Michaelis Menten equation
Summary
TLDRThe 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
- π§ͺ The Michaelis-Menten equation describes the relationship between enzyme kinetics and substrate concentration.
- π 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.
- π Initially, the reaction rate increases linearly with substrate concentration, indicating first-order kinetics.
- π At high substrate concentrations, the reaction rate plateaus, indicating zeroth-order kinetics where the rate is independent of substrate concentration.
- π‘ 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.
- βοΈ The Michaelis constant (Km) is defined as the substrate concentration at which the reaction rate is half of its maximum velocity (Vmax).
- π The equation incorporates the concept that the rate of formation of the enzyme-substrate complex equals the rate of its breakdown.
- π The total enzyme concentration is the sum of free enzyme and enzyme bound to the substrate.
- π At maximum velocity (Vmax), all enzyme molecules are bound to the substrate, and no free enzyme is left.
- π 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
π§ͺ 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.
π 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.
Mindmap
Keywords
π‘Michaelis Menten equation
π‘Enzyme
π‘Substrate
π‘Product
π‘Reaction velocity
π‘First-order reaction kinetics
π‘Zeroth order reaction kinetics
π‘Vmax (maximum velocity)
π‘Km (Michaelis Menten constant)
π‘Pseudo steady state hypothesis
π‘Law of mass action
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
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