Test: Michaelis Menten Kinetics - Chemistry MCQ

Miachelis Menten equation is given by 
Rearranging, 

K_m is defined as the enzyme’s binding efficiency with its appropriate substrate through optimized multiple non-covalent interactions. K_m is also referred to as the substrate concentration at which the reaction occurs at half of the maximum rate. K_cat is referred to as turnover number that denotes the number of catalytic turn over events that happen per unit time. Catalytic efficiency is referred to K_cat/K_m. The high value of this indicates collision frequencies between enzyme and substrate molecule and low value indicates the equilibrium assumption status. V_max is the maximum rate of the reaction.

Miachelis Menten equation is given bywhere
V₀ = initial velocity, V_max = maximum rate, K_m = Miachelis Menten constant and [S] = substrate concentration.
According to this equation, V_o versus [S] plot giving a hyperbolic curve is referred to as Miachelis Menten plot. The tangent to the curve at the origin goes through the point (V₀ = V_max), ([S] = K_m). The substrate concentration, which gives a rate of half the maximum reaction velocity, is equal to the K_m.

Hanes plot equation is based on rearrangement of the Lineweaver Burk plot equation by multiplication of [S0] factor and is given by
where,
V₀ = initial velocity, V_max = maximum rate, K_m = Miachelis Menten constant and [S] = substrate concentration.
The graphical representation of [S₀]/V₀ versus [S₀] is called the Hanes plot. One of the drawbacks of this approach is that neither the ordinate nor the abscissa represents independent variable, both are dependent on substrate concentration.

K_cat is referred to as turn over number which denotes the number of catalytic turn over events that happens per unit time. Catalytic efficiency is given by K_cat/K_m. Miachelis Menten constant is given by K_m. Substrate concentration is the amount substrate used in an enzyme catalyzed reaction.

4*10⁷ is the value of catalytic efficiency of catalase. Catalytic efficiency is referred to as K_cat/K_m. High value indicates that the collision frequencies between enzyme and substrate molecule and low value indicates that the equilibrium assumption status. As 4*10⁷ M^-1s^-1 is the value of catalytic varies from less than 1 M^-1s^-1 to greater than 108 M^-1s^-1.

Hanes plot is a graphical representation of [S₀]/V₀ is plotted against [S₀] which is based on the equation, 
where
V₀ = initial velocity, V_max = maximum rate, K_m = Miachelis Menten constant and [S] = substrate concentration.
This plot yields a straight line of slope 1/V_max, a y-intercept of K_m/V_max and an x-intercept of -K_m.

The Miachelis Menten equation is proved to be unsatisfactory for the following reasons:
The graph proposed is not following a proper mathematical model.
The graph is following a tangent model and hence it is difficult to calculate an exact K_m and V_max.
Hence Lineweaver and Burk came up with a suitable solution to solve this problem. The equation

represents Lineweaver Burk equation where,
V0 = initial velocity, V_max = maximum rate, K_m = Miachelis Menten constant and [S] = substrate concentration.

The flexible nature of enzymes was not dealt by lock and key model, but the induced fit model. This model dealt with change in shape after enzyme substrate interaction. The following assumptions were made in rapid equilibrium model:
* The substrate concentration will always be higher than enzyme concentration. [E] >> [S]
* An equilibrium state is assumed between reactants and products. [E]+[S]⇌[ES]
* It is the initial substrate concentration [S_o] that determines the efficacy of an enzyme to mediate a reaction.

The main difference between Henri and Miachelis Menten model is that Miachelis and Menten did a strong experimental work to prove that any enzyme catalyzing single substrate reaction will possess a hyperbolic curve. The unique feature of this model is assumption of rapid equilibrium between reactants and ES complex, where the ES complex will slowly decompose to form free enzyme and products. Hence it is appropriate to term this model as “rapid equilibrium model”. Hence the above statement is true.