This question asks to identify the correct Eadie-Hofstee plot for an enzyme exhibiting Michaelis-Menten kinetics in the presence of an uncompetitive inhibitor.

Understanding Eadie-Hofstee Plots

The Eadie-Hofstee plot graphs the initial velocity ($v_0$) on the y-axis against the ratio $v_0/[S]$ (where $[S]$ is substrate concentration) on the x-axis. The equation is represented as: $v_0 = V_{max} - K_m \frac{v_0}{[S]}$ This equation is in the form $y = c + mx$, where:

• $y = v_0$
• $x = v_0/[S]$
• $c = V_{max}$ (y-intercept)
• $m = -K_m$ (slope)

Effect of Uncompetitive Inhibition

An uncompetitive inhibitor binds exclusively to the enzyme-substrate (ES) complex. This type of inhibition affects the enzyme kinetics by:

• Decreasing the maximum velocity ($V_{max}$).
• Decreasing the Michaelis constant ($K_m$).

Eadie-Hofstee Plot Changes with Uncompetitive Inhibition

Based on the Eadie-Hofstee equation and the effects of uncompetitive inhibition:

• Y-intercept ($V_{max}$): Since $V_{max}$ decreases, the y-intercept of the plot shifts downwards in the presence of the inhibitor.
• Slope ($-K_m$): Since $K_m$ decreases, the value of $-K_m$ becomes less negative (i.e., the slope increases towards zero). The slope becomes less steep.

Therefore, the line representing the inhibited enzyme (+I, solid line) should be positioned below the uninhibited enzyme line (-I, dotted line) and have a less steep slope.

Analyzing the Options

We need to find the plot that shows a decreased y-intercept and a less steep slope.

• Option 1 (Plot 1): Shows a decreased y-intercept and a less steep slope. The lines intersect on the x-axis. This is consistent with the theoretical model of uncompetitive inhibition.
• Option 2 (Plot 2): Shows a decreased y-intercept but a steeper slope (more negative). This pattern is characteristic of competitive inhibition.
• Option 3 (Plot 3): Shows a decreased y-intercept, but the slope change is less clear or potentially constant. This does not perfectly fit the expected changes for uncompetitive inhibition.
• Option 4 (Plot D): Shows a decreased y-intercept ($V_{max}$) and a less steep slope (increased $-K_m$, meaning decreased $K_m$). The solid line (+I) is below and less steep than the dotted line (-I). This plot visually matches the expected changes in intercept and slope for uncompetitive inhibition.

Plot 4 (Option D) best depicts the decrease in both $V_{max}$ (y-intercept) and $K_m$ (slope) characteristic of uncompetitive inhibition on an Eadie-Hofstee plot.