Michaelis Menten equation

Summary

The video script explains the Michaelis-Menten equation, a fundamental concept in enzyme kinetics. It describes how enzyme and substrate interact, leading to product formation. The script outlines the initial linear relationship between reaction rate and substrate concentration, known as first-order kinetics, and the subsequent plateau where the rate reaches a maximum, or Vmax, indicative of zeroth-order kinetics. The Michaelis-Menten equation is derived to mathematically model both kinetics, incorporating the enzyme-substrate complex, equilibrium assumption, and the pseudo-steady state hypothesis. The equation ultimately relates reaction velocity (V0), maximum velocity (Vmax), and substrate concentration, with a focus on the Michaelis constant (Km), which is the substrate concentration at half-maximal velocity.

Takeaways

• 🧪 The Michaelis-Menten equation describes the relationship between enzyme kinetics and substrate concentration.
• 📈 The velocity of a reaction, which is the rate of product formation, can be plotted against substrate concentration to observe first-order and zeroth-order kinetics.
• 🔍 Initially, the reaction rate increases linearly with substrate concentration, indicating first-order kinetics.
• 🏁 At high substrate concentrations, the reaction rate plateaus, indicating zeroth-order kinetics where the rate is independent of substrate concentration.
• 💡 The Michaelis-Menten equation is derived from the equilibrium assumption and the pseudo-steady state hypothesis, which assumes a constant concentration of the enzyme-substrate complex.
• ⚖️ The Michaelis constant (Km) is defined as the substrate concentration at which the reaction rate is half of its maximum velocity (Vmax).
• 🔄 The equation incorporates the concept that the rate of formation of the enzyme-substrate complex equals the rate of its breakdown.
• 🌐 The total enzyme concentration is the sum of free enzyme and enzyme bound to the substrate.
• 📉 At maximum velocity (Vmax), all enzyme molecules are bound to the substrate, and no free enzyme is left.
• 🔄 The final form of the Michaelis-Menten equation is V0 = Vmax * [S] / (Km + [S]), which can describe both first-order and zeroth-order kinetics.

Q & A

What is the Michaelis-Menten equation?

The Michaelis-Menten equation is a mathematical model that describes the initial velocity of an enzyme-catalyzed reaction as a function of substrate concentration. It helps to establish a relationship between the initial velocity (V0), maximum velocity (Vmax), and substrate concentration (S).

What is the significance of the slope in a graph that shows the rate of reaction with respect to time?

The slope in a graph that shows the rate of reaction with respect to time represents the velocity of the reaction, which is the rate at which the substrate is converted into product.

What does the linear increase in the graph of reaction velocity versus substrate concentration indicate?

The linear increase in the graph indicates first-order reaction kinetics, where the rate of reaction increases linearly with substrate concentration.

What is meant by the plateau region in the graph of reaction velocity versus substrate concentration?

The plateau region in the graph indicates zeroth-order reaction kinetics, where the velocity of the reaction no longer increases with substrate concentration, reaching a maximum velocity (Vmax).

Why is the simple first-order equation not applicable to the plateau region of the reaction velocity graph?

The simple first-order equation is not applicable to the plateau region because, in this region, the velocity of the reaction is independent of substrate concentration, which contradicts the assumption of first-order kinetics.

What is the equilibrium assumption in the context of the Michaelis-Menten equation?

The equilibrium assumption states that the enzyme-substrate complex (ES) formed during the reaction is in a dynamic equilibrium, meaning the rate of formation of ES is equal to the rate of its breakdown into enzyme (E) and substrate (S) or product (P).

What is the pseudo-steady state hypothesis in enzymatic reactions?

The pseudo-steady state hypothesis assumes that the concentration of the enzyme-substrate complex (ES) remains approximately constant during the reaction, implying that the rate of formation of ES is equal to the rate of its breakdown.

How is the Michaelis constant (Km) defined in the context of the Michaelis-Menten equation?

