Enrichment analysis

Enrichment analysis#

requires

  • some cluster of proteins/genes (e.g. upregulated proteins/genes in a certain condition)

  • functional annotations, i.e. a category summarizing a set of proteins/genes.

You can start with watching Lars Juhl Jensen’s brief introduction to enrichment analysis on youtube.

Here we use as example data from an ovarian cancer dataset: PXD010372

First make sure you have the required packages installed:

# ToDo: Improve VueCore dependencies
%pip install acore vuecore python-louvain snfpy

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Note: you may need to restart the kernel to use updated packages.

from pathlib import Path

import dsp_pandas
import pandas as pd
import plotly.graph_objects as go
from vuecore import viz

import acore
import acore.differential_regulation
import acore.enrichment_analysis

dsp_pandas.format.set_pandas_options(max_colwidth=60)

Parameters of this notebook

base_path: str = (
    "https://raw.githubusercontent.com/Multiomics-Analytics-Group/acore/refs/heads/main/"
    "example_data/PXD010372/processed"
)
omics: str = f"{base_path}/omics.csv"
meta_pgs: str = f"{base_path}/meta_pgs.csv"
meta: str = f"{base_path}/meta_patients.csv"
features_to_sample: int = 100

Load processed data#

from our repository. See details on obtaining the data under the example data section on this page

df_omics = pd.read_csv(omics, index_col=0)
df_meta_pgs = pd.read_csv(meta_pgs, index_col=0)
df_meta = pd.read_csv(meta, index_col=0)
df_omics
P04217 Q9NQ94-6 P01023 A8K2U0 Q9NPC4 Q9NRG9 Q86V21 Q7RTV5 Q6PD74 A0A096LP25 ... P06889 P07951-2 P09493-3 P09493-8 P0DMW5 P23083 P80748 Q29967 Q5T8P6-2 Q5T8P6-3
Patient02 31.692 28.418 33.330 24.592 24.250 29.019 29.245 NaN 26.173 28.495 ... 25.704 32.095 30.611 NaN NaN 25.947 27.607 28.401 24.711 28.975
Patient24 32.113 27.401 33.009 25.149 24.902 29.400 28.924 NaN 24.706 27.410 ... 24.301 33.191 30.633 30.067 NaN 29.286 27.957 27.551 24.391 29.047
Patient08 31.097 28.432 31.600 25.151 NaN 29.252 26.575 NaN NaN 28.213 ... 23.590 32.968 31.439 28.936 NaN 28.306 29.456 29.775 25.486 28.924
Patient03 30.995 28.365 33.827 22.606 23.793 29.446 29.296 NaN 24.301 28.854 ... NaN 32.578 31.484 27.719 NaN 26.100 28.598 27.193 NaN 30.021
Patient13 32.037 NaN 33.761 23.823 NaN 28.945 27.177 NaN 24.637 28.921 ... NaN 34.461 32.920 28.884 NaN 29.893 31.016 29.931 NaN 29.517
Patient18 31.855 NaN 34.705 25.289 25.377 27.779 26.758 NaN 24.226 27.896 ... 24.383 33.344 31.891 27.841 NaN 29.193 28.310 30.401 NaN 27.910
Patient25 30.773 NaN 32.751 NaN NaN 28.813 28.589 NaN 24.396 28.315 ... NaN 30.589 29.244 24.012 NaN 27.692 24.011 27.139 25.195 29.448
Patient14 30.435 28.195 32.463 NaN NaN 29.564 28.233 NaN 25.189 30.207 ... 23.700 33.071 31.503 26.714 NaN 28.491 28.122 30.373 26.393 29.849
Patient05 30.219 26.704 32.468 22.564 NaN 28.719 29.265 23.019 25.624 29.525 ... NaN 30.435 29.425 25.293 NaN 27.293 27.931 30.291 26.618 29.479
Patient20 31.078 NaN 34.063 25.315 24.377 28.385 27.472 NaN 24.626 28.666 ... NaN 32.109 30.750 26.679 NaN 25.503 NaN 29.367 24.658 28.802
Patient21 30.912 NaN 33.287 NaN NaN 29.188 28.756 NaN NaN 28.396 ... NaN 33.239 31.750 27.464 NaN 29.800 29.206 30.769 NaN 30.355
Patient11 30.697 28.426 32.712 22.730 23.259 29.753 28.441 NaN 24.970 26.765 ... 23.929 32.397 30.945 27.180 19.654 25.578 27.736 26.040 25.767 30.056
Patient23 31.175 28.184 32.586 24.601 NaN 29.202 28.150 22.956 24.361 28.326 ... NaN 34.423 32.661 28.921 NaN 25.794 27.847 28.916 25.984 29.626
Patient16 30.172 27.839 32.827 30.132 NaN 29.329 28.857 NaN 22.695 29.167 ... 23.819 32.130 31.584 26.226 NaN 26.428 27.499 25.790 24.300 29.740
Patient07 30.991 27.558 32.742 21.468 NaN 28.534 25.345 NaN 24.528 28.065 ... NaN 33.581 32.539 28.420 NaN 27.072 23.853 28.670 24.996 28.872
Patient17 31.484 27.751 34.503 23.818 NaN 29.059 27.084 NaN 25.798 28.339 ... NaN 32.383 31.135 26.782 NaN 25.634 27.485 29.994 25.876 29.284
Patient04 31.410 28.070 33.947 23.039 24.354 29.062 28.640 NaN 26.040 28.909 ... NaN 32.452 31.515 25.965 20.206 25.193 25.081 27.299 25.836 29.756
Patient10 30.540 26.970 33.911 24.601 NaN 29.826 28.359 NaN 24.734 29.186 ... 25.039 33.270 31.977 28.255 20.992 25.832 28.539 27.989 25.638 29.984
Patient12 31.881 27.155 33.990 23.756 NaN 28.367 27.276 NaN 24.930 28.589 ... 26.967 33.719 32.595 28.613 NaN 29.269 28.899 27.364 25.619 28.604
Patient06 31.969 NaN 33.707 22.169 24.041 29.420 27.533 NaN NaN 28.196 ... NaN 33.199 31.595 26.842 NaN 27.593 29.836 30.685 NaN 29.132
Patient09 30.657 27.128 34.230 NaN NaN 29.205 27.669 NaN 25.924 28.201 ... NaN 31.685 31.324 25.805 NaN 27.592 26.667 29.753 25.349 28.876
Patient15 30.606 NaN 34.209 NaN NaN 28.476 26.708 NaN NaN 28.343 ... NaN 32.300 30.295 27.085 NaN 28.329 26.651 29.954 24.755 29.945
Patient22 30.311 NaN 33.014 NaN NaN 30.312 28.655 NaN 26.169 28.945 ... NaN 33.099 31.663 28.124 NaN 26.345 26.829 31.376 25.959 30.301
Patient19 30.641 28.844 32.556 21.944 NaN 28.835 27.235 NaN 23.146 29.000 ... 27.079 34.425 33.490 29.931 NaN 25.061 29.803 29.947 24.917 29.669
Patient01 31.957 27.237 33.766 NaN NaN 29.325 28.526 NaN 25.355 27.734 ... NaN 33.243 31.817 28.737 NaN 26.888 28.780 29.021 24.186 29.075

