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To nd kcat, we use the Vmax value determined by the CB E method and the enzyme concentration: (0.73-mM substrate/min)/0.050-mM enzyme) 15 min 1 0.25 s 1. 5. Hanes plots yield slopes of 1/Vmax and y intercepts of Km =Vmax . So, from the values given, Vmax 0:0100 mM=min and Km 2:0 10 5 mM, or 20 pM. Speci c activity is calculated from Vmax 0:0100 I:U:=L, since enzyme concentration is known to be 10 ng/mL (i.e., 0.010 mg/L): (0.0100 I.U./L)/(0.010 mg/L) 1.0 I.U./mg. CHAPTER 3 1. The kinetic method requires [S] < 0.1 Km , since initial rates are measured, and these depend linearly on [S] only under these conditions. 2. For a substrate assay, [S] < 0.1 Km , and for an activity assay, [S] > 10 Km . 3. Detection limits would be considerably improved (lower) if the indicator reaction generates and inhibitor of a uorophore-producing enzymatic reaction, because of the additional catalytic ampli cation provided by this reaction. 4. (a) Only the rst reaction is critical for the AP assay. The other three reactions are indicator reactions that could be used with any primary reaction producing FAD. (b) 0.1 mmol substrate/L converted in 10 min 1 10 5 mmol/(min mL) 1 10 5 I.U./mL. (c) Calculate Vmax 3:2 s 1 1.2 10 8 M enzyme) 4.32 10 8 M/s; after 10 min (600 s), 4.32 10 8 M/s 600 s 2.59 10 5 M substrate has been converted. Since 1:1 stoichiometry prevails, the absorbance change is (2.3 104 M 1cm 1) (1 cm)(2.59 10 5 M) 0.60 AU. (d) In the activity assay, 1.2 10 8 M enzyme would yield and absorbance change of 0.3 AU. Assuming a linear relationship between A and [S], 0.4 10 8 M enzyme would yield 0.1 AU, and 8.0 10 8 M would give 2.0 AU. The approximate dynamic range of the alkaline phosphatase assay is thus 0.004 0.080 mM. Since kcat 3.6 s 1 (or 216 min 1), and Vmax kcat[E], the Vmax values range from 0.86 mM/min to 17 mM/min. These values convert to 8.6 10 4 and 1.7 10 2 I.U./mL. 5. From Beer s law, [ABTS]ox 0.174 AU/(3.48 104 M 1 cm 1 1 cm) 5.00 10 6 M. The AG/ABTS stoichiometry is 1:1, so taking dilution into account, the original [AG] was 5.00 10 5 M. Converting units yields [AG] 8.20 mg/mL, indicating that the patient is diabetic. CHAPTER 4 1. Steps consist of support activation, enzyme coupling, and column packing. Polystyrene must rst be activated to generate suitable functional groups for
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immobilization. This requires nitration, reduction, and diozotization in the activation step. The subsequent coupling step to immobilize the enzyme then consists of exposing the support to a buffered aqueous solution containing cholesterol oxidase. Following this mild coupling step, the polystyrene particles are ltered, rinsed, and packed into a column. Cholesterol oxidase, like other oxidase enzymes, generates hydrogen peroxide which can be detected amperometrically at 0.7 V versus SCE. To use an absorbance detector, peroxidase must be coimmobilized with the cholesterol oxidase, and a dye reagent must be included in the mobile phase so that a colored reaction product is generated. 2. (a) This copolymer yields residual carboxylate groups after immobilization. The negative charge attracts counterions including H , so that local pH at the particle surface is lower than bulk pH. This means that the apparent pH optimum will be higher for the immobilized enzyme than for the dissolved, homogeneous enzyme. This applies to any enzyme immobilized on ethylene/ malic anhydride copolymer. (b) Due to the stagnant (diffusion) layer at the particle surface, the apparent Km for urea will be larger than the homogeneous Km . The same is true for any immobilized enzyme. 3. (a) This is a physical immobilization method. The enzyme is trapped between membranes, but is not chemically bound. The effect of this immobilization on Km could be to increase it slightly (Km is never lower for immobilized enzymes), but the pH optimum is not expected to change. In effect, the enzyme exists in solution that is trapped between membranes, but it is not chemically bound to the surface. Physical immobilization methods have less effect on Km and pH optima than do chemical methods. (b) Response increases linearly with [acetylcholine], then levels off at high 0 concentrations. Km occurs at half-maximal response. (c) Same as Figure 2.12. 4. (a) Silanol groups are derivatized using APTS, giving primary amine groups. These can be reacted directly with protein carboxylate groups, using a dehydrating reagent such as a carbodiimine/NHS reaction; alternately, the primary amines can be diazotized, then coupled to protein residues. (b) From Eq. 4.23, capacity C kETb {(1.45 103 s 1)(0.3-g enzyme)/ (5 104 g/mol} (3 mL/5mL) 3.5 10 3 mol/s 0.21 mol min 1. 0 (c) From Eq. 4.24, substitute C 0.21 mol/min, P 0.95 and given Km values. Using the homogeneous Km value, maximum ow rates of 1.2 104, 1.2 104 and 9.2 103 L/min are obtained with the values given (this column has an extremely large capacity). CHAPTER 5 1. Preparation A is more concentrated, since it must be diluted to a much greater extent to reach the dilute end of the equivalence agglutination zone.
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