Steady-state kinetic cycle

Figure 9. Steady-state kinetic cycle for the reduction of 7,8-DHF to 5,6,7,8-THF via DHFR.

Fig. 9. The MoFe protein cycle of molybdenum nitrogenase. This cycle depicts a plausible sequence of events in the reduction of N2 to 2NH3 + H2. The scheme is based on well-characterized model chemistry (15, 105) and on the pre-steady-state kinetics of product formation by nitrogenase (102). The enzymic process has not been chsiracter-ized beyond M5 because the chemicals used to quench the reactions hydrolyze metal nitrides. As in Fig. 8, M represents an aji half of the MoFe protein. Subscripts 0-7 indicate the number of electrons trsmsferred to M from the Fe protein via the cycle of Fig. 8.

The values of x = 0.5 and = 1 for the kinetic orders in acetone [1] and aldehyde [2] are not trae kinetic orders for this reaction. Rather, these values represent the power-law compromise for a catalytic reaction with a more complex catalytic rate law that corresponds to the proposed steady-state catalytic cycle shown in Scheme 50.3. In the generally accepted mechanism for the intermolecular direct aldol reaction, proline reacts with the ketone substrate to form an enamine, which then attacks the aldehyde substrate." A reaction exhibiting saturation kinetics in [1] and rate-limiting addition of [2] can show apparent power law kinetics with both x and y exhibiting orders between zero and one. 

The calculated conversions presented in Table VIII used Eq. (57). They are quite remarkable. They reproduce experimental trends of lower conversion and higher peak bed temperature as the S02 content in the feed increases. Bunimovich et al. (1995) compared simulated and experimental conversion and peak bed temperature data for full-scale commercial plants and large-scale pilot plants using the model given in Table IX and the steady-state kinetic model [Eq. (57)]. Although the time-average plant performance was predicted closely, limiting cycle period predicted by the... 

Fig. 17. Comparison of the variation of the time-average S02 conversion and the maximum bed temperature predicted for stationary cycling condition by an unsteady-state and a steady-state kinetic model for a packed-bed S02 converter operating with periodic flow reversal...

This reaction cycle has more steps than the simple Michaelis-Menten scheme. Nonetheless, the steady-state rate equations describing these reaction cycles have indistinguishable functions, and one cannot determine the number of intermediary steps by steady-state kinetics alone. 

To conclude this Section, we would like to stress that both experimental and theoretical analyses of the non-steady-state kinetics of the tunnelling luminescence of defects in insulators after the step-like stimulation allow us to distinguish the anisotropic defect rotation and diffusion. For the defect rotation, sharp increases of the I(t) and its smooth decrease are observed for the temperature stimulation cycle, whereas an opposite effect occurs for the defect diffusion. 

The most important observation in the pre-steady-state kinetics of the CN system is that after a short lag (100 msec) there is a phase (lasting about 3 sec) where the evolution of H2 is linear and only after these 3 sec does CN reduction occur. This long lag prior to CN reduction would correspond to 18 to 20 electron transfer steps from the Fe protein. More realistically this delay probably involves a CN -induced modification of the enzyme, such as a ligand substitution reaction (this modified state of the enzyme is designated as. E in Figure 21). However, this modification step is too slow to be part of the steady-state cycle for CN reduction. Also, it cannot be a slow activation of the enzyme prior to turnover, since the onset of H2 evolution is the same in both the presence and the absence of CN . Steady-state observations indicate that cyanide binds to a more oxidized form of the MoFe protein than binds N2, but that state cannot be defined because of the long lag phase. 

A final conclusion can be formulated as follows. The number of the parameters that cannot be determined from the steady-state kinetic data is the same as the number of steps that do not enter into the cycles. The source of indeterminacy of the parameters implies "buffer sequences [Fig. 3(b)] and "bridges between the cycles [Fig. 3(d)]. Note that this estimate refers only to the graph structure when individual reaction weights have not been specified. 

The oxidation of propylene oxide on porous polycrystalline Ag films supported on stabilized zirconia was studied in a CSTR at temperatures between 240 and 400°C and atmospheric total pressure. The technique of solid electrolyte potentiometry (SEP) was used to monitor the chemical potential of oxygen adsorbed on the catalyst surface. The steady state kinetic and potentiometric results are consistent with a Langmuir-Hinshelwood mechanism. However over a wide range of temperature and gaseous composition both the reaction rate and the surface oxygen activity were found to exhibit self-sustained isothermal oscillations. The limit cycles can be understood assuming that adsorbed propylene oxide undergoes both oxidation to CO2 and H2O as well as conversion to an adsorbed polymeric residue. A dynamic model based on the above assumption explains qualitatively the experimental observations. 