25 rows × 8946 columns

ax = (
    df_omics.notna()
    .sum()
    .sort_values(ascending=True)
    .plot(xlabel="Protein groups", ylabel="Number of non-NaN values (samples)")
)
../_images/6ad9cb3593726b4092cd784d470752c031b01e07844eae0b22885d777fd038f8.png

Keep only features with a certain amount of non-NaN values and select 100 of these for illustration. Add always four which were differently regulated in the ANOVA using all the protein groups.

idx_always_included = ["Q5HYN5", "P39059", "O43432", "O43175"]

Hide code cell source

 
df_omics = (
    df_omics
    # .dropna(axis=1)
    .drop(idx_always_included, axis=1)
    .dropna(thresh=18, axis=1)
    .sample(
        features_to_sample - len(idx_always_included),
        axis=1,
        random_state=42,
    )
    .join(df_omics[idx_always_included])
)
df_omics
P62699 Q9UID3 P05186 Q9NZ08-2 Q8TF74 O15230 Q4LDE5 Q96MG7 Q96MM6 Q9Y6M1 ... Q9UKU7 Q96SY0 Q13247 Q9NQG5 H3BPE1 Q02833 Q5HYN5 P39059 O43432 O43175
Patient02 25.744 27.646 24.825 30.105 27.181 30.261 24.238 24.996 23.847 31.927 ... 27.326 28.245 32.740 30.372 31.685 27.180 21.868 27.572 28.485 33.119
Patient24 24.782 28.443 29.958 30.665 27.706 31.103 24.776 25.533 26.667 33.517 ... 28.354 28.067 33.131 31.254 31.339 27.098 28.910 29.459 28.228 34.151
Patient08 26.635 28.011 28.743 29.763 27.332 30.480 25.142 24.687 24.214 29.387 ... 29.053 28.057 33.009 30.139 32.116 27.397 22.516 29.585 28.366 33.274
Patient03 26.761 28.331 31.520 30.090 28.091 31.936 23.985 26.385 25.443 32.362 ... 28.245 27.612 33.184 30.992 31.345 27.867 21.852 28.343 28.733 34.434
Patient13 27.491 28.966 25.042 30.876 28.581 32.188 23.905 NaN 23.498 32.105 ... 29.292 27.442 32.153 30.045 33.332 27.116 22.424 28.045 27.983 34.268
Patient18 NaN 28.413 26.452 31.216 26.199 31.185 NaN NaN 25.005 29.415 ... 28.315 26.442 30.620 30.013 32.085 26.713 20.567 27.846 28.193 31.871
Patient25 26.072 28.371 29.305 30.088 27.197 31.111 NaN 24.499 24.883 32.270 ... 30.104 28.211 32.010 30.054 31.429 27.101 32.377 26.086 29.177 32.313
Patient14 25.697 28.411 29.425 30.873 28.360 30.412 24.295 25.174 24.068 29.663 ... 29.632 27.428 32.530 30.974 31.788 27.049 22.130 26.888 28.299 32.963
Patient05 25.790 27.874 24.818 30.635 26.518 30.998 22.597 24.534 23.701 30.797 ... 30.055 27.575 32.700 31.005 32.052 27.766 20.647 26.527 28.401 34.023
Patient20 24.959 28.080 28.632 31.084 27.257 31.072 NaN 26.595 26.129 30.246 ... 29.512 27.605 31.557 30.284 32.153 26.902 23.337 26.162 28.947 32.507
Patient21 26.374 28.163 26.020 32.343 28.301 32.388 NaN 27.555 25.467 32.892 ... 27.160 28.573 32.214 30.846 33.233 NaN 26.163 29.583 29.314 35.208
Patient11 26.322 28.512 24.235 30.513 27.941 29.219 22.882 25.260 24.900 31.671 ... 28.757 29.051 33.398 31.657 31.656 27.653 21.419 27.526 27.870 36.087
Patient23 27.373 28.389 30.295 29.885 27.726 31.278 25.704 25.357 25.495 31.612 ... 28.840 26.112 32.362 30.252 33.521 27.126 34.031 25.931 28.749 32.247
Patient16 26.506 28.278 25.537 31.184 27.227 31.622 NaN 25.053 23.493 30.575 ... 29.774 28.135 32.817 30.031 32.910 27.223 21.429 27.865 28.570 33.674
Patient07 25.715 28.380 23.654 30.521 26.910 31.911 25.611 23.744 24.818 31.005 ... 29.628 27.409 32.266 31.832 31.961 26.905 22.464 27.488 28.138 33.236
Patient17 25.473 28.345 30.136 30.880 26.721 31.207 24.561 24.923 25.746 32.288 ... 28.751 27.704 32.410 30.878 31.450 26.455 29.921 27.244 28.630 33.756
Patient04 25.822 28.670 24.103 29.637 27.581 30.972 23.876 25.153 24.173 32.007 ... 30.339 28.168 32.742 32.067 32.545 26.369 22.766 27.709 28.948 35.473
Patient10 25.030 28.168 26.021 28.449 27.842 30.552 23.629 25.732 23.999 30.608 ... 28.969 28.068 32.337 30.069 32.492 26.901 21.094 27.315 27.512 34.164
Patient12 25.973 28.266 26.580 30.112 26.236 31.083 24.757 24.533 27.254 31.241 ... 27.793 27.567 31.930 30.296 31.856 26.808 31.242 26.390 28.174 33.836
Patient06 25.617 28.657 26.296 31.600 27.061 32.144 23.811 25.055 23.839 32.003 ... 28.889 27.420 32.057 31.404 32.079 26.577 NaN 25.560 27.818 33.526
Patient09 25.055 27.873 31.705 30.227 26.819 29.953 25.248 23.154 24.546 31.707 ... 29.256 28.608 32.115 31.012 32.551 26.535 22.485 26.217 28.025 33.992
Patient15 25.904 28.484 26.286 31.581 27.025 31.919 NaN 24.286 25.358 29.530 ... 29.986 26.993 32.577 30.992 31.949 25.985 26.292 27.203 27.812 32.633
Patient22 27.152 28.855 27.813 30.987 25.051 31.263 NaN 25.648 25.047 31.950 ... 28.964 27.956 32.560 31.377 35.067 27.832 28.504 25.517 29.120 32.710
Patient19 25.428 27.820 25.893 31.397 26.895 31.800 25.152 24.925 28.137 32.429 ... 28.720 26.959 32.432 30.829 31.956 27.395 26.936 26.108 29.104 32.940
Patient01 26.674 27.999 29.158 31.028 28.454 31.230 24.325 25.249 23.878 29.512 ... 29.177 28.620 31.388 30.507 33.021 28.021 22.630 26.846 28.062 33.601

