Constraint-based analysis mass-balance constraints

Whereas detailed dynamic models can precisely answer questions on cellular behavior, the widespread application of such approaches has been hampered by the lack of kinetic information. In the absence of kinetic information, a method known as flux balance analysis (FBA) has been developed to analyze the metabolic capabilities of a cellular system based on mass balance constraints [Varma and Palsson 1994 Edwards et al. 1999 Edwards and Palsson 2000],... 

In close analogy to flux-balance analysis, we thus extend the constraint-based description of metabolic networks to incorporate (local) dynamic properties. Recall the expansion of the mass-balance equation into a Taylor series, already given in Eq. (68)... 

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. 

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. 

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]. 

Metabolic networks can be quantitatively and qualitatively studied without enzyme kinetic parameters by using a constraints-based approach. Metabolic networks must obey the fundamental physicochemical laws, such as mass, energy, redox balances, diffusion, and thermodynamics. Therefore, when kinetic constants are unavailable, cellular function can still be mathematically constrained based on the mass and energy balance. Flux balance analysis (FBA) is a mathematical modeling framework that can be used to study the steady-state metabolic capabilities of cell-based physicochemical constraints. ... 

The equality constraints composed of the mass and heat balances and the performance equations in each subsystem, thermodynamic properties of the flows, and specifications for design are represented by the functions h which are in the form of n equations with m+n variables. These equations are easily arranged in the order of precedence based on structural analysis. The number of independent variables (parameters), y, corresponds to the degrees of freedom in the system. When the value of the parameters is given, n equations are solved with respect to n variables, z. Thereupon, the inequality constraints, if any, are checked and the objective functions are calculated. Therefore, the problem is rewritten simply as follows ... 

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