# A tale of two cell populations: integrating RNA velocity information in single cell transcriptomic data visualization with VeloViz

Oct 6, 2021

## Introduction

We recently developed a single-cell transcriptomic data visualization
method called `VeloViz`

now published in Oxford Bioinformatics. In addition to using each cell’s observed
transcriptional state from single-cell transcriptomic data, `VeloViz`

also integrates information regarding each cell’s predicted future
transcriptional state inferred from RNA velocity analysis to create 2D
and 3D embeddings of the data. More details regarding how the method
works and its applications can be found in this paper in the journal
Bioinformatics. `VeloViz`

is implemented as an R software package
avaialble at https://jef.works/veloviz/ and on
Bioconductor.

In this blog post, I will use simulations to tell a story about two cell populations, who (transcriptionally) look quite similar to each other but are going in different paths (towards divergent terminal cell fates). I hope this story will be a fun demonstration of the potential utility of integrating RNA velocity information in visualizing cell populations and their relationships.

## Background and Theory

RNA velocity analysis uses the relative abundance of nascent (unspliced) and mature (spliced) mRNA to estimate the rates of gene splicing and degradation in order to predict the future transcriptional state of individual cells. In RNA velocity modeling, cells with levels of unspliced transcripts higher than expected in steady state are interpreted as having positive velocity or upregulation of the gene, while cells with levels of unspliced transcripts lower than expected at steady state are interpreted as having negative velocity or downregulation of the gene. This combination of velocities across all modeled genes can then used to estimate the future transcriptional state of each individual cell. Such RNA velocity analysis has also been adapted for transcriptomic imaging data using the relative abundance of nuclear and cytoplasmic mRNA.

_{(RNA velocity diagram. Source: https://www.embopress.org/doi/full/10.15252/msb.202110282)}

Generally, in order to visualize these predicted future transcriptional states
inferred from RNA velocity analysis, visualization with principal
components, t-distributed stochastic neighbor embedding, and other
embeddings derived from the observed transcriptional states are often
used. In the rest of this blog post, I will use a very crude simulation to
demonstrate the potential utility of integrating the predicted future
transcriptional state information from RNA velocity in deriving
embeddings for visualization purposes using `VeloViz`

.

## A tale of two cell populations (a simulation)

Let’s simulate some steady state cells and two intermediate cell
populations. We will simulate two steady state cell populations (`A`

and
`B`

) as well as two intermediate cell populations (`SA`

and `SB`

). In
our simulation, steady state cell populations `A`

and `B`

have distinct
transcriptional profiles. In contrast, intermediate cell populations
`SA`

and `SB`

will express genes found in both A and B. However, we will
(crudely) simulate such that `SA`

cells are actively upregulating genes
expressed in `A`

, while `SB`

cells are actively upregulating genes
expressed in `B`

following the theory behind RNA velocity. In
particular, both `SA`

and `SB`

will have comparable levels of spliced
RNAs but `SA`

will have more unspliced RNAs for genes expressed in `A`

while `SB`

will have more unspliced RNAs for genes expressed in `B`

.

```
nc <- 100
ncss <- 50
## spliced (same)
g1s <- c(rep(10,nc), rep(10,nc))
## unspliced (one high, one low)
g1us <- c(rep(15,nc), rep(5,nc))
## simulate steady state cells
ssg1s <- c(rep(0, ncss), rep(20, ncss))
ssg1us <- c(rep(0, ncss), rep(20, ncss))
## simulated ground truth expression
gts <- c(g1s, ssg1s)
gtus <- c(g1us, ssg1us)
## group annotations
com <- c(rep('SA', nc), rep('SB', nc), rep('B', ncss), rep('A', ncss))
cell.colors <- MERINGUE:::fac2col(com)
names(gts) <- names(gtus) <- names(com) <- names(cell.colors) <- paste0('cell', 1:c(2*nc+2*ncss))
## plot
veloviz::plotEmbedding(cbind(gts, gtus), groups=com, cex=3,
xlab='Spliced', ylab='Unspliced', mark.clusters=TRUE)
```

```
## using provided groups as a factor
```

We can add some noise to the simulated data. Let’s also expand to 6
genes with the same upregulation trends as described previously. Note
that if we were to only look at the spliced gene expression levels, `SA`

and `SB`

cells are transcriptionally indistinguishable. If we look at
the total gene expression levels, `SA`

