INITIAL RATE ENZYME DATA

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. 

Figure 8 Plot of the initial rate of the enzyme-catalyzed oxidation of 1-phenylpropanol as a function of % ee. The solid line represents a fit of the data to the Michaelis-Menten formalism for competitive inhibition where [S] = [ -(60)] and [ ] = [ -(60)]. The total alcohol concentration was maintained constant at lOmM.100...

Data of chemical composition 106 Pressure changes 145 Variables related to composition 164 Half iife and initial rate data 177 Temperature variation. Activation energy Homogeneous catalysis 202 Enzyme and solid catalysis 210 Flow reactor data 222 CSTR data 231 Complex reactions 238... 

The tabulated data of initial rates and concentrations were obtained for enzyme conversion of a substrate at 37 C, pH 6.5. 

These initial rate data of an enzyme catalyzed reaction are known ... 

In the second and most commonly used method, the investigator studies the alterations in the patterns of the initial rate data (usually graphically presented as doublereciprocal plots). In these studies of multisubstrate and multiproduct enzyme-catalyzed reactions, an investigator can measure the rate of the reaction by either by observing any increase in the concentration of a common... 

Then, k equals the observed reaction rate divided by the initial reactant concentration i.e., k = Vinitiai/[Ainitiai])-This method is most useful when one has an assay method that is sufficiently sensitive to ensure that only a small fraction, say 3-5%, of the reactant is depleted during the rate measurements. Typically, this is satisfactorily achieved with a UV-visible spectrophotometer, a fluorescence spectrometer, or a radioactively labeled reactant. The initial rate method is extremely convenient, and the preponderance of enzyme rate data has been obtained by initial rate measurements. Finally, one should note that the initial rate method can yield erroneous results if the initial reactant concentration is in doubt. This is not true for the plots of ln ([Ao] - [At]/([Ao] -[Aoo]) versus reaction time because one is considering the fraction of reactant A remaining. 

The components of the coupling system should neither inhibit nor activate the primary enzyme. Moreover, care must be exercized to ascertain that the auxiliary enzyme (s) is not contaminated with other minor enzyme activities capable of influencing the primary enzymatic activity. The results from any coupled enzyme assay must exactly match the results obtained with other valid initial rate assays to ensure that the presence of the auxiliary system in no way affects the activity of the primary enzyme. This is typically accomplished by comparing data obtained from the coupled assay with stopped-time assay results to ensure that similar results are obtained. 

A graphical procedure " for plotting enzyme initial rate data as v versus v/[S] (also known as the Woolf-Au-gustinsson-Hofstee plot), where the initial velocity v is the so-called (y)-axis variable and v divided by the initial substrate concentration [S] is the so-called (v)-axis variable, such that the vertical-axis intercept equals Vmax, the slope equals and the horizontal-axis intercept is V IK... 

The initial rate assumption is one of the most powerful and widely used assumptions in the kinetic characterization of enzyme action. The proper choice of reaction conditions that satisfy the initial rate assumption is itself a challenge, but once conditions are established for initial rate measurements, the kinetic treatment of an enzyme s rate behavior becomes much more tractablek In reporting initial rate data, investigators would be well advised to provide the following information ... 

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... 

Wilkinson and Cleland have pointed out the importance of proper weighting of initial rate data in the study of enzyme-catalyzed reactions. If the initial velocities vary by a factor of five or less, the weighting factor involves terms. If the velocities differ by a factor of ten or more, Cleland has suggested that the variance of... 

Most literature on enzyme kinetics is devoted to initial rate data and the analysis of reversible effects on enzyme activity. In many applications and process settings, however, the rate at which the enzyme activity declines is of critical importance. This is especially true when considering its long-term use in continuous reactors. In such situations the economic feasibility of the process may hinge on the useful lifetime of the enzyme biocatalyst. The focus of this section is on the mechanisms and kinetics of loss of enzyme activity. It should also be recognised that the alteration of protein structure is central to the practical manipulation of proteins (e.g. precipitation, affinity and other forms of protein chromatography, and purification in general). 

From a series of batch runs with a constant enzyme concentration, the following initial rate data were obtained as a function of initial substrate concentration. 

Enzyme kinetics are normally determined under steady-state, initial-rate conditions, which place several constraints on the incubation conditions. First, the amount of substrate should greatly exceed the enzyme concentration, and the consumption of substrate should be held to a minimum. Generally, the amount of substrate consumed should be held to less than 10%. This constraint ensures that accurate substrate concentration data are available for the kinetic analyses and minimizes the probability that product inhibition of the reaction will occur. This constraint can be problematic when the Km of the reaction is low, since the amount of product (10% of a low substrate concentration) may be below that needed for accurate product quantitation. One method to increase the substrate amount available is to use larger incubation volumes. For example, a 10-mL incubation has 10 times more substrate available than a 1-mL incubation. Another method is to increase the sensitivity of the assay, e.g., using mass spectral or radioisotope assays. When more than 10% of the substrate is consumed, the substrate concentration can be corrected via the integrated form of the rate equation (Dr. James Gillette, personal communication) ... 

A number of questions might be addressed in the discussion of the results. How reproducible are the initial rate measurements (Note that runs D5 and E3 are duplicates also, runs El and the standard assay for enzyme activity have identical initial concentrations.) Are the enzyme-catalyzed data compatible with the Michaelis-Menten mechanism Do the data from both runs C and D follow apparent zero-order kinetics, and how does this agree with expectations based on comparing (S) with KJ Which of the two types of analysis, Lineweaver-Burk or Eadie-Hofstee, seems to give the better results and why How does 2 agree with the estimate of the turnover number based on the specific activity Are the acid-catalyzed data consistent with the rate law given in Eq. (10) ... 

The HPLC assay method is particularly useful when it is necessary to obtain initial rate data for a study of an enzymatic activity. Optimal assay conditions for the HPLC must be established first. Usually, the optimization process involves the determination of several variables, such as the optimal substrate concentration, pH, temperature, and enzyme concentration. It is assumed that the reader is familiar with the problems associated with assay conditions such as pH, buffer, and temperature. This chapter discusses only factors that might present problems for the HPLC assay method. For additional information, see the works cited in the General References. 

The significance of obtaining rate data for the study of enzymes has been discussed elsewhere, and the reader is referred to the General References for additional information. Although usually relevant to the in-depth study of the mechanism of an enzyme reaction, such concerns are beyond the scope of the present discussion. Of concern in this text are the problems associated with obtaining initial rate data with the HPLC assay method. 

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