Multi-omics integration by causal network inference using CORNETO

This is a group project based tutorial first presented at the 2026 EMBL-EBI Introduction to multi-omics data integration and visualisation training. The fundamental idea of the project is to infer molecular activities (e.g. transcription factor or kinase activities) from different omics modalities, map the activities to a prior-knowledge network, and then use optimisation methods to infer networks that the most plausibly explain the activity patterns given the known perturbations. This project carries quite some similarities with the COSMOS project led by Aurelien Dugourd (Dugourd et al., 2021; 2024). However, there are important differences:

• The COSMOS project uses metabolomics in addition to transcriptomics, while here we can use phosphoproteomics, proteomics, and secretomics
• The COSMOS project uses the cosmosR R package with its dedicated prior-knowledge network: this is an out-of-the-box solution which uses the old R implementation of the CARNIVAL (Liu et al., 2019) network optimisation method
• Within the next 1-2 years the original COSMOS will be replaced by much more customisable and feature-rich solutions within the Python ecosystem
• In this project, we use the already available new Python components to perform a workflow very similar to COSMOS: we have to do more things "by hand", which allows us more freedom and also helps understanding

Data and study background

Our example data comes from a study of kidney fibrosis by Tüchler et al. (2025). It employs an in vitro model of TGF-beta-induced fibrotic transformation of PDGFR-beta positive patient derived kidney mesenchymal cells. These cells are similar to myofibroblasts, the main cell type responsible for excess extracellular matrix (ECM) deposition in fibrosis. The study generated a comprehensive time-resolved multi-omics dataset spanning 7 time points (5 min to 96 h) and 4 omics modalities under 10 ng/l TGF-beta stimulation, quantifying over 14,000 biomolecules. The omics modalities include transcriptomics, phosphoproteomics, proteomics, and secretomics, complemented with imaging of collagen I deposition. Furthermore, it also correlates and validates its results by comparing to kidney fibrosis patient data, as well as in vitro data from patient lung fibroblasts and tissue slices. Another important validation is the quantification of collagen I deposition under knock-down of transcription factors most significant based on the main experiment. Importantly, while we also measure collagen I as transcript and protein, the actual ECM fiber deposition doesn't only depend on collagen I, but several further proteins which cross-link with it, or build or degrade the ECM. A general observation in the study is that the early (especially 1h) and late response to TGF-beta is different. To model the time dynamics, multiple network inference steps are performed: the initial with TGF-beta as the only perturbation is responsible for the early TF and kinase activity patterns; then the early activities (plus TGF-beta) become the inputs and the early secretomics hits are the targets; next the early transcriptomics considered to be the perturbations and the late activities are the outputs; and finally, the connections between these late activity hits and the late secretomics are inferred.

Tools

Our workflow consists of tools developed in the Saez Lab:

• Decoupler (Badia-i-Mompel et al., 2022) for activity inference
• OmniPath (Türei et al., 2026) for prior knowledge network retrieval
• CORNETO (Rodriguez-Mier et al., 2025) for integer linear (ILP) network optimization

These are the key components of the mechanistic modeling approach used and developed in our group. To use better the limited time available in the training, we will focus 90% on the CORNETO part, using only corneto (with its dependencies) and standard data handling and visualisation tools.

References

• Tüchler N, Burtscher ML et al. "Dynamic multi-omics and mechanistic modeling approach uncovers novel mechanisms of kidney fibrosis progression." Mol. Syst. Biol. 21:1030–1065 (2025). doi:10.1038/s44320-025-00116-2
• Rodriguez-Mier P, Garrido-Rodriguez M, Gabor A, Saez-Rodriguez J. "Unifying multi-sample network inference from prior knowledge and omics data with CORNETO." Nat. Mach. Intell. 7:1168–1186 (2025). doi:10.1038/s42256-025-01069-9
• Türei D, Schaul J, Palacio-Escat N, Bohár B et al. "OmniPath: integrated knowledgebase for multi-omics analysis." Nucleic Acids Res. 54(D1):D652–D660 (2026). doi:10.1093/nar/gkaf1126
• Badia-i-Mompel P et al. "decoupleR: ensemble of computational methods to infer biological activities from omics data." Bioinform. Adv. 2:vbac016 (2022). doi:10.1093/bioadv/vbac016
• Liu A, Trairatphisan P, Gjerga E et al. "From expression footprints to causal pathways: contextualizing large signaling networks with CARNIVAL." npj Syst. Biol. Appl. 5:40 (2019). doi:10.1038/s41540-019-0118-z
• Dugourd A et al. "Causal integration of multi-omics data with prior knowledge to generate mechanistic hypotheses." Mol. Syst. Biol. 17:e9730 (2021). doi:10.15252/msb.20209730
• Dugourd A, Lafrenz P, Mañanes D, Paton V, Fallegger R, Kroger AC, Türei D, Shtylla B, Saez-Rodriguez J. "Modeling causal signal propagation in multi-omic factor space with COSMOS." bioRxiv (2024). doi:10.1101/2024.07.15.603538
• Kuppe C et al. "Decoding myofibroblast origins in human kidney fibrosis." Nature 589:281–286 (2021). doi:10.1038/s41586-020-2941-1

Setup

We will use uv for an efficient and clean management of dependencies and our environment. In the training we use Python 3.12 because it's the default version on the virtual machines. The first step is to clone the project repository where I included all the required data, documentation, example scripts and results.

git clone https://github.com/saezleb/corneto-ebi-multiomics

The repo contains the environment definition in pyproject.toml, you can set up the enviromnent with uv:

cd corneto-ebi-multiomics
uv sync

Alternatively, install in a virtual environment:

uv venv
uv pip install -e .

