Mathematical modeling cellular metabolism

These differences probably contribute to the fact that mathematical modeling is, as yet, not seen as a mainstream research tool in many areas of molecular biology. However, as will be described in the remainder of this chapter, many obstacles in the construction of kinetic models of cellular metabolism can be addressed using a combination of novel and established experimental and computational techniques, enabling the construction of metabolic models of increasing complexity and size. 

The systematization of biological data through mathematical modeling is not a trivial task and requires the intensive use of material and human resources. Moreover, the models often incorporate experimental uncertainties that do not always allow the identification of the trends of the culture, with the desired precision. Figure 8.1 summarizes the main types of models applied to the description of cellular metabolism, according to the classification proposed by Tsuchiya et al., (1966). 

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. ... 

Finally, mathematical modeling in biology can provide valuable insight into the integrative behavior of cellular networks. For example, FBA can be used to predict the metabolic by-products in E. coli that are formed during aerobic and anaerobic metabo-lism.f Furthermore, FBA has been utilized to generate several novel hypotheses regarding the function of the E. coli metabolic network. These were demonstrated to be consistent with available experimental data.P"... 

The calculation of metabolic fluxes based on isotopomer distribution has gained importance as a quantitative and reliable tool for the study of cellular physiology. Metabolic fluxes are mainly calculated during steady-state conditions, which limits their applicability to scale-down dynamic studies. Nevertheless, research efforts with labeling experiments and mathematical models have allowed important advances in the dynamic C-based metabolic flux analysis [37-39], from which scale-down studies would be much benefited. An interesting example... 

A kinetic model consists of a set of mathematical expressions that relate the rates of cellular growth and metabolism to the composition of the medium. With... 

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