Sweetzyme IT Extra is a trademarked immobilized enzyme formulation of glucose isomerase sold by the Danish company Novozymes. The following reaction is carried out in a 4.0 L reactor in the presence of an non-competitive inhibitor, I: E + G <=1=> EG =2=> E + F EG+1 <=3 => EIG G = glucose, F = fructose The Sweetzyme beads added to the reactor have a total surface area, a = 342 cm². Kinetic Parameters k₁= 0.00820 M-¹ s¹ k.₁ 0.00190 s¹¹ k₂ = 0.570 s¹ Initial/Total Enzyme concentration: Initial Bulk Substrate Concentration: Mass transfer coefficient, Eo 2.30 x 105 M Sb = 0.152 M k₁= 9.15 x 10 cm/s A. What is the maximum reaction velocity with no inhibitor (in mol/L-s)? (recall that Rapid Equilibrium and Quasi steady state approaches predict the same value for Vmax for this mechanism) B. What is the maximum reaction velocity (in mol/L-s) with the non-competitive inhibitor, I, at a concentration of [1] = 0.0029 M, with K₁= 1.8 x 10³ M.

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Author:Reginald H. Garrett, Charles M. Grisham
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Chapter18: Glycolysis
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6.
Sweetzyme® IT Extra is a trademarked immobilized enzyme formulation of glucose isomerase sold by the Danish company
Novozymes. The following reaction is carried out in a 4.0 L reactor in the presence of an non-competitive inhibitor, I:
E + G <=1=> EG = 2 => E + F
EG+1 <=3=> EIG
G=glucose, F = fructose
The Sweetzyme beads added to the reactor have a total surface area, a = 342 cm².
Kinetic Parameters
k₁ = 0.00820 M₁¹ S¹
k.₁ = 0.00190 s¹
k₂ = 0.570 s¹
Initial/Total Enzyme concentration:
Initial Bulk Substrate Concentration:
Mass transfer coefficient,
Eo 2.30 x 105 M
Sb = 0.152 M
k₁ = 9.15 x 10 cm/s
A. What is the maximum reaction velocity with no inhibitor (in mol/L-s)?
(recall that Rapid Equilibrium and Quasi steady state approaches predict the same value for Vmax for this mechanism)
B. What is the maximum reaction velocity (in mol/L-s) with the non-competitive inhibitor, I, at a concentration of [1] =
0.0029 M, with K₁ = 1.8 x 10³ M.
C. Calculate the Dahmköhler number to determine if the reaction is diffusion-limited or reaction-limited
(i) when there is no inhibitor
(ii) when the uncompetitive inhibitor is present at [1] = 0.0029 M
Note: Use k₁ a, where a = surface area over reactor volume, when determining the Damkohler number.
D. Calculate KM using the Rapid Equilibrium approach (we've solved for this in the class notes) and determine the actual
reaction velocity for the bulk substrate concentration given, S, = 0.152 M with [1] = 0.0029 M. Will the inhibited
reaction with immobilized enzyme be reaction or diffusion limited? Determine the production rate of fructose.
Transcribed Image Text:6. Sweetzyme® IT Extra is a trademarked immobilized enzyme formulation of glucose isomerase sold by the Danish company Novozymes. The following reaction is carried out in a 4.0 L reactor in the presence of an non-competitive inhibitor, I: E + G <=1=> EG = 2 => E + F EG+1 <=3=> EIG G=glucose, F = fructose The Sweetzyme beads added to the reactor have a total surface area, a = 342 cm². Kinetic Parameters k₁ = 0.00820 M₁¹ S¹ k.₁ = 0.00190 s¹ k₂ = 0.570 s¹ Initial/Total Enzyme concentration: Initial Bulk Substrate Concentration: Mass transfer coefficient, Eo 2.30 x 105 M Sb = 0.152 M k₁ = 9.15 x 10 cm/s A. What is the maximum reaction velocity with no inhibitor (in mol/L-s)? (recall that Rapid Equilibrium and Quasi steady state approaches predict the same value for Vmax for this mechanism) B. What is the maximum reaction velocity (in mol/L-s) with the non-competitive inhibitor, I, at a concentration of [1] = 0.0029 M, with K₁ = 1.8 x 10³ M. C. Calculate the Dahmköhler number to determine if the reaction is diffusion-limited or reaction-limited (i) when there is no inhibitor (ii) when the uncompetitive inhibitor is present at [1] = 0.0029 M Note: Use k₁ a, where a = surface area over reactor volume, when determining the Damkohler number. D. Calculate KM using the Rapid Equilibrium approach (we've solved for this in the class notes) and determine the actual reaction velocity for the bulk substrate concentration given, S, = 0.152 M with [1] = 0.0029 M. Will the inhibited reaction with immobilized enzyme be reaction or diffusion limited? Determine the production rate of fructose.
Expert Solution
Answer to A

Vmax = k2[E0]          =0.570 s-1 × 2.30×10-5 M         = 1.311×10-5 M s-1

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