From now on, every time you want to run something in this environment, just add uv run in front of the command; and if you want to install more dependencies, you can use uv add <package-name>. For example, to start a Python shell:

uv run python

Repository structure

data/
  differential/
    diff_expr_all.tsv.gz       # Differential expression, all omics & time points
    activities.tsv             # TF and kinase activity scores
  network/
    paper_edges.tsv            # Published network edges (for comparison)
    paper_nodes.tsv            # Published network nodes (for comparison)
  imaging/
    col1_timecourse.tsv        # COL1 imaging data (for interpretation)
scripts/
  01_decoupler_demo.py         # TF activity inference with Decoupler
  02_prepare_inputs.py         # Data preparation and PKN retrieval
  03_corneto_network.py        # CARNIVAL network optimization
  04_visualize_results.py      # Network visualization and interpretation
results/                       # Generated outputs (networks, figures)

Group project schedule

Session 1 (1:45 h): Intro and activity inference with Decoupler

We start by demonstrating how transcription factor (TF) activities can be inferred from transcriptomics data using Decoupler (Badia-i-Mompel et al., 2022) and the CollecTRI regulon database. This shows how abstract molecular activities can be estimated from omics measurements, motivating the network integration step.

Script: scripts/01_decoupler_demo.py

Session 2 (2:15 h): Data preparation and prior knowledge network

We load the differential omics data, select time points and modalities, and prepare the inputs for CORNETO. We retrieve a signed, directed protein interaction network from OmniPath (Türei et al., 2026), filter it for expressed genes, and prune it for reachability.

Script: scripts/02_prepare_inputs.py

Session 3 (2:00 h): Network inference with CORNETO

Using the CARNIVAL algorithm (Liu et al., 2019) implemented in CORNETO (Rodriguez-Mier et al., 2025), we find an optimal subnetwork of the prior knowledge network that connects upstream perturbations (TGF-beta stimulus, kinase and TF activities) to downstream measurements (secreted protein changes). We can do more than one network inference, depending on time maybe we start network inference already in the previous session. In this project, because the longitudinal nature of the data poses additional challenge, we can infer an early and a late network, following similar steps as in the paper.

Script: scripts/03_corneto_network.py

Session 4 (3:30 h): Visualization and interpretation

We visualize the inferred network, the activities, compare them to the published results, and interpret the findings in the context of kidney fibrosis biology. We also have available the collagen I deposition data from imaging.

Script: scripts/04_visualize_results.py

Data description

The input data comes from the supplementary tables of Tüchler et al. (2025):

• Differential expression (diff_expr_all.tsv.gz): Log fold changes and adjusted p-values for all omics modalities (rna, proteomics, phosphoproteomics, secretomics) across 7 time points after TGF-beta stimulation vs. control. 391,105 measurements.

• Molecular activities (activities.tsv): Transcription factor and kinase activity scores inferred by Decoupler from transcriptomics (for TFs, using CollecTRI) and phosphoproteomics (for kinases, using a kinase-substrate network). 287 TFs and 157 kinases across 7 time points (3,108 rows total).

• Imaging data (col1_timecourse.tsv): Collagen I fluorescence intensity from immunofluorescence microscopy across the time course, providing a phenotypic readout of fibrotic ECM deposition.

Key concepts

• Activity inference: when the state captured in omics data is in part a mechanistic consequence of certain molecular activities and robust relationships between activities and omics measurements exist in prior-knowledge (these are called signatures or footprints), it is possible to estimate the activities from the omics data by simple statistics similar to enrichment analysis (Badia-i-Mompel et al., 2022). The simplest concrete example is transcription factor (TF) activity inference: if we know the target genes of a TF from prior-knowledge (this is the footprint of the TF, aka its regulon), and the majority of those target genes show a positive fold change in transcriptomics data, we can infer that the TF gets activated in the given condition. Read more in the Decoupler manual.

• Prior knowledge network (PKN): A signed, directed graph of known protein-protein regulatory interactions from OmniPath (Türei et al., 2026). Edges indicate activation (+1) or inhibition (-1), making it a causal network suitable for mechanistic modeling.

• Network optimisation: a procedure which, given a set of constraints (patterns of molecular activities, perturbations) and a causal prior-knowledge network, searches for subnetworks which achieve the least amount of logical contradiction between the constaints and the network by using the lowest number of nodes and edges from the PKN

• CORNETO: "Core network optimiser" (Rodriguez-Mier et al., 2025) - a Python framework that is able to deliver diverse network optimisation problems by diverse formulations to a number of optimisation solvers (backends). Read more in the CORNETO documentation .

• CARNIVAL: An optimisation method (Liu et al., 2019) that finds a subnetwork of the PKN consistent with observed perturbations (inputs) and measurements (outputs), while penalizing network complexity (L0 regularization on edges). This method is called causal reasoning, and it is one of the many optimisation methods CORNETO supports. Read more in the CARNIVAL paper.

• CarnivalFlow: The current CORNETO implementation of CARNIVAL, using a flow-based formulation that supports multi-sample analysis with structured sparsity regularization. Read more here.

Further materials

• This is a notebook from another training , you find a lot of background information and examples in it