(JUNE 2018)
36. The V_max and K_m from a Lineweaver-Burk plot of an enzyme reaction where ¹/_v = 40µM^-1
min at ¹/_[S] = 0 and ¹/_[S] = -1.5 x 10² mM^-1 at ¹/_v = 0 are
(1) 0.025 µM min^-1 and 0.67 x 10^-2mM
(2) 0.025 µM^-1 min and 0.67 x 10^-2
(3) 0.025 µM min^-1 and 1.5 x 10² mM^-1
(4) 0.038 µM min^-1 and 0.67 x 10^-2mM

The correct answer is (1) 0.025 µM min−1−1 and 0.67 \times 10^{-2}$$ mM.

Introduction

The Lineweaver-Burk plot, a double reciprocal graph of the Michaelis-Menten equation, is a classical method used to estimate kinetic parameters such as maximum velocity VmaxVmax and Michaelis constant KmKm of enzyme reactions. Given intercepts from the plot, these parameters can be calculated directly. This article clarifies how to derive VmaxVmax and KmKm given specific plot intercepts, tailored for academic rigor and practical enzyme kinetics understanding.

Given Data from the Lineweaver-Burk Plot

• 1/v=40 μM−1 min1/v=40μM−1min at $1/[S]=0$ (Y-intercept)

• 1/[S]=−1.5×102 mM−11/[S]=−1.5×102mM−1 at $1/v=0$ (X-intercept)

Understanding the Lineweaver-Burk Equation

The Lineweaver-Burk plot plots 1vv1 against 1[S][S]1. The equation is:

1v=KmVmax1[S]+1Vmaxv1=VmaxKm[S]1+Vmax1

• Y-intercept =1Vmax=Vmax1

• X-intercept =−1Km=−Km1

Calculation of VmaxVmax

From the Y-intercept:

1Vmax=40 μM−1 minVmax1=40μM−1min

Calculate VmaxVmax:

Vmax=140=0.025 μM min−1Vmax=401=0.025μMmin−1

Calculation of KmKm

From the X-intercept:

−1Km=−1.5×102 mM−1−Km1=−1.5×102mM−1

Solve for KmKm:

Km=11.5×102=6.67×10−3 mM=0.0067 mMKm=1.5×1021=6.67×10−3mM=0.0067mM

Equivalent to 0.67×10−2 mM0.67×10−2mM.

Interpretation and Significance

• Vmax=0.025 μM min−1Vmax=0.025μMmin−1 represents the maximum reaction velocity when enzyme is saturated.

• Km=6.67×10−3 mMKm=6.67×10−3mM indicates that half-maximal velocity occurs at this substrate concentration, reflecting substrate affinity.

Summary Table

Conclusion

By analyzing the intercepts of a Lineweaver-Burk plot, VmaxVmax and KmKm can be precisely calculated. For the given data, the maximum velocity is 0.025 μM min−10.025μMmin−1, and the Michaelis constant is approximately $0.0067\text{mM}$. This process is fundamental in enzymology for characterizing enzyme behavior and substrate interactions accurately.