



Goal:
Kinetic data is presented for the alcohol dehydrogenase catalyzed oxidation of ethanol to acetaldehyde. The results
are analyzed within
the context of the MichaelisMenten mechanism for enzyme action. Prerequisites: An introductory knowledge of kinetics, including a few examples of mechanisms and how they give rise to a specific rate equation. While not necessary, background preparation for this exercise might include the derivation of the MichaelisMenten equation. Resources you will need: This exercise should be carried out within a software environment that is capable of data manipulation, which can generate a bestfit line for an xy data set, and can also determine the uncertainties in the slope and intercept of the bestfit line. You will also be graphing the data along with the fitted function. Background: Enzymes are large, threedimensional proteins that catalyze a wide range of biochemical reactions. Enzymes normally show a remarkable specificity for catalyzing the reaction of only certain substrates. This specificity exists because the mechanism for catalysis involves the binding of the enzyme and a particular substrate in a “lock and key” fashion (i.e. evolution has favored the development of certain enzymes that have a threedimensional surface that contours to the shape of a specific substrate). The rate of the reaction increases because intermolecular interactions that accompany binding lower the activation energy. A simple model for enzyme action is represented by where E is the enzyme, S is the substrate, ES is called the enzymesubstrate complex, and P is the product. The rate equation associated with this mechanism is worked out in most physical chemistry textbooks, and is given by
(1)
where R is the rate of reaction and [E]_{t} represents the concentration of both bound and unbound enzyme in solution (i.e. [E]_{t} = [E] + [ES]). The ratio of rate constants that appears in the denominator of equation (1) is simply equal to another constant. Consequently, equation (1) can be written more compactly as
(2)
where K_{m} is called the Michaelis constant, and equation (2) is called the MichaelisMenten equation. In real biochemical systems, the enzyme is normally present at extraordinarily small concentrations in comparison to the substrate (i.e. [E]<<[S]). As the substrate concentration is increased, very little unbound enzyme will remain. In other words, the enzyme in the system will eventually become saturated with substrate (i.e. [E]_{t} = [ES]) and the maximum possible rate for the reaction will be observed in this limit. Referring to equation (2), the maximum rate is achieved when [S] >> K_{m} , meaning K_{m} can be neglected in the denominator and equation (2) becomes (3)
With the definition of R_{max}, we can rewrite the MichaelisMenten rate equation in the form
(4)
The constants K_{m} and R_{max} each quantify a characteristic of our enzymesubstrate system. K_{m} can be interpreted as the concentration of substrate that is required to achieve onehalf the maximum rate. This can be verified by substituting K_{m} = [S] in equation (4) which yields
(5)
If an enzymesubstrate system has a relative small value of K_{m}, then we know that that enzyme has a very high affinity for binding that substrate. Alternatively, the constant R_{max} is simply a measure of the inherent ability of the enzyme to act as a catalyst (an enzymesubstrate system with a large R_{max} value is going to occur at a relatively fast rate). Equation (4) is plotted in figure (1) for arbitrary values of K_{m} and R_{max}; initially, the rate increases at a rapid rate with increasing [S], but levels out as the enzyme becomes saturated (i.e. R converges on R_{max} as [S] becomes large). How does one evaluate the constants K_{m} and R_{max} for a particular enzymesubstrate system? The most common method involves measuring the rate of reaction at several different concentrations of substrate and subsequently fitting the data to equation (4). This process is made easier by taking the reciprocal of equation (4), which yields (6)
In other words, a plot of 1/R versus 1/[S] should be linear (if the enzymesubstrate system obeys the MichaelisMenten mechanism), and the slope and intercept can be used to evaluate the parameters K_{m} and R_{max}. Such a plot is called a LineweaverBurk plot. In the exercise below, you will be presented with some kinetic data for the oxidation of ethanol to acetaldehyde. This reaction is catalyzed in the human body by an enzyme called alcohol dehydrogenase. The data will be analyzed within the context of the MichaelisMenten mechanism to determine the constants K_{m} and R_{max}. Experimental Data: The following data where obtained from K. Bendinskas, C. DiJiacomo, A. Krill, and E. Vitz, Journal of Chemical Education, 82(7), 1068 (2005). In this study, the enzyme alcohol dehydrogenase (ADH) is used to catalyze the conversion of ethanol (the substrate) to acetaldehyde (the product). Eight kinetic trials were carried out in a pH 9.0 buffer; only the concentration of ethanol was varied from one trial to the next. The reaction was followed spectrophotometrically, although in an indirect fashion. Specifically, the direct conversion of ethanol to acetaldehyde only gives rise to absorbance changes in the UV portion of the spectrum, which is difficult to follow with standard lab spectrometers and cuvettes. The authors were able to coupled the ethanol reaction to another reaction that gives rise to a color change in the visible region (through a coupling scheme that can be read about in the above reference, dichlorophenolindophenol undergoes a synchronous redox reaction which causes the solution to go from blue to colorless; the authors monitored this change at 635 nm). The initial rate of reaction was defined as the slope of absorbance at 635 nm versus time plot that was recorded for each trial (these dA/dt values are given in the table below, and represent the rate of reaction, R).
Exercise: 1. Enter the raw data into an appropriate quantitative analysis software environment and plot R versus [S]. Estimate values for K_{m} and R_{max} for this system by simply inspecting the graph. 2. Manipulate the data into a form that will allow you to generate a LineweaverBurk plot. Generate this plot, include a bestfit line, and use the slope and intercept to calculate values of K_{m} and R_{max}. Do these numbers agree with the estimates that you obtained in step (1)? 3. LineweaverBurk plots, which are doublereciprocal plots, are sometimes problematic because they tend to cluster all the large substrate concentration data to one side of the plot. Also, the few points corresponding to smaller substrate concentrations tend to be noisy because they are obtained by taking the reciprocal of a small number that contains a relatively high degree of random error. These difficulties can sometimes be avoided by plotting the data in an alternate fashion. One such method is known as a HanesWoolf plot, and is obtained by multiplying both sides of equation (6) by [S], which yields
(7)
Generate a HanesWoolf plot, include a bestfit line, and calculate values of K_{m} and R_{max}. Comment about the similarities (dissimilarities) of the plots and the values of K_{m} and R_{max} obtained in steps (2) and (3). 4. MORE CHALLENGING: Using a software environment that is capable of determining the standard deviation in the slope and intercept of a bestfit line, and by propagating that error into K_{m} and R_{max}, determine whether the HanesWoolf method yields K_{m} and R_{max} values with more or less uncertainty in comparison to the LineweaverBurk method. 

Suggestions
for improving this web site are welcome. You are
also encouraged to submit your own datadriven exercise to
this
web archive. All inquiries should be directed to the curator:
Tandy
Grubbs, Department of Chemistry, Unit 8271, Stetson University, DeLand,
FL 32720.
