Multiple-substrate/product steady state kinetic

Multiple-substrate/product steady state kinetics... 

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... 

Peller, L. Alberty, R. A. (1959). Multiple intermediates in steady state enzyme kinetics I. The mechanism involving a single substrate and product. J. Amer. Chem. Soc. 81, 5907-5914. 

Although steady-state kinetic methods cannot establish the complete enzyme reaction mechanism, they do provide the basis for designing the more direct experiments to establish the reaction sequence. The magnitude of kcm will establish the time over which a single enzyme turnover must be examined for example, a reaction occurring at 60 sec will complete a single turnover in approximately 70 msec (six half-lives). The term kcJKm allows calculation of the concentration of substrate (or enzyme if in excess over substrate) that is required to saturate the rate of substrate binding relative to the rate of the chemical reaction or product release. In addition, the steady-state kinetic parameters define the properties of the enzyme under multiple turnovers, and one must make sure that the kinetic properties measured in the first turnover mimic the steady-state kinetic parameters. Thus, steady-state and transient-state kinetic methods complement one another and both need to be applied to solve an enzyme reaction pathway. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

The next level of complexity is to review the situation of a single-substrate biocatalyst with a single catalytic site that is responsible for more than one product-forming/release step (a multiple-product situation). This scenario will be analysed by means of the Briggs-Haldane steady state approach with reference to the indicated Uni Bi kinetic scheme, where Uni refers to one substrate and Bi to the evolution of two products. Irreversibility is also assumed (Scheme 8.7). By analogy with the previous treatments above, we may derive two equations ... 

The on rate, kon, is equivalent to k, and the off rate, off> is equivalent to the sum of all pathways of E-I breakdown, in this case, A i - - k2. It is possible that multiple products are formed, and the rates of formation of these should be included in the koff term. A progress curve or continuous assay is the best way to determine the kon and Ki of an alternate substrate. Addition of an alternate substrate inhibitor to an enzyme assay results in an exponential decrease in rate to some final steady-state turnover of substrate (Fig. 13.1). In an individual assay, both the rate of inhibition (kobs) and the final steady-state rate (C) will depend on the concentration of inhibitor. Care must be taken to have a sufficient excess of inhibitor over enzyme concentration present, since the inhibitor is consumed during the process. Where possible, working at assay conditions well below the of the assay substrate simplifies the kinetics, as the substrate will not interfere in the inhibition. If the... 

For the purpose of the present discussion the term transient kinetics is applied to the time course of a reaction from the moment when enzyme and substrate are mixed, t=0, until either a steady state or equilibrium is established. The difference between the kinetic problems discussed in section 3.3 and in the present section is, respectively, the presence of catalytic as distinct from catalytic concentrations of enzyme. Here we are concerned with the stoichiometry of enzyme states. Transient kinetic experiments with enzymes can be divided into two types. The first of these (multiple turnover) is carried out under the condition that the initial concentrations of substrate and enzyme are Cs(0) Ce(0) and c it) can, therefore, be regarded as constant throughout the course of the reaction until a steady state is attained. Alternatively, in a single turnover reaction, when Cs(0)reaction intermediates is observed until the overall process is essentially complete. These two possibilities will be illustrated with specific examples. In connection with a discussion of the approach to the steady state, in section 3.3 it was emphasized that, at t = 0, the concentrations of the intermediates, enzyme-substrate and enzyme-product complexes, are zero and, therefore, the rate of product formation is also zero. Under the experimental conditions used for steady state rate measurements and for enzyme assays, the first few seconds after the initiation of a reaction are ignored. However, when the experimental techniques and interpretation discussed below are used, events during the first few milliseconds of a reaction can be analysed and provide important information. With suitable monitors it is possible to follow the formation and decay of enzyme complexes with substrates and... 

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