL,
return.details = FALSE, expression.scaling = FALSE, ...)
{
randomize <- FALSE
if (do.par)
par(mfrow = c(1, 1), mar = c(3.5, 3.5, 2.5, 1.5), mgp = c(2,
0.65, 0), cex = 0.85)
celcol <- "white"
if (is.null(show.cell)) {
celcol <- cell.colors[rownames(emb)]
}
plot(emb, bg = celcol, pch = 21, col = ac(1, alpha = cell.border.alpha),
xlab = xlab, ylab = ylab, ...)
em <- as.matrix(vel$current)
ccells <- intersect(rownames(emb), colnames(em))
em <- em[, ccells]
emb <- emb[ccells, ]
nd <- as.matrix(vel$deltaE[, ccells])
cgenes <- intersect(rownames(em), rownames(nd))
nd <- nd[cgenes, ]
em <- em[cgenes, ]
if (randomize) {
nd <- t(apply(nd, 1, function(x) (rbinom(length(x), 1,
0.5) * 2 - 1) * abs(sample(x))))
}
if (is.null(cc)) {
cat("delta projections ... ")
if (scale == "log") {
cat("log ")
cc <- velocyto.R:::colDeltaCorLog10(em, (log10(abs(nd) + 1) *
sign(nd)), nthreads = n.cores)
}
else if (scale == "sqrt") {
cat("sqrt ")
cc <- velocyto.R:::colDeltaCorSqrt(em, (sqrt(abs(nd)) * sign(nd)),
nthreads = n.cores)
}
else if (scale == "rank") {
cat("rank ")
cc <- velocyto.R:::colDeltaCor((apply(em, 2, rank)), (apply(nd,
2, rank)), nthreads = n.cores)
}
else {
cat("linear ")
cc <- velocyto.R:::colDeltaCor(em, nd, nthreads = n.cores)
}
colnames(cc) <- rownames(cc) <- colnames(em)
diag(cc) <- 0
}
cat("knn ... ")
if (n > nrow(cc)) {
n <- nrow(cc)
}
emb.knn <- velocyto.R:::balancedKNN(t(emb), k = n, maxl = nrow(emb), dist = "euclidean",
n.threads = n.cores)
diag(emb.knn) <- 1
cat("transition probs ... ")
tp <- exp(cc/corr.sigma) * emb.knn
tp <- t(t(tp)/Matrix::colSums(tp))
tp <- as(tp, "dgCMatrix")
cat("done\n")
if (!is.null(show.cell)) {
i <- match(show.cell, rownames(emb))
if (is.na(i))
stop(paste("specified cell", i, "is not in the embedding"))
points(emb, pch = 19, col = ac(val2col(tp[rownames(emb),
show.cell], gradient.range.quantile = 1), alpha = 0.5))
points(emb[show.cell, 1], emb[show.cell, 2], pch = 3,
cex = 1, col = 1)
di <- t(t(emb) - emb[i, ])
di <- di/sqrt(Matrix::rowSums(di^2)) * arrow.scale
di[i, ] <- 0
dir <- Matrix::colSums(di * tp[, i])
dic <- Matrix::colSums(di * (tp[, i] > 0)/sum(tp[, i] >
0))
dia <- dir - dic
suppressWarnings(arrows(emb[colnames(em)[i], 1], emb[colnames(em)[i],
2], emb[colnames(em)[i], 1] + dic[1], emb[colnames(em)[i],
2] + dic[2], length = 0.05, lwd = 1, col = "blue"))
suppressWarnings(arrows(emb[colnames(em)[i], 1], emb[colnames(em)[i],
2], emb[colnames(em)[i], 1] + dir[1], emb[colnames(em)[i],
2] + dir[2], length = 0.05, lwd = 1, col = "red"))
suppressWarnings(arrows(emb[colnames(em)[i], 1] + dic[1],
emb[colnames(em)[i], 2] + dic[2], emb[colnames(em)[i],
1] + dir[1], emb[colnames(em)[i], 2] + dir[2],
length = 0.05, lwd = 1, lty = 1, col = "grey50"))
suppressWarnings(arrows(emb[colnames(em)[i], 1], emb[colnames(em)[i],
