Initial-rate kinetics

Fig. 2. Initial rate kinetics for the enantioselective ring opening of the ECH with HjO catalyzed by the monomer and dimer chiral (salenlCoAlXa catalysts.

H. J. Fromm, Initial Rate Kinetics, Springer-Verlag, NY, 1975. 

Applying the Haldane relation to obtain an equilibrium constant from initial rate kinetics. Because of the inherently greater uncertainty in determinations of rate parameters, this method often proves to be unreliable ... 

A potential limitation encountered when one seeks to characterize the kinetic binding order of certain rapid equilibrium enzyme-catalyzed reactions containing specific abortive complexes. Frieden pointed out that initial rate kinetics alone were limited in the ability to distinguish a rapid equilibrium random Bi Bi mechanism from a rapid equilibrium ordered Bi Bi mechanism if the ordered mechanism could also form the EB and EP abortive complexes. Isotope exchange at equilibrium experiments would also be ineffective. However, such a dilemma would be a problem only for those rapid equilibrium enzymes having fccat values less than 30-50 sec h For those rapid equilibrium systems in which kcat is small, Frieden s dilemma necessitates the use of procedures other than standard initial rate kinetics. 

A linear graphical method for analyzing the initial rate kinetics of enzyme-catalyzed reactions. In the Hanes plot, [A]/v is plotted as a function of [A], where v is the initial rate and [A] is the substrate concentration ". ... 

Initial rate kinetics of bovine brain hexokinase (A) with glucose and ATP as substrates, and (B) with fructose and ATP. Note that the apparent parallel-line kinetics observed with glucose conform to a rate equation lacking a < 12 term. 

If the concentration of substrate is not at least 100 times the concentration of enzyme, the steady state will not persist over the time course of most experiments. In such cases, the resulting initial rate data cannot be analyzed by standard initial rate kinetic procedures. See also Enzyme Kinetics Numerical Integration... 

A good illustration of the influence of an impurity can be provided by noting the effect on initial-rate kinetics by the presence of a particular type of inhibitor in the substrate stock solution. Substrates and competitive inhibitors are often structural analogs of each other. It would not be surprising if an unknown competitive inhibitor was present with the substrate. Hence, upon serial dilutions of the stock substrate solution, the inhibitor concentration would be in constant ratio relative to the substrate. Thus, the initial rate expression in the presence of a competitive inhibitor,... 

An appropriate incubation time should also be evaluated to measure initial rate kinetics (depletion) of the most extensively metabolized substrate while maintaining sensitivity of the least metabolized substrate. 

The initial rate kinetics for hydrogenation, double bond migration and ci —trans isomerisation are shown in Table 10. The activation energies for isomerisation and hydrogenation are shown in Table 11. 

Initial rate kinetics and activation energies for acetylene hydrogenation... 

Over all the metals studied, except cobalt, nickel and copper, the selectivity and stereoselectivity decreased slightly as the reaction proceeded. In addition to the products shown in Table 20, in the rhodium- and iridium-catalysed reactions small yields (2—3%) of buta-1 2-diene were also observed. For all the catalysts, except rhodium, iridium and platinum, which were not investigated, the initial rate kinetic orders were unity in hydrogen and zero or slightly negative (Ni) in but-2-yne. 

The kinetics of the condensation of the Cr(H20)63+ ion and its corresponding deprotonated species have been studied in the pH region 3.5-5.0 [25°C, I = 1.0 M(NaC104)] (201). The study of this reaction is complicated by the formation of higher oligomers. Chromatographic analysis of the products as a function of time established the dinuclear species to be the main product for the first 5% of reaction, and the initial-rate kinetics of condensation were studied by a pH-stat technique. The observed pH dependence of the rate was interpreted in terms of the second-order rate constants defined by Eq. (44), and values for... 

