PBMC

Library imports

import os
import sys

import numpy as np
import pandas as pd
import torch

import matplotlib.pyplot as plt
import mplscience
import seaborn as sns

import scanpy as sc
import scvelo as scv
import scvi
from scvelo.plotting.simulation import compute_dynamics
from velovi import preprocess_data, VELOVI
from velovi._model import _compute_directional_statistics_tensor

sys.path.append("../..")
from paths import DATA_DIR, FIG_DIR

Global seed set to 0

General settings

scvi.settings.dl_pin_memory_gpu_training = False

sns.reset_defaults()
sns.reset_orig()
scv.settings.set_figure_params('scvelo', dpi_save=400, dpi=80, transparent=True, fontsize=20, color_map='viridis')

SAVE_FIGURES = True
if SAVE_FIGURES:
    os.makedirs(FIG_DIR / 'pbmc', exist_ok=True)

Function definition

def fit_velovi(bdata):
    VELOVI.setup_anndata(bdata, spliced_layer="Ms", unspliced_layer="Mu")

    vae = VELOVI(bdata)

    vae.train()

    df = vae.history["elbo_train"].iloc[20:].reset_index().rename(columns={'elbo_train': 'elbo'})
    df['set'] = 'train'

    _df = vae.history["elbo_validation"].iloc[20:].reset_index().rename(columns={'elbo_validation': 'elbo'})
    _df['set'] = 'validation'

    df = pd.concat([df, _df], axis=0).reset_index(drop=True)

    with mplscience.style_context():
        sns.set_style(style="whitegrid")
        fig, ax = plt.subplots(figsize=(6, 4))
        sns.lineplot(data=df, x='epoch', y='elbo', hue='set', palette=['#0173B2', '#DE8F05'], ax=ax)

    latent_time = vae.get_latent_time(n_samples=25)
    velocities = vae.get_velocity(n_samples=25, velo_statistic="mean")

    t = latent_time
    scaling = 20 / t.max(0)

    bdata.layers["velocities_velovi"] = velocities / scaling
    bdata.layers["latent_time_velovi"] = latent_time

    bdata.var["fit_alpha"] = vae.get_rates()["alpha"] / scaling
    bdata.var["fit_beta"] = vae.get_rates()["beta"] / scaling
    bdata.var["fit_gamma"] = vae.get_rates()["gamma"] / scaling
    bdata.var["fit_t_"] = (
        torch.nn.functional.softplus(vae.module.switch_time_unconstr)
        .detach()
        .cpu()
        .numpy()
    ) * scaling
    bdata.layers["fit_t"] = latent_time.values * scaling[np.newaxis, :]
    bdata.var['fit_scaling'] = 1.0

    return vae

def compute_sign_variance(adata, vae):
    v_stack = vae.get_velocity(n_samples=50, velo_statistic="mean", return_mean=False)
    pos_freq = (v_stack >= 0).mean(0)
    # neg_freq = (v_stack < 0).mean(0)

    adata.layers["velocity"] = v_stack.mean(0)

    var_freq = pos_freq * (1 - pos_freq)
    adata.obs["sign_var"] = var_freq.mean(1)

    adata.layers["sign_var"] = var_freq
    adata.layers["variance"] = v_stack.var(0)

def compute_sign_var_score(adata, labels_key, vae):
    compute_sign_variance(adata, vae)

    sign_var_df = adata.to_df("sign_var")
    expr_df = adata.to_df("Ms")

    prod_df = sign_var_df * np.abs(expr_df)
    prod_df[labels_key] = adata.obs[labels_key]
    prod_df = prod_df.groupby(labels_key).mean()

    sign_var_df[labels_key] = adata.obs[labels_key]
    sign_var_df = sign_var_df.groupby(labels_key).mean()

    return sign_var_df.mean(0)

def gene_rank(adata, vkey="velocities_velovi"):
    from scipy.stats import rankdata
    scv.tl.velocity_graph(adata, vkey=vkey)
    tm = scv.utils.get_transition_matrix(
        adata, vkey=vkey, use_negative_cosines=True, self_transitions=True
    )
    tm.setdiag(0)
    adata.layers["Ms_extrap"] = tm @ adata.layers["Ms"]
    adata.layers["Ms_delta"] = adata.layers["Ms_extrap"] - adata.layers["Ms"]

    prod = adata.layers["Ms_delta"] * adata.layers[vkey]
    ranked = rankdata(prod, axis=1)
    adata.layers["product_score"] = prod
    adata.layers["ranked_score"] = ranked

def plot_phase_portrait(adata, gene, color, figsize=(6, 6)):
    fig, ax = plt.subplots(figsize=figsize)

    df = pd.DataFrame(
        {
            'unspliced': adata[:, gene].layers['Mu'].squeeze().copy(),
            'spliced': adata[:, gene].layers['Ms'].squeeze().copy(),
            'color': color
        }
    )

    with mplscience.style_context():
        sns.scatterplot(data=df, x='spliced', y='unspliced', c=color, s=25, ax=ax);