2], emb[colnames(em)[i], 1] + dia[1], emb[colnames(em)[i],
2] + dia[2], length = 0.05, lwd = 1, col = "black"))
}
else {
cat("calculating arrows ... ")
arsd <- data.frame(t(velocyto.R:::embArrows(emb, tp, arrow.scale,
n.cores)))
rownames(arsd) <- rownames(emb)
if (expression.scaling) {
tpb <- tp > 0
tpb <- t(t(tpb)/colSums(tpb))
es <- as.matrix(em %*% tp) - as.matrix(em %*% as.matrix(tpb))
pl <- pmin(1, pmax(0, apply(as.matrix(vel$deltaE[,
colnames(es)]) * es, 2, sum)/sqrt(colSums(es *
es))))
arsd <- arsd * pl
}
ars <- data.frame(cbind(emb, emb + arsd))
colnames(ars) <- c("x0", "y0", "x1", "y1")
colnames(arsd) <- c("xd", "yd")
rownames(ars) <- rownames(emb)
ars$col <- celcol
cat("done\n")
if (show.grid.flow) {
cat("grid estimates ... ")
rx <- range(c(range(ars$x0), range(ars$x1)))
ry <- range(c(range(ars$y0), range(ars$y1)))
gx <- seq(rx[1], rx[2], length.out = grid.n)
gy <- seq(ry[1], ry[2], length.out = grid.n)
if (is.null(grid.sd)) {
grid.sd <- sqrt((gx[2] - gx[1])^2 + (gy[2] -
gy[1])^2)/2
cat("grid.sd=", grid.sd, " ")
}
if (is.null(min.arrow.size)) {
min.arrow.size <- sqrt((gx[2] - gx[1])^2 + (gy[2] -
gy[1])^2) * 0.01
cat("min.arrow.size=", min.arrow.size, " ")
}
if (is.null(max.grid.arrow.length)) {
max.grid.arrow.length <- sqrt(sum((par("pin")/c(length(gx),
length(gy)))^2)) * 0.25
cat("max.grid.arrow.length=", max.grid.arrow.length,
" ")
}
garrows <- do.call(rbind, lapply(gx, function(x) {
cd <- sqrt(outer(emb[, 2], -gy, "+")^2 + (x -
emb[, 1])^2)
cw <- dnorm(cd, sd = grid.sd)
gw <- Matrix::colSums(cw)
cws <- pmax(1, Matrix::colSums(cw))
gxd <- Matrix::colSums(cw * arsd$xd)/cws
gyd <- Matrix::colSums(cw * arsd$yd)/cws
al <- sqrt(gxd^2 + gyd^2)
vg <- gw >= min.grid.cell.mass & al >= min.arrow.size
cbind(rep(x, sum(vg)), gy[vg], x + gxd[vg], gy[vg] +
gyd[vg])
}))
colnames(garrows) <- c("x0", "y0", "x1", "y1")
if (fixed.arrow.length) {
suppressWarnings(arrows(garrows[, 1], garrows[,
2], garrows[, 3], garrows[, 4], length = 0.05,
lwd = arrow.lwd))
}
else {
alen <- pmin(max.grid.arrow.length, sqrt(((garrows[,
3] - garrows[, 1]) * par("pin")[1]/diff(par("usr")[c(1,
2)]))^2 + ((garrows[, 4] - garrows[, 2]) *
par("pin")[2]/diff(par("usr")[c(3, 4)]))^2))
suppressWarnings(lapply(1:nrow(garrows), function(i) arrows(garrows[i,
1], garrows[i, 2], garrows[i, 3], garrows[i,
4], length = alen[i], lwd = arrow.lwd, col=celcol[i])))
}
if (plot.grid.points)
points(rep(gx, each = length(gy)), rep(gy, length(gx)),
pch = ".", cex = 0.1, col = ac(1, alpha = 0.4))
cat("done\n")
if (return.details) {
cat("expression shifts .")
scale.int <- switch(scale, log = 2, sqrt = 3,
1)
if (!expression.scaling) {
tpb <- tp > 0
tpb <- t(t(tpb)/colSums(tpb))
es <- as.matrix(em %*% tp) - as.matrix(em %*%
as.matrix(tpb))
}
cat(".")
