Regulated Flux-Balance Analysis (rFBA)

1. Regulated Flux-Balance Analysis (rFBA) Speack: Zhu YANG 2006.10.04

2. Reference • Covert, M.W., Schilling, C.H., and Palsson, B.Ø. 2001. Regulation of gene expression in flux balance models of metabolism. J. Theor. Biol. 213: 73–88.

3. Background • FBA (Flux-Balance Analysis) Model hase assumed that all gene products in the metabolic reaction network are available to contribute to an optimal solution. • These regulatory effects have not been accounted for in previous FBA models, which leads to certain incorrect predictions of cellular-level behavior. • regulatory constraints are self-imposed by the organism, and presumably represent the result of an optimal evolutionary process. • Detailed deterministic and stochastic models require extensive information, such as temperature, substrate availability, the presence of signaling molecules, and other environmental parameters, many of which have yet to be completely specified.

4. Methods

5. Constrains-based analysis

6. 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.

7. Representing Transcriptional Regulatory Constraints • Cells are subject to both invariant and adjustable constraints. • Invariant constraints are physico-chemical in origin and include stoichiometric, capacity and thermodynamic constraints. • Adjustable constraints are biological in origin, and they can be used to further limit allowable behavior. These constraints will change in a condition-dependent manner.

8. Regulatory constraints change the solution space.

9. Regulatory Constructure Described Boolean Logic Representation

10. Time Course of Growth • The quasi-steady-state assumption • The experimental time is divided into small time steps, . • Beginning at where the initial conditions of the experiment are specified,

11. Example of a sample network

12. Reactions and Regulatory Rules

13. Instances of Transcriptional Regulation were Examined • Preferential carbon source uptake/catabolite repression • Anaerobic growth. • Amino acid biosynthesis pathway repression. • Transcriptional regulation to maintain concentration levels of important metabolites.

14. Diauxie on Two Carbon Sources

15. Aerobic/Anaerobic-Diauxie

16. Growth on Carbon and Amino AcidWith Carbon in Excess

17. Growth on Carbon and Amino AcidWith Amino Acid in Excess

18. Complex Medium

19. Complex Medium (Cont’d)

20. Discussion • Major advantages over FBA • Quantitative dynamic simulation of substrate uptake, cell growth and by-product secretion; • Qualitative simulation of gene transcription events and the presence of proteins in the cell; • Investigation of the systemic e!ects of imposing temporary regulatory constraints on the solution space.

21. Discussion (Cont’d) • The sample network examined here, although two orders of magnitude smaller than the metabolic networks of commonly studied bacteria, exhibits surprisingly complex behavior, as shown by the unusual intermediate flux distributions during growth on the complex medium. • Besides simply determining whether or not regulatory constraints are implemented, the environment also has an important influence on the regulatory constraints themselves. • The use of Boolean logic to represent genetic regulatory networks qualitatively has grown in sophistication, including such features as multilevel logic variables and asynchronous updating of protein synthesis