There are well-established methods for obtaining the type of inhibition and the value of the inhibition constants from initial-rate kinetics, often from linearized plots such as lineweaver-Burk, Eadie-Hofstee, or Hanes. As these procedures are covered very well by a range of basic textbooks on biochemistry and kinetics (see the list of Suggested Further Reading ) we will not repeat these procedures here. Instead, we will discuss the situation in which an enzyme reaction is followed over more than just the initial range of conversion. Towards this end, the rate equation,... 

In this section, we will discover that inhibition, which tends to be a nuisance at low conversion in initial-rate kinetics studies, can become very detrimental if high degrees of conversions are sought, such as in any situation in synthesis or large-scale processing. 

Given that binding can occur very quickly, the transient kinetic period is important for determining the association constant and the methods to determine its value have been demonstrated previously [11]. Generally, in this initial rate kinetic method, at f = 0, the equation for initial rate analysis is ... 

A kinetic method for determination of aromatic amines was proposed, based on measuring the development of azo dyes (134) resulting from coupling a diazonium ion derived from a PAA analyte and the chromophoric substrate 1 -(4-hydroxy-6-methylpyrimidin-2-yl)-3-methylpyrazolin-5-one (133), as shown in equation 22. After a short induction period initial rate kinetics can be measured when the process is quite advanced, absorbance reaches a maximum and starts to recede due to oxidation of the azo dye by excess nitrous acid. Each PAA has to be calibrated for its molar absorption coefficient and reaction rate, for optimal measurement. A tenfold excess of 133 over the analytes ensures a pseudo... 

Wang, E.J., C.N. Casciano, R.P. Clement and W.W. Johnson. Two transport binding sites of P-glycoprotein are unequal yet contingent initial rate kinetic analysis by ATP hydrolysis demonstrates intersite dependence. Biochim. Biophys. Acta 1481 63-74, 2000. 

The second objective Is to examine the Influence of reversed micellar solution parameters, Including the Interaction of substrates with the surfactant Interface, on observed Initial rate kinetics. This Is of Interest because a number of reports have Indicated that enzymes In reversed micellar solutions exhibit an enhanced reactivity, or "super-activity" (7-9I. As a model system, the hydrolysis reactions of synthetic substrates of a-chymotrypsln were studied In a reversed micellar solution. Nuclear magnetic resonance was used to examine the Interactions between these substrates and the micellar environment. 

Methods. Z-Tyr-Gly-NH2 was synthesized from Z-Tyr-OMe and Gly-NH2 In reversed micellar solutions containing 0.15 M DTAB as the surfactant In a 1 5 volume mixture of n-hexanol and n-octane. Hexanol acts as a cosurfactant and aids In solubilizing the Z-Tyr-OMe. Initial rate kinetic studies employed the hydrolysis of the synthetic substrates GPANA and BTPNA In reversed micelles of CTAB In a... 

Figure 7-17. Methods of parameter identification A by fitting initial rate kinetic data, and B by fitting the time-course of a reaction.

A distinction between the different mechanisms is best done using initial rate kinetic measurements as described in detail in the literature. For reaction engineering purposes only a proper fit of reactor data is desired, using a minimum amount of kinetic parameters for statistical reasons. 

The kinetics within Fig. 7-24 do not represent initial rate kinetics, but the reaction rate during the conversion S - P plotted versus the remaining substrate concentration (initial concentration [S]o = 1 mmol L-1). 

To study the kinetics of immobilized enzymes a recirculation reactor may be used. This reactor allows one to perform kinetic measurements with defined external mass transfer effects, reached by establishing a high flow rate near the catalyst, minimizing mass transfer resistance. The reactor behaves as a differential gradientless reactor allowing initial-rate kinetic measurements to be made. 

Determination of Initial Rate Kinetics on />-nitrophenol P-D xylopyranoside... 

