Question

Properties of an Enzyme of Prostaglandin Synthesis Prostaglandins are one class of the fatty acid derivatives called eicosanoids. Prostaglandins produce fever and inflammation, as well as the pain associated with inflammation. The enzyme prostaglandin endoperoxide synthase, a cyclooxygenase, uses oxygen to convert arachidonic acid to \(\mathrm{PGG}_{2}\), the immediate precursor of many different prostaglandins (prostaglandin synthesis is described in Chapter 21 . Ibuprofen inhibits prostaglandin endoperoxide synthase, thereby reducing inflammation and pain. The kinetic data given in the table are for the reaction catalyzed by prostaglandin endoperoxide synthase in the absence and presence of ibuprofen. a. Based on the data, determine the \(V_{\max }\) and \(K_{\mathrm{m}}\) of the enzyme. \(\begin{array}{ccc}\begin{array}{c}\text { [Arachidonic } \\ \text { acid] }(\mathrm{mM})\end{array} & \begin{array}{c}\text { Rate of formation of } \\\ \mathrm{PGG}_{2}\left(\mathrm{mM} \mathrm{min}^{-1}\right)\end{array} & \begin{array}{c}\text { Rate of formation of } \\ \mathrm{PGG}_{2} \text { with } 10 \mathrm{mg} / \mathrm{mL}\end{array}\end{array}\) \begin{tabular}{ccc} ibuprofen & \(\left(\mathrm{mM}^{-1} \mathrm{~min}^{-1}\right)\) \\ \hline \(0.5\) & \(23.5\) & \(16.67\) \\ \(1.0\) & \(32.2\) & \(30.49\) \\ \(1.5\) & \(36.9\) & \(37.04\) \\ \(2.5\) & \(41.8\) & \(38.91\) \\ \(3.5\) & \(44.0\) & 25 \\ \hline \end{tabular} b. Based on the data, determine the type of inhibition that ibuprofen exerts on prostaglandin endoperoxide synthase.

Short answer

\(V_{max} \approx 45\, \text{mM/min}, K_m \approx 0.8\, \text{mM}\). Ibuprofen is a competitive inhibitor.

Step-by-step solution

Understand the Enzyme Kinetics Problem

In this problem, we aim to determine the maximum velocity \(V_{\max}\) and the Michaelis constant \(K_m\) of the enzyme prostaglandin endoperoxide synthase based on provided kinetic data. Additionally, we need to identify the type of inhibition exerted by ibuprofen.

Plot the Rate versus Substrate Concentration

Plot the rates of reaction (without ibuprofen) against the corresponding arachidonic acid concentrations. You will notice the formation of a curve typical for enzyme kinetics, indicating saturation as the substrate concentration increases.

Determine \(V_{max}\) and \(K_m\) Without Ibuprofen

To determine \(V_{max}\) and \(K_m\), a Lineweaver-Burk plot can be used, where we plot \(1/\text{Rate}\) against \(1/[\text{Arachidonic Acid}]\). The intercept on the y-axis gives \(1/V_{max}\) and the slope gives \(K_m/V_{max}\). Using the given data:- Without ibuprofen, \(V_{max} \approx 45\, \text{mM/min}\) and \(K_m \approx 0.8\, \text{mM}\).

Analyze Data With Ibuprofen

Check the rates in the presence of ibuprofen. Notice how ibuprofen alters the rate at various substrate concentrations compared to the rates without ibuprofen.

Determine the Effect of Ibuprofen

On plotting a second Lineweaver-Burk plot for the data with ibuprofen, the lines will become steeper, indicating the presence of an inhibitor. In this scenario, ibuprofen increases the apparent \(K_m\), while \(V_{max}\) remains unchanged. This is characteristic of a competitive inhibition.

Identify the Type of Inhibition

Given that ibuprofen increases the apparent \(K_m\) but \(V_{max}\) stays the same, ibuprofen acts as a competitive inhibitor for prostaglandin endoperoxide synthase.

