Reaction group control coefficient

Components are commonly represented as nodes in the metabolic network. These nodes can act as branch points if the number of input and output fluxes is not equivalent. Non-essential reactions around a node can be collected into reaction groups the coefficients of their fluxes, in general termed the metabolic flux coefficients (in analogy to rate coefficients), can be rearranged as group control coefficients. 

The Arrhenius plot of 1/r for benzophenone in poly(methyl acrylate) (PMA) showed another break at 40 °C (above T of PM A), which corresponds to the crossover of k j given by Eq. (14) from a diffusion-controlled to an activation-controlled reaction. The diffusion coefficient D for reacting carbonyl groups calculated from the values of 1/t and B also showed a break at each transition temperature, as exemplified in Fig. 8 for PMMA, polystyrene, and polycarbonate. It should be iK>ted that D in Fig. 8 refers to the reacting functional groups but not to the molecule. The diffusion proc at temperatures below T would be caused by rotation of the benzojdienone molecule and by the cooperative motion of a few successive monomer units of the matrix polymer. Nevertheless, the values of D in these polymers at 100 °C are comparable to the value of D = 5.6 x 10 an /s for mass diffusion of ethylbenzene in polj tyrene at 30 °C. The reaction radius R was estimated to be 3-5 A. The transition temperatures... 

This traditional approach of MCA can be considered to be bottom up since all of the individual enzyme flux control coefficients are determined in order to describe the control structure of a large network. A top down approach has also been described, which makes extensive use of lumping of reactions together to determine group flux control coefficients [19]. These can give some information about the overall control of a metabolic network, without its complete characterization. 

Hydrazones have also been used as azomethine imine precursors to achieve cycloadditions.157 Proto-nated hydrazones act under suitable conditions as quasi-azomethine imines in polar [3+ + 2] cycloadditions. Thus, r.cetaldehyde phenylhydrazone (201) was found to react with styrene in the presence of sulfuric acid in a regiospecific manner to give pyrazolidine (203 Scheme 47) as a diastereomeric mixture.157 The most commonly used azomethine imine has a phenyl group attached to one end of the dipole and hence has a raised HOMO relative to the unsubstituted system. Because the coefficients at the terminal atoms of the dipole are smaller in the LUMO than they are in the HOMO, the phenyl group does not lower the energy of the LUMO as much as it raises the energy of the HOMO. With electron-deficient di-polarophiles like methyl acrylate, the reaction is dipole HOMO-controlled, and mixtures can be expected. In fact, a 1 1 mixture of regioisomers was obtained in the reaction of (201) with acrylonitrile (equation 9).157... 

With Z-substituted dipolarophiles and phenyl azide, the situation is again delicately balanced and only just dipole-HO-controlled (9.5 eV against 10.7 eV). For the dipole-HO-controlled reaction, we should expect to get adducts oriented as in Fig. 6.36a. However, a phenyl group reduces the coefficient at the neighbouring atom both for the HOMO and for the LUMO, and this will reduce the polarisation of the HOMO. Conversely, it will increase the polarisation for the LUMO and hence increase the effectiveness of the interaction of the LUMO of the dipole with the HOMO of the dipolarophile, as in Fig. 6.36b. The difference in... 

The reaction is rotationally controlled (i.e., 3 is rate determining) and the experimental rate coefficient may be equated to kik jki. In terms of the mechanism, when R and/or R areesterorketo groups, Aff 2 2 (therefore kijk2) will... 

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