Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Derive: Michaelis-Menten Kinetics

\( r_p = k_3 (E \cdot S)(W) \)

\( r_{E.S} = 0 = k_1 (E)(S) - k_2 (E \cdot S) - k_3 W (E \cdot S) \)

\( (E \cdot S) = \frac{k_1 (E)(S)}{k_2 + k_3 W} \)

\( E_t = (E) + (E \cdot S) \)

\( (E) = \frac{E_t}{1 + \frac{k_1 S}{k_2 + k_3 W}} \)

\( r_p = k_3 (E \cdot S)(W) = \frac{V_{\max} k_3 W E_t S}{k_2 + k_3 W + S} \frac{k_1}{K_m} \)

\( r_p = \frac{V_{\max} S}{K_m + S} \)

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