Mathematical modeling computational metabolic models

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. 

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. 

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). 

The computer simulation is one of the essential means to investigate dynamic and steady-state behavior as well as control of metabolic pathways. A metabolic simulator is a computer program that performs one or several of the tasks including solving the steady state of a metabolic pathway, dynamically simulating a metabolic pathway, or calculating the control coefficient of a metabolic pathway. Its mathematical model generally consists of a set of differential equations derived from rate equations of the enzymatic reactions of the pathway. 

Figure 3. This kinetic model for zinc in humans was based on averaged data obtained following oral and i.v. administration of Zn to 17 patients with abnormalities of taste and smell. The compartmental model used all kinetic data from Zn activity in plasma, red blood cells, urine, liver, and thigh as well as stable zinc parameters, including dietary intake, serum, and urinary concentration. The SAAM27 computer program was used to obtain the simplest set of mathematical relationships that would satisfy the data characteristics for each measurement time in the study and remain consistent with accepted concepts of zinc metabolism. Although the short physical half-life of Zn limited the data collection period, this model allowed for analysis of the rapid phases of zinc metabolism (about 10% of total body zinc) and derivation of a number of fundamental steady state...

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