The Michaelis constant (Km) is defined as the substrate concentration at which the reaction velocity is half of the maximum velocity (Vmax). It is also the ratio of the rate constants for the breakdown of the enzyme-substrate complex to its formation.

What does Vmax represent in the Michaelis-Menten equation?

Vmax represents the maximum velocity of the enzyme-catalyzed reaction, which is the highest rate that can be achieved when all enzyme molecules are saturated with substrate.

How is the velocity of the reaction (V0) related to the substrate concentration (S) and the Michaelis constant (Km) in the Michaelis-Menten equation?

The velocity of the reaction (V0) is related to the substrate concentration (S) and the Michaelis constant (Km) by the equation V0 = Vmax * S / (Km + S), which describes how the reaction velocity changes with substrate concentration.

Outlines

00:00

🧪 Understanding Michaelis-Menten Equation

This paragraph introduces the Michaelis-Menten equation, which is fundamental to understanding enzyme kinetics. It explains how the enzyme acts on the substrate, leading to the conversion of substrate into product, and how this process can be visualized through a graph showing the rate of reaction (velocity) with respect to time. The velocity is directly related to the change in concentration of the substrate and product. The graph typically starts with a linear region representing first-order kinetics, where the reaction rate increases linearly with substrate concentration, and then plateaus in a zeroth-order kinetics region where the reaction rate reaches a maximum (Vmax) and becomes independent of substrate concentration. The paragraph also introduces the mathematical representation of these kinetics, starting with a simple first-order equation and setting the stage for the derivation of the Michaelis-Menten equation, which will account for both first and zeroth-order kinetics.

05:01

🔍 Deriving the Michaelis-Menten Equation

This paragraph delves into the derivation of the Michaelis-Menten equation, which is crucial for describing enzyme kinetics under various substrate concentrations. It starts by establishing the relationship between initial velocity (V0), maximum velocity (Vmax), and the Michaelis constant (Km). The paragraph outlines the assumptions made in the derivation, including the equilibrium assumption and the pseudo-steady state hypothesis. These assumptions lead to the formulation of the Michaelis-Menten constant (Km), which is defined as the substrate concentration at which the reaction velocity is half of Vmax. The paragraph then proceeds to derive the equation that relates V0 to Vmax, Km, and substrate concentration (S), culminating in the classic Michaelis-Menten equation: V0 = Vmax * S / (Km + S). This equation is key to understanding how enzyme activity is regulated and how it responds to changes in substrate concentration.

Keywords

💡Michaelis Menten equation

The Michaelis Menten equation is a mathematical model that describes the initial rate of an enzyme-catalyzed reaction. It is fundamental to understanding enzyme kinetics. In the video, this equation is used to explain the relationship between the initial reaction velocity (V0), the maximum reaction velocity (Vmax), and the substrate concentration ([S]). The equation is derived to account for both first-order and zero-order kinetics, showing how the reaction velocity changes with different substrate concentrations.

💡Enzyme

An enzyme is a biological catalyst that speeds up chemical reactions in the body. In the context of the video, the enzyme acts on the substrate to convert it into a product, which is a key part of many biochemical processes. The enzyme's efficiency and the rate at which it works are central to the discussion on enzyme kinetics.

💡Substrate

A substrate is the molecule upon which an enzyme acts to catalyze a reaction. In the video, the substrate's concentration is shown to have a direct impact on the reaction rate, particularly in the initial stages of the reaction where the rate increases linearly with substrate concentration.

💡Product

The product is the result of the enzymatic reaction where the substrate is converted. The video explains that as the substrate concentration decreases over time, the product concentration increases, which is indicative of the progress of the enzymatic reaction.

💡Reaction velocity

Reaction velocity, also known as the rate of reaction, is the speed at which a chemical reaction proceeds. It is measured by the change in concentration of reactants or products over time. In the video, the velocity of the reaction is used to describe how quickly the enzyme converts substrate into product.