        _, unspliced, spliced = compute_dynamics(adata, basis=gene, extrapolate=True, sort=True)
        df = pd.DataFrame(
            {
                'unspliced': unspliced.squeeze(),
                'spliced': spliced.squeeze(),
            }
        )

        ax.plot(spliced, unspliced, color="purple", linewidth=2)

        spliced_steady_state = np.linspace(np.min(spliced), np.max(spliced))
        unspliced_steady_state = adata.var.loc[gene, 'fit_gamma'] / adata.var.loc[gene, 'fit_beta'] * (spliced_steady_state - np.min(spliced_steady_state)) + np.min(unspliced)
        ax.plot(spliced_steady_state, unspliced_steady_state, color='purple', linestyle="--", linewidth=2);

    ax.axis('off')
    if SAVE_FIGURES:
        fig.savefig(
            FIG_DIR / 'pbmc' / f'phase_portrait_{gene}.svg',
            format="svg",
            transparent=True,
            bbox_inches='tight'
        )

def plot_phase_portrait(adata, gene, color, permuted=False, figsize=(6, 6)):
    fig, ax = plt.subplots(figsize=figsize)

    df = pd.DataFrame(
        {
            'unspliced': adata[:, gene].layers['Mu'].squeeze().copy(),
            'spliced': adata[:, gene].layers['Ms'].squeeze().copy(),
            'color': color
        }
    )

    with mplscience.style_context():
        sns.scatterplot(data=df, x='spliced', y='unspliced', c=color, s=25, ax=ax);

        _, unspliced, spliced = compute_dynamics(adata, basis=gene, extrapolate=True, sort=True)
        df = pd.DataFrame(
            {
                'unspliced': unspliced.squeeze(),
                'spliced': spliced.squeeze(),
            }
        )

        ax.plot(spliced, unspliced, color="purple", linewidth=2)

        spliced_steady_state = np.linspace(np.min(spliced), np.max(spliced))
        unspliced_steady_state = adata.var.loc[gene, 'fit_gamma'] / adata.var.loc[gene, 'fit_beta'] * (spliced_steady_state - np.min(spliced_steady_state)) + np.min(unspliced)
        ax.plot(spliced_steady_state, unspliced_steady_state, color='purple', linestyle="--", linewidth=2);

    ax.axis('off')
    
    if SAVE_FIGURES:
        if permuted:
            fname = f'phase_portrait_{gene}_permuted'
        else:
            fname = f'phase_portrait_{gene}'
        fig.savefig(
            FIG_DIR / 'pbmc' / f'{fname}.svg',
            format="svg",
            transparent=True,
            bbox_inches='tight'
        )

def plot_perm_scores(adata, perm_scores, gene, color_label, figsize=(6, 4)):
    df = pd.DataFrame(perm_scores.loc[gene])
    df["Cell type"] = df.index
    order = adata.obs[color_label].cat.categories.tolist()
    
    with mplscience.style_context():
        sns.set_style(style="whitegrid")
        fig, ax = plt.subplots(figsize=figsize)
        sns.barplot(
            data=df,
            y=gene,
            x="Cell type",
            palette=adata.uns[f"{color_label}_colors"],
            order=order,
            ax=ax,
        )

    if SAVE_FIGURES:
        fig.savefig(
            FIG_DIR / 'pbmc' / f'permutation_score_{gene}.svg',
            format="svg",
            transparent=True,
            bbox_inches='tight'
        )

Data loading

adata = sc.read(DATA_DIR / 'pbmc' / 'pbmc_10k.h5ad')
adata

AnnData object with n_obs × n_vars = 11950 × 58367
    obs: 'celltype'
    uns: 'celltype_colors'
    layers: 'spliced', 'unspliced'

Data preprocessing

scv.pp.filter_and_normalize(adata, min_shared_counts=20, n_top_genes=2000)
scv.pp.moments(adata, n_pcs=30, n_neighbors=30)
adata = preprocess_data(adata)

