Introduction to Constraint-Based Modelling

Constraint-based modelling of metabolism — a short course in three lectures.

Dario Pescini · University of Milano-Bicocca · Department of Statistics and Quantitative Methods

Abstract

A metabolic network constrains what a cell can do long before any kinetics are known. This course takes that idea as far as it goes: from a reaction network and its stoichiometry to the set of flux distributions a cell could reach, then to Flux Balance Analysis, which picks one of them by assuming the cell optimises something. We check that answer against a real measurement, find where it disagrees, and trace the disagreement back to defects in the reconstruction itself. The last lecture asks how much of the answer was ever determined — through flux variability, gene deletions and sampling — and what to do when "optimal" is the wrong assumption.

The emphasis throughout is on what a model does not tell you. All the calculations in the slides are reproduced by a hands-on exercise you run yourself, in Python with COBRApy.

Contents

I — From Network to Solution Space	networks and fluxes · reconstruction · the steady-state assumption · constraints · the solution space
II — Flux Balance Analysis	linear programming · alternative optima and pFBA · growth yield against experiment · nine diagnostic checks and how to fix what they find
III — Beyond the Optimum	flux variability · perturbations and deletions · sub-optimality · sampling · ensembles
Capstone	ENGRO 1: constrain a cancer core model, break it, and explain what it predicts

Each lecture has a hands-on file with worked solutions and a skeleton to fill in. Models used: a 19-reaction toy model you can hold in your head, e_coli_core, and ENGRO 1.

Getting set up

Everything you need is in this folder. With mamba or conda installed:

mamba env create -f environment.yml
mamba activate cbm-course

Then check it works:

python -c "import cobra; print(cobra.io.load_model('textbook').slim_optimize())"
# 0.8739215069684307

That is the growth rate of E. coli on glucose, and it is the first number in Lecture II. If you get it, you are ready.

How to work through it

slides/	the three lectures, as PDFs
CBM_L0N_exercises.md	the exercises, with worked solutions folded away — try before opening
CBM_L0N_functionsRecap.md	every function used, its aim, its parameters, and where the docs are
CBM_L0N_Scheletro.py	a skeleton to fill in, if you prefer starting from one
CBM_L04_capstone.md	the capstone: one model, everything from all three lectures
models/	the models — nothing downloads at run time
scripts/diagnose.py	the diagnostics tool, used in Lecture II exercise 6

Run everything from this folder, so the paths in the exercises resolve:

cd CBM_course
mamba activate cbm-course
python scripts/diagnose.py models/toymodel.xml

Exercises are plain .py and .md files — no notebooks. Solutions are in each exercises file under Show solution; every one of them runs.