# CellRank meets pseudotime#

In this tutorial, you will learn how to…

compute a pseudotime using Diffusion pseudotime (DPT) [Haghverdi

*et al.*, 2016]set up CellRank’s PseudotimeKernel to compute a transition matrix based on

*any*pseudotime of your liking.visualize the transition matrix in a low-dimensional embedding.

Along the way, we’ll see an example where RNA velocity does not work well; this motivates us to use the `PseudotimeKernel`

.

We summarize the workflow, from a pseudotime up to the transition matrix, in the following figure:

**Fig** | We infuse directionality into a kNN graph using any pseudotime; edges that point into the pseudotemporal “past” are donw-weighted. This can be understood as an adapted, soft version of the Palantir algorithm [Setty *et al.*, 2019].

To demonstrate the appproach in this tutorial, we will use a scRNA-seq dataset of human bone marrow [Setty *et al.*, 2019].

Important

If you want to run this on your own data, you will need…

a scRNA-seq dataset for which you have computed a pseudotime using a tool like DPT [Haghverdi

*et al.*, 2016], Palantir [Setty*et al.*, 2019] or Slingshot [Street*et al.*, 2018].

This tutorial notebook can be downloaded using the following link.

## Import packages & data#

```
[1]:
```

```
import sys
if "google.colab" in sys.modules:
!pip install -q git+https://github.com/theislab/cellrank@dev
!pip install python-igraph
```

```
[2]:
```

```
import scvelo as scv
import scanpy as sc
import cellrank as cr
import numpy as np
scv.settings.verbosity = 3
scv.settings.set_figure_params("scvelo")
cr.settings.verbosity = 2
```

```
[3]:
```

```
import warnings
warnings.simplefilter("ignore", category=UserWarning)
warnings.simplefilter("ignore", category=FutureWarning)
warnings.simplefilter("ignore", category=DeprecationWarning)
```

```
[4]:
```

```
adata = cr.datasets.bone_marrow()
adata
```

```
[4]:
```

```
AnnData object with n_obs × n_vars = 5780 × 27876
obs: 'clusters', 'palantir_pseudotime', 'palantir_diff_potential'
var: 'palantir'
uns: 'clusters_colors', 'palantir_branch_probs_cell_types'
obsm: 'MAGIC_imputed_data', 'X_tsne', 'palantir_branch_probs'
layers: 'spliced', 'unspliced'
```

## Check RNA velocity on this data#

Before diving into the actual `PseudotimeKernel`

, let’s motivate this choice a bit. We’ve seen that RNA velocity works well across a range of datasets including the pancres data from the Cellrank meets RNA velocity tutorial; so let’s check how RNA velocity performs on this dataset [Bergen *et al.*, 2020].

We’ll check the ratio of spliced to unspliced counts, go through some basic preprocessing, run scVelo, compute a transition matrix using the `VelocityKernel`

and visualize it. To learn more about these steps, please see the Cellrank meets RNA velocity tutorial.

```
[5]:
```

```
scv.pl.proportions(adata)
```

This looks fine, the percentage of unspliced reads is about what we would expect for 10x Chromium data [La Manno *et al.*, 2018]. Next, filter out genes which don’t have enough spliced/unspliced counts, normalize and log transform the data and restrict to the top highly variable genes. Further, compute principal components and moments for velocity estimation. These are standard scanpy/scvelo functions, for more information about them, see the scVelo
API.

```
[6]:
```

```
scv.pp.filter_and_normalize(adata, min_shared_counts=20, n_top_genes=2000, subset_highly_variable=False)
sc.tl.pca(adata)
sc.pp.neighbors(adata, n_pcs=30, n_neighbors=30)
scv.pp.moments(adata, n_pcs=None, n_neighbors=None)
```

```
Filtered out 20068 genes that are detected 20 counts (shared).
Normalized count data: X, spliced, unspliced.
Extracted 2000 highly variable genes.
Logarithmized X.
computing moments based on connectivities
finished (0:00:03) --> added
'Ms' and 'Mu', moments of un/spliced abundances (adata.layers)
```