Filtered out 48988 genes that are detected 20 counts (shared).
Normalized count data: X, spliced, unspliced.
Extracted 2000 highly variable genes.
Logarithmized X.
computing neighbors
    finished (0:00:19) --> added 
    'distances' and 'connectivities', weighted adjacency matrices (adata.obsp)
computing moments based on connectivities
    finished (0:00:01) --> added 
    'Ms' and 'Mu', moments of un/spliced abundances (adata.layers)
computing velocities
    finished (0:00:00) --> added 
    'velocity', velocity vectors for each individual cell (adata.layers)

sc.tl.umap(adata)
scv.pl.scatter(adata, basis='umap', c='celltype', legend_loc='right', s=5, dpi=200)

Model training

vae = fit_velovi(adata)

/home/icb/philipp.weiler/miniconda3/envs/velovi-py39/lib/python3.9/site-packages/torch/distributed/_sharded_tensor/__init__.py:8: DeprecationWarning: torch.distributed._sharded_tensor will be deprecated, use torch.distributed._shard.sharded_tensor instead
  warnings.warn(
GPU available: True, used: True
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]
Set SLURM handle signals.

Epoch 276/500:  55%|█████▌    | 276/500 [03:40<02:59,  1.25it/s, loss=-2.59e+03, v_num=1]
Monitored metric elbo_validation did not improve in the last 45 records. Best score: -2679.995. Signaling Trainer to stop.

scv.tl.velocity_graph(adata, vkey="velocities_velovi", sqrt_transform=False)
scv.tl.velocity_embedding(
    adata, vkey="velocities_velovi", use_negative_cosines=True, self_transitions=True
)

computing velocity graph (using 1/64 cores)

    finished (0:00:35) --> added 
    'velocities_velovi_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity embedding
    finished (0:00:02) --> added
    'velocities_velovi_umap', embedded velocity vectors (adata.obsm)

fig, ax = plt.subplots(figsize=(6, 4))
scv.pl.velocity_embedding_stream(
    adata, vkey="velocities_velovi", color=["celltype"], cmap="viridis", legend_loc=False, title='', ax=ax
)

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'velocity_stream.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

Uncertainty

Extrinsic

extrapolated_cells_list = []
for i in range(25):
    vkey = "velocities_velovi_{i}".format(i=i)
    v = vae.get_velocity(n_samples=1, velo_statistic="mean")
    adata.layers[vkey] = v
    scv.tl.velocity_graph(adata, vkey=vkey, sqrt_transform=False, approx=True)
    t_mat = scv.utils.get_transition_matrix(
        adata, vkey=vkey, self_transitions=True, use_negative_cosines=True
    )
    extrapolated_cells = np.asarray(t_mat @ adata.layers["Ms"])
    extrapolated_cells_list.append(extrapolated_cells)
extrapolated_cells = np.stack(extrapolated_cells_list)

computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_0_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_1_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_2_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_3_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_4_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:06) --> added 
    'velocities_velovi_5_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_6_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_7_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_8_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_9_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_10_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_11_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_12_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_13_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_14_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_15_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_16_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:08) --> added 
    'velocities_velovi_17_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_18_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_19_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_20_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:06) --> added 
    'velocities_velovi_21_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_22_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_23_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity graph (using 1/64 cores)

    finished (0:00:07) --> added 
    'velocities_velovi_24_graph', sparse matrix with cosine correlations (adata.uns)

df, _ = _compute_directional_statistics_tensor(extrapolated_cells, n_jobs=4, n_cells=adata.n_obs)

INFO     velovi: Computing the uncertainties...                                              

[Parallel(n_jobs=4)]: Using backend LokyBackend with 4 concurrent workers.
Global seed set to 0
Global seed set to 0
Global seed set to 0
Global seed set to 0
[Parallel(n_jobs=4)]: Done  24 tasks      | elapsed:   15.6s
[Parallel(n_jobs=4)]: Done 3348 tasks      | elapsed:   18.5s
[Parallel(n_jobs=4)]: Done 11819 tasks      | elapsed:   25.1s
[Parallel(n_jobs=4)]: Done 11950 out of 11950 | elapsed:   25.2s finished

for c in df.columns:
    adata.obs[c + "_extrinsic"] = np.log10(df[c].values)

with mplscience.style_context():
    fig, ax = plt.subplots(figsize=(6, 4))
    scv.pl.umap(adata, color='directional_cosine_sim_variance_extrinsic', perc=[5, 95], cmap='viridis', ax=ax)