gs <- do.call(cbind, parallel::mclapply(gx, function(x) {
cd <- sqrt(outer(emb[, 2], -gy, "+")^2 + (x -
emb[, 1])^2)
cw <- dnorm(cd, sd = grid.sd)
gw <- Matrix::colSums(cw)
cws <- pmax(1, Matrix::colSums(cw))
cw <- t(t(cw)/cws)
gxd <- Matrix::colSums(cw * arsd$xd)
gyd <- Matrix::colSums(cw * arsd$yd)
al <- sqrt(gxd^2 + gyd^2)
vg <- gw >= min.grid.cell.mass & al >= min.arrow.size
if (any(vg)) {
z <- es %*% cw[, vg]
}
else {
NULL
}
}, mc.cores = n.cores, mc.preschedule = T))
if (scale == "log") {
nd <- (log10(abs(nd) + 1) * sign(nd))
}
else if (scale == "sqrt") {
nd <- (sqrt(abs(nd)) * sign(nd))
}
cat(".")
gv <- do.call(cbind, parallel::mclapply(gx, function(x) {
cd <- sqrt(outer(emb[, 2], -gy, "+")^2 + (x -
emb[, 1])^2)
cw <- dnorm(cd, sd = grid.sd)
gw <- Matrix::colSums(cw)
cws <- pmax(1, Matrix::colSums(cw))
cw <- t(t(cw)/cws)
gxd <- Matrix::colSums(cw * arsd$xd)
gyd <- Matrix::colSums(cw * arsd$yd)
al <- sqrt(gxd^2 + gyd^2)
vg <- gw >= min.grid.cell.mass & al >= min.arrow.size
if (any(vg)) {
z <- nd %*% cw[, vg]
}
else {
NULL
}
}, mc.cores = n.cores, mc.preschedule = T))
cat(". done\n")
return(invisible(list(tp = tp, cc = cc, garrows = garrows,
arrows = as.matrix(ars), vel = nd, eshifts = es,
gvel = gv, geshifts = gs, scale = scale)))
}
}
else {
apply(ars, 1, function(x) {
#print(x)
foocol = ac(x[5], alpha = arrow.alpha)
## unclear why this is needed frankly
x <- as.numeric(x[1:4])
#print(x)
if (fixed.arrow.length) {
suppressWarnings(arrows(x[1], x[2], x[3], x[4],
length = 0.05, lwd = arrow.lwd, col=foocol))
}
else {
ali <- sqrt(((x[3] - x[1]) * par("pin")[1]/diff(par("usr")[c(1,
2)]))^2 + ((x[4] - x[2]) * par("pin")[2]/diff(par("usr")[c(3,
4)]))^2)
suppressWarnings(arrows(x[1], x[2], x[3], x[4],
length = min(0.05, ali), lwd = arrow.lwd, col=foocol))
}
})
}
}
return(invisible(list(tp = tp, cc = cc)))
}
animation::saveGIF(
expr = {
sapply(seq(0.1, 1, 0.1), function(i) {
show.velocity.on.embedding.cor2(scale(emb.veloviz), vel,
n = 50,
scale='sqrt', fixed.arrow.length=TRUE,
cex=0, arrow.scale=i, show.grid.flow=FALSE,
arrow.lwd=2, arrow.alpha = 0.5, do.par = FALSE,
cell.colors=cell.cols, main='VeloViz', axes=FALSE)
})
},
movie.name = "veloarrows.gif"
)
animation::saveGIF(
expr = {
sapply(seq(0.1, 1, 0.1), function(i) {
show.velocity.on.embedding.cor2(scale(emb.umap), vel,
n = 50,
scale='sqrt', fixed.arrow.length=TRUE,
cex=0, arrow.scale=i, show.grid.flow=FALSE,
arrow.lwd=2, arrow.alpha = 0.5, do.par = FALSE,
cell.colors=cell.cols, main='UMAP', axes=FALSE)
})
},
movie.name = "umaparrows.gif"
)
RECENT POSTS
- Animating RNA velocity with moving arrows on 15 October 2021
- A tale of two cell populations: integrating RNA velocity information in single cell transcriptomic data visualization with VeloViz on 06 October 2021
- Story-telling with Data Visualization on 12 August 2021
- Complementing single-cell clustering analysis with MERINGUE spatial analysis on 21 June 2021
- Randomly Generating Music with R on 19 April 2021
- Animating the Cell Cycle on 28 December 2020
- Using R To Find The Missing Faculty on 30 November 2020
- Using scVelo in R using Reticulate on 25 August 2020
- A Guide to Responding to Scientific Peer Review on 17 June 2020
- Quickly Creating Pseudobulks on 06 April 2020