Biochemistry
Biochemistry
9th Edition
ISBN: 9781305961135
Author: Mary K. Campbell, Shawn O. Farrell, Owen M. McDougal
Publisher: Cengage Learning
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Chapter 6, Problem 29RE

MATHEMATICAL The hydrolysis of a phenylalanine-containing peptide is catalyzed by α -chymotrypsin with the following results. Calculate K M and V max for the reaction.

Peptide Concentration  ( M ) Velocity  ( M min 1 ) 2.5 × 10 4 5.0 × 10 4 10.0 × 10 4 15.0 × 10 4 2.2 × 10 6 5.8 × 10 6 5.9 × 10 6 7.1 × 10 6

Expert Solution & Answer
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Interpretation Introduction

Interpretation:

The values of KM and Vmax of the hydrolysis reaction of phenylalanine-containing peptide, which is catalyzed by alpha-chymotrypsin, is to be determined.

Concept introduction:

In an enzymatic reaction, Vmax is maximum rate of the reaction, KM is substrate concentration of the reaction that reaches half of its maximum velocity.

The Vmax and KM of a reaction can be calculated with the help of the Lineweaver–Burk plot. In this plot, the substrate concentration, (1[S]), is along the X-axis and the velocity of the reaction 1V is along the Y-axis.

Answer to Problem 29RE

Biochemistry, Chapter 6, Problem 29RE

The graph shows a straight line and on extrapolating the line, it intersects X-axis as well as Y-axis, and the desired value is determined.

The value of the Y-intercept is 450, which also represents (1Vmax).

So, the value of Vmax is calculated as,

(1Vmax)=(1450)Vmax=2.2×103Msec1

Conversion of Msec1 into Mmin1.

60sec=1min1=1min60sec2.2×103Msec=60sec1min×2.2×103Msec=1.32×103Mmin1

The value of the X- intercept is -800, which represents the value of (1KM).

So, the value of KM is calculated as,

(1KM)=(1800)KM=1.25×103M

Explanation of Solution

Given information:

Peptide Concentration           (M)Velocity(M min-1)2.5×1042.2×1065.0×1045.8×10610.0×1045.9×10615.0×1047.1×106

The reciprocal of the substrate concentration and the velocity is required to draw the respective plots. Before plotting the graph, the data must be converted. The reaction velocity data is given in mole/min. It needs to be converted into mole/sec by dividing by 60.

peptide concentration(M)pepetide concentration        (1M)concentation in milimoles            (mmol)velocity (V)=(1V)Mmin1velocity(1V)Msec12.5×1040.400×10440002.2×106=0.4545×1067575.55.0×1040.200×10420005.8×106=0.1724×1062873.310.0×1040.100×10410005.9×106=0.1694×1062823.315.0×1040.067×1046707.1×106=0.1408×1062346.61

In enzyme kinetics, the values of KM and Vmax of a reaction can be determined with the help of the Michaelis–Menten equation. The equation is as follows:

V=Vmax[S]KM+[S]

This equation is further modified so that it can represent in a straight line.

Modification of the equation is,

1V=KMVmax×1[S]+1Vmax

From this equation, the values of both KM and Vmax can be determined. In the given plot, the values are calculated as follows:

KM=1value intersect at x-axis

Vmax=1value intersect at Y-axis

Conclusion

With the help of the Lineweaver–Burk plot, the values of both KM and Vmax is determined. The value of Vmax is 1.32×103 Mmin1 and the value of KM is 1.25×103M.

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Chapter 6 Solutions

Biochemistry

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