Chemistry:
A kinetic study of an intestinal peptidase using glycylglycine as the substrate produced the experimental data shown in the table.
glycylglycine 
glycine
[S]  | Product formed  |
| 1.5 | 0.21 |
| 2.0 | 0.24 |
| 3.0 | 0.28 |
| 4.0 | 0.33 |
| 8.0 | 0.40 |
| 16.0 | 0.45 |
Use the Lineweaver-Burk equation to determine the 
and 
for this enzyme preparation and substrate.
The correct answer and explanation is:
The calculated values for the enzyme kinetics using the Lineweaver-Burk plot are:
- KmK_m (Michaelis constant) = 2.14 mM
- VmaxV_{max} (Maximum reaction velocity) = 0.50 units
Explanation:
The Lineweaver-Burk equation is derived from the Michaelis-Menten equation: 1V=KmVmax⋅[S]+1Vmax\frac{1}{V} = \frac{K_m}{V_{max} \cdot [S]} + \frac{1}{V_{max}}
where:
- VV is the reaction velocity,
- [S][S] is the substrate concentration,
- VmaxV_{max} is the maximum velocity,
- KmK_m is the Michaelis constant.
By plotting 1/V1/V against 1/[S]1/[S], we obtain a straight line where:
- The slope is Km/VmaxK_m / V_{max},
- The y-intercept is 1/Vmax1/V_{max}.
From the experimental data, we calculated the reciprocals of substrate concentration and reaction velocity. Using linear regression, we obtained the equation of the line: y=4.27x+1.997y = 4.27x + 1.997
From the intercept (1/Vmax=1.9971/V_{max} = 1.997), we calculate: Vmax=11.997=0.50V_{max} = \frac{1}{1.997} = 0.50
From the slope (Km/Vmax=4.27K_m / V_{max} = 4.27), we calculate: Km=4.27×0.50=2.14 mMK_m = 4.27 \times 0.50 = 2.14 \text{ mM}
These values describe the enzyme’s efficiency in catalyzing the reaction. The KmK_m value indicates the substrate concentration at which the enzyme operates at half its maximum velocity. A lower KmK_m means higher affinity, while VmaxV_{max} represents the enzyme’s full catalytic potential.
The Lineweaver-Burk plot provides a clear method to determine these kinetic parameters and analyze enzyme efficiency.