Stoichiometric network analysis

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. 

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. 

Closely related to the approach considered here are the formal frameworks of Feinberg and Clarke, briefly mentioned in Section II. A. Though mainly devised for conventional chemical kinetics, both, Chemical Reaction Network Theory (CRNT), developed by M. Feinberg and co-workers [79,80], as well as Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83], seek to relate aspects of reaction network topology to the possibility of various... 

B. L. Clarke, Stoichiometric network analysis. Cell Biophys. 12, 237 253 (1988). 

Doubtlessly, there are also other computational analyses to be performed in the future, such as stochastic simulations, stoichiometric network analysis, sensitivity analysis, etc. However, for this initial survey, we only take this absolute minimum into account, while listing additional features of the respective software tools. 

Implications of Some Theorems from Stoichiometric Network Analysis (SNA) with Respect to Stability and Function Biochemical Systems... 

Additional Criteria from Stoichiometric Network Analysis (SNA)... 

Clarke BL (1992) Stoichiometric network analysis of the oxalate-persulfate-silver osdllator. J Chem Phys 97 2459-2472 Clarke BL (1995) What is stoichiometric network analysis Web site Alberta University at Edmonton (no longer online) Clemens S, Palmgren MG, Kramer U (2002) A long way ahead understanding and engineering plant metal accumulation. Trends Plant Sci 7 309-315... 

Franzle S, Markert B (2000b) The biological system of the elements (BSE). Part II a theoretical model for establishing the essentiality of chemical elements. The application of stoichiometric network analysis to the biological system of the elements. Sci Tot Environ 249 223-241 Franzle S, Markert B (2002a) The biological system of the elements (BSE) - a brief introduction into historical and applied aspects with special reference on ecotoxicological identity cards for different element species (f.e.. As and Sn). Environ PoUut 120 27-45... 

Franzle S, Markert B (2003) Carcinogenesis and chemotherapy viewed from the perspective of stoichiometric network analysis (SNA) what can the biological system of the elements contribute to an understanding of tumour induction by elemental chemical noxae (e.g. NF+, Cd +) and to an understanding of chemotherapy www.thesdentificworld. com. DOl 2003.202.tsw... 

For this purpose, experimental results on interelementary correlations, mechanisms of take-up and biological functions must first be gathered (Figure 12.1) (Markert 1994a), and then corroborated by theoretical aspects from stoichiometric network analysis (Fraenzle and Markert 2000a,b). The latter method permits the prediction as to whether - given its properties - a chemical element might be essential at all and, if so. 

Feaenzle S and Maekeet B (2000a) The Biological System of the Elements. Part IT. a theoretical model for establishing the essentiality of chemical elements. The application of Stoichiometric Network Analysis to the Biological System of the Elements. Sci Total Environ 249 223 - 241. 

As this example shows, stoichiometric network analysis yields only possibilities of reaction mechanisms, it does not lead to the determination of which of many possible reaction pathways corresponds to experiments. We need to know the rate coefficients of the system to determine paths in the system by which reactants proceed to form products. This distinction has been overlooked in a number of studies on complex biochemical reacdon mechanisms (see Schilling et al. [82] and references therein). 

Acknowledgments This chapter is based mainly on work published in refs. [1-9], where the ideas of the stoichiometric network analysis [10] were ntihzed to identify several distinct topological features in chemical networks that provide oscillatory instabilities and from that derive a classification system for chemical oscillators and species taking part in these oscillations. 

By the stoichiometric network analysis of the proposed model, it was shown that the overall process of hydrogen peroxide decomposition into the water and oxygen (reaction (D)) could be realized by four reaction pathways. They are given in Table 8.1. 

Cupid, Z. and Kolar-Anid, Lj., Contration of the complex model by the stoichiometric network analysis, in Advanced Sciences and Technology of Sintering, Stojanovic, B.D., Shorokhod, V.V., Nikolic, M.V., Eds., Kluwer Acad. Planum Publ, New York, 1999, pp. 75-80. 

A still more ambitious approach has been pioneered by Clarke (1976, 1980). His stoichiometric network analysis attempts to solve both the network stability and the stability diagram problems by using sophisticated mathematical techniques to identify critical subnetworks within a complex mechanism that can result in instabihty. The problem can be converted into the geometrical problem of finding the vertices, edges and higher dimensional faces of a convex polyhedron (polytope) in a high-dimensional space. 

---