Scaling of metabolism

West GB, Woodruff WH, Brown JH. Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci USA 2002 99 Suppl 1 2473-8. 

For the quantitative description of the metabolic state of a cell, and likewise which is of particular interest within this review as input for metabolic models, experimental information about the level of metabolites is pivotal. Over the last decades, a variety of experimental methods for metabolite quantification have been developed, each with specific scopes and limits. While some methods aim at an exact quantification of single metabolites, other methods aim to capture relative levels of as many metabolites as possible. However, before providing an overview about the different methods for metabolite measurements, it is essential to recall that the time scales of metabolism are very fast Accordingly, for invasive methods samples have to be taken quickly and metabolism has to be stopped, usually by quick-freezing, for example, in liquid nitrogen. Subsequently, all further processing has to be performed in a way that prevents enzymatic reactions to proceed, either by separating enzymes and metabolites or by suspension in a nonpolar solvent. 

West GB, Brown JH, Enquist BJ (1999) The fourth dimension of life fractal geometry and allometric scaling of organisms. Science 284 1677-1679 West GB, Woodruff WH, Brown JH (2002) Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci USA 99 2473-2478 Westerhoff HV, van Workum M (1990) Control of DNA structure and gene expression. Biomed Biochim Acta 49 839-853... 

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. 

Sato et al. (1991) expanded their earlier PBPK model to account for differences in body weight, body fat content, and sex and applied it to predicting the effect of these factors on trichloroethylene metabolism and excretion. Their model consisted of seven compartments (lung, vessel rich tissue, vessel poor tissue, muscle, fat tissue, gastrointestinal system, and hepatic system) and made various assumptions about the metabolic pathways considered. First-order Michaelis-Menten kinetics were assumed for simplicity, and the first metabolic product was assumed to be chloral hydrate, which was then converted to TCA and trichloroethanol. Further assumptions were that metabolism was limited to the hepatic compartment and that tissue and organ volumes were related to body weight. The metabolic parameters, (the scaling constant for the maximum rate of metabolism) and (the Michaelis constant), were those determined for trichloroethylene in a study by Koizumi (1989) and are presented in Table 2-3. 

In addition to the mechanistic simulation of absorptive and secretive saturable carrier-mediated transport, we have developed a model of saturable metabolism for the gut and liver that simulates nonlinear responses in drug bioavailability and pharmacokinetics [19]. Hepatic extraction is modeled using a modified venous equilibrium model that is applicable under transient and nonlinear conditions. For drugs undergoing gut metabolism by the same enzymes responsible for liver metabolism (e.g., CYPs 3A4 and 2D6), gut metabolism kinetic parameters are scaled from liver metabolism parameters by scaling Vmax by the ratios of the amounts of metabolizing enzymes in each of the intestinal enterocyte compart-... 

Figure 10.13 Hyphae of Fusarium alkanophllum from light hydrocarbons producing important amounts of metabolic water from the substrate. In cultures for more than 90 days, drops of water associated to the soluble degraded products were observed. Scale = 10.5 xm (Light Microscope image). (Reproduced from Marcanoa, 2002, by permission of Elsevier)...

Finally, Section X provides a summary of the results and outlines the path toward large-scale kinetic models of metabolism. 

A considerable improvement over purely graph-based approaches is the analysis of metabolic networks in terms of their stoichiometric matrix. Stoichiometric analysis has a long history in chemical and biochemical sciences [59 62], considerably pre-dating the recent interest in the topology of large-scale cellular networks. In particular, the stoichiometry of a metabolic network is often available, even when detailed information about kinetic parameters or rate equations is lacking. Exploiting the flux balance equation, stoichiometric analysis makes explicit use of the specific structural properties of metabolic networks and allows us to put constraints on the functional capabilities of metabolic networks [61,63 69]. 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

Consequently, we have to touch upon at least some operational issues to define our approach to the ways and means of constructing models of metabolism. At the most basic level, surveying the current literature, we face a strong dichotomy between a quest for elaborate large-scale models of cellular pathways and minimal (skeleton) models, tailored to explain specific dynamic phenomena only. 

Figure 4. Following the scheme described by Wiechert and Takors [97], a mathematical model of metabolism is easily constructed. However, in practice, a number of obstacles hamper the construction of large scale kinetic models.

Note that Eq. (6) includes thermodynamic equilibrium (v° = 0) as a special case. However, usually the steady-state condition refers to a stationary nonequilibrium state, with nonzero net flux and positive entropy production. We emphasize the distinction between network stoichiometry and reaction kinetics that is implicit in Eqs. (5) and (6). While kinetic rate functions and the associated parameter values are often not accessible, the stoichiometric matrix is usually (and excluding evolutionary time scales) an invariant property of metabolic reaction networks, that is, its entries are independent of temperature, pH values, and other physiological conditions. 

The stoichiometric matrix N is one of the most important predictors of network function [50,61,63,64,68] and encodes the connectivity and interactions between the metabolites. The stoichiometric matrix plays a fundamental role in the genome-scale analysis of metabolic networks, briefly described in Section V. Here we summarize some formal properties of N only. 

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