Flux Balance Analysis Formulation

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About This MicroSim

This MicroSim demonstrates Flux Balance Analysis (FBA) — the mathematical framework for predicting metabolic fluxes in genome-scale metabolic models. Students see a small metabolic network alongside its stoichiometric matrix S, adjust exchange reaction bounds with sliders, and step through the linear programming formulation.

Key Concepts

Stoichiometric matrix (S) — Rows are metabolites, columns are reactions. Each entry is the stoichiometric coefficient (negative for substrates, positive for products).
Steady-state constraint — \(S \cdot v = 0\), where \(v\) is the flux vector. At steady state, the net production and consumption of each internal metabolite must balance.
Flux bounds — Each reaction has upper and lower bounds on its flux (determined by enzyme capacity, thermodynamics, or experimental measurements).
Objective function — Typically maximizing biomass production or ATP yield.
Linear programming — FBA solves for the flux distribution that maximizes the objective while satisfying stoichiometric and bound constraints.

How to Use

Exchange reaction sliders — Adjust the upper and lower bounds on nutrient uptake and product secretion rates
Step through the LP formulation — See how the objective function, constraints, and bounds are assembled
Observe the metabolic network — See how the network diagram maps to the stoichiometric matrix

Iframe Embed Code

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        height="562"
        width="100%"
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Lesson Plan

Grade Level

College introductory bioinformatics

Duration

20-25 minutes

Prerequisites

Understanding of metabolic reactions and stoichiometry
Basic concept of steady-state in biological systems
Familiarity with linear equations and constraints

Activities

Exploration (5 min): Examine the metabolic network and its stoichiometric matrix. Verify that each column of S corresponds to a reaction in the network, with correct signs for substrates and products.
Bound Manipulation (5 min): Adjust the glucose uptake bound. What happens to the feasible flux space? What does it mean biologically when you restrict nutrient uptake?
LP Formulation (5 min): Step through the formulation. Identify the objective function, the equality constraints (S*v = 0), and the inequality constraints (bounds).
Discussion (5 min): FBA predicts optimal flux distributions but assumes cells maximize growth. When might this assumption be wrong?
Assessment (5 min): Answer the reflection questions below.

Assessment

What does the steady-state constraint \(S \cdot v = 0\) mean biologically?
Why are exchange reactions important in FBA, and what do their bounds represent?
If you set glucose uptake to zero, what would FBA predict for biomass production?
What are the limitations of FBA compared to kinetic modeling?