Use the dynamical model from scVelo to estimate model parameters and compute velocities. On my MacBook using 8 cores, the below cell takes about 2 min to execute.

```
[7]:
```

```
scv.tl.recover_dynamics(adata, n_jobs=8)
scv.tl.velocity(adata, mode="dynamical")
```

```
recovering dynamics (using 8/8 cores)
```

```
finished (0:02:42) --> added
'fit_pars', fitted parameters for splicing dynamics (adata.var)
computing velocities
finished (0:00:03) --> added
'velocity', velocity vectors for each individual cell (adata.layers)
```

Set up the `VelocityKernel`

from the `adata`

object containing the scVelo-computed velocities and compute a cell-cell transition matrix.

```
[8]:
```

```
vk = cr.kernels.VelocityKernel(adata)
vk.compute_transition_matrix()
```

```
Computing transition matrix using `'deterministic'` model
```

```
Using `softmax_scale=1.7071`
```

```
```

```
Finish (0:00:04)
```

```
```

```
[8]:
```

```
VelocityKernel
```

Visualize via stream lines an a t-SNE embedding:

```
[9]:
```

```
vk.plot_projection(basis='tsne')
```

```
Projecting transition matrix onto `tsne`
Adding `adata.obsm['T_fwd_tsne']`
Finish (0:00:01)
```

Warning

That’s a bit concerning, arrows point **exactly opposite** the known differentiation trajectory in which hematopoietic stems cells (HSCs) differentiate via intermediate states towards Monocyotes (Mono), Dendritic cells (DCs), etc [Setty *et al.*, 2019]. That’s not just a result of the low-dimensional representation, feel free to use CellRank to compute initial and terminal states on this data (see our initial and terminal states
tutorial) and you’ll find them to be inconsistend with biological knowledge as well.

To explore why this may be the case, let’s look into the most influential genes driving the velocity flow here:

```
[10]:
```

```
top_genes = adata.var['fit_likelihood'].sort_values(ascending=False).index
scv.pl.scatter(adata, basis=top_genes[:10], ncols=5, frameon=False)
```

In all of the top likelihood genes, the common lymphoid progenitor cells (CLPs) are a massive outlier! Since the current scVelo model does not account for state-dependent kinetic parmeters, this means the CLPs bias the parameter values for all other cells. We explored what happens if we remove CLPs and re-run the above analysis steps:

Warning

Even with CLPs removed, projected velocities still point oppposite to what’s known. The top-likelihood genes look different now - the CLP outliers have been removed; however, many of these top-influential genes show signs of state and time-dependent kinetic parameters. For example, in *ANK1*, Erythroid cells seem to require their own parameter set and in *RPS16*, the direction is inverted, i.e., an up-regulation is detected as a down-regulation, probably due to transcriptional bursting
[Barile *et al.*, 2021, Bergen *et al.*, 2021].

There’s an easy way in CellRank to overcome these difficulties - use another kernel! In this tutorial, we’ll use the `PseudotimeKernel`

because hematopoiesis is a well-studied system where traditional pseutodime methods work well.

## Choosing the right pseudotime#

There are [Saelens *et al.*, 2019] of pseudotime algorithms out there, so how do you choose the right one for your data? We’ll do a very superficial analysis here and just compare two methods: diffusion pseudotime (DPT) and the Palantir pseudotime [Haghverdi *et al.*, 2016, Setty *et al.*, 2019].

The Palantir pseudotime has been precomputed for this dataset, check the original tutorial and the scanpy interface to learn how to do this. To compute DPT on this dataset, we’ll start by computing a diffusion map [Coifman *et al.*, 2005, Haghverdi *et al.*, 2015]. Feel free to check out scanpy
tutorials, in particular the PAGA tutorial, to learn more.

```
[11]:
```

```
sc.tl.diffmap(adata)
```

For DPT, we manually have to suply a root cell (recall, we’re not using any RNA velocity here). One (semi-manual) way of doing this is by using extrema of diffusion components:

```
[12]:
```

```
root_ixs = 2394 # has been found using `adata.obsm['X_diffmap'][:, 3].argmax()`
scv.pl.scatter(adata, basis='diffmap', c=['clusters', root_ixs], legend_loc='right', components=['2, 3'])
adata.uns['iroot'] = root_ixs
```