25 rows × 100 columns

And we have the following patient metadata, from which we will use the Status column as our dependent variable and the PlatinumValue as a covariate.

df_meta
PlatinumValue Days to platinum resistance Disease free days Overall survival days Status Refractory
Patient_id
Patient02 Resistant -54 114 241 deceased y
Patient24 Sensitive 2,584 2,754 2,903 deceased n
Patient08 Resistant 31 211 228 deceased n
Patient03 Resistant -22 114 1,489 deceased y
Patient13 Sensitive 382 573 1,479 deceased n
Patient18 Sensitive 971 1,133 1,716 deceased n
Patient25 Sensitive 3,100 3,229 3,229 alive n
Patient14 Sensitive 440 580 1,106 deceased n
Patient05 Resistant 18 161 363 deceased n
Patient20 Sensitive 1,111 1,296 3,046 alive n
Patient21 Sensitive 1,271 1,498 1,573 deceased n
Patient11 Resistant -37 391 567 deceased n
Patient23 Sensitive 2,478 2,603 2,603 alive n
Patient16 Sensitive 462 663 1,347 deceased n
Patient07 Resistant 20 210 345 deceased n
Patient17 Sensitive 864 1,008 1,528 deceased n
Patient04 Resistant 29 155 485 deceased n
Patient10 Resistant 104 366 922 deceased n
Patient12 Sensitive 366 552 973 deceased n
Patient06 Resistant 52 190 790 deceased n
Patient09 Resistant 134 335 1,118 deceased n
Patient15 Sensitive 397 588 1,078 deceased n
Patient22 Sensitive 1,665 1,804 1,804 alive n
Patient19 Sensitive 1,051 1,188 1,467 alive n
Patient01 Resistant 11 113 280 deceased y

ANOVA: Compute upregulated genes for each condition#

These will be used to find enrichments in the set of both upregulated pathways in deceased and alive patients.

group = "Status"
diff_reg = acore.differential_regulation.run_anova(
    df_omics.join(df_meta[[group]]),
    drop_cols=[],
    subject=None,
    group=group,
)
diff_reg.describe(exclude=["float"])
identifier test correction rejected group1 group2 Method
count 100 100 100 100 100 100 100
unique 100 1 1 2 1 1 1
top P62699 t-Test FDR correction BH False deceased alive Unpaired t-test
freq 1 100 100 96 100 100 100 
diff_reg["rejected"] = diff_reg["rejected"].astype(bool)  # ! needs to be fixed in anova
diff_reg.query("rejected")
identifier T-Statistics pvalue mean(group1) mean(group2) std(group1) std(group2) log2FC test correction padj rejected group1 group2 FC -log10 pvalue Method
32 Q96JJ3 -3.897 0.001 28.031 28.584 0.562 0.119 -0.553 t-Test FDR correction BH 0.018 True deceased alive 0.682 3.139 Unpaired t-test
97 P39059 5.938 0.000 27.561 25.961 1.057 0.235 1.600 t-Test FDR correction BH 0.000 True deceased alive 3.031 5.324 Unpaired t-test
98 O43432 -6.045 0.000 28.278 29.019 0.414 0.155 -0.741 t-Test FDR correction BH 0.001 True deceased alive 0.598 4.873 Unpaired t-test
99 O43175 5.248 0.000 33.864 32.543 0.945 0.256 1.321 t-Test FDR correction BH 0.001 True deceased alive 2.498 4.533 Unpaired t-test

Download functional annotations, here pathways, for the protein groups#

in our selection of the dataset.

Check the acore.io.uniprot module for more details on how to fetch and process annotations from UniProt, especially check the link given there on all the available fields: return_fields

from urllib.error import HTTPError

from acore.io.uniprot import fetch_annotations, process_annotations

# annotations are cached in the repository to avoid querying UniProt on each docs build
fname_annotations = (
    f"example_data/PXD010372/processed/annotations_{features_to_sample}.csv"
)
fname = Path(fname_annotations)
url_annotations = f"{base_path}/annotations_{features_to_sample}.csv"
try:
    annotations = pd.read_csv(fname, index_col=0)
    print(f"Loaded annotations from {fname}")
except FileNotFoundError:
    try:
        annotations = pd.read_csv(url_annotations, index_col=0)
        print(f"Loaded annotations from {url_annotations}")
    except (FileNotFoundError, HTTPError):
        annotations = None
if annotations is None:
    print(f"Fetching annotations for {df_omics.columns.size} UniProt IDs.")
    # adding 'go' leads to duplicates which are filtered out by `process_annotations`
    FIELDS = "go_p,go_c,go_f,go"
    annotations = fetch_annotations(df_omics.columns, fields=FIELDS)
    annotations = process_annotations(annotations, fields=FIELDS)
    # cache the annotations
    fname.parent.mkdir(exist_ok=True, parents=True)
    annotations.to_csv(fname, index=True)
annotations

