Constraint-based analysis

Famili I, Forster J, Nielsen J, Palsson BO. Saccharomyces cerevisiae phenotypes can be predicted by using constraint-based analysis of a genome-scale reconstructed metabolic network. Proc Natl Acad Sci USA 2003 100 13134-9. 

Despite its widely recognized limitations, flux balance analysis has resulted in a large number of successful applications [35, 67, 72 74], including several extensions and refinements. See Ref. [247] for a recent review. Of particular interest are recent efforts to augment the stoichiometric balance equations with thermodynamic constraints providing a link between concentration and flux in the constraint-based analysis of metabolic networks [74, 149, 150]. For a more comprehensive review, we refer to the very readable monograph of Palsson [50]. 

Part II of this book represents the bulk of the material on the analysis and modeling of biochemical systems. Concepts covered include biochemical reaction kinetics and kinetics of enzyme-mediated reactions simulation and analysis of biochemical systems including non-equilibrium open systems, metabolic networks, and phosphorylation cascades transport processes including membrane transport and electrophysiological systems. Part III covers the specialized topics of spatially distributed transport modeling and blood-tissue solute exchange, constraint-based analysis of large-scale biochemical networks, protein-protein interactions, and stochastic systems. 

Analysis of biochemical systems, with their behaviors constrained by the known system stoichiometry, falls under the broad heading constraint-based analysis, a methodology that allows us to explore computationally metabolic fluxes and concentrations constrained by the physical chemical laws of mass conservation and thermodynamics. This chapter introduces the mathematical formulation of the constraints on reaction fluxes and reactant concentrations that arise from the stoichiometry of an integrated network and are the basis of constraint-based analysis. 

Figure 9.6 Small network example to illustrate the application of thermodynamic constraints in constraint-based analysis.

Introducing the chemical potential (or free energy) and the thermodynamic constraint provides a solid physical chemistry foundation for the constraint-based analysis approach to metabolic systems analysis. Treatment of the network thermodynamics not only improves the accuracy of the predictions on the steady state fluxes, but can also be used to make predictions on the steady state concentrations of metabolites. To see this, we substitute the relation between reaction Gibbs free energy (ArG ) of the th reaction and the concentrations of biochemical reactants... 

Mathematical optimization deals with determining values for a set of unknown variables x, X2, , x , which best satisfy (optimize) some mathematical objective quantified by a scalar function of the unknown variables, F(xi, X2, , xn). The function F is termed the objective function bounds on the variables, along with mathematical dependencies between them, are termed constraints. Constraint-based analysis of metabolic systems requires definition of the constraints acting on biochemical variables (fluxes, concentrations, enzyme activities) and determining appropriate objective functions useful in determining the behavior of metabolic systems. 

Applying mass-balance and thermodynamic constraints typically leaves one without a precisely defined (unique) solution for reaction fluxes and reactant concentration, but instead with a mathematically constrained feasible space for these variables. Exploration of this feasible space is the purview of constraint-based analysis. It has so far been left unstated that any application in this area starts with the determination of the reactions in a system, from which the stoichiometric matrix arises. This first step, network reconstruction, integrates genomic and proteomic data to determine carefully the enzymes present in an organism, cell, or subcellular compartment. The network reconstruction process is described elsewhere [107]. 

Special topics - explores spatially distributed systems, constraint-based analysis for large-scale networks, protein-protein interaction, and stochastic phenomena in biochemical... 

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