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handout4 - Department of Chemical Engineering University of...

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Unformatted text preview: Department of Chemical Engineering University of California, Santa Barbara ChE 170 Fall 2010 Handout 4 Michaelis-Menten enzyme kinetics E = enzyme S = substrate P = product Full reaction kinetics for this system: Approach 1: quasi steady-state approximation for ES 0 Using Substituting in above for and solving for , ⁄ where we have made the definition: Now compute the rate of product formation: Make the definition: max Then the rate is given by, max Approach 2: rapid equilibrium approximation for Assume that substrate binding is in equilibrium with the reactants. Then, Solving for , Combining with the mass balance equation Solving for , , If we now define Then, And the remainder of the derivation proceeds as before. Therefore the quasi steady-state and equilibrium approximations lead to slightly different expressions for the Michaelis constant . For reactions that are rate-limited in the formation of the product, , the two approaches are roughly equivalent. ...
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