Question

Prostaglandins are a class of eicosanoids (fatty acid derivatives) with a variety of extremely potent actions on vertebrate tissues. They are responsible for producing fever and inflammation and its associated pain. Prostaglandins are derived from the 20-carbon fatty acid, arachidonic acid, in a reaction catalyzed by the enzyme, prostaglandin endoperoxide synthase. This uses oxygen to convert arachidonic acid to PGG2 (a prostaglandin). Ibuprofen inhibits this enzyme and is a fever reducer and anti-inflammatory agent. The kinetic data is given below for prostaglandin endoperoxide synthase in the presence and absence of ibuprofen. enzyme (a) Use a double reciprocal plot (Lineweaver-Burke) to determine the Km and Vmax with and without inhibitor and determine the type of inhibition for ibuprofen. S] mM arachidonic acid V (mmol/ml min) V (mmol/ml min) V (mmol/ml min) with 0.3mM your without ibuprofen With 0.2mM ibuprofen compound 0.2 5.0 3.0 2.0 0.4 7.5 5.0 3.0 0.8 10.0 7.5 4.0 1.0 10.7 8.3 4.3 2.0 12.5 10.7 5.0 4.0 13.6 12.5 5.5 Suppose you have synthesized a new compound that also inhibits prostaglandin endoperoxide synthase and have collected kinetic data in the presence and absence of your new compound. (b) Use the same graph paper and to graph a Lineweaver Burke graph to determine the Km and Vmax with your inhibitor and determine the type of inhibition for the compound you made. (c) Determine the Km apparent and the Ki for the competitive inhibitor.

Answer 1

Using the data given, we plot Lineweaver Burke double reciprocal graph which is a plot of 1/V as a function 1/S. The plot gives, y- and x- intercepts.

Y-intercept gives 1/V_max

while x-intercept gives -1/K_m

s (mM)	V(no inhibitor)	V(with Ibuprofen)	V(your compound)	1/s	1/V(no inhibitor)	1/V (ibuprofen)	1/V (your compound)
0.2	5	3	2	5	0.2	0.333333333	0.5
0.4	7.5	5	3	2.5	0.133333333	0.2	0.333333333
0.8	10	7.5	4	1.25	0.1	0.133333333	0.25
1	10.7	8.3	4.3	1	0.093457944	0.120481928	0.23255814
2	12.5	10.7	5	0.5	0.08	0.093457944	0.2
4	13.6	12.5	5.5	0.25	0.073529412	0.08	0.181818182

0.6 1/V 0.066 1/S0.166 0.5 R2 1 0.4 N-0.053 1/s0.066 - No inhibitor 0.3 With Ibuprofen Your compound 0.2 Linear (No inhibitor) 1/V 0.026*1/S+0.066 R2 1 Linear (With lbuprofen) 0.1 Linear (Your compound) -3 -1 1 2 4 6 -0.1 1/S -0.2 un LD

Based on the graph we find for Ibuprofen,

1/V = 0.053*1/S + 0.066

At y-intercept,

x=0

i.e when 1/S =0, V = V_max

Therefore,

1/V_max = 0.066

therefore V_max for inburprofen = 1/0.066 = 15.15 mmol/ml min

At x- intercept

y = 0

Therefore, when 1/V = 0, x-intercept = -1/K_m

=> 0 = 0.053*(-1/K_m) + 0.066

=> K_m for ibuprofen = 0.053/0.066 = 0.803 mM

2) For your compound, the equation is

1/V = 0.066*1/S + 0.166

Therefore V_max is given by

1/V_max = 0.166

V_max for your compound = 1/0.166 = 6.024 mmol/ml min

Therefore K_m is given by

0 = 0.066*-1/K_m + 0.166

K_m of your compound = 0.066/0.166 = 0.3975 mM

As we can see, your compound reduces V_max but does not affect the K_m. Such a tyoe of inhibition is called noncompetitive inhibition. Therefore, your compound exhibits noncompetitive inhibition.

K_I is the inhibitor concentration for V = V_max/2

For your compound V_max = 6.024

Therefore, V_max/2 = 3, at which the inhibitor concentration is 0.3 mM of your compound. Therefore

K_i of your compound = 0.3 mM