Steady-state enzyme kinetic data

Table 9.3. Steady-State Enzyme Kinetic Data...

Since the concentrations of all the intermediate states are constant under steady state conditions, all of these states can, at least formally, be incorporated into a single kinetic intermediate state. It follows that under steady state conditions, kinetic data can provide no information about the existence and kinetic properties of intermediate enzyme-substrate complexes. An understanding of the mechanism of an enzyme catalysed reaction needs information about these intermediate states, which is therefore usually obtained from kinetic studies before steady state has been established, usually by rapid reaction methods. Comprehensive coverage of the techniques and methods of analysis of pre-steady state kinetics is beyond the scope of this chapter, but we discuss here methods for analysing simple exponential processes. Two approaches are used. In the first, the observed signal S(t) is fitted to an exponential function of the following form ... 

Data for the matrix of values of Rg as a function of values of both 9 and c is conventionally visualised in a Zimm plot (Figure 4.30). As with families of double-reciprocal plots in steady-state enzyme kinetics, parameters are now extracted computationally, but presented graphically. The functions, however, are not simple and need not be linear. The ordinate is KcjRg, but the abscissa is sin (0/2) + kc, where c is the concentration of the polymer and k is an arbitrary constant chosen so that the y intercept of families of plots at constant c or constant 9 is constant. 

Not all data points are created equal. Your lab partner, who is both systematic and frugal, decides to perform a series of enzyme assays at substrate concentrations of 1, 2, 4, and 8 xM. You argue for doing the experiments at [S] = 1, 4, 16, and 100 p.M. Try both sets of experiments using the simulated enzyme kinetics lab in the Steady-State Enzyme Kinetics Conceptual Insights module. Who had the better idea, and why ... 

One of the critical factors in the design of experiments to determine the values of steady-state enzyme kinetic parameters is the optimal choice of a range of substrate concentrations. On the basis of the data in Fig. 5-28, suggest a possible optimal range of substrate concentrations. 

Even under seemingly ideal conditions, the steady-state concentration of the first reaction product may exceed the inhibitory constant for the binding of that product to the primary enzyme. In such cases, the linearity of the coupled assay can be misleading, and the investigator must validate the coupled enzyme kinetic data by direct comparison with the results obtained by another technique such as a stopped-time radiometric assay. This... 

In the determination of steady state reaction kinetic constants of enzyme-substrate reactions, FABMS also provides some very unique capabilities. Since these studies are best performed in the absence of glycerol in the reaction mixture, the preferred method is that which analyzes aliquots which are removed from a batch reaction at timed intervals. Quantitation of the reactants and products of interest is essential. When using internal standards, generally, the closer in mass the ion of interest is to that of the internal standard, the better is the quantitative accuracy. Using these techniques in the determination of kinetic constants of trypsin with several peptide substrates, it was found that these constants could be easily measured (8). FABMS was used to follow the decrease in the reactant substrate and/or the increase in the products with time and with varying concentrations of substrate. Rates of reactions were calculated from these data for each of the several substrate concentrations used and from the Lineweaver-Burk plot, the values of Km and Vmax are obtained. 

The initial acceleration of enzyme reactions can be observed by a study of the rate of appearance of the final product during the short time interval between mixing of enzyme and substrate and the attainment of the steady-state concentrations of all the intermediate compounds. Apart from the final steady-state velocity, this method can, in principle, give information about the kinetics of two reaction steps. In the first place, the second-order constant ki which characterizes the initial enzyme-substrate combination can be determined when [ S]o, the initial substrate concentration, is sufficiently small to make this step rate-determining during the pre-steady-state period. Kinetic equations for the evaluation of rate constants from pre-steady-state data have recently been derived (4). Under suitable conditions ki can be evaluated from... 

Although the steady state treatment is the preferred approach for analyzing enzyme kinetic data, the applications of both kinetic treatments in general enzyme reactions will be considered. 

The steady-state kinetic treatment of random reactions is complex and gives rise to rate equations of higher order in substrate and product terms. For kinetic treatment of random reactions that display the Michaelis-Menten (i.e. hyperbolic velocity-substrate relationship) or linear (linearly transformed kinetic plots) kinetic behavior, the quasi-equilibrium assumption is commonly made to analyze enzyme kinetic data. 

Should one use the Hill plot in practice to examine the initial velocity behavior of enzymes Because infinite cooperativity is assumed to be the basis of the Hill treatment, only rapidly equilibrating systems are suitable for the Hill analysis. However, enzyme systems displaying steady-state kinetic behavior will not satisfy this requirement for this reason, one must avoid the use of kinetic data in any application of the Hill equation to steady-state enzyme systems. 

