Transient-state kinetic analysis steps

Unlike the standard protocols for steady-state kinetic analysis, transient kinetic analysis is dependent on the availability of signals to measure individual steps of the reaction. Moreover, the observable kinetics change and can be complex or deceivingly simple depending on the relative magnitudes of sequential steps in a pathway. The rule of thumb is that one exponential phase exists in the time dependence of a reaction for each step in the pathway. For example, the kinetics of signals observable according to Scheme 2 will follow a triple exponential function Y =Ai e A- + A2 - A3 -f c. Moreover,... 

The kinetic analysis of an enzyme mechanism often begins by analysis in the steady state therefore, we first consider the conclusions that can be derived by steady-state analysis and examine how this information is used to design experiments to explore the enzyme reaction kinetics in the transient phase. It has often been stated that steady-state kinetic analysis cannot prove a reaction pathway, it can only eliminate alternate models from consideration (5). This is true because the data obtained in the steady state provide only indirect information to define the pathway. Because the steady-state parameters, kcat and K, are complex functions of all of the reactions occurring at the enzyme surface, individual reaction steps are buried within these terms and cannot be resolved. These limitations are overcome by examination of the reaction pathway by transient-state kinetic methods, wherein the enzyme is examined as a stoichiometric reactant, allowing individual steps in a pathway to be established by direct measurement. This is not to say that steady-state kinetic analysis is without merit rather, steady-state and transient-state kinetic studies complement one another and analysis in the steady state should be a prelude to the proper design and interpretation of experiments using transient-state kinetic methods. Two excellent chapters on steady-state methods have appeared in this series (6, 7) and they are highly recommended. 

This study has important lessons for enzyme kinetic analysis. The use of pH variation and examination of isotope elfects can be a powerful combination to explore the chemistry of enzyme-catalyzed reactions and to dissect the contributions of individual reaction steps to the net steady-state turnover (27). Examination of the effects of pH on each step of the reaction pathway could resolve the contributions of ionizable groups toward ground-state binding energy and transition-state stabilization. The use of isotope effects by transient-state kinetic methods is more limited than in the steady state due to the errors involved in comparing two rate measurements. In the steady state, the ratio method has allowed isotope effects of less than 1% to be measured accurately (8a, 58). By transient-state kinetics, one would require at least a 10-20% change in rate to demonstrate a convincing difference between two rate measurements in most instances. 

A large amount of N2O was formed from the initial stage over LaM03 (M = Co, Mn, Fe, Cr, Ni) at 573 K. The time course of the NO+CO reaction (performed in a batch recirculation system) reflects this situation. These results support a two-step reaction pathway in which N2O is an intermediate for nitrogen formation, deal et al. (1994) confirm the role of N2O as intermediate in this reaction over perovskite oxides. They used steady-state isotopic transient kinetic analysis to study the mechanism of NO + CO reaction over LaCo03. They concluded that N2O was an intermediate in the formation of N2 at T < 873 K. They also concluded that at high temperature CO2 desorption became the rate-limiting step of the overall reaction. This is likely due to the rapid formation and slow decomposition of very stable carbonates on the perovskite surface as reported by Milt et al. (1996). 

Steady-state isotopic transient kinetic analysis (SSITKA) involves the replacement of a reactant by its isotopically labelled counterpart, typically in the form of a step or pulse input function. Producing an input function with isotope-labelled reactants permits the monitoring of isotopic transient responses, while maintaining the total concentration of labelled plus nonlabelled reactants, adsorbates, and products at steady-state conditions. It is assumed that there are no effects due to differences in kinetic behavior of the isotopic species from unmarked atomic species. However, for instance, deuterium substitution exhibits isotopic effects that can not be neglected. 

The plug flow reactor is increasingly being used under transient conditions to obtain kinetic data by analysing the combined reactor and catalyst response upon a stimulus. Mostly used are a small reactant pulse (e.g. in temporal analysis of products (TAP) [16] and positron emission profiling (PEP) [17, 18]) or a concentration step change (in step-response measurements (SRE) [19]). Isotopically labeled compounds are used which allow operation under overall steady state conditions, but under transient conditions with respect to the labeled compound [18, 20-23]. In this type of experiments both time- and position-dependent concentration profiles will develop which are described by sets of coupled partial differential equations (PDEs). These include the concentrations of proposed intermediates at the catalyst. The mathematical treatment is more complex and more parameters are to be estimated [17]. Basically, kinetic studies consist of ... 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

Knowledge about transient episodes in catalytic conversions may contribute to the understanding of their stationary state. In Fischer-Tropsch CO-hydrogenation, the mechanism is undoubtedly complex, and the reaction steps occur among chemisorbed species their rates are not directly measurable, however, they can be calculated with the help of a kinetic model. Particular methods of performing the reaction and the sampling and analysis of the products are required to obtain the time resolution of reaction rates and selectivities. 

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