Loaded annotations from example_data/PXD010372/processed/annotations_100.csv
identifier source annotation
0 P62699 Gene Ontology (biological process) cell population proliferation [GO:0008283]
1 P62699 Gene Ontology (cellular component) centrosome [GO:0005813]
2 P62699 Gene Ontology (GO) extracellular region [GO:0005576]
3 P62699 Gene Ontology (GO) ficolin-1-rich granule lumen [GO:1904813]
4 P62699 Gene Ontology (GO) GID complex [GO:0034657]
... ... ... ...
1,723 O43175 Gene Ontology (GO) electron transfer activity [GO:0009055]
1,724 O43175 Gene Ontology (GO) L-malate dehydrogenase (NAD+) activity [GO:0030060]
1,725 O43175 Gene Ontology (GO) NAD binding [GO:0051287]
1,726 O43175 Gene Ontology (GO) phosphoglycerate dehydrogenase activity [GO:0004617]
1,727 O43175 Gene Ontology (GO) L-serine biosynthetic process [GO:0006564]

1728 rows × 3 columns

See how many protein groups are associated with each annotation. We observe that most functional annotations are associated only to a single protein group in our dataset.

Hide code cell source

 
s_count_pg_per_annotation = (
    annotations.groupby("annotation").size().value_counts().sort_index()
)
_ = s_count_pg_per_annotation.plot(
    kind="bar",
    xlabel="Number of protein groups associated with annotation",
    ylabel="Number of annotations",
)
s_count_pg_per_annotation.to_frame("number of annotations").rename_axis(
    "N protein groups"
).T
N protein groups 1 2 3 4 5 6 7 8 9 10 11 16 17 19 22 37 39 42 51
number of annotations 844 133 45 17 7 5 3 2 1 2 2 1 1 2 1 1 1 1 1
../_images/31867ceec24278a4f87044a383841a61e275c42407a5330fd35782daf425176d.png 
annotations.groupby("annotation").size().value_counts(ascending=False)

1    844
2    133
3     45
4     17
5      7
6      5
7      3
11     2
8      2
19     2
10     2
9      1
42     1
39     1
17     1
22     1
37     1
51     1
16     1
Name: count, dtype: int64

Enrichment analysis#

Is done separately for upregulated genes in each group as it’s assumed that biological processes are regulated in one direction together. The minimum absolut log2 fold change is 0.553 for the statistically significant protein groups in this example.

Hide code cell source

 
diff_reg.query("rejected")[
    [
        "identifier",
        "group1",
        "group2",
        "pvalue",
        "padj",
        "rejected",
        "log2FC",
        "FC",
    ]
].sort_values("log2FC")
identifier group1 group2 pvalue padj rejected log2FC FC
98 O43432 deceased alive 0.000 0.001 True -0.741 0.598
32 Q96JJ3 deceased alive 0.001 0.018 True -0.553 0.682
99 O43175 deceased alive 0.000 0.001 True 1.321 2.498
97 P39059 deceased alive 0.000 0.000 True 1.600 3.031

Running the enrichment analysis for the up- and down regulated protein groups separately with the default settings of the function, i.e. a log2 fold change cutoff of 1 and at least 2 protein groups detected in the set of proteins defining the functional annotation.

ret = acore.enrichment_analysis.run_up_down_regulation_enrichment(
    regulation_data=diff_reg,
    annotation=annotations,
    pval_col="padj",
    min_detected_in_set=2,
    lfc_cutoff=1,
)
ret

No significant enrichment found with the given parameters. Returning an empty DataFrame.
No significant enrichment found for comparison deceased~alive (upregulated in alive).
terms identifiers foreground background foreground_pop background_pop pvalue padj rejected direction comparison
0 extracellular exosome [GO:0070062] P39059,O43175 2 17 2 100 0.035 0.035 True upregulated in deceased deceased~alive

we can decrease the cutoff for the log2 fold change to 0.5 and see that we retain all targets from the differential expression analysis.

ret = acore.enrichment_analysis.run_up_down_regulation_enrichment(
    regulation_data=diff_reg,
    annotation=annotations,
    pval_col="padj",
    min_detected_in_set=2,
    lfc_cutoff=0.5,  # ! the default is 1
)
ret
terms identifiers foreground background foreground_pop background_pop pvalue padj rejected direction comparison
0 extracellular exosome [GO:0070062] P39059,O43175 2 17 2 100 0.035 0.035 True upregulated in deceased deceased~alive
0 cytosol [GO:0005829] Q96JJ3,O43432 2 40 2 100 0.174 0.174 False upregulated in alive deceased~alive

And even more if we do not restrict the analysis of finding at least two proteins of a functional set in our data set (i.e. we only need to find one match from the set).

