Flux balance analysis . computational

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. 

Equation (64) justifies the application of flux-balance analysis even in the face of (i) fast short-term fluctuations and (ii) periodic long term for example, circadian variability. The steady state balance condition restricts the feasible steady-state flux distributions to the flux cone P = v° G IRr IVv0 = 0. The reduction of the admissible flux space, with some of its algebraic properties already summarized in Section III.B, is exploited by several computational approaches, most notably Flux Balance Analysis (FBA) [61, 71, 235] and elementary flux modes (EFMs) [96, 236 238],... 

Flux balance analysis has been used for over 15 yr to study the metabolic flux distribution. Initially, the applications of FBA were primarily educational however, recently, the utility has grown. The FBA has been applied to study the effect of gene deletions, the design of bacterial metabolism for industrial and environmental applications, or for the computational exploration of cellular physiology. Metabolic engineering has been successfully applied to engineer micro-organisms to produce valuable biochemicals... 

Kaleta C, de Figueiredo LF, Werner S, Guthke R, Ristow M, Schuster S (2011) In Silico Evidence for gluconeogenesis from fatty acids in humans. PLoS Comput Biol 7 el002116 Kauffman KJ, Prakash P, Edwards JS (2003) Advances in flux balance analysis. Curr Opin Biotechnol 14 491-496... 

W. J. Heuett and H. Qian. Combining flux and energy balance analysis to model large-scale biochemical networks../. Bioinform. Comput. Biol., 4 1227-1243,... 

Kobayashi (143) presented the first computer simulations that considered the determination of the crystal radius as part of the analysis but avoided the capillary problem by considering a flat melt-ambient surface, which is consistent with <)>o = 99°. Calculations were performed for a fixed crystal radius, and then the growth rate was adjusted to balance the heat flux into the crystal. Crowley (148) was the first to present numerical calculations of a conduction-dominated heat-transfer model for the simultaneous determination of the temperature fields in crystal and melt and of the shapes of the melt-crystal and melt-ambient surfaces for an idealized system with a melt pool so large that no interactions with the crucible are considered. She used a time-dependent formulation of the thermal-capillary model and computed the shape of an evolving crystal from a short initial configuration. 

We have defined the flux equations for the free species as well as the adsorbed species. Now we substitute them into the mass balance equation to obtain the necessary mass balance equation for computational analysis. This is done next. 

The authors analysis (38) uses film theory on the gas-side and penetration theory on the liquid side. The penetration theory was adopted as offering a more realistic basis to describe the diffusion and reaction. The set of parabolic partial differential equations which describe this diffusion and reaction were solved in conjunction with the customary boundary conditions, plus a number of subsidiary relationships which ensure electrical neutrality and are compatible with the initial loadings of reagent amine. Equilibrium was assumed to be established in the bulk, but otherwise the fluxes were not jointed to the overall material balances on the gas and liquid phases. Even so, the computation appears quite formidable. 

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