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'directional_cosine_sim_variance_extrinsic.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

df = pd.DataFrame(
    {
        'Clusters': adata.obs['celltype'],
        'Extrinsic directional cosine sim. variance': adata.obs['directional_cosine_sim_variance_extrinsic']
    }
)
palette = dict(zip(adata.obs['celltype'].cat.categories, adata.uns['celltype_colors']))

with mplscience.style_context():
    sns.set_style(style="whitegrid")
    fig, ax = plt.subplots(figsize=(6, 4))
    sns.violinplot(data=df, x="Clusters", y="Extrinsic directional cosine sim. variance", palette=palette, ax=ax);
    ax.set_ylabel('')

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'extrinsic_directional_cosine_sim_variance_violin.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

Velocity coherence

sign_score = compute_sign_var_score(adata, 'celltype', vae)

gene_rank(adata)

computing velocity graph (using 1/64 cores)

    finished (0:00:36) --> added 
    'velocities_velovi_graph', sparse matrix with cosine correlations (adata.uns)

Monocytes

cell_subset = adata.obs.query("celltype == 'Mono'").index
cluster_data = adata[cell_subset]
cluster_data.obs['mean_product_score_per_cell_mono'] = cluster_data.layers['product_score'].mean(axis=1)
cluster_data.var['mean_product_score_per_gene_mono'] = cluster_data.layers['product_score'].mean(axis=0)

fig, ax = plt.subplots(figsize=(6, 4))
sns.histplot(data=cluster_data.var, x='mean_product_score_per_gene_mono', ax=ax);

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'mean_product_score_per_gene_mono_histogram.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

B cells

cell_subset = adata.obs.query("celltype == 'B'").index
cluster_data = adata[cell_subset]
cluster_data.obs['mean_product_score_per_cell_b'] = cluster_data.layers['product_score'].mean(axis=1)
cluster_data.var['mean_product_score_per_gene_b'] = cluster_data.layers['product_score'].mean(axis=0)

fig, ax = plt.subplots(figsize=(6, 4))
sns.histplot(data=cluster_data.var, x='mean_product_score_per_gene_b', ax=ax);

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'mean_product_score_per_gene_b_histogram.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

NK cells

cell_subset = adata.obs.query("celltype == 'NK'").index
cluster_data = adata[cell_subset]
cluster_data.obs['mean_product_score_per_cell_nk'] = cluster_data.layers['product_score'].mean(axis=1)
cluster_data.var['mean_product_score_per_gene_nk'] = cluster_data.layers['product_score'].mean(axis=0)

fig, ax = plt.subplots(figsize=(6, 4))
sns.histplot(data=cluster_data.var, x='mean_product_score_per_gene_nk', ax=ax);

if SAVE_FIGURES:
    fig.savefig(
        FIG_DIR / 'pbmc' / 'mean_product_score_per_gene_nk_histogram.svg',
        format="svg",
        transparent=True,
        bbox_inches='tight'
    )

Permutation analysis

perm_scores, permuted_adata = vae.get_permutation_scores(labels_key='celltype')

INFO     Input AnnData not setup with scvi-tools. attempting to transfer AnnData setup       
INFO     Input AnnData not setup with scvi-tools. attempting to transfer AnnData setup       

full_perm_df = pd.DataFrame(columns=["Score", "Dataset"])

max_ratio = np.nanmax(perm_scores.values, axis=1)
scores = max_ratio.tolist()
dataset = ['PBMC'] * len(max_ratio)

full_perm_df["Score"] = scores
full_perm_df["Dataset"] = dataset

color = adata.obs['celltype'].astype(str).replace(
    dict(zip(adata.obs['celltype'].cat.categories, adata.uns['celltype_colors']))
).tolist()

Lowest ranked genes

for gene in adata.var_names[np.argsort(scores)[:5]]:
    plot_phase_portrait(adata, gene, color)
    plot_phase_portrait(permuted_adata, gene, color, permuted=True)
    plot_perm_scores(adata, perm_scores, gene, 'celltype')

Highest ranked genes

for gene in adata.var_names[np.argsort(scores)[-5:]]:
    plot_phase_portrait(adata, gene, color)
    plot_phase_portrait(permuted_adata, gene, color, permuted=True)
    plot_perm_scores(adata, perm_scores, gene, 'celltype')