Traditional steady-state kinetic studies rely on indirect observation of catalysis by monitoring the accumulation of product or consumption of substrate as a consequence of many reaction cycles with a trace of catalyst. Conclusions are limited to inference of the possible pathways for the order of addition of multiple substrates and release of products and quantification of two bulk kinetic parameters, kcat and kcaJKm- The parameter kcat defines the maximum rate of conversion of enzyme-bound substrate to product released into solution, but it cannot be used to establish whether the maximum rate of reaction is limited by enzyme conformational changes, rates of chemical reaction, or rates of product release per se it does, however, set a lower... 

Pre-steady-state kinetic studies established that the appearance of the NADH chromophore on addition of substrate was a two-step process, and these steps can now be identified as closure of the active site and hydride transfer. This study indicated that the on-enzyme equilibrium for addition of water or homocysteine to the enone was close to unity (and the value in free solution), whereas the equilibrium for oxidation of NAD by bound adenosine was 10 times more favourable than in free solution. The focusing of the catalytic power of the enzyme on the oxidation step avoids the formation of abortive complexes by hydride transfer between enone and NADH, yielding 4,5-dehydroadenosine and NAD ". This happens about 10 " times faster than productive hydride transfer at the beginning and end of the catalytic cycle, with the slow rate (close to that of model reactions) apparently arising from a conformationally modulated increase in the distance the hydride has to be transferred. 

The PMM/PGM is activated by glucose 1,6-bisphosphate, and exhibits substrate inhibition in steady-state kinetic assays. The substrate inhibition can be relieved by increased concentrations of glucose 1,6-bisphosphate, which is, of course, the intermediate in the reaction with phosphoglucose. Presumably, mannose 1,6-bisphosphate activates PMM/PGM as well, but this has not been tested. The substrate inhibition and its relief by the intermediate provide strong evidence for the proposed chemical mechanism. The inhibition arises when the bisphosphorylated intermediate dissociates prematurely from the enzyme during the catalytic cycle, and substrate binding to the unphosphorylated enzyme creates a dead-end complex. 

Fig. 5. Effect of cycle period and inlet SO2 concentration on the performance of flow reversal reactor. (1-3) SO2 conversion predicted with dynamic kinetic model, (l -3 ) SO2 conversion predicted with steady-state kinetic model. (1,1 ) 9 % SO2 in the reactor inlet, (2,2 ) 6 % SO2, and (3,3) 3 % SO2.

The reactions of Compound I and Compound II with ferrocyanide were investigated independently on a stopped-flow apparatus, and the over-all reaction cycle was investigated using steady-state kinetics. The two approaches are self-consistent. Details of the investigation, now available in thesis form 17), will be published elsewhere 18),... 

The steady state kinetics of arsenite oxidoreductase from A. faecalis indicate a so-called double displacement (or ping-pong ) mechanism (15) in which the enzyme cycles between oxidized and reduced forms in its reaction with arsenite and azurin (or cytochrome c). This overall kinetic scheme is common in redox-active proteins. Arsenite must bind, the oxygen atom transfer chemistry take place, and arsenate dissociate before the subsequent reaction of a second molecule of substrate. Since arsenate is not an inhibitor of arsenite oxidoreductase (43), product dissociation must be effectively irreversible. The turnover number (kcai) of 27 sec and for arsenite of 8 pM are reasonable parameters for the detoxification of arsenite, especially since A. faecalis is able to survive in at least 80 mM (1%) sodium arsenite. The considerable catalytic power of the enzyme is reflected by the kinetic parameter k JK of 3.4 X 10 M sec , which is fairly close to the diffusion-controlled maximum of 10 -10 M sec for proteins in... 

With the exception of a study carried out with a partially characterized multicopper oxidase isolated from tea leaves (85), there has been very little detailed work concerned with the steady state kinetic behavior of laccases. Early work on the transient kinetics indicated, however, that (1) enzyme bound Cu + was reduced by substrate and reoxidized by O2, and (2) substrate was oxidized in one-electron steps to give an intermediate free radical in the case of the two electron donating substrates such as quinol and ascorbic acid. The evidence obtained suggested that free radicals decayed via a non-enzymatic disproportionation reaction rather than by a further reduction of the enzyme (86—88). In the case of substrates such as ferrocyanide only one electron can be donated to the enzyme from each substrate molecule. It was clear then that the enzjmie was acting to couple the one-electron oxidation of substrate to the four-electron reduction of oxygen via redox cycles involving Cu. 

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