Question

1. Graphic depictions of enzyme kinetic data can aid in evaluation of reversible enzyme inhibition. Please use the data below to determine type of inhibition for using two different concentrations (in blue and purple). Be sure to include graphical representation (Michaelis-Menton, Lineweaver-Burk plots), type of inhibition, appropriate kinetic schemes and rate equations. The enzyme concentration at its initial state E, was kept constant. All data points are given in arbitrary units. Completely justify your answer. Use Excel or graphing paper provided (or you may use your own graph paper). (15 points) Extra Credit: Discuss in details how Km and Vmax are affected by inhibition. How can changing the substrate concentration help to achieve Vmax ? No Inhibition Inhibitor at concentration A 1/v Inhibitor at concentration B 1/v [S] 1/[] V 1/v v 1.0 1.0 12 0.083 7.8 0.128 4.3 0.233 2.0 0.50 20 0.050 13.7 0.073 8.0 0.125 4.0 0.25 29 0.034 21.8 0.046 14.0 0.071 8.0 0.125 35 0.029 30.3 0.033 21.0 0.048 12.0 0.083 40 0.025 34.5 0.029 26.0 0.038

Answer 1

Enzyme kinetics involves the study of an enzyme catalyzed reaction by determining the various kinetic parameters through equations and graphs. The fundamental equation for determining the kinetic parameters such as Km and Vmax is Michaelis-Menten equation, which is as the following:

Vo= Vmax. [S]/ Km +[S]

where, Vo or v is the initial velocity

Vmax is the maximum velocity

[S] is the substrate concentration

Km is the Michaelis constant or the enzyme affinity for the substrate

When a graph is plotted through this equation, approximate values of Km and Vmax are observed.

Therefore, to get exact values of Km and Vmax, the inverse of Michaelis-Menten equation is derived which is called Lineweaver Burk or LB equation, which is as the following:

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

This equation can be compared to a straight line equation:

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

y = m . x + c

where

y=1/Vo; m= Km/Vmax; x= 1/[S]; c=1/Vmax

So, y-axis: 1/Vo, and x-axis: 1/[S]

y-intercept= 1/Vmax; x-intercept= -1/Km

m= slope of the straight line

The given data is as the following:

[S]	v (no inhibition)	v (inhibitor at conc. A)	v (inhibitor at conc. B)	1/[S]	1/v (no inhibitor)	1/v (Inhibitor at conc. A)	1/v (inhibitor at conc. B)
1	12	7.8	4.3	1	0.083333	0.128205	0.232558
2	20	13.7	8	0.5	0.05	0.072993	0.125
4	29	21.8	14	0.25	0.034483	0.045872	0.071429
8	35	30.3	21	0.125	0.028571	0.033003	0.047619
12	40	34.5	26	0.083333	0.025	0.028986	0.038462

Michaelis-Menten Plot is hyperbolic in nature. The following plot is obtained by using the substrate concentration [S] and initial velocity v values. The velocity increases with the substrate but with further increase in the substrate concentration, not much change is observed in the velocity of the reaction. This velocity attained by the enzyme is maximum and called Vmax. The velocity of the reaction does not increase beyond Vmax. This happens due to complete saturation of the active sites with the substrate and any further addition of substrate gives no additional enhancement in the velocity or the rate of the reaction.

The substrate concentration at which the velocity of the reaction is equal to the half of the maximum velocity, is called Km or the Michaelis constant. It determines the affinity of the enzyme towards the substrate, higher the Km, lower is the affinity, lower the Km, higher is the affinity for the substrate.

Any change in the Km and Vmax in presence of inhibitors, help in determining the type of inhibitor.

45 40 35 30 25 20 v (no inhibition) v (inhibitor at conc. A) -V (inhibitor at conc. B) 15 LO 5 0 0 5 10 15 [S]

Lineweaver Burk (LB) plot is prepared by taking the inverse values of [S] and initial velocity (v) values.

0.25 0.2 0.15 A/L 0.1 -1/v(no inhibitor) -1/v (Inhibitor at conc. A) -1/v (inhibitor at conc. B) 0.05 -0.6 -0.4 -0.2 012 0.4 016 0.8 12 0.05 -0.1 1/[S]

From the LB plot, it is evident that Km of the enzyme is increasing in the presence of the inhibitor, and it further increases with the increase in the inhibitor concentration. But, the maximum velocity Vmax of the reaction remains same in each case. Km in absence and presence of the inhibitor can be calculated from the x-intercepts, while Vmax is determined from the y-intercept. The LB plot indicates competitive inhibition by the inhibitor, it is increasing the Km, but does not affect the velocity of the reaction..

Competitive inhibition is one of the types of reversible inhibition. In this, the inhibitor and the substrate have similar structure, hence the inhibitor competes with the substrate for the active site and prevents the substrate binding. This lowers the affinity of the enzyme towards the substrate, hence increasing the Km of the enzyme. The inhibition can be reversed by increasing the substrate concentration, which causes the binding of substrate to the active site instead of the inhibitor, thus reversing the effect of the inhibitor.