💡First-order reaction kinetics

First-order reaction kinetics refers to a scenario where the rate of reaction is directly proportional to the concentration of the substrate. The video script describes the initial linear portion of the reaction velocity graph as an example of first-order kinetics, where the rate increases linearly with substrate concentration.

💡Zeroth order reaction kinetics

Zeroth order reaction kinetics is characterized by a reaction rate that is independent of substrate concentration, reaching a plateau where increasing substrate concentration does not increase the reaction rate. The video explains this concept as the enzyme becomes saturated with substrate, and the reaction rate levels off at Vmax.

💡Vmax (maximum velocity)

Vmax, or maximum velocity, is the highest rate of reaction that an enzyme can achieve. It occurs when all the enzyme's active sites are occupied by the substrate. In the video, Vmax is described as the point at which the reaction velocity plateaus, indicating that the enzyme is working at its full capacity.

💡Km (Michaelis Menten constant)

Km is the Michaelis Menten constant, which is a measure of the affinity of an enzyme for its substrate. It is the substrate concentration at which the reaction velocity is half of Vmax. The video script uses Km to derive the Michaelis Menten equation and to explain the relationship between substrate concentration and reaction velocity.

💡Pseudo steady state hypothesis

The pseudo steady state hypothesis is an assumption used in enzyme kinetics that the concentration of the enzyme-substrate complex (ES) remains relatively constant during the reaction. This assumption simplifies the derivation of the Michaelis Menten equation by allowing the rates of formation and breakdown of the ES complex to be considered equal.

💡Law of mass action

The law of mass action is a principle in chemical kinetics that states that the rate of a reaction is proportional to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. In the video, this law is used to establish the relationship between the forward (kf) and reverse (kr) rate constants for the enzyme-substrate reaction.

Highlights

The Michaelis-Menten equation describes the kinetics of enzyme-catalyzed reactions.

The substrate is converted into product by the enzyme, affecting substrate and product concentrations over time.

The rate of reaction, or velocity, can be determined by the slope of the graph representing concentration change over time.

At low substrate concentrations, the reaction rate increases linearly, following first-order kinetics.

A plateau in the graph indicates a maximum reaction velocity (Vmax) where further substrate concentration increases do not affect the reaction rate, known as zeroth-order kinetics.

The linear portion of the graph can be described by the equation y = mx + c, where y is velocity, m is the slope, c is the y-intercept, and x is substrate concentration.

The Michaelis-Menten equation is necessary to explain the plateau region where velocity is independent of substrate concentration.

The enzyme-substrate complex formation is a reversible reaction, described by the equilibrium assumption.

The pseudo steady-state hypothesis posits that the concentration of the enzyme-substrate complex remains constant during the reaction.

The Michaelis constant (Km) is derived from the ratio of the association and dissociation constants, representing the substrate concentration at which the reaction rate is half of Vmax.

The velocity of the reaction (V0) can be expressed in terms of the enzyme-substrate complex and the catalytic constant (kcat).

Total enzyme concentration is the sum of free enzyme and enzyme bound to the substrate.

At maximum velocity (Vmax), all enzyme molecules are bound with the substrate, and no free enzyme is left.

The Michaelis-Menten equation is rearranged to express V0 in terms of Vmax, Km, and substrate concentration (s).

When substrate concentration is much greater than Km, the equation simplifies to V0 = Vmax, indicating that the reaction rate is at its maximum.

At half of Vmax, the substrate concentration is equal to Km, which is a key parameter in enzyme kinetics.

