Chapter 6, Problem 14P

(a)

Summary Introduction

To determine: The value of V_max and K_m of enzyme prostaglandin endoperoxide synthase.

Introduction:

Prostaglandin is class of lipid which is present at a site of injury and tissue damage in body. It is involved in healing process and induces inflammation, and initiation of pain.

Explanation of Solution

Pictorial representation:

Table 1 shows the rate of formation of prostaglandin from arachidonic acid and Fig.1 shows the Lineweaver Burk plot, a double reciprocal plotting for 1/V₀ Vs. 1/[S].

Table 1

Fig.1: Lineweaver Burk plot.

Lineweaver-Burk equation is the reciprocal of Michaelis-Menten equation, and given as:

Michaelis-Menten equation $V_{°}=\frac{V\max \left[\text{S}\right]}{Km+\left[\text{S}\right]}$

Lineweaver-Burk equation $\frac{1}{V_{°}}=\frac{Km}{V\max \left[\text{S}\right]}+\frac{1}{V\max }$

So, by reciprocating the values given in first and second columns of the given table, we get 1/[S] and 1/V₀ values in absence of the inhibitor, as mentioned in Table 1. By plotting these values we obtain the Lineweaver-Burk graph depicted in Fig.1. From the graph, calculating the V max in the absence of inhibitor:

$\begin{array}{l}\text{y-axis}\text{intercept}\text{=}\frac{\text{-1}}{V\max }\\ V\max =\frac{-1}{-0.0194}\\ =51.54\text{mM}\\ \simeq 51.\text{5 mM/min}\\ \end{array}$

Calculating the Km in the absence of inhibitor:

$\begin{array}{l}\text{x-axis}\text{intercept}\text{=}\frac{\text{-1}}{Km}\\ Km=\frac{-1}{-1.7}\\ =0.588\text{mM}\\ \simeq \text{0}\text{.59 mM}\end{array}$

Conclusion

The V_max of enzyme in the absence of inhibitor is 51.5mM/min, while K_m of enzyme in the absence of inhibitor is 0.59mM.

(b)

Summary Introduction

To determine: The type of inhibition that ibuprofen exerts on prostaglandin endoperoxide synthase.

Introduction:

Enzyme inhibitors are defined as chemical molecules that bind at active site of enzymes and prevent the binding of substrate with enzyme. There are two types of inhibitors such as reversible and irreversible inhibitors.

Explanation of Solution

Lineweaver-Burk equation is the reciprocal of Michaelis-Menten equation is given as:

Michaelis-Menten equation $V_{°}=\frac{V\max \left[\text{S}\right]}{Km+\left[\text{S}\right]}$

Lineweaver-Burk equation $\frac{1}{V_{°}}=\frac{Km}{V\max \left[\text{S}\right]}+\frac{1}{V\max }$

So, by reciprocating the given values in column first and third, we get the rate of formation of prostaglandin from arachidonic acid in presence of inhibitor ibuprofen, as mentioned in Table 1. By plotting these values we obtain the Lineweaver-Burk graph for 1/[S] and 1/V₀ in presence of inhibitor, as depicted in Fig.1.

Calculating the Vmax in presence of inhibitor:

V_max in the presence of inhibitor:

$\begin{array}{c}\text{y axis-intercept}=\frac{-1}{V\text{max}}\\ V\text{max}=\frac{\text{-1}}{\text{y axis-intercept}}\\ =\frac{-1}{-0.0194}\\ =51.54\text{mM}/\min \end{array}$

Km of enzyme in the presence of inhibitor:

$\begin{array}{c}\text{x axis-intercept}=\frac{-1}{Km}\\ K_m=\frac{-1}{\text{x axis-intercept}}\\ =\frac{-1}{-1.2}\\ =0.83\text{mM}\end{array}$

The V_max of enzyme both in the presence and absence of inhibitor is 51.54 mM/min, while K_m of enzyme in the presence and absence of inhibitor is 0.83mM and 0.59mM.

Prostaglandin is involved in initiation of pain, and it is synthesized by prostaglandin endoperoxide synthase. Ibuprofen inhibits the activity of this enzyme by binding at the active site and preventing binding of substrate with enzyme. The double reciprocal graph in Fig.1 shows when competitive inhibitor ibuprofen is present, the V_max remains unchanged while K_m increases. Thus, -1/Km value is closer to the origin in the graph depicted in Fig.1. In competitive inhibition, V_max remains unchanged while K_m increases. Therefore, ibuprofen is a competitive inhibitor of prostaglandin.

Conclusion

The inhibition of prostaglandin by ibuprofen is example of competitive inhibition.