## Kinetics of Enzymatic Reactions: The Michaelis-Menten Equation

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The rate limiting step in the enzyme catalyzed transformation of substrate S into product P is the breakdown of the ES complex: Since the ES concentration is not easily measured experimentally, Leonor Michaelis and Maud Menten have given an alternative expression for the determination of the rate of such enzymatic reactions: where KM, the Michaelis constant is defined as: Several algebraic transformations to a linear form have been proposed for this equation which are more useful in the analysis of the experimental data: Lineweaver-Burk, Eadie and Dixon.

Given the following data for the hydrolysis of sucrose by the enzyme invertase, find which equation has the best correlation coefficient, determine the Michaelis constant and kb - the maximum turnover number:

 [S] 0.0292 0.0584 0.0876 0.117 0.146 0.146 0.175 0.234 k 0.182 0.265 0.311 0.33 0.349 0.349 0.372 0.371

In the Dixon expression, which has the best correlation, the substrate concentration [S] is correlated to the ratio of the substrate concentration [S] to the rate k. The maximum turnover number is the reciprocal of the slope, and the Michaelis constant is the product of the intercept with the maximum turnover number. Question:

1. Calculate the Michaelis constant and the maximum turnover number according the other two equations. Are the differences significant?