Whole-organ metabolic modeling

Darveau et al. (2002, 2003) propose that the relationship between body mass and metabolic rate reflects the contribution of multiple factors - ATP-utilization processes in parallel, supply processes in series - that each have different power functions. This hierarchical layering results in an allometric cascade that has different scaling implications for different measures of metabolism. They contend that only a multiple-factor account, and not West s (or any) single-cause account, can explain the scaling difference between basal and maximum metabolic rate (Bishop, 1999). However, the mathematical formulation of their model has been severely criticized (Banavar etal., 2003 West etal., 2003), and in any case it does not provide an account of why individual processes scale as power functions of mass or why the causal cascade results in a whole-organism metabolism that approximates the 3/4 rule (Bokma, 2004 West et al., 2003 West and Brown, 2004). 

PBPK models have also been used to explain the rate of excretion of inhaled trichloroethylene and its major metabolites (Bogen 1988 Fisher et al. 1989, 1990, 1991 Ikeda et al. 1972 Ramsey and Anderson 1984 Sato et al. 1977). One model was based on the results of trichloroethylene inhalation studies using volunteers who inhaled 100 ppm trichloroethylene for 4 horns (Sato et al. 1977). The model used first-order kinetics to describe the major metabolic pathways for trichloroethylene in vessel-rich tissues (brain, liver, kidney), low perfused muscle tissue, and poorly perfused fat tissue and assumed that the compartments were at equilibrium. A value of 104 L/hour for whole-body metabolic clearance of trichloroethylene was predicted. Another PBPK model was developed to fit human metabolism data to urinary metabolites measured in chronically exposed workers (Bogen 1988). This model assumed that pulmonary uptake is continuous, so that the alveolar concentration is in equilibrium with that in the blood and all tissue compartments, and was an expansion of a model developed to predict the behavior of styrene (another volatile organic compound) in four tissue groups (Ramsey and Andersen 1984). 

A recent paper clearly highlighted the limitations of in vitro systems in modeling whole-organism responses, which should be considered when developing biomarkers of in vivo toxicity. Dere and colleagues (58) compared the temporal gene expression profiles of Hepalclc mouse hepatoma cells and of the mice liver after treatment with a dioxin. The analysis revealed that Hepalclc cells were able to model the induction of xenobiotic metabolism in vivo. On the other hand, responses associated with cell cycle progression and proliferation were unique to the in vitro system, while lipid metabolism and immune responses were not replicated effectively in the Hepalclc cells. 

Using an erythrocytes-containing medium for perfusion one has to take into account the putative involvement of the erythrocytes themselves with respect to uptake of the candidate compound. Therefore, not only the erythrocyte-free perfusate but also the erythrocytes fraction should be included in the analysis of the candidate compound, separately. In our hands the model of isolated perfused liver is metabolically active for up to 3 hours and during this time no decline in hepatic metabolic activity becomes obvious. However, bile flow declined during the perfusion experiments. Therefore, our total perfusion time of isolated livers in our standard experimental setup is limited to 2 hours. The tissue level of the candidate compound analyzed after 2 hours in the liver is a measure for the total amount of compound in the whole organ. This does not necessarily mean the presence of the candidate compound in hepatocytes but additionally in the capillary and biliary space of the liver. 

This section mainly builds upon classic biochemistry to define the essential building blocks of metabolic networks and to describe their interactions in terms of enzyme-kinetic rate equations. Following the rationale described in the previous section, the construction of a model is the organization of the individual rate equations into a coherent whole the dynamic system that describes the time-dependent behavior of each metabolite. We proceed according to the scheme suggested by Wiechert and Takors [97], namely, (i) to define the elementary units of the system (Section III. A) (ii) to characterize the connectivity and interactions between the units, as given by the stoichiometry and regulatory interactions (Sections in.B and II1.C) and (iii) to express each interaction quantitatively by... 

Following the scheme presented in Fig. 4, we now have assembled the building blocks that are necessary for the formulation of an explicit kinetic model. Although currently often restricted to medium-scale representations of metabolic pathwaysor (sub)networks, the parts may now be organized into a coherent whole, building the kinetic model of a metabolic network. 

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