Guide

CORNETO (Constraint-based Optimization for the Reconstruction of NETworks from Omics) is a python package for unified biological network inference and contextualisation from prior knowledge, developed and maintained by the Saez-Rodriguez Lab at EMBL-EBI and Heidelberg University.

CORNETO employs mathematical programming to translate network inference problems into exact, unified reformulations on top of Network Flows, and then uses mathematical solvers to find optimal solutions. It offers flexibility for various applications:

• Provides modular building blocks for diverse network inference problems.

• Reimplements methodologies such as Shortest Paths, Steiner Trees, Prize Collecting Steiner Forest, and more.

• Supports different types of prior knowledge, including protein-protein interactions, signalling networks, and genome-scale metabolic networks.

• Introduces novel methods for network inference and contextualisation.

The library is designed with minimal dependencies and is easily extendable, making it a powerful tool for both end-users and developers.

• Getting started
  • Prior Knowledge and Graphs
    • Manually creating a graph
    • Edge attributes
    • Modyfing attributes
    • Importing graphs
    • Saving and reading
    • Hypergraphs
  • Working with data
    • Samples and features
    • Creating a dataset
    • Querying measurements
    • Copying and extending data
    • Saving and loading data
    • Using data with methods
  • Plotting
    • 1. Basic graph visualization
    • 2. Visual encoding from values
    • 3. Presets for common workflows
    • 4. Theme customization
    • 5. Export and interoperability
    • 6. Browser/WASM rendering
    • 7. Custom processors
  • Constrained Optimization
    • The Knapsack Problem
• Network methods
  • Shortest paths
    • Creating a weighted graph
    • Random graphs
  • Multi-sample shortest paths
  • Multi-commodity Network Flows
  • Acyclic Flows
    • Largest DAG from a given source and sink vertex
    • Largest DAG from any source to any sink
  • Steiner trees
    • What are Steiner Trees?
    • How CORNETO Solves Steiner Tree Problems
    • Importing data to CORNETO
    • Solving the problem with the exact steiner tree
    • Extracting the tree and plotting
    • Directed graphs
    • Mixed graphs
  • Prize-Collecting Steiner Trees (PCST)
    • Directed
    • Select a specific root vertex
  • Multi-sample PCST
    • Using CORNETO
    • Multi-sample PCST
    • Testing the effect of \(\lambda\)
• Metabolism
  • Flux balance analysis
    • From COBRApy to CORNETO
    • Extend the optimization problem
    • Solve multiple media conditions
    • Sparse FBA
  • Multi-condition FBA
    • Independent and coupled formulations
    • Why is this different from pairwise comparisons?
    • Relation to COBRApy
    • Example: shared and context-specific metabolism
    • Define the metabolic conditions
    • Establish each condition’s growth capacity
    • Require growth and favor a compact reaction union
    • What happens in separate two-condition analyses?
    • Solve all conditions jointly
    • Interpretation and limitations
  • Integrating gene expression into metabolic models
    • One established approach: iMAT
    • From genes to reaction evidence
    • Relationship to COBRApy
    • Example: selecting an anaerobic fermentation program
    • Advanced: compute and supply reaction scores directly
    • Interpretation and limitations
  • Multi-condition gene expression integration
    • What changes in the multi-condition formulation?
    • Example: aerobic respiration and anaerobic fermentation
    • Balance expression evidence across conditions
    • Independent iMAT as a reference
    • Solve both expression contexts jointly
    • Shared and condition-specific metabolism
    • Interpretation and limitations
• Signaling
  • CARNIVAL
    • Creating a toy example
    • CarnivalFlow
    • Carnival ILP
    • Old implementation
  • Multi-sample CARNIVAL
    • Toy example
    • Multi-sample CARNIVAL
    • Plotting solutions on top of the PKN
    • Penalizing indirect signaling rules
    • Single sample using the same multi-sample method
  • PHONEMeS
    • Choosing the appropriate PHONEMeS workflow
    • Understanding phosphosite scores
    • Computing scores from differential results
    • Inferring a network for one condition
    • Reading and plotting the inferred subnetwork
    • Controlling network size with edge costs
    • Comparing multiple conditions
    • Advanced: implementation in CORNETO
  • Global upstream and downstream PHONEMeS
    • A small runnable example
    • Reading the inferred network
    • Choosing how anchors participate
    • Multiple conditions
    • Why this differs from original upside-down PHONEMeS
    • Scores and edge costs in real analyses
    • Advanced: the general Data interface
    • Advanced: implementation in CORNETO
  • Inferring intracellular signaling models with CellNOptDAG
    • One signaling model, several perturbation conditions
    • Relationship to CellNOptR
    • Example: perturbations and two signaling readouts
    • Fit one pathway to the complete experiment
    • Which signaling reactions are supported?
    • Does the model reproduce the measured responses?
    • A pathway reaction can be present but inactive
    • A compact view for larger signaling experiments
    • Under the hood
    • Biological interpretation and limitations
    • Connection to causal structure learning
• Interoperability
  • COBRApy: Constraint-based metabolic modeling in Python
    • Flux Balance Analysis with COBRA and CORNETO
  • LIANA+: An all-in-one cell-cell communication framework
  • Decoupler: Ensemble of methods to infer biological activities
  • Omnipath: intra- & intercellular signaling knowledge
  • NetworkX: Network Analysis in Python
  • AnnNet
    • Convert a CORNETO graph
    • Scope and limitations
  • CVXPY: Convex optimization, for everyone
  • PICOS: A Python interface to conic optimization solvers