Mathematical models metabolism

In the case of dmg interactions involving metabolic inhibition, little increase in the substrate concentration is expected when the inhibition constant (K ) determined in in vitro studies using human liver samples is larger than the inhibitor concentration in vivo. Various approaches have been adopted using mathematical models in attempts to quantitatively predict in vivo dmg interactions from in vitro data [5]. 

It is important that chemical engineers master an understanding of metabolic engineering, which uses genetically modified or selected organisms to manipulate the biochemical pathways in a cell to produce a new product, to eliminate unwanted reactions, or to increase the yield of a desired product. Mathematical models have the potential to enable major advances in metabolic control. An excellent example of industrial application of metabolic engineering is the DuPont process for the conversion of com sugar into 1,3-propanediol,... 

Femandez JG, Humbert BE, Droz PO, et al. 1977. Trichloroethylene exposure. Simulation of uptake, excretion and metabolism using a mathematical model. Br J Ind Med 34 43-55. 

Morgan, J.A. and Rhodes, D., Mathematical modeling of plant metabolic pathways, Metabol. Eng. 4, 80, 2002. 

Gruetter, R., Seaquist, E. R. and Ugurbil, K. A mathematical model of compartmentalized neurotransmitter metabolism in the human brain. Am. J. Physiol. 281, E100-112, 2001. 

Mathematical modeling of radiotracers of the radiotracer uptake to obtain the biological parameters of interest (receptor density, affinity, glucose metabolism, etc.) plays an extremely important role in PET and SPECT imaging, much more so than in many other areas of imaging. 

HEINRICH, R., RAPOPORT, S.M., RAPOPORT, T.A., Metabolic regulation and mathematical models, Progr. Biophys. Mol. Biol., 1977,32,1-82. 

When evaluating the safety of chemicals in humans, it is very important to know the fate of chemicals in the human body and the amounts of exposure in daily activity. This section reviews the metabolic reactions of pyrethroids in humans, and the biomonitoring of pyrethroid metabolites in human urine for the exposure assessment. Mathematical modeling is a useful tool to predict the fate of chemicals in humans. This section also deals with the recent advance of mathematical modeling of pyrethroids to predict the pharmacokinetics of pyrethroids. 

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. 

As outlined in the previous section, there is a hierarchy of possible representations of metabolism and no unique definition what constitutes a true model of metabolism exists. Nonetheless, mathematical modeling of metabolism is usually closely associated with changes in compound concentrations that are described in terms of rates of biochemical reactions. In this section, we outline the nomenclature and the essential steps in constructing explicit kinetic models of metabolic networks. 

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.

To illustrate the actual importance of dynamic properties for the functioning of metabolic networks, we briefly describe and summarize a recent computational study on a model of human erythrocytes [296]. Erythrocytes play a fundamental role in the oxygen supply of cells and have been subject to extensive experimental and theoretical research for decades. In particular, a variety of explicit mathematical models have been developed since the late 1970s [108, 111, 114, 123, 338 341], allowing us to test the reliability of the results in a straightforward way. 

H. G. Holzhtitter, G. Jacobasch, and A. Bisdorff, Mathematical modeling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate kinase deficient red blood cells. Eur. J. Biochem. 149(1), 101 111 (1985). 

R. Schuster and H. G. Holzhiitter, Use of mathematical models for predicting the metabolic effect of large scale enzyme activity alterations. Application to enzyme deficiencies of red blood cells. Eur. J. Biochem. 229(2), 403 418 (1995). 

M. Rizzi, M. Baltes, U. Theobald, and M. Reuss, In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae-. II. Mathematical model. Biotechnol. Bioeng. 55, 592 608 (1997). 

H. Assmus, Mathematical modeling of potato tuber carbohydrate metabolism. Ph.D. thesis, Oxford Brookes University (2005). 

C. De Maria, D. Grassini, F. Vozzi, B. Vinci, A. Landi, A. Ahluwalia, and G. Vozzi, Hemet Mathematical model of biochemical pathways for simulation and prediction of hepatocyte metabolism. Comput. Methods Programs Biomed. (2008). 

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