ret = acore.enrichment_analysis.run_up_down_regulation_enrichment(
    regulation_data=diff_reg,
    annotation=annotations,
    pval_col="padj",
    min_detected_in_set=1,
    lfc_cutoff=0.5,  # ! the default is 1
)
ret
terms identifiers foreground background foreground_pop background_pop pvalue padj rejected direction comparison
0 (R)-2-hydroxyglutarate (NAD+) dehydrogenase activity [GO... O43175 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
1 L-malate dehydrogenase (NAD+) activity [GO:0030060] O43175 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
2 L-serine biosynthetic process [GO:0006564] O43175 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
3 NAD binding [GO:0051287] O43175 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
6 collagen type XV trimer [GO:0005582] P39059 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
17 phosphoglycerate dehydrogenase activity [GO:0004617] O43175 1 0 2 100 0.020 0.063 False upregulated in deceased deceased~alive
5 brain development [GO:0007420] O43175 1 1 2 100 0.040 0.069 False upregulated in deceased deceased~alive
4 basement membrane [GO:0005604] P39059 1 1 2 100 0.040 0.069 False upregulated in deceased deceased~alive
14 extracellular matrix structural constituent conferring t... P39059 1 1 2 100 0.040 0.069 False upregulated in deceased deceased~alive
11 extracellular exosome [GO:0070062] P39059,O43175 2 17 2 100 0.035 0.069 False upregulated in deceased deceased~alive
8 electron transfer activity [GO:0009055] O43175 1 1 2 100 0.040 0.069 False upregulated in deceased deceased~alive
13 extracellular matrix organization [GO:0030198] P39059 1 2 2 100 0.059 0.094 False upregulated in deceased deceased~alive
10 endoplasmic reticulum lumen [GO:0005788] P39059 1 4 2 100 0.098 0.143 False upregulated in deceased deceased~alive
12 extracellular matrix [GO:0031012] P39059 1 5 2 100 0.117 0.159 False upregulated in deceased deceased~alive
18 signal transduction [GO:0007165] P39059 1 6 2 100 0.136 0.172 False upregulated in deceased deceased~alive
9 endoplasmic reticulum [GO:0005783] P39059 1 10 2 100 0.209 0.248 False upregulated in deceased deceased~alive
15 extracellular region [GO:0005576] P39059 1 18 2 100 0.345 0.386 False upregulated in deceased deceased~alive
16 membrane [GO:0016020] P39059 1 21 2 100 0.393 0.415 False upregulated in deceased deceased~alive
7 cytosol [GO:0005829] O43175 1 41 2 100 0.666 0.666 False upregulated in deceased deceased~alive
3 cell chemotaxis [GO:0060326] Q96JJ3 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
2 actin filament organization [GO:0007015] Q96JJ3 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
7 eukaryotic translation initiation factor 4F complex [GO:... O43432 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
4 cell motility [GO:0048870] Q96JJ3 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
12 regulation of vasculogenesis [GO:2001212] Q96JJ3 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
11 regulation of translational initiation [GO:0006446] O43432 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
10 receptor tyrosine kinase binding [GO:0030971] Q96JJ3 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
9 positive regulation of translation [GO:0045727] O43432 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
14 translation factor activity, RNA binding [GO:0008135] O43432 1 0 2 100 0.020 0.056 False upregulated in alive deceased~alive
13 spermatid development [GO:0007286] O43432 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
15 translation initiation factor activity [GO:0003743] O43432 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
16 translational initiation [GO:0006413] O43432 1 1 2 100 0.040 0.056 False upregulated in alive deceased~alive
1 RNA cap binding [GO:0000339] O43432 1 2 2 100 0.059 0.078 False upregulated in alive deceased~alive
6 cytosol [GO:0005829] Q96JJ3,O43432 2 40 2 100 0.174 0.211 False upregulated in alive deceased~alive
0 RNA binding [GO:0003723] O43432 1 16 2 100 0.313 0.354 False upregulated in alive deceased~alive
8 membrane [GO:0016020] Q96JJ3 1 21 2 100 0.393 0.418 False upregulated in alive deceased~alive
5 cytoplasm [GO:0005737] O43432 1 38 2 100 0.630 0.630 False upregulated in alive deceased~alive

Multiple testing correction: Benjamini-Hochberg vs. empirical FDR (eFDR)#

The classic Benjamini-Hochberg (BH) procedure (correction="fdr_bh", the default) corrects the p-values of all tested annotations using only the p-values themselves. The empirical FDR (eFDR, correction="efdr") instead estimates the FDR from permutations, as done in the mulea R package (Turek et al. 2024): in each permutation a random foreground set of the original size is drawn from all measured features and the test is repeated for all annotations. For each p-value threshold \(t\) the eFDR is the average number of annotations with a p-value \(\leq t\) in the permuted data divided by the number of annotations with a p-value \(\leq t\) in the observed data. This takes into account the overlap between annotations (one feature belongs to many GO terms) and the discreteness of Fisher’s exact test p-values, which violate the assumptions of the BH procedure.

To use it, set correction="efdr" and the number of permutations (use a large number, e.g. 10000, for stable estimates). Set a seed to make the permutations reproducible.

enrichment_kwargs = dict(
    regulation_data=diff_reg,
    annotation=annotations,
    pval_col="padj",
    min_detected_in_set=1,
    lfc_cutoff=0.5,
)
ora_bh = acore.enrichment_analysis.run_up_down_regulation_enrichment(
    **enrichment_kwargs, correction="fdr_bh"
)
ora_efdr = acore.enrichment_analysis.run_up_down_regulation_enrichment(
    **enrichment_kwargs, correction="efdr", permutations=1000, seed=42
)

Both runs test the same annotations and share the same Fisher’s exact test p-values. Only the adjusted p-values (padj) and thereby the rejected decision differ. Here the comparison for the annotations with the smallest p-values:

keys = ["comparison", "direction", "terms"]
comparison_ora = (
    ora_bh.set_index(keys)[["foreground", "pvalue", "padj", "rejected"]]
    .join(
        ora_efdr.set_index(keys)[["padj", "rejected"]],
        lsuffix=" BH",
        rsuffix=" eFDR",
    )
    .sort_values("pvalue")
)
comparison_ora.head(10)
foreground pvalue padj BH rejected BH padj eFDR rejected eFDR
comparison direction terms
deceased~alive upregulated in deceased (R)-2-hydroxyglutarate (NAD+) dehydrogenase activity [GO:0120568] 1 0.020 0.063 False 1.000 False
L-malate dehydrogenase (NAD+) activity [GO:0030060] 1 0.020 0.063 False 1.000 False
L-serine biosynthetic process [GO:0006564] 1 0.020 0.063 False 1.000 False
NAD binding [GO:0051287] 1 0.020 0.063 False 1.000 False
collagen type XV trimer [GO:0005582] 1 0.020 0.063 False 1.000 False
phosphoglycerate dehydrogenase activity [GO:0004617] 1 0.020 0.063 False 1.000 False
upregulated in alive regulation of vasculogenesis [GO:2001212] 1 0.020 0.056 False 1.000 False
cell chemotaxis [GO:0060326] 1 0.020 0.056 False 1.000 False
receptor tyrosine kinase binding [GO:0030971] 1 0.020 0.056 False 1.000 False
cell motility [GO:0048870] 1 0.020 0.056 False 1.000 False

Number of annotations considered significant (adjusted p-value <= 0.05) by each procedure:

comparison_ora[["rejected BH", "rejected eFDR"]].sum().to_frame("n significant")
n significant
rejected BH 0
rejected eFDR 0

In this small example most annotations are supported by a single protein group and share the same discrete p-value of 0.02. In the permuted data many annotations reach this p-value just by chance, so the eFDR of these annotations is 1 and none of them is called significant, whereas BH, which treats the p-values as independent continuous values, only just misses the cutoff. An example where eFDR calls more annotations significant than BH is shown in the comparison with mulea.