Once we found a root cell we’re happy with (a cell from the HSC cluster), we can compute DPT and compare it with the precomputed Palantir pseudotime:

```
[13]:
```

```
sc.tl.dpt(adata)
scv.pl.scatter(adata, basis='tsne', color=['dpt_pseudotime', 'palantir_pseudotime'], color_map='gnuplot2')
```

It seems like DPT is a bit biased towards the CLPs; it assigns very high values to that cluster which masks variation among the other states. We can further explore this with violin plots to visualize the distribution of pseudotime values per cluster, restricted to those clusters we expect to belong to a certain trajectory, e.g. the Monocyte or Erythroid trajectories:

```
[14]:
```

```
mono_trajectory = ['HSC_1', 'HSC_2', 'Precursors', 'Mono_1', 'Mono_2']
ery_trajectory = ['HSC_1', 'Ery_1', 'Ery_2']
# plot the Monocyte trajectory
mask = np.in1d(adata.obs['clusters'], mono_trajectory)
sc.pl.violin(adata[mask], keys=['dpt_pseudotime', 'palantir_pseudotime'], groupby='clusters', rotation=-90,
order=mono_trajectory)
# plot the Erythroid trajectory
mask = np.in1d(adata.obs['clusters'], ery_trajectory)
sc.pl.violin(adata[mask], keys=['dpt_pseudotime', 'palantir_pseudotime'], groupby='clusters', rotation=-90,
order=ery_trajectory)
```

This is a really coarse analysis and only meant to give us a rough idea of which pseudotime to use; generally speaking, they both look good on this dataset. As expected, pseudotimes on average increase as we go towards more mature states. As the Palantir pseudotime appears to be less biased towards CLPs, let’s use that for the `PseudotimeKernel`

below.

## Running the `PseudotimeKernel`

#

Let’s use the palantir pseudotime to compute a directed cell-cell transition matrix using the `PseudotimeKernel`

:

```
[15]:
```

```
pk = cr.kernels.PseudotimeKernel(adata, time_key='palantir_pseudotime')
pk.compute_transition_matrix()
print(pk)
```

```
Computing transition matrix based on pseudotime`
```

```
```

```
Finish (0:00:03)
```

```
PseudotimeKernel[dnorm=False, scheme='hard', frac_to_keep=0.3]
```

We can again visualize this transition matrix via streamlines in the t-SNE embedding.

Important

We do not make use of RNA velocity here, CellRank implements a general way of visualizing kNN-graph-based transition matrices via streamlines in any embedding. Thus, the dynamics in the following plot are purely informed by the pseudotime and the kNN graph, and not by RNA velocity.

```
[16]:
```

```
pk.plot_projection(basis='tsne', recompute=True)
```

```
Projecting transition matrix onto `tsne`
Adding `adata.obsm['T_fwd_tsne']`
Finish (0:00:01)
```

This looks much better, the projected dynamics now agree with what is known from biology.

Warning

This is only a low dimensional representation which we shouldn’t trust too much; CellRank contains powerful tools to asses the dynamics in high dimensionional data directly, see the next section.

## What’s next?#

In this tutorial, you learned how to use CellRank to compute a transition matrix using any precomputed pseudotime and how it can be visualized in low dimensions. The real power of CellRank comes in when you use estimators to analyze the transition matrix directly, rather than projecting it. For the next steps, we recommend…

going through the initial & terminal states tutorial to learn how to use the transition matrix to automatically identify initial and terminal states.

taking a look at the full API to learn about parameter values you can use to adapt these computations to your data.

exploring the vast amount of pseudotime methods to find the one that works best for your data [Saelens

*et al.*, 2019].

Important

If you encounter any bugs in the code, our if you have suggestions for new features, please open an issue. If you have a general question or something you would like to discuss with us, please post on the scverse discourse.

## Package versions#

```
[17]:
```

```
cr.logging.print_versions()
```

```
cellrank==1.5.1+g4bab618c.d20220621 scanpy==1.7.2 anndata==0.8.0 numpy==1.21.4 numba==0.51.2 scipy==1.5.3 pandas==1.3.3 pygpcca==1.0.2 scikit-learn==0.24.0 statsmodels==0.12.1 python-igraph==0.8.3 scvelo==0.2.4 pygam==0.8.0 matplotlib==3.3.3 seaborn==0.11.0
```