In conclusion, the steady-state kinetics of mannitol phosphorylation catalyzed by II can be explained within the model shown in Fig. 8 which was based upon different types of experiments. Does this mean that the mechanisms of the R. sphaeroides II " and the E. coli II are different Probably not. First of all, kinetically the two models are only different in that the 11 " model is an extreme case of the II model. The reorientation of the binding site upon phosphorylation of the enzyme is infinitely fast and complete in the former model, whereas competition between the rate of reorientation of the site and the rate of substrate binding to the site gives rise to the two pathways in the latter model. The experimental set-up may not have been adequate to detect the second pathway in case of II " . The important differences between the two models are at the level of the molecular mechanisms. In the II " model, the orientation of the binding site is directly linked to the state of phosphorylation of the enzyme, whereas in the II" model, the state of phosphorylation of the enzyme modulates the activation energy of the isomerization of the binding site between the two sides of the membrane. Steady-state kinetics by itself can never exclusively discriminate between these different models at the molecular level since a condition may be proposed where these different models show similar kinetics. The II model is based upon many different types of data discussed in this chapter and the steady-state kinetics is shown to be merely consistent with the model. Therefore, the II model is more likely to be representative for the mechanisms of E-IIs. 

In steady-state kinetic studies, the total concentration of the enzyme should be much less than the concentration of the substrate(s), product(s), and effector(s) typically, by at least a thousandfold. When this condition is not true, the steady-state condition will not be valid and other methods, such as global analysis, have to be utilized to analyze the kinetic data. 

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. 

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... 

One less kinetic parameter can be obtained from an analysis of the data for a ping-pong mechanism than can be obtained for ordered reactions. Nevertheless, in Eq. 9-47, twelve rate constants are indicated. At least this many steps must be considered to describe the behavior of the enzyme. Not all of these constants can be determined from a study of steady-state kinetics, but they may be obtained in other ways. 

Steady state kinetic measurements on an enzyme usually give only two pieces of kinetic data, the KM value, which may or may not be the dissociation constant of the enzyme-substrate complex, and the kcM value, which may be a microscopic rate constant but may also be a combination of the rate constants for several steps. The kineticist does have a few tricks that may be used on occasion to detect intermediates and even measure individual rate constants, but these are not general and depend on mechanistic interpretations. (Some examples of these methods will be discussed in Chapter 7.) In order to measure the rate constants of the individual steps on the reaction pathway and detect transient intermediates, it is necessary to measure the rate of approach to the steady state. It is during the time period in which the steady state is set up that the individual rate constants may be observed. 

The enzyme has been shown to be specific for the (3 form by rapid reaction measurements on a time scale faster than that for the interconversion of the anomers, and also by determination of the activity toward model substrates that are locked in either of the configurations. By using sufficient enzyme to phos-phorylate all the active anomer of the substrate before the two forms can reequilibrate, it is found that 80% of the substrate reacts rapidly, and that the remaining 20% reacts at the rate constant for the anomerization. The kinetics were followed both by quenched flow using [y-32P]ATP10 and by the coupled spectrophotometric assay of equation 6.4.11 The other evidence comes from the steady state data on the following substrates 12... 

The enzyme-product complexes of the yeast enzyme dissociate rapidly so that the chemical steps are rate-determining.31 This permits the measurement of kinetic isotope effects on the chemical steps of this reaction from the steady state kinetics. It is found that the oxidation of deuterated alcohols RCD2OH and the reduction of benzaldehydes by deuterated NADH (i.e., NADD) are significantly slower than the reactions with the normal isotope (kn/kD = 3 to 5).21,31 This shows that hydride (or deuteride) transfer occurs in the rate-determining step of the reaction. The rate constants of the hydride transfer steps for the horse liver enzyme have been measured from pre-steady state kinetics and found to give the same isotope effects.32,33 Kinetic and kinetic isotope effect data are reviewed in reference 34 and the effects of quantum mechanical tunneling in reference 35. 

In disagreement with the above indications was the finding of Aldridge et al. (146) that for enzyme which was phosphorylated at pH 5.5 with inorganic phosphate and rapidly mixed with buffer at pH 8.4, the rate of dephosphorylation was twice as fast as the turnover of the enzyme at pH 8.0. Also, transient state kinetic studies by Femley and Walker (99, 110) showed a rapid release (burst) of phenol followed by a steady state release of phenol, only at pH < 7. Thus, these data would seem to indicate that at pH >7 the rate determining step is phosphorylation. 

Enzymes are biocatalysts, as such they facilitate rates of biochemical reactions. Some of the important characteristics of enzymes are summarized. Enzyme kinetics is a detailed stepwise study of enzyme catalysis as affected by enzyme concentration, substrate concentrations, and environmental factors such as temperature, pH, and so on. Two general approaches to treat initial rate enzyme kinetics, quasi-equilibrium and steady-state, are discussed. Cleland s nomenclature is presented. Computer search for enzyme data via the Internet and analysis of kinetic data with Leonora are described. 

---