Metabolic network analysis stoichiometric reactions

Nonetheless, the topological and stoichiometric analysis of metabolic networks is probably the most powerful computational approach to large-scale metabolic networks that is currently available. Stoichiometric analysis draws upon extensive work on the structure of complex reaction systems in physical chemistry in the 1970s and 1980s [59], and can be considered as one of the few theoretically mature areas of Systems Biology. While the variety and amount of applications of stoichiometric analysis prohibit any comprehensive summary, we briefly address some essential aspects in the following. 

Stoichiometric analysis goes beyond topological arguments and takes the specific physicochemical properties of metabolic networks into account. As noted above, based on the analysis of the nullspace of complex reaction networks, stoichiometric analysis has a long history in the chemical and biochemical sciences [59 62]. At the core of all stoichiometric approaches is the assumption of a stationary and time-invariant state of the metabolite concentrations S°. As already specified in Eq. (6), the steady-state condition... 

Besides the two most well-known cases, the local bifurcations of the saddle-node and Hopf type, biochemical systems may show a variety of transitions between qualitatively different dynamic behavior [13, 17, 293, 294, 297 301]. Transitions between different regimes, induced by variation of kinetic parameters, are usually depicted in a bifurcation diagram. Within the chemical literature, a substantial number of articles seek to identify the possible bifurcation of a chemical system. Two prominent frameworks are Chemical Reaction Network Theory (CRNT), developed mainly by M. Feinberg [79, 80], and Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83]. An analysis of the (local) bifurcations of metabolic networks, as determinants of the dynamic behavior of metabolic states, constitutes the main topic of Section VIII. In addition to the scenarios discussed above, more complicated quasiperiodic or chaotic dynamics is sometimes reported for models of metabolic pathways [302 304]. However, apart from few special cases, the possible relevance of such complicated dynamics is, at best, unclear. Quite on the contrary, at least for central metabolism, we observe a striking absence of complicated dynamic phenomena. To what extent this might be an inherent feature of (bio)chemical systems, or brought about by evolutionary adaption, will be briefly discussed in Section IX. 

The catabolism of 2 includes 118 reactions many of which are reversible (Fig. 3.5). Since kinetic data on micro-metabolites are difficult to determine experimentally, and in order to obtain an overall view of the xenobiotic metabolism, a stoichiometric model of the full network of degradation pathways of 2 was set up in addition to the network shown in Fig. 3.5. This network was then analyzed by means of elementary flux mode analysis [78]. 

A more popular form of stoichiometric analysis is the analysis of flux distributions that are consistent with system steady state (Note that in the terminology of metabolic modelling, the rate of a reaction at system steady state is referred to as a flux.) This type of analysis can be done directly on the N matrix because of its central role in the description of the mass balances of all the variable intermediates in a network. 

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