Transcripts

hey guys click by chemistry basics here

is took about Michaelis Menten equation

when the enzyme acts on the substrate

the substrate gets converted into

product and the product is finally

released

hence with respect to time the

concentration of substrate decreases and

the concentration of product increases

taking slope of the graph gives

information about the rate of reaction

there is change in the concentration

with respect to time hence we can also

call this as velocity of the reaction

now when we measure velocity of reaction

at different substrate concentration

then what we get is a graph which looks

like this if we observe this graph

carefully then what we can see is that

the first part of the graph is linear

where the rate of reaction increases

linearly with the substrate

concentration this linear increase is

called first-order reaction kinetics

then the graph shows a plateau region

where the increase in substrate

concentration no longer increases the

velocity of the reaction at this stage

the velocity have reached maximum

velocity or remax this plateau region is

known as zeroth order reaction kinetics

which means velocity is independent of

substrate concentration

now the first-order reaction kinetics

can be explained easily with the

equation y is equal to MX plus C where Y

is the velocity and mr. slope C is the

intercept on y-axis and X is the

substrate concentration

however this equation cannot be used for

the Plato region as the velocity is

independent of the substrate

concentration and this is the reason why

we need to derive Michaelis Menten

equation now the Michaelis Menten

equation explained this curl

mathematically the aim of this equation

is to establish a mathematical relation

between V 0 V Max and game such that

both first order and zero order kinetics

can be explained

so here we go the enzyme acts on the

substrate and forms enzyme substrate

complex this is a reversible reaction

under equilibrium this is also known as

equilibrium assumption

according to law of mass action II into

s into K F is equal to e s into K R

if we take a ratio key are two key F

number to get is that this Association

constant the disassociation constant is

represented by term KD

besides equilibrium assumption there is

a second assumption known as pseudo

steady state hypothesis according to

this the concentration of es complex

remains constant during enzymatic

reaction

when we say the concentration of es

complex remains constant this means rate

of formation of es is equal to rate of

breakdown of es complex

es is formed by the forward reaction

between enzyme and substrate

therefore es formation is equal to KS

into e into s

es complex is broken down into E and s

or E and B therefore es breakdown is

equal to kr into es plus K cat into yes

as es formation is equal to es breakdown

we can say KS into e into S is equal to

kr into es plus K cat into es

now on the right hand side we can take

es common so that KF into e into s is

equal to es into bracket kr plus K cat

so taking the ratio e into s upon e s is

equal to kr plus K k't divided by K F

this is known as km or Michaelis Menten

constant

now let's go back to our aim our aim is

to establish a mathematical relation

between v-0 we max and km

now II into s upon e s is equal to km is

one equation that we have now we need to

think about equation for the velocity

and maximum velocity V Max

the velocity of the reaction is DP by DT

rate of product formation per unit time

and product formation depends on this

association of es complex so velocity

can be expressed as V zero is equal to K

CAD into e s

in this system there will be some free

enzyme molecules which are not bound

with the substrate and other enzyme

molecules bound with the substrate so

total enzyme concentration can be given

as e zero is equal to e plus es

now watch carefully when all enzyme

molecules are bound with the substrate

there is no free enzyme left hence a

zero is equal to es as all enzyme sites

are occupied by the substrate the

velocity reaches maximum velocity or

v-max therefore v-max is equal to K cat

into e0 where a 0 is equal to es

now let's rearrange the equation to get

one single equation e zero is equal to e

plus yes

taking es on the other side we get e

zero minus es is equal to e

this can be replaced in the equation of

KM

therefore km is equal to e0 minus es

into s / yes

now let's multiply s with the term a

zero

- yes so we get km is equal to e 0 into

S minus e s into s / e yes

now let's rearrange es and the equation

becomes something like this

km is equal to e0 into s upon s - s

now the term is zero can be replaced as

we max by k-kat

of cake at and es is v-0

if we take - s on the other side with km

then what we get is km plus s is equal

to we max into s divided by V 0 and

finally if we rearrange km plus s and V

0 then we get V 0 is equal to we max

into s upon km plus s

now let's try to understand this

equation when the substrate

concentration is very large the value of

km will be very less as compared to

value of s hence km can be ignored

when compared to s so the equation now

becomes we zero is equal to we max into

s divided by s hence we zero becomes

equal to v-max

now let's consider the case where we

zero is half of VMAX

in this case half of VMAX

becomes equal to we max into s upon km +

s

if we rearrange this equation then what

we get is km is equal to s which is

nothing but the definition of km the

substrate concentration at which

velocity becomes half of VMAX