1. Flux Balance Analysis

2. 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

3. FBA Step I: system definition Step II: mass balance Step III: defining measurable fluxes Step IV: optimization The immediate goal is to identify the steady state of the system.

4. 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

5. 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).

6. Step II – mass balance Stoichiometric matrix S Flux matrix v S · v = 0 in steady state.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. FBA An E. coli (ECK12) system definition is available on the website of Palsson’s group.website of Palsson’s group Free LP package (GLPK, simplex) is freely available on the Internet.GLPK LP solvers are available in Matlab® optimization toolbox.Matlab® optimization toolbox FBA course at Palsson’s group website http://gcrg.ucsd.edu/classes/be203.htm http://gcrg.ucsd.edu/classes/be203.htm