Question

Kinetic Inhibition Patterns Indicate how the observed \(K_{\mathrm{m}}\) of an enzyme would change in the presence of inhibitors having the given effect on \(a\) and \(\alpha^{\prime}\) : a. \(\alpha>\alpha^{\prime} ; \alpha^{\prime}=1.0\) b. \(\alpha^{\prime}>\alpha\) c. \(\alpha=\alpha^{\prime} ; \alpha^{\prime}>1.0\) d. \(\alpha=\alpha^{\prime} ; \alpha^{\prime}=1.0\)

Short answer

a: Increase, b: Decrease, c: Unchanged, d: Unchanged.

Step-by-step solution

Recall the Enzyme Kinetics Modification

In enzyme kinetics, under the influence of inhibitors, the apparent Michaelis-Menten constant \(K_{\mathrm{m, app}}\) is given by \(K_{\mathrm{m, app}} = \frac{\alpha K_{\mathrm{m}}}{\alpha^{\prime}}\). Here, \(\alpha\) and \(\alpha^{\prime}\) are modification factors due to competitive and uncompetitive inhibition, respectively.

Analyze Situation a: \(\alpha > \alpha^{\prime}\); \(\alpha^{\prime} = 1.0\)

When \(\alpha > \alpha^{\prime}\) and \(\alpha^{\prime} = 1.0\), it implies that only \(\alpha\) impacts the modification (competitive inhibition). Hence, \(K_{\mathrm{m, app}} = \alpha K_{\mathrm{m}}\). The observed \(K_{\mathrm{m}}\) increases.

Analyze Situation b: \(\alpha^{\prime} > \alpha\)

If \(\alpha^{\prime} > \alpha\), it suggests predominant uncompetitive inhibition, therefore \(K_{\mathrm{m, app}} = \frac{\alpha K_{\mathrm{m}}}{\alpha^{\prime}}\). \(K_{\mathrm{m, app}}\) will decrease since \(\alpha^{\prime}\) is greater than \(\alpha\).

Analyze Situation c: \(\alpha = \alpha^{\prime} > 1.0\)

For \(\alpha = \alpha^{\prime} > 1.0\), both competitive and uncompetitive inhibitions affect equally, so \(K_{\mathrm{m, app}} = K_{\mathrm{m}}\). The observed \(K_{\mathrm{m}}\) remains unchanged.

Analyze Situation d: \(\alpha = \alpha^{\prime} = 1.0\)

When \(\alpha = \alpha^{\prime} = 1.0\), there is no inhibition effect, and hence \(K_{\mathrm{m, app}} = K_{\mathrm{m}}\). The observed \(K_{\mathrm{m}}\) remains unchanged.

Key concepts

Michaelis-Menten constant

The Michaelis-Menten constant, often symbolized as \(K_{\mathrm{m}}\), is a crucial concept in enzyme kinetics. This constant helps us understand how efficient an enzyme is at converting a substrate into a product. Put simply, it's the substrate concentration at which the reaction rate is at half its maximum velocity.
Understanding \(K_{\mathrm{m}}\) gives insights into the affinity of an enzyme for its substrate; a low \(K_{\mathrm{m}}\) means high affinity and vice versa.

• Key to enzyme kinetics: Shows enzyme efficiency
• Low values mean high affinity for substrates
• Helps in comparing different enzyme-substrate interactions

When inhibitors are present, apparent changes to \(K_{\mathrm{m}}\) can occur, depending on the nature and type of inhibition, affecting the enzyme’s catalytic action.

Competitive inhibition

Competitive inhibition is when a substance mimics the substrate and competes for the enzyme's active site. This type of inhibition can significantly affect enzyme kinetics by increasing the apparent Michaelis-Menten constant, \(K_{\mathrm{m, app}}\).
Why does this happen? Because the inhibitor, resembling the substrate, occupies the active site, preventing the substrate from binding. The more inhibitor is present, the more the substrate needs to outcompete it, raising the apparent \(K_{\mathrm{m}}\):

• Directly competes with substrate for active site
• Raises \(K_{\mathrm{m}}\) since higher substrate concentration is needed
• Vmax remains unaffected as inhibitor effect reduces with high substrate concentrations

A good example of competitive inhibition is drugs that block enzyme activity by occupying the active site. Despite raising \(K_{\mathrm{m}}\), it doesn’t change the maximum velocity of the reaction, as the inhibition can be overcome by increasing substrate concentration.

Uncompetitive inhibition

Uncompetitive inhibition occurs when the inhibitor only binds to the enzyme-substrate complex, not the free enzyme. This binding affects the enzyme in a way that prevents the reaction from completing, thus influencing both the \(K_{\mathrm{m, app}}\) and the maximum velocity (Vmax) of the reaction.
This particular form of inhibition reduces APK, the apparent constant. It lowers both \(K_{\mathrm{m}}\) and \(V_{\mathrm{max}}\), allowing the system to work on a new level:

• Bind to enzyme-substrate complex, not free enzyme
• Decreases both \(K_{\mathrm{m}}\) and \(V_{\mathrm{max}}\)
• Cannot be overcome by increasing substrate concentration

What is fascinating about uncompetitive inhibition is how it creates a type of balance. Both the affinity and maximum capacity for the substrate lower simultaneously, meaning it reduces the reaction rate under all substrate concentrations.