Constraint-based analysis of biochemical systems

When mechanistic information is available or obtainable for the components of a system, it is possible to develop detailed analyses and simulations of that system. Such analyses and simulations may be deterministic or stochastic in nature. (Stochastic systems are the subject of Chapter 11.) In either case, the overriding philosophy is to apply mechanistic rules to predict behavior. Often, however, the information required to develop mechanistic models accounting for details such as enzyme and transporter kinetics and precisely predicting biochemical states is not available. Instead, all that may be known reliably about certain large-scale systems is the stoichiometry of the participating reactions. As we shall see in this chapter, this stoichiometric information is sometimes enough to make certain concrete determinations about the feasible operation of biochemical networks. 

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. 

As we shall see, linear algebraic constraints arising from steady state mass balance form the basis of metabolic flux analysis (MFA) and flux balance analysis (FBA). Thermodynamic laws, while introducing inherent non-linearities into the mathematical description of the feasible flux space, allow determination of feasible reaction directions and facilitate the introduction of reactant concentrations to the constraint-based framework. 

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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. 

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. 

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... 

One can view biochemical systems as represented at the most basic level as networks of given stoichiometry. Whether the steady state or the kinetic behavior is explored, the stoichiometry constrains the feasible behavior according to mass balance and the laws of thermodynamics. As we have seen in this chapter, some analysis is possible based solely on the stoichiometric structure of a given system. Mass balance provides linear constraints on reaction fluxes non-linear thermodynamic constraints provide information about feasible flux directions and reactant concentrations. 

Several other natural products systems have been studied, some quite extensively, by NMR methodology, however space constraints prohibt detailed discussion of these systems therefore only important leading references will be given. Extensive NMR studies on amino acids and small peptides have been performed by Lauterwein and coworkers [116-119], by Fiat and coworkers [120-123] and others [124]. Several studies have used l O-enriched dioxygen and carbon monoxide to study by NMR techniques the interactions of these biochemically important small molecules with various proteins [125-128]. A number of investigators have explored the properties and interactions of nucleic acid bases [129,130], nucleosides [131,132], nucleotides [133-138] and one report has appeared in which NMR spectroscopy approaches were applied to the study of small molecule-DNA interactions [139]. A recent report describes the careful analysis of the effect of structure on NMR chemical shifts of over forty hydroxyterpenoids [140]. A study of the 1 0 NMR spectroscopy of over thirty steroid ketones, acids, esters and alcohols enriched with has recently appeared [141]. 

E. coli metabohsm. The effects of gene deletions in the central metabolic pathways on the ability of the in silico metabolic networks to support growth were assessed and the in silico predictions were compared with experimental observations. It was shown that, based on stoichiometric and capacity constraints, the in silico analysis was able to qualitatively predict the growth potential of mutant strains in 86% of the cases examined. The synthesis of in silico metabolic genotypes based on genomic, biochemical and strain-specific information is possible, and systems analysis methods are available to analyze and interpret the metabolic phenotype. ... 

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