Lineweaver-Burk Plots – MCAT Biochemistry | MedSchoolCoach

## Sample MCAT Biochem Question

Which of the following best represents a Lineweaver-Burk plot for competitive inhibition?

a) The x-intercept shifts further from zero

b) The y-intercept increases

c) The x-intercept shifts closer to zero

d) The y-intercept decreases

C is correct: The x-intercept shifts closer to zero.

The Lineweaver-Burk plot is a graphical method of analyzing the Michaelis–Menten equation and the enzyme-substrate-inhibitor relationship. The x-axis in the graph is 1/[S], and the y-axis is 1/V. In competitive inhibition, the inhibitor decreases the binding affinity for the enzyme to the substrate by competing with the substrate for the active site. This competition increases the Km, since it will take more substrate to outcompete the inhibitor and move the reaction forward. Increasing the Km will cause the x-intercept of the Lineweaver-Burk plot to shift closer to zero (choice A is incorrect). Answer choices B and D are incorrect, the y-intercept will not change.

### What is a Lineweaver-Burk plot?

A Lineweaver-Burk plot is another way of representing the data of Michaelis-Menten saturation curves is through Lineweaver-Burk plots. The Lineweaver-Burk plot is derived from the Lineweaver-Burk equations, which themselves are derived from the Michaelis-Menten equation:

Vo = Vmax [S] / Km + [S]

The reciprocal of this equation is:

1 / Vo = (Km / Vmax [S]) + (1 / Vmax)

From this, the Lineweaver-Burk equation becomes:

1 / Vo = (Km / Vmax ) (1 / [S]) + (1 / Vmax)

One thing to note about the Lineweaver-Burk equation is that when plotted as a graph, it is a linear line with the equation y = mx + b (Figure 1). As a line, interpreting the data points is straightforward. The Michaelis-Menten saturation curve, on the other hand, is more challenging to interpret at times due to the different data points and the hyperbolic nature of the graph.

In terms of the Lineweaver-Burk plot, the slope is equal to Km / Vmax, the x-intercept is equal to -1 / Km, and the y-intercept is equal to 1 / Vmax . The Lineweaver–Burk plot is the graphical representation of enzyme kinetics without an enzyme inhibitor. The x-axis and y-axis can also be interpreted as 1 / substrate concentration, or 1 / [S] and 1 / V. In this way, the Lineweaver-Burk plot is often also called the double reciprocal plot. Increasing the substrate concentration decreases the value of 1 / [S] because the denominator is getting larger. Therefore, going left on the x-axis indicates an increasing substrate concentration. Likewise, a greater reaction velocity decreases the value of 1 / V. Therefore, going left and down the Lineweaver-Burk plot indicates an increasing substrate concentration, which would naturally create a greater reaction velocity, since there is more substrate to react with the enzyme pushing the reaction forward.

One crucial point about the Lineweaver-Burk plot is that the x-axis goes into negative values. However, there is no such thing as negative substrate concentrations. Instead, researchers can use this graph to extrapolate data from a hypothetical situation in which a negative substrate concentration exists.

### Lineweaver-Burk Plot & Enzyme Inhibition

It is easy to visualize the effects of different types of inhibitors on an enzymatic reaction using the Lineweaver-Burk plot. Figure 2 shows Lineweaver-Burk plots with the effects of competitive, uncompetitive, and mixed inhibitors.

In terms of competitive inhibitors, recall that they compete directly with the substrate to bind to the active site of the enzyme. In turn, they will decrease the affinity of the enzyme for the substrate, which will increase the Km. As stated above, the x-intercept is equal to -1 / Km. Increasing the value of the Km will then decrease the value of the x-intercept. Decreasing the value of the x-intercept will shift the line closer to zero. Also, the y-intercept will stay the same because competitive inhibitors do not affect the maximum velocity of the reaction. In competitive inhibitors, the slope of the graph increases, the x-intercept shifts to the right, and the y-intercept is unchanged.

For uncompetitive inhibitors, both the Km and the Vmax will be reduced. Recall that since uncompetitive inhibitors increase the affinity of the enzyme for the substrate, Km decreases. Also, since the x-intercept is equal to -1 / Km, a smaller Km would give a larger value for the x-interceptor. In this way, the x-intercept will shift to the left. Also, since uncompetitive inhibitors also decrease the maximum reaction velocity, the value of the y-intercept, or 1 / Vmax , will increase. Increasing the y-intercept will shift the line upwards. Therefore, uncompetitive inhibitors will result in a parallel line to the original graph, in which both the x and y-intercepts have changed.

Lastly, for mixed inhibitors, the Km is unaffected, and the Vmax decreases. Recall that the Km of mixed inhibitors is variable, depending on the specific inhibitor being used. However, mixed inhibitors are a form of noncompetitive inhibition, and with noncompetitive inhibition, the Vmax decreases. However, the Km is unchanged. Therefore, the x-intercept stays the same; however, since the Vmax decreases, the y-intercept shifts upward.

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