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

For users of the Mathcad browser: wmc-rmm1.mcd
(23 KB, ver. 5.0)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 *K*M,
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 *k*b - 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 |
0.330 | 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:**

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

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