Flux Balance Analysis

FBA articles

Advances in flux balance analysis. K. Kauffman, P. Prakash, and J. Edwards. Current Opinion in Biotechnology 2003, 14:4910496

Analysis of optimality in natural and perturbed metabolic networks. D. Segre et al. PNAS 2002, 99:1511-15117

FBA

Step I: system definitionStep II: mass balanceStep III: defining measurable fluxesStep IV: optimization

The immediate goal is to identify the steady state of the system.

Step I – system definition

All reactions and metabolites Regulations could be neglected in primitive

model

Transport mechanisms, definition of system boundary Diffusion across membranes Active transport systems

A model system comprising three metabolites (A, B and C) with three reactions (internal fluxes, vi

including one reversible reaction) and three exchange fluxes (bi).

Step II – mass balance

Stoichiometric matrix SFlux matrix vS · v = 0 in steady state.

Mass balance equations accounting for all reactions and transport mechanisms are written for each species. These equations are then rewritten in matrix form. At steady state, this reduces to S ·

V=0.

Step III – defining measurable fluxes & constraints

Dependences among components of flux vector (? – to be confirmed)

Ranges of fluxes, including hypothesis-driven values and experimental measurements V < 0 to allow reversible reactions

Constraints C=0

At this stage, feasible solution space for v could be solved. Analysis of v could be used to study organizing principles of metabolism.

The fluxes of the system are constrained on the basis of thermodynamics and experimental

insights. This creates a flux cone corresponding to the metabolic capacity of the organism.

Step 4 – optimization

Define of objective function Z E.g., biomass production in defined proportion.

A well-formulated optimization problem P: Maximize (or min.) Z, subject to,

1. S · v = 0;

2. C = 0;

If Z is linear, then P could be solved through LP techniques.

Optimization of the system with different objective functions (Z). Case I gives a single optimal point, whereas case II gives multiple optimal points lying

along an edge.

FBA

An E. coli (ECK12) system definition is available on the website of Palsson’s group.

Free LP package (GLPK, simplex) is freely available on the Internet.

LP solvers are available in Matlab® optimization toolbox.

FBA course at Palsson’s group website http://gcrg.ucsd.edu/classes/be203.htm