Metabolism network

This is not the place to expose in detail the problems and the solutions already obtained in studying biochemical reaction networks. However, because of the importance of this problem and the great recent interest in understanding metabolic networks, we hope to throw a little light on this area. Figure 10.3-23 shows a model for the metabolic pathways involved in the central carbon metabolism of Escherichia coli through glycolysis and the pentose phosphate pathway [22]. 

This has been done illustrating a feed-forward process [3]. Another application of these multistep reactions is the study of metabolic networks. Kier and colleagues have reported on such an example [4],... 

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. 

While metabolic engineers traditionally sought the rate-limiting enzyme to unlock flow through a pathway, now they understand that there may be many points of control and feedback with the metabolic network, and seek to empirically determine the dynamics of the interactions between rate controllers and other factors. For example, the sizes of metabolic precursor pools and the catabolism or sequestration of products affect accumulation as well as flux through the pathway. 

After measuring the fluxes through the metabolic network, it is necessary to determine the extent to which each pathway or enzyme controls the net fluxes. Metabolic control analysis (MCA) is a technique used to elucidate how flux control is distributed in a metabolic network, thereby providing the information for identification of potential targets for metabolic engineering [8],... 

How could such difficulties be avoided Shapiro lists minerals which could have served either as the first replicators or as highly selective polymerases. He also considers a further possibility life may have begun as a metabolic network of reactions which involved monomers the replicators may have evolved in a later evolutionary phase. The misgivings mentioned, and the open questions referred to in earlier chapters, indicate that a de novo synthesis of RNA under the conditions present on the young Earth was almost impossible. Thus, models were and are being looked for which could bypass as many as possible of the problems referred to. 

Schuster S et al. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechnol 2000 18 326-332. 

Nonetheless, the construction of explicit kinetic models allows a detailed and quantitative interrogation of the alleged properties of a metabolic network, making their construction an indispensable tool of Systems Biology. The translation of metabolic networks into ordinary differential equations, including the experimental accessibility of kinetic parameters, is one of the main aspects of this contribution and is described in Section III. 

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. 

Despite its predictive power and successful application on a variety of large-scale metabolic networks, stoichiometric analysis also encompasses a few inadequacies. In particular, stoichiometric analysis largely relies on the steady-state assumption and is not straightforwardly applicable to analyze complex time-dependent dynamics in metabolic systems. Similarly, stoichiometric analysis does not allow us to account for allosteric regulation, considerably delimiting its capabilities to predict dynamic properties. See also Section V.C for a discussion of the limits of stoichiometric analysis. 

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. 

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... 

We seek to describe the time-dependent behavior of a metabolic network that consists of m metabolic reactants (metabolites) interacting via a set of r biochemical reactions or interconversions. Each metabolite S, is characterized by its concentration 5,(f) > 0, usually measured in moles/volume. We distinguish between internal metabolites, whose concentrations are affected by interconversions and may change as a function of time, and external metabolites, whose concentrations are assumed to be constant. The latter are usually omitted from the m-dimensional time-dependent vector of concentrations S(t) and are treated as additional parameters. If multiple compartments are considered, metabolites that occur in more than one compartments are assigned to different subscripts within each compartment. 

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