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In the twentieth century, many scientists were working on kinetics. But Leanor Michaelis and Maud Leonora Menten have proposed a theory on kinetics. It is mainly used in or dealing with chemical reactions and enzymatic reactions. We know that enzymes are used to speed up chemical reactions. It also helps to determine at which speed the reaction is going on when a catalyst is added to that particular chemical reaction. The theory of Michaelis-Menten Kinetics completely deals with how the catalyst is speeding up the reaction, the mechanism behind the speed-up of reaction, the speed at which the enzyme or catalyst is working and the speed of reaction increased when the catalyst or enzyme is added. It is mainly designed to explain the velocity of enzyme-catalyzed reactions and their gross mechanism. This Michaelis Menten hypothesis is used the most among all the best models.
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Key takeaways: first order reaction, zero order reaction, enzyme reaction, chemical kinetics, substrate, concentration.
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Basic Enzyme Reaction
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When the enzyme acts on the substrate, the substrate gets converted into the product. The product is finally released. Hence with respect to time, the substrate concentration decreases, and the concentration of the product increases. The slope of the graph gives information about the rate of reaction. There is a change in the concentration to time. Hence, we can also call this as velocity of the given reaction.
The reaction velocity is calculated as:
Rate = – d[s]/dt = d[p]/dt.
According to the graph we obtained by velocity v/s substrate, we can say that the first part of the graph is linear. It is meant that the reaction rate increases linearly with respect to substrate concentration. This linear increase in the velocity is called the first-order reaction kinetics. Then the graph curve shows that very less increase in the velocity even the substrate is increasing. At this point, we can say that velocity has reached its maximum point. Hence, it is called Vmax. This region is called zero-order kinetics. Here the velocity of the reaction is independent of the substrate concentration. This is called zero-order kinetics.
It can be defined in a mathematical format such as y= mx + c. where,
Y = velocity
M = slope
X = substrate
C = intercept on y-axis.
This cannot be used in the curved region that is zero order velocity, because the velocity is independent of the substrate concentration. This particularly fits for the first order kinetics because the velocity is increasing linearly. Now this Michaelis-Menten kinetics explains the curve of first order kinetics mathematically.
Aim
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The main target of this equation is to create a mathematical relation between velocity and substrate concentration at the curved area. Then they tried to establish a relation between V0, Vmax. Such that both zero order and first order kinetics can be explained.
Read More: Elementary Reactions
Derivation
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E + S → ES (Kf)
E + S ← ES (Kr)
This is an equilibrium assumption.
According law of mass action:
Kf [E] [S] = Kr [ES]
[E] [S] / [ES] = Kr / Kf = Kd
It is called a dissociation constant; it is represented by Kd.
Another assumption is the pseudo-steady-state hypothesis.
ES à E + P (Kcat as a catalyst)
Here we can say that the concentration of ES complex is constant. This is called as rate of formation of ES is equal to rate of break down of ES. ES is formed by the reaction between enzyme and substrate.
[ES] formation = [ES] breakdown
[ES] formation = Kf [E] [S]
[ES] breakdown = Kr [ES] + Kcat [ES]
Kf [E] [S] = Kr [ES] + Kcat [ES]
Kf [E] [S] = [ES] (Kr+Kcat)
[E] [S] / [ES] = Kr+Kcat / Kf = Km
Relation between V0, Vmax and Km
Velocity (V0) = d[p] / dt
V0 = Kcat [ES]
E0 = E + ES
Vmax = Kcat [E0]
Km = [E] [S] / [ES] = [E0-ES] [S] / [ES]
Km = [E0] [S] – [ES] [S] / [ES]
Km = [E0] [S] / [ES] – [S] /1
Km = Vmax [S] / Kcat [ES] – [S] /1
Km + [S] = Vmax [S] / V0
V0 = Vmax [S] /Km + [S]
Cases in the derived equation
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Case1: According to the equation, when the concentration of substrate is very large then Km is very low. S>>>Km then we can ignore Km such that:
V0 = Vmax
Case2: Half of Vmax
V0 = Vmax / 2
Vmax / 2 = Vmax [S] / Km + [S]
Km = [S]
Hence, this is the reaction we obtained by using the Michaelis-Menten hypothesis.
Read More: Diatomic
Things to Remember
- Michaelis-Menten's hypothesis is majorly used to find the speed of the reactions when enzymes are added.
- There are two regions in the reaction: zero order and first order.
- In the zero-order area, the velocity of the reaction will linearly increase with respect to the substrate concentration
- In the first order we find a curve at which the rate is not constant and can’t be determined.
- According to the equation, when the concentration of substrate is very large then Km is very low then, V0 = Vmax
- When V0 is equal to half of Vmax then, Km = [S]
Read More: Dalton’s atomic theory
Sample Questions
Ques: What does the Michaelis-menten equation explain to us? (2 marks)
Ans: This tells and explains to us that when there is a very low concentration the rate of an enzyme is directly proportional to the substrate concentration. At very high concentrations, the rate of enzyme operation reaches the maximum and it is called maximum velocity.
Ques: What are the factors affecting the Michaelis-Menten constant? (2 marks)
Ans: Factors such as:
- pH
- temperature
- ionic strengths
- the nature of substrate
Ques: what is the reason that Vmax depends on the enzyme concentration? (2 marks)
Ans: In fact, chemical kinetics states that the reaction rate is dependent on the concentration of the reactants. Although enzymes, Vmax is also dependent on the enzyme concentration. This is due to the more enzyme molecules will increase the rate by reacting with more molecules. Thus more substrate is formed fastly.
Ques: What is the type of curve obtained in the Michaelis-menten kinetics? (2 marks)
Ans: In the Michaelis-Menten hypothesis the velocity and substrate concentration is represented in the graph format. This gives us a hyperbola shape when we draw it. It represents that the first half is linear and then we obtain a curve that results in the shape of a hyperbola.
Ques: Is there an increase in Vmax when pH is increased? (2 marks)
Ans: Yes, the enzyme reaction and activity are high when the new pH is created. Because when we add the enzyme and with the enzyme-substrate reaction gets increased and new products will be forming with the new pH. Thus, this affects the Vmax.
Ques: Is there any change in Vmax due to a change in temperature? (2 marks)
Ans: Both the Vmax and km are dependent on temperature. It ranges from 13 to 55 degrees Celsius. Vmax values increased steadily until the denaturation point with all enzymes, the effect of temperature on Km was more variable.
Ques: What are the factors affecting the Vmax of an enzyme? (2 marks)
Ans: Vmax is affected by factors such as:
- Enzyme concentration
- Temperature
- pH
Ques: which enzyme doesn’t follow Km kinetics? (2 marks)
Ans: Allosteric enzyme is the enzyme that doesn’t follow the Michaelis-Menten constant and it shows a sigmoid saturation curve whereas this shows the hyperbola.
Ques: A first-order reaction has a rate constant of 1.15 x 10-3 s-1. How long will 5g of this reactant take to reduce to 3g? (2 marks)
Ans: t = 2.303/k log[R0]/[R]
= 2.303/1.15x10-3 log(5/3)
= 2.00x103 log(1.667)
= 444s
Ques: Time required to decompose SO2CL2 to half of its initial amount is 60 minutes. If the decomposition is a first-order reaction, calculate the rate constant of the reaction. (2 marks)
Ans: t1/2 = 60min = 3600 sec
t ½ = 0.693/k
3600=0.693/k
K= 0.0001925.
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