Matrix pathway analysis

Fig. 2.1 (continued) fixed flux r, = 1. Metabolic Pathway Analysis The elementary mode matrix EM of this network calculated by METATOOL contains 11 unique EMs, 5 of which are ExPas (shown in asterisks), (c) Pictorial Representation ExPas above) and EMs below) calculated for this metabolic network, (d) Geometric Interpretation of Analysis The admissible polyhedral flux cone represents all possible pathways within the network spaimed by 5 ExPas. MFA identifies a pathway that lies within the cone and is in accordance with the measured fluxes, while FBA also finds a single pathway that solves the objective function. MPA finds all genetically independent pathways within the admissible flux cone. ExPas circles) and EMs triangles)... 

The basic idea is very simple In many scenarios the construction of an explicit kinetic model of a metabolic pathway is not necessary. For example, as detailed in Section IX, to determine under which conditions a steady state loses its stability, only a local linear approximation of the system at this respective state is needed, that is, we only need to know the eigenvalues of the associated Jacobian matrix. Similar, a large number of other dynamic properties, including control coefficients or time-scale analysis, are accessible solely based on a local linear description of the system. 

Proceeding with the large-R analysis of the ionization matrix element, (f V i), we find that at large Kr2-X separations it decreases as 1/R r2 x. As a result, the contribution of the two-electron recombination - ionization pathway to the decay width depends on the cluster geometry as l/-R r Kr Kr2-x-Since the decomposition of the (Kr+)2X cluster along the Kr+-Kr+ coordinate automatically means elongation of the Kr2-X distance as well, the power law exponents are effectively summed, resulting in the l/R Kr dependence. A detailed analysis shows that this type of power law is characteristic of all the possible decay pathways. 

Another application of the analysis of the stoichiometric matrix is flux balance analysis (Edwards et al. 2002). Often the number of fluxes in the system exceeds the number variable metabolites making equation (3) an underdetermined set of linear equations, that is, many different combinations of fluxes are consistent with system steady state. One approach is to measure the fluxes that enter and exit the cell. Because intracellularly there are many redundant pathways, this does not enable one to determine all fluxes. Isotope labelling may help then (Wiechert 2002). Another approach to then find a smaller number of solutions is to postulate that the solution should satisfy an additional objective. This objective is taken to be associated with optimal functioning of the network, for instance maximization of some flux or combination... 

---