State flux maximization

The selective flux maximization from the FOIST scheme shown in Fig. 2 is achieved by altering the spatial profile of the initial state to be subjected to the photolysis pulse and since changes in flux are due to the flow of probability density, it is useful to examine the attributes of the probability density profiles from the field optimized initial states. 

Enforcing stoichiometric, capacity, and thermodynamic constraints simultaneously leads to the definition of a solution space that contains all feasible steady-state flux vectors. Within this set, one can find a particular steady-state metabolic flux vector that optimizes the network behavior toward achieving one or more goals (e g., maximize or minimize the production of certain metabolites). Mathematically speaking, an objective function has to be defined that needs to be minimized or maximized subject to the imposed constraints. Such optimization problems are typically solved via linear programming techniques. 

The problem of controlling the outcome of photodissociation processes has been considered by many authors [63, 79-87]. The basic theory is derived in detail in Appendix B. Our set objective in this application is to maximize the flux of dissociation products in a chosen exit channel or final quantum state. The theory differs from that set out in Appendix A in that the final state is a continuum or dissociative state and that there is a continuous range of possible energies (i.e., quantum states) available to the system. The equations derived for this case are... 

Regardless of the flux mechanism, it is clear upon examination of permeability expressions that flux is proportional to the concentration differential across the total barrier to mass transport. This flux is maximal in a given system for a permeant when the penetrating agent is present in the applied phase in a saturated state. There are many situations of pharmaceutical interest where this solubility... 

Fig. 16. Bifurcation diagram of temporal dissipative structures, c (maximal amplitude of the oscillation minus the homogeneous steady-state value) is sketched versus B for a two-dimensional system with zero flux boundary conditions. The first bifurcation occurs at B = Bn and corresponds to a stable homogeneous oscillation. At B, two space-dependent unstable solutions bifurcate simultaneously. They become stable at B a and Bfb. Notice that as it is generally the case Bfa Bfb.

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... 

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