Site specific enrichment analysis#

The basic example uses a modified peptide sequence to demonstrate the enrichment analysis.

TODO: The example on how to do that needs a PTM focused dataset. The details of how site specific enrichment analysis is done will depend on the dataset and the question at hand.

If the identifiers contain PTMs this information is removed to match it to the annotation using a regular expression (in the function). For example:

import re

regex = "(\\w+~.+)_\\w\\d+\\-\\w+"
identifier_ckg = "gnd~P00350_T10-WW"
match = re.search(regex, identifier_ckg)
match.group(1)

'gnd~P00350'

# ToDo: Add example for site specific enrichment analysis

Single sample GSEA (ssGSEA)#

Run a gene set enrichment analysis (GSEA) for each sample. The ssGSEA is a method that the proteins (genes) are ordered for each sample and the ranking of proteins (genes) associated to a functional annotation (pathway, GO term, etc.) is used to compute an enrichment score for that sample for that functional annotation.

Method description accoring to Barbie et. al. (2009)

Note: The call functional annotation “signature” in the original article.

“This was accomplished by a ‘single sample’ extension of GSEA that allows one to define an enrichment score that represents the degree of absolute enrichment of a gene set in each sample within a given data set. The gene expression values for a given sample were rank-normalized, and an enrichment score was produced using the Empirical Cumulative Distribution Functions (ECDF) of the genes in the signature and the remaining genes. This procedure is similar to GSEA but the list is ranked by absolute expression (in one sample). The enrichment score is obtained by an integration of the difference between the ECDF. For a given signature \(G\) of size \(N_G\) and single sample \(S\), of the data set of \(N\) genes, the genes are replaced by their ranks according the their absolute expression: \(L=\{r_1, r_2, \ldots, r_N\}\). The list is then ordered from the highest rank \(N\) to the lowest \(1\). An enrichment score \(ES(G,S)\) is obtained by a sum (integration) of the difference between a weighted ECDF of the genes in the signature \(P_{G}^w\) and the ECDF of the remaining genes \(P_{NG}\):

\(ES(G,S) = \sum_{i=1}^{N} \left| P_{G}^{w}(G,S,i) - P_{N_G}(G,S,i) \right|\)

where

\(P_{G}^{w}(G,S,i)= \sum_{r_j \in G, j \leq i} \frac{|r_j|^\alpha}{\sum_{r_{j \in G}} |r_j|^\alpha}\) and \(P_{N_G}(G,S,i)= \sum_{r_j \notin G, j \leq i} \frac{1}{N - N_G}\)

This calculation is repeated for each signature and each sample in the data set. Note that the exponent of this quantity (\(α\)) is set to 1/4, and adds a modest weight to the rank. In the regular GSEA a similar enrichment score is used, but the weight is typically set to 1. Also, instead of the sum over \(i\), the enrichment score is computed according to the largest difference. This quantity is slightly more robust and more sensitive to differences in the tails of the distributions than the Kolmogorov–Smirnov statistic. It is particularly well suited to represent the activation score of gene sets on the basis of a relatively small subset of the genes attaining high expression values.” (Barbie et al., 2009)

See the above details from the article and the package gseapy for more details.

enrichtments = acore.enrichment_analysis.run_ssgsea(
    data=df_omics,
    annotation=annotations,
    min_size=2,
)
enrichtments

2026-10-26 17:02:11,202 [WARNING] Input data contains NA, filled NA with 0
Term ES NES
Name
Patient13 regulation of telomere maintenance [GO:0032204] -49.490 -0.503
Patient24 signaling receptor binding [GO:0005102] -49.403 -0.502
Patient20 telomere maintenance [GO:0000723] 48.985 0.497
Patient18 telomere maintenance [GO:0000723] 48.985 0.497
Patient15 telomere maintenance [GO:0000723] 48.980 0.497
... ... ... ...
Patient18 positive regulation of glycolytic process [GO:0045821] 0.029 0.000
Patient11 response to hypoxia [GO:0001666] 0.029 0.000
Patient24 mitochondrion [GO:0005739] -0.014 -0.000
Patient11 neuromuscular junction [GO:0031594] 0.011 0.000
Patient12 protein kinase activity [GO:0004672] -0.008 -0.000

5650 rows × 3 columns

enrichtments.iloc[0].to_dict()

{'Term': 'regulation of telomere maintenance [GO:0032204]',
 'ES': -49.48979591836735,
 'NES': -0.5025615257756797}

ax = enrichtments["NES"].plot.hist()
../_images/139b72db2c47a6a36ff469a6e7cc2942146d881a9787bd9adf028f680ed2ad5f.png

The normalised enrichment score (NES) can be used in a PCA plot to see if the samples cluster according to the enrichment of the gene sets.

