(JUNE 2012)
33. A plot of V/[S] versus V is generated for an enzyme catalyzed reaction, and a straight line is obtained. Indicate the information that can be obtained from the plot.
(1) V_max and K_m can be obtained only from a plot of 1/V versus 1/[S].
(2) K_m/V_max from the slope
(3) V_max and K_m                                              (4) only K_m

The correct answer is (2) Km/Vmax from the slope.

Introduction

Enzyme kinetics is often studied by plotting various transformations of reaction velocity and substrate concentration to linearize data and extract meaningful parameters. One such transformation is the Eadie-Hofstee plot, where the ratio $V/[S]$ is plotted against reaction velocity $V$. If this plot yields a straight line, key parameters like the Michaelis constant (KmKm) and maximum velocity (VmaxVmax) can be determined directly. This article explains the significance of a $V/[S]$ vs. $V$ plot and how to interpret it to calculate these enzymatic constants.

The Michaelis-Menten Equation

The fundamental Michaelis-Menten equation is:

V=Vmax[S]Km+[S]V=Km+[S]Vmax[S]

Where

• $V$ is the reaction velocity

• VmaxVmax is the maximum velocity

• $[S]$ is substrate concentration

• KmKm is the Michaelis constant

Rearranging for the $V/[S]$ vs. $V$ Plot (Eadie-Hofstee Plot)

Divide both sides by $[S]$:

V[S]=VmaxKm+[S][S]V=Km+[S]Vmax

Using algebraic manipulation, it can be shown that:

V=−Km×V[S]+VmaxV=−Km×[S]V+Vmax

This is a straight-line equation of the form:
$y=mx+c$
Where,

• $y=V$

• x=V[S]x=[S]V

• Slope m=−Kmm=−Km

• Intercept c=Vmaxc=Vmax

What Information Does This Plot Provide?

• The slope of the straight line gives −Km−Km, so the absolute value of the slope equals the Michaelis constant.

• The y-intercept corresponds to the maximum velocity VmaxVmax.

This linearization helps overcome common issues with other plots (e.g., Lineweaver-Burk) such as unequal error distribution and compression of data points at high substrate concentrations.

Why Is This Useful?

• Allows direct determination of KmKm and VmaxVmax from experimental data.

• More robust to data uncertainties compared to double reciprocal plots.

• Represents enzyme kinetics data in a form conducive to rapid parameter estimation.

Summary Table

Conclusion

A plot of $V/[S]$ versus $V$ that yields a straight line is known as an Eadie-Hofstee plot. From this plot, the Michaelis constant (KmKm) can be estimated from the slope, while the maximum reaction velocity (VmaxVmax) is determined from the y-intercept. This approach provides an alternative and useful method for analyzing enzyme kinetics data with greater accuracy and insight.