, `SB`

, `A`

, and `B`

cells are be
distinct.

```
## add some noise
jitteramount <- 1
## make gene expression matrix with 6 genes
## where genes are upregulated in one of the intermediate populations
## to be more or less like the steady state populations (3 each)
spliced = rbind(jitter(c(g1s, ssg1s), jitteramount),
jitter(c(g1s, ssg1s), jitteramount),
jitter(c(g1s, ssg1s), jitteramount),
jitter(20-c(g1s, ssg1s), jitteramount),
jitter(20-c(g1s, ssg1s), jitteramount),
jitter(20-c(g1s, ssg1s), jitteramount))
colnames(spliced) <- paste0('cell', 1:ncol(spliced))
rownames(spliced) <- paste0('gene', 1:nrow(spliced))
unspliced = rbind(jitter(c(g1us, ssg1us), jitteramount),
jitter(c(g1us, ssg1us), jitteramount),
jitter(c(g1us, ssg1us), jitteramount),
jitter(20-c(g1us, ssg1us), jitteramount),
jitter(20-c(g1us, ssg1us), jitteramount),
jitter(20-c(g1us, ssg1us), jitteramount))
spliced[spliced < 0] <- 0
unspliced[unspliced < 0] <- 0
mat <- spliced + unspliced
colnames(unspliced) <- paste0('cell', 1:ncol(unspliced))
rownames(unspliced) <- paste0('gene', 1:nrow(unspliced))
## plot as heatmap
library(gplots)
```

```
##
## Attaching package: 'gplots'
## The following object is masked from 'package:stats':
##
## lowess
```

```
gplots::heatmap.2(spliced, Rowv=NA, trace='none', ColSideColors = cell.colors, scale='none', col = colorRampPalette(c('blue', 'white', 'red'))(100))
```

```
## Warning in gplots::heatmap.2(spliced, Rowv = NA, trace = "none", ColSideColors =
## cell.colors, : Discrepancy: Rowv is FALSE, while dendrogram is `both'. Omitting
## row dendogram.
```

```
gplots::heatmap.2(mat, Rowv=NA, trace='none', ColSideColors = cell.colors, scale='none', col = colorRampPalette(c('blue', 'white', 'red'))(100))
```

```
## Warning in gplots::heatmap.2(mat, Rowv = NA, trace = "none", ColSideColors =
## cell.colors, : Discrepancy: Rowv is FALSE, while dendrogram is `both'. Omitting
## row dendogram.
```

Another way of looking at this is that if we were to create an UMAP
embedding on the spliced gene expression levels, `SA`

and `SB`

cells
would be intermixed. Alternatively, if we were to create an UMAP
embedding on the total gene expression levels, all 4 cell populations
would form distinct clusters.

```
set.seed(1)
emb.umap.spliced <- uwot::umap(t(spliced), min_dist = 1, n_neighbors = 5)
rownames(emb.umap.spliced) <- colnames(spliced)
par(mfrow=c(1,1))
veloviz::plotEmbedding(emb.umap.spliced, groups=com)
```

```
## using provided groups as a factor
```

```
set.seed(1)
emb.umap <- uwot::umap(t(mat), min_dist = 1, n_neighbors = 5)
rownames(emb.umap) <- colnames(spliced)
par(mfrow=c(1,1))
veloviz::plotEmbedding(emb.umap, groups=com)
```

```
## using provided groups as a factor
```

We can apply RNA velocity analysis to now predict the future
transcriptional states of our cells. Indeed, as simulated, `gene1`

,
which is expressed in `A`

cells but not `B`

cells, is being upregulated
in `SA`

cells and downregulated in `SB`

cells while `gene4`

, which is
expressed in `B`

cells but not `A`

cells, is being upregulated in `SB`

cells and downregulated in `SA`

cells.

```
library(velocyto.R)
```

```
## Loading required package: Matrix
```

```
cell.dist = dist(t(mat))
library(velocyto.R)
vel = velocyto.R::gene.relative.velocity.estimates(spliced, unspliced, mult=1,
kCells = 10,
cell.dist = cell.dist)
```

```
## calculating cell knn ... done
## calculating convolved matrices ... done
## fitting gamma coefficients ... done. succesfful fit for 6 genes
## calculating RNA velocity shift ... done
## calculating extrapolated cell state ... done
```

```
## show gene trend
emb.test <- cbind(spliced[1,], unspliced[1,])
gene <- "gene1"
velocyto.R::gene.relative.velocity.estimates(spliced, unspliced,
deltaT=100,
kCells = 10,
kGenes=1,
fit.quantile=0.1,
cell.emb=emb.test,
cell.colors=cell.colors,
cell.dist=cell.dist,
show.gene=gene,
old.fit=vel,do.par=T)
```

```
## calculating convolved matrices ... done
```

```
## [1] 1
```

```
gene <- "gene4"
velocyto.R::gene.relative.velocity.estimates(spliced, unspliced,
deltaT=100,
kCells = 10,
kGenes=1,
fit.quantile=0.1,
cell.emb=emb.test,
cell.colors=cell.colors,
cell.dist=cell.dist,
show.gene=gene,
old.fit=vel,do.par=T)
```

```
## calculating convolved matrices ... done
```

```
## [1] 1
```