nes = enrichtments.set_index("Term", append=True).unstack()["NES"].convert_dtypes()
nes
Term 5'-deoxyribose-5-phosphate lyase activity [GO:0051575] ATP binding [GO:0005524] ATP hydrolysis activity [GO:0016887] DNA damage response [GO:0006974] DNA-binding transcription factor binding [GO:0140297] EKC/KEOPS complex [GO:0000408] GID complex [GO:0034657] Golgi apparatus [GO:0005794] INTAC complex [GO:0160232] LBD domain binding [GO:0050693] ... transcription coregulator activity [GO:0003712] transcription corepressor activity [GO:0003714] translation initiation factor activity [GO:0003743] translational initiation [GO:0006413] tubulin binding [GO:0015631] ubiquitin ligase complex [GO:0000151] ubiquitin protein ligase activity [GO:0061630] ubiquitin protein ligase binding [GO:0031625] visual perception [GO:0007601] zinc ion binding [GO:0008270]
Name
Patient01 0.210 0.061 0.302 -0.229 0.137 0.157 -0.149 0.014 -0.102 0.204 ... -0.034 0.023 0.051 0.051 0.063 -0.111 -0.062 0.028 0.090 0.154
Patient02 0.396 0.046 0.216 -0.098 0.162 0.135 -0.160 -0.045 -0.115 -0.176 ... 0.114 0.195 0.151 0.151 0.061 -0.140 -0.023 0.075 0.082 0.154
Patient03 0.436 0.047 0.328 -0.223 0.092 0.135 -0.088 -0.077 -0.170 0.147 ... 0.116 0.178 0.101 0.101 0.007 -0.122 -0.246 -0.003 0.065 -0.040
Patient04 0.352 0.021 0.221 -0.193 0.110 0.151 -0.147 -0.029 -0.102 0.218 ... 0.081 0.117 0.158 0.158 0.056 -0.124 -0.103 0.036 0.150 0.014
Patient05 0.157 0.019 0.223 -0.100 0.151 0.099 -0.146 0.002 -0.190 0.192 ... -0.062 0.014 0.134 0.134 0.045 -0.108 -0.031 0.059 0.040 0.127
Patient06 0.358 0.037 0.225 -0.207 0.068 0.166 -0.166 0.024 -0.114 0.055 ... 0.041 0.034 0.110 0.110 0.049 -0.200 -0.248 0.032 0.013 0.115
Patient07 0.174 0.046 0.243 -0.337 0.100 0.162 -0.125 -0.005 -0.170 0.179 ... -0.062 -0.053 0.097 0.097 0.121 -0.135 -0.205 -0.006 0.082 0.029
Patient08 0.217 0.061 0.252 -0.176 0.157 0.197 -0.139 -0.074 -0.171 0.170 ... -0.058 0.052 0.115 0.115 0.030 -0.130 -0.154 0.015 0.148 -0.004
Patient09 0.188 0.045 0.364 -0.139 0.093 0.130 -0.134 -0.003 -0.028 0.216 ... 0.003 -0.018 0.057 0.057 0.026 -0.112 -0.057 0.057 0.039 0.095
Patient10 0.250 0.084 0.205 -0.043 0.142 0.212 -0.142 0.010 -0.168 0.176 ... 0.024 0.080 0.078 0.078 0.089 -0.120 -0.128 0.084 0.032 -0.077
Patient11 0.145 0.072 0.246 -0.031 0.123 -0.103 -0.106 -0.015 -0.012 0.001 ... -0.026 -0.075 0.134 0.134 0.125 -0.086 -0.111 0.077 0.064 0.070
Patient12 0.305 0.003 0.212 -0.148 0.126 0.150 -0.163 0.010 -0.191 0.087 ... 0.007 0.086 0.077 0.077 0.043 -0.185 -0.089 0.034 0.020 0.128
Patient13 0.345 0.049 0.208 -0.354 0.068 0.136 -0.002 0.018 -0.254 0.021 ... -0.001 0.079 0.023 0.023 0.118 -0.073 -0.309 -0.012 0.116 0.062
Patient14 0.159 0.065 0.292 -0.210 0.097 0.259 -0.132 -0.048 -0.150 0.058 ... -0.074 -0.108 0.124 0.124 0.020 -0.110 -0.113 -0.007 -0.002 0.096
Patient15 0.198 0.097 0.248 -0.098 0.153 0.213 -0.087 0.008 -0.160 0.181 ... -0.040 -0.004 0.129 0.129 0.041 -0.055 -0.030 0.095 0.043 0.162
Patient16 0.218 0.038 0.204 -0.180 0.121 0.088 -0.133 0.003 -0.198 0.184 ... 0.048 0.035 0.088 0.088 0.054 -0.119 -0.152 0.017 0.023 0.074
Patient17 0.415 0.032 0.298 -0.282 0.100 0.135 -0.182 -0.040 -0.181 0.165 ... 0.146 0.154 0.093 0.093 0.045 -0.194 -0.191 0.019 0.044 0.080
Patient18 0.182 0.069 0.294 -0.195 0.093 0.124 -0.211 0.006 -0.206 0.133 ... -0.127 -0.112 0.160 0.160 0.131 -0.249 -0.180 0.030 0.091 0.186
Patient19 0.382 0.027 0.216 -0.191 0.074 0.166 -0.188 -0.031 -0.228 0.106 ... 0.043 0.086 0.126 0.126 0.085 -0.243 -0.219 0.032 0.015 0.116
Patient20 0.179 0.054 0.295 -0.164 0.028 0.021 -0.204 0.006 -0.093 0.126 ... -0.133 -0.148 0.067 0.067 0.042 -0.254 -0.219 0.037 0.084 0.146
Patient21 0.436 0.004 0.231 -0.340 0.107 0.166 -0.110 -0.078 -0.065 0.056 ... 0.138 0.153 0.185 0.185 0.079 -0.148 -0.314 -0.026 0.014 0.099
Patient22 0.277 0.022 0.177 -0.133 0.113 0.202 -0.046 0.014 -0.119 0.204 ... 0.048 0.075 0.115 0.115 0.064 -0.053 -0.127 0.055 0.058 0.060
Patient23 0.291 0.005 0.315 -0.109 0.143 0.187 -0.079 -0.029 -0.280 0.134 ... 0.052 0.112 0.145 0.145 0.074 -0.100 -0.031 0.077 0.099 0.109
Patient24 0.415 0.025 0.307 -0.119 0.156 0.062 -0.216 0.031 -0.208 0.172 ... 0.194 0.232 0.098 0.098 0.034 -0.171 -0.093 0.048 0.121 0.102
Patient25 0.159 0.059 0.277 -0.073 0.070 0.255 -0.120 -0.090 -0.138 0.070 ... -0.080 -0.107 0.088 0.088 -0.017 -0.131 -0.064 0.119 0.045 0.096