Key concepts

Prostaglandin Synthesis

Prostaglandins are vital components in our body, closely related to processes such as inflammation, pain, and fever. They belong to a group of molecules known as eicosanoids, which are derived from fatty acids. One key enzyme involved in prostaglandin synthesis is prostaglandin endoperoxide synthase, often referred to as a cyclooxygenase. This enzyme acts on arachidonic acid, a polyunsaturated fatty acid found in the body's phospholipids. By using oxygen, it converts arachidonic acid into \(\text{PGG}_2\), a precursor molecule that leads to the formation of various other prostaglandins.

The importance of prostaglandin synthesis lies in its critical role in maintaining physiological functions and also in the pathogenesis of diseases where inflammation is persistent. Understanding the synthesis process provides insight into how therapeutic agents like ibuprofen function to alleviate pain and reduce inflammation. When enzymes like cyclooxygenase are inhibited, the production of prostaglandins decreases, thus reducing symptoms associated with their excessive release.

Competitive Inhibition

In enzyme kinetics, understanding the types of inhibition is crucial for deciphering how substances like drugs can affect enzyme activity. Competitive inhibition occurs when an inhibitor resembles the substrate, in this case, arachidonic acid, and competes for binding at the active site of the enzyme.

Ibuprofen, a common pain reliever, is an example of a competitive inhibitor. It attaches to prostaglandin endoperoxide synthase similarly to how arachidonic acid would. When ibuprofen binds to this active site, it effectively prevents the enzyme from converting arachidonic acid into \(\text{PGG}_2\), thereby reducing the rate of prostaglandin formation.

• Key indicators of competitive inhibition include an increase in \(K_m\) while \(V_{max}\) remains unchanged.
• This type of inhibition is often reversible, meaning that increasing substrate concentration can overcome the inhibitor's effect.

Through this mechanism, drugs like ibuprofen alleviate pain and inflammation by directly interfering with the enzyme's ability to function properly.

Lineweaver-Burk Plot

The Lineweaver-Burk plot is a common graphical representation in enzyme kinetics, useful for determining key kinetic parameters of an enzyme. This double-reciprocal plot transforms the Michaelis-Menten equation into a straight line, making it easier to extract values for \(V_{max}\) and \(K_m\).

The plot displays \(1/\text{Rate}\) against \(1/[\text{Substrate}]\). Through linear transformation, we achieve a straight line with a y-intercept at \(1/V_{max}\) and a slope equal to \(K_m/V_{max}\). This helps in visually distinguishing the effect of inhibitors like ibuprofen.

With competitive inhibition, multiple Lineweaver-Burk plots can be drawn, reflecting changes in the presence of the inhibitor. In these plots, the slopes increase, indicating a higher apparent \(K_m\) while the y-intercept remains the same, confirming that \(V_{max}\) is unaffected. This visual tool is an invaluable resource in enzyme kinetics, facilitating the interpretation of how substrates and inhibitors influence enzymatic reactions.

Michaelis-Menten Equation

The Michaelis-Menten equation lays the foundation for understanding enzyme kinetics, describing the rate of enzymatic reactions in relation to substrate concentration. This equation is fundamental for calculating two important kinetic parameters: \(V_{max}\), the maximum rate of the reaction, and \(K_m\), the substrate concentration at which the reaction rate is half of \(V_{max}\).

The equation is represented as \(v = \frac{V_{max}[S]}{K_m + [S]}\), where \([S]\) denotes the substrate concentration. It models how variations in substrate concentration affect the speed of enzymatic reactions, producing a hyperbolic curve when graphed.

Understanding the Michaelis-Menten equation is crucial when studying enzyme inhibition. In the case of competitive inhibitors such as ibuprofen, \(K_m\) appears to increase because a higher concentration of the substrate is needed to reach \(V_{max}/2\). However, \(V_{max}\) remains constant, indicating that the enzyme can still reach its maximum rate given enough substrate. This equation provides insights into how competitive inhibitors alter enzyme activity.