Therefore, at a future time point, we would expect the expression level
of `gene1`

in `SA`

cells to be higher, like that in `A`

cells, while the
expression level of `gene1`

in `SB`

cells to be lower, like that in `B`

cells. Likewise, we would expect the expression level of `gene4`

in `SA`

cells to be lower, like that in `A`

cells, while the expression level of
`gene4`

in `SB`

cells to be higher, like that in `B`

cells.

```
curr = vel$current
proj = vel$projected
par(mfrow=c(1,2))
veloviz::plotEmbedding(cbind(mat[1,], curr[1,]), groups=com,
xlab='Observed Total', ylab='Current Spliced', mark.clusters=TRUE)
```

```
## using provided groups as a factor
```

```
veloviz::plotEmbedding(cbind(mat[1,], proj[1,]), groups=com,
xlab='Observed Total', ylab='Projected Spliced', mark.clusters=TRUE)
```

```
## using provided groups as a factor
```

`VeloViz`

can take into consideration this predicted future
transcriptional state in creating the embedding and visualizing these
cell populations. By taking into consideration the predicted future
transcriptional states, we can see more clearly see in the `VeloViz`

embedding that `SA`

cells are closer to `A`

cells while `SB`

cells are
closer to `B`

cells.

```
library(veloviz)
# build VeloViz graph
veloviz = veloviz::buildVeloviz(
curr = curr, proj = proj,
normalize.depth = FALSE,
use.ods.genes = FALSE,
pca = FALSE,
k = 5,
similarity.threshold = 0,
distance.weight = 1,
distance.threshold = 0,
weighted = TRUE,
seed = 0,
verbose = FALSE
)
```

```
## [1] "Done finding neighbors"
## [1] "calculating weights"
## [1] "Done making graph"
```

```
emb.veloviz = veloviz$fdg_coords
par(mfrow=c(1,1))
veloviz::plotEmbedding(emb.veloviz, groups=com, mark.clusters = TRUE)
```

```
## using provided groups as a factor
```

We can further visualize RNA velocity arrows on each of these embeddings to get a sense for how these 4 cell populations (SA, SB, A, and B) may be related to each other.

```
par(mfrow=c(1,1))
show.velocity.on.embedding.cor(scale(emb.umap.spliced), vel,n=100,scale='sqrt',cell.colors=cell.colors, arrow.scale = 0.5, arrow.lwd=1, do.par = FALSE, show.grid.flow=TRUE,min.grid.cell.mass=0.5,grid.n=20)
```

```
## delta projections ... sqrt knn ... transition probs ... done
## calculating arrows ... done
## grid estimates ... grid.sd= 0.1621915 min.arrow.size= 0.00324383 max.grid.arrow.length= 0.08212338 done
```

```
show.velocity.on.embedding.cor(scale(emb.umap), vel,n=100,scale='sqrt',cell.colors=cell.colors, arrow.scale = 0.5, arrow.lwd=1, do.par = FALSE, show.grid.flow=TRUE,min.grid.cell.mass=0.5,grid.n=20)
```

```
## delta projections ... sqrt knn ... transition probs ... done
## calculating arrows ... done
## grid estimates ... grid.sd= 0.1348527 min.arrow.size= 0.002697054 max.grid.arrow.length= 0.08212338 done
```

```
show.velocity.on.embedding.cor(scale(emb.veloviz), vel,n=100,scale='sqrt',cell.colors=cell.colors, arrow.scale = 0.5, arrow.lwd=1, do.par = FALSE, show.grid.flow=TRUE,min.grid.cell.mass=0.5,grid.n=20)
```

```
## delta projections ... sqrt knn ... transition probs ... done
## calculating arrows ... done
## grid estimates ... grid.sd= 0.146899 min.arrow.size= 0.002937981 max.grid.arrow.length= 0.08212338 done
```

Indeed, by taking into consideration the predicted
future transcriptional states, we can see more clearly see in the
`VeloViz`

embedding that `SA`

cells are transcriptionally moving towards
`A`

cells while `SB`

cells are transcriptionally moving towards `B`

cells. In contrast, UMAP embeddings that take into consideration only
the observed spliced or total gene expression levels are not able to
preserve such transcriptional relationships between populations.

Of course, this is a very crude and simple simulation highlighting the theoretical utility of taking into consideration information from RNA velocity information in visualizing cellular trajectories. Try it out for yourself! Can you simulate a scenario where taking into consideration RNA velocity information in visualizing cellular trajectories better recapitulates the underlying expected cell population relationships? What about a scenario where taking into consideration RNA velocity information misleads by suggesting a relationship between cell populations that should not exist? Are there instances with real data where these scenarios may apply? What orthogonal evidence and experiments can you do to follow up?

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