Initial rate kinetic assays were conducted at 37 C in 50 mM citrate buffer at pH 4.8 in 96-well microtiter plates using /)-nitrophenol P-D-xylopyranoside. For all assays, the XlnD was loaded at 1.5 p.g/ml of reaction, and initial substrate concentrations were varied from 0.1 to 3.2 mM. The release of pNP was monitored every 15 s for the initial 10 min of each reaction by measming the absorbance at 405 nm on a SpectraMax 190 UV/VIS microplate scanner from the Molecular Devices (Sunnyvale, CA). End product inhibition by D-xylose was confirmed by ranning identical assays to those described above with initial D-xylose concentrations ranging from 3.33 to 40 mM. Triplicate analyses of all assays were run at all conditions. All parameters estimated in this study were calculated using standard Michaelis-Menten kinetics as described previously [11]. 

A , is the rate constant for combination of A with the free enzyme E. However, = ( 4 6 + 4 7 + k k-j)/k k kj. This involves 5 rate constants Aj, A4, Aj, Ag and kj all of which involve both A and B or, in the case of Ag and k-, both corresponding products. Thus is unlikely to be independent of the nature of A for this mechanism. Clearly this criterion will distinguish between two mechanisms shown in Schemes 5 and 8, and in fact the prediction is unique to the ping-pong mechanism. Another distinctive test of the ping-pong mechanism is the Haldane relationship. Haldane pointed out that from the initial rate kinetic parameters for the forward and reverse directions of a reversible enzyme-catalysed-reaction it was possible to obtain an expression for the overall equilibrium constant [66]. 

Casazza, J.P. Fromm, H.J. Purification and initial rate kinetics of acyl-phos-phate-hexose phosphotransferase from Aerobacter aerogenes. Biochemistry, 16, 3091-3097 (1977)... 

Note that we are suggesting you plot several rates versus concentration, while other reactant concentrations are kept constant. However, reaction rates depend upon the concentration of the species involved and they change with time. Hence, in this experiment, we need to measure the rates at equivalent points. One must measure the various rates starting at points in time where the concentrations of those species whose concentrations are being kept constant are relatively invariant. Initial-rate kinetics, which is described later in this chapter, is particularly useful in this regard. In contrast, if we algebraically incorporate concentration into the rate constant, we can plot rate constants as a function of concentration to determine kinetic orders (wait until the section on pseudo-first order kinetics to understand this fully). 

For elementary reactions the kinetics are relatively simple, and there are straightforward mathematical expressions that allow us to solve for rate constants. These simple mechanisms are those we analyze first. They involve first and second order kinetics, along with variations including pseudo-first order and equilibrium kinetics. We also look at a method to measure rate constants known as initial-rate kinetics. We analyze complex reactions only under the simplifying assumption of the steady state approximation (Section 7.5.1), and show how kinetic orders can change with concentration. More advanced methods for analyzing complex reactions are left to texts that specialize in kinetics. 

We commonly encounter reactions that are slow enough that it is difficult to follow them to several half-lives in order to obtain a reliable rate constant. Further, many reactions start to have significant competing pathways as the reaction proceeds, causing deviations from the ideal behaviors discussed above. In these cases we often turn to initial-rate kinetics. In this procedure we only follow the reaction to 5% or 10% completion, thereby avoiding complications that may arise later in the reaction and/or allowing us to solve for rate constants in a reasonable time period. This approach is inherently less accurate than a full monitoring of a reaction over several half-lives, but often it is the best we can do. 

Now that we have looked at some of the most common scenarios, it is useful to tabulate these along with more complex ones. This should serve as a simple reference table for you to apply when implementing kinetic experiments. Table 7.2 shows several reaction stoichiometries along with the rate laws and the integrated rate laws. Almost all of these scenarios are amenable to reduction to simpler forms when a large excess of one reagent is used or an initial-rate kinetic treatment is applied. 

Two Transport Binding Sites of P-Glycoprotein are Unequal Yet Contingent Initial Rate Kinetic Analysis by ATP Hydrolysis Demonstrates Intersite Dependence. 

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