25 rows × 226 columns

import acore.exploratory_analysis as ea

pca_result, pca_annotation = ea.run_pca(
    data=nes.join(df_meta[[group]]),
    drop_cols=[],
    annotation_cols=[],
    group=group,
    components=2,
    dropna=False,
)
resultDf, loadings, var_exp = pca_result
resultDf
group x y
0 deceased -0.750 -0.301
1 deceased 0.715 0.435
2 deceased 0.946 -0.077
3 deceased 0.496 0.231
4 deceased -0.598 -0.001
5 deceased 0.557 0.236
6 deceased -0.520 -0.541
7 deceased -0.282 -0.401
8 deceased -0.532 0.179
9 deceased -0.026 0.325
10 deceased -0.675 0.943
11 deceased 0.395 -0.218
12 deceased 0.605 -0.270
13 deceased -0.763 0.107
14 deceased -0.625 0.229
15 deceased -0.204 0.042
16 deceased 0.832 -0.182
17 deceased -0.768 -0.408
18 alive 0.625 -0.128
19 alive -0.898 -0.149
20 deceased 1.048 -0.017
21 alive 0.070 0.403
22 alive 0.239 -0.281
23 deceased 0.901 -0.096
24 alive -0.790 -0.058

The loadings show how the variables are correlated with the principal components.

loadings
x y value
positive regulation of stem cell proliferation [GO:2000648] 0.280 -0.107 0.299
endodermal cell differentiation [GO:0035987] 0.289 0.070 0.297
stem cell differentiation [GO:0048863] 0.289 0.070 0.297
response to virus [GO:0009615] 0.289 0.005 0.289
heterochromatin formation [GO:0031507] 0.286 0.001 0.286
... ... ... ...
chromosome [GO:0005694] 0.004 0.006 0.007
cell migration [GO:0016477] 0.003 0.004 0.005
plasma membrane [GO:0005886] 0.003 -0.001 0.004
electron transfer activity [GO:0009055] -0.002 -0.003 0.003
tubulin binding [GO:0015631] -0.000 -0.000 0.000

226 rows × 3 columns

We will plot both on the sample plot (samples on the first two principal components and loadings of variables). We use the vuecore package for this, which is also developed by the Multiomics Analytics Group.

args = {"factor": 2, "loadings": 2}  # increase number of loadings or scaling factor
#! pca_results has three items, but docstring requests only two -> double check
figure = viz.get_pca_plot(data=pca_result, identifier="PCA enrichment", args=args)
figure = go.Figure(data=figure["data"], layout=figure["layout"])
figure

GSEA (Gene Set Enrichment Analysis)#

GSEA ranks all measured features (e.g. proteins) by a continuous metric such as the log2 fold-change from differential expression analysis and tests whether the members of a gene set are enriched at the top or bottom of this ranked list.

Unlike overrepresentation analysis (ORA), GSEA does not require a significance cutoff to define a foreground set: it uses the full ranked list and is therefore less sensitive to the choice of an arbitrary threshold.

Here we use gseapy.prerank under the hood, which implements the classic weighted Kolmogorov–Smirnov enrichment statistic described in Subramanian et al. (2005).

See gseapy.prerank for more details.

gsea_results = acore.enrichment_analysis.run_gsea(
    regulation_data=diff_reg,
    annotation=annotations,
    identifier="identifier",
    ranking_col="log2FC",
    annotation_col="annotation",
    identifier_col="identifier",
    min_size=1,
    permutation_num=100,
    seed=42,
    correction_alpha=0.05,
)
gsea_results
Term ES NES NOM p-val FDR q-val FWER p-val Tag % Gene % Lead_genes rejected
0 extracellular matrix organization [GO:0030198] 0.969 1.633 0.000 0.160 0.130 2/3 4.23% P39059;B1ALD9 False
1 calcium ion binding [GO:0005509] -0.971 -1.505 0.000 0.802 0.540 2/2 7.04% P05186;H3BPE1 False
2 extracellular matrix structural constituent conferring t... 0.975 1.488 0.020 0.760 0.650 1/2 1.41% P39059 False
3 skeletal system development [GO:0001501] -0.971 -1.463 0.000 0.763 0.750 1/2 2.82% P05186 False
4 signal transduction [GO:0007165] 0.764 1.407 0.000 1.000 0.920 1/5 1.41% P39059 False
... ... ... ... ... ... ... ... ... ... ...
835 cytosol [GO:0005829] -0.172 -0.539 0.977 1.000 1.000 4/38 11.27% O43432;Q9NYB9;Q96JJ3;Q9Y6M1 False
836 mitochondrion [GO:0005739] 0.269 0.526 0.981 0.994 1.000 2/6 22.54% Q9Y320;Q9P0J0 False
837 integrin-mediated signaling pathway [GO:0007229] -0.333 -0.519 0.935 0.999 1.000 2/2 69.01% O15230;P08631 False
838 intracellular signal transduction [GO:0035556] -0.333 -0.502 0.983 0.998 1.000 2/2 69.01% Q9Y6E0-2;P08631 False
839 flavin adenine dinucleotide binding [GO:0050660] -0.300 -0.448 1.000 0.999 1.000 1/2 23.94% Q9UKU7 False

840 rows × 10 columns

The normalised enrichment score (NES) summarises the enrichment: positive values indicate that the gene set is enriched among the up-regulated features and negative values indicate enrichment among the down-regulated features.

gseapy reports a permutation-based FDR q-val for each gene set (derived from the NES null distribution), so no further correction is needed. The rejected column flags gene sets with FDR q-val <= correction_alpha.

gsea_results[["Term", "NES", "NOM p-val", "FDR q-val", "rejected"]]
Term NES NOM p-val FDR q-val rejected
0 extracellular matrix organization [GO:0030198] 1.633 0.000 0.160 False
1 calcium ion binding [GO:0005509] -1.505 0.000 0.802 False
2 extracellular matrix structural constituent conferring t... 1.488 0.020 0.760 False
3 skeletal system development [GO:0001501] -1.463 0.000 0.763 False
4 signal transduction [GO:0007165] 1.407 0.000 1.000 False
... ... ... ... ... ...
835 cytosol [GO:0005829] -0.539 0.977 1.000 False
836 mitochondrion [GO:0005739] 0.526 0.981 0.994 False
837 integrin-mediated signaling pathway [GO:0007229] -0.519 0.935 0.999 False
838 intracellular signal transduction [GO:0035556] -0.502 0.983 0.998 False
839 flavin adenine dinucleotide binding [GO:0050660] -0.448 1.000 0.999 False

840 rows × 5 columns

ax = gsea_results["NES"].plot.hist(title="Distribution of NES", xlabel="NES")
../_images/4f3ee7941f7da88a014d065012c6c227aa1fadb815e8c1993edfa9796d08df64.png

Done.