Computer-Assisted Data Analysis of Enzyme Kinetics Marvin Bishop and Edgardo Zamora Fordham University 60th Street and Columbus Avenue New York. NY 10023 Several programs treating enzymes have appeared in the JOURNAL OF CHEMICALEDUCATION. Wolf (19)simulated a model enzyme, while Eades, Douglass, and Brown (20) generated data sheets for pre-laboratory practice. Our proeram is eeared to on-line laboratorv analysis and aives stuients the option of collecting more data while the experiment is still in Dromess. Graphs enable erroneous data points to he easily spdtte;i and thedifferent data fits allow an-assessment of the quality of the results. The Ieaction pathway of an enzyme-catalyzed reaction is generally depicted in terms of an enzyme-substrate complex. The simple enzyme mechanism is represented by the equation k-1
in which E, S, ES, and P are the enzyme, substrate, complex, and product concentrations respectively, and the k's are the specific rate constants. A steady-state analysis yields the Michaelis-Menten equation (21):
Here. Vo is the initial reaction velocity, V ~ a is x the maximum initial reaction velocity, S is the substrate concentration, and K M is the Michaelis-Menten constant. K M is characteristic of; given enzyme-substrate system and is equal to the sub-
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strate concentration a t which the initial reaction velocity is half the maximum. The Michaelis-Menten equation has the form of a rectangular hyperbola passing through the origin with the line Vo = VMAXas a horizontal asymptote. Measurement of Vo as a function of Sdetermines VMAXand KM.Sis known from the dilutions of stock substrate employed in the experiment. Vo is determined from the initial slope of a plot of the amount of product vs. time. The amount of product present is conveniently measured hy comparing optical densities to those of a series of standard dilutions (22). However, KM and VMAXare not easy to obtain accurately from eqn. (2). Various transformations have been suggested to put eqn. (2) into linear form. Three common fitting forms are: the Lineweaver-Burk (23) (LB), 1 - KM 1 (3) Vo VMAXS ~ M A X the Eadie-Hofstee (24-25) (EH), - K ~ v o + vM*x v, = S
(4)
and the Dixon-Webb (26) (DW),
The constants, KM and VMAX,are easily obtained from the slope and intercept of these straight lines. Table 1 indicates the appropriate variable to plot as well as the resultant slope and intercept for each of the linear forms. Students enter their Vo and S data and select the linear fitting form to he used. The computer prints a title for the selected form, the equation of the form, the correlation coefficient of the fit, VMAXand K Mas well as a tahle listing the input data and the data predicted from the fit. In addition, a graph is drawn on the teletype comparing the actual data to the fit. This graph cannot he used for quantitative purposes but it enables students to easily obtain a 'feel' for the quality of the fit. Program Kinetidteractive BASIC, 400 statements, 60 comments. Students run Kinet via teletypes connected to a DEC 20. Documentation includes listing and a sample execution. Copies of the listing and sample execution will be provided free when a self-addressed, stamped envelope is supplied with request. This research was supported in part by the donors of the Petroleum Research Fund of the American Chemical Society and by the Fordham University Computer Center. We thank Maria Nowak for bringing this application of data analysis to our attention.
Volume 58 Number 3 March 1981
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