Michaelis menten

Enzyme Kinetics
M.Sc. IV Semester
2/28/2020 singhkalpana297@gmail.com 1

• To study enzymes, first order kinetics must be followed!
The velocity increases as the substrate concentration is increased
up to a point where the enzyme is "saturated" with substrate.
At this point the rate of the reaction (v) reaches a maximal value
and is unaffected by further increases in substrate because all of
the enzyme active site is bound to substrate

Michaelis Menten Equation

Comparison First Order Reaction & MM Equation………
Straight Line
• First Order Reaction
Hyperbola

• If there are two substrates, one of them is held at a high concentration
(0 order) and the other substrate is studied at a lower concentration so
that for that substrate, it is a first order reaction.
• This leads us to the M and M equation.

The Theory is based upon following assumptions
1. Only a single substrate and single product are involved
2.Process proceeds essentially to completion
3The concentration of the substrate is much greater than that
of the Enzyme in action
4.An Intermediate Enzyme –Substrate complex is formed
5.The rate of decomposition of the substrate is proportional
to the concentration of the Enzyme substrate complex

• An enzyme-catalyzed reaction of substrate S to product P, can be written
S → P
Actually, the enzyme and substrate must combine and E recycled after the
reaction is finished, just like any catalyst.
Because the enzyme actually binds the substrate the reaction can be
written as:
E + S ↔ ES → P+E………………………………….1.
The simplest reaction is a single substrate going to a single product.
k
1
k-1
k 2

Rate/ velocity of the reaction depends on the formation of ES
 The P -> ES is ignored
 The equilibrium constant 𝐾𝑒𝑞 is based on the idea that the reaction
is limited to the formation of the ES complex and that only 𝐾1and
𝐾−1are involved because the thermodynamics of the reversal of 𝐾2
cause it to be minimal
 𝐾𝑒𝑞 =
𝐾1
𝐾−1
How fast an enzyme catalyzes a reaction is it's rate. The rate of the
reaction is in the number of moles of product produced per
second
Rate of the reaction (V) =
𝑑 [𝑃]
𝑑𝑡
= 𝐾2[ ES]……………………2.

• The maximum reaction rate 𝑉𝑚 will be reached when the total enzyme
𝐸𝑡 is bound to the substrate
• 𝑉𝑚 = k (𝐸𝑡)………………………..3.
• Dividing equation 2 by3
•
𝑉
𝑉 𝑚
=
[𝐸𝑆]
[𝐸𝑡
……………………………4.
• Considering equation 1.
•
𝑑 [𝐸 𝑆]
𝑑𝑡
= 𝑘1[E] [S]- 𝑘−1[ES]- 𝑘2[ES]…….5.

• In most of the Enzyme catalyzed reactions conc. of enzyme is very low
compared with the concentration of the substrate
• Conversion of some or even all of the enzyme in ES will cause only a
relatively minute decrease in [S]
• When enzyme is first added to the solution of the substrate, for a brief
period when [ES] increases and [E] decreases, soon there is a steady
state in which [ES] is relatively constant
• In the steady state, the rates of formation and breakdown of ES have
become essentially equal, and
𝑑[𝐸𝑆]
𝑑𝑡
≈ 0 from equation 5, we then have

• 𝑘1[E] [S] = 𝑘−1[ES] +𝑘2[ES]……………..6.
• 𝑘1[E] [S] = [ES](𝑘−1+𝑘2)
• [ES] = 𝑘1[E] [S]/(𝑘−1+𝑘2)………………7.
• In equation 5-7, E refers to the concentration of free Enzyme, not the
total concentrartion of enzyme. If Total concentration of Enzyme is
represented by [𝐸 𝑇]
• [E] = [𝐸 𝑇] - [ES]……………………….8.
• Combining equation 7 and 8 gives
• [ES] =
{[ 𝐸 𝑇] − [ES]} [S] 𝑘1
( 𝑘−1+ 𝑘2)
………………9.
• Substituting 𝐾 𝑚 =
( 𝑘−1+ 𝑘2)
𝑘1
……………..10 in equation 9.

• [ES]=
{[ 𝐸 𝑇] − [ES]} [S]
𝐾 𝑚
…………………………11
• On rearrangement
• [ES] =
[ 𝐸 𝑇] [S]
𝑆 +𝐾 𝑚
……………………………………12.
• Combining equation 2 and 12
• v=
𝐾2[ 𝐸 𝑇] [S]
𝑆 +𝐾 𝑚
……………………………………..13
• The product 𝐾2[𝐸 𝑇] is the maximum rate of reaction
• 𝑉𝑚𝑎𝑥 = 𝐾2[𝐸 𝑇] substituting value in equation 13
• v=
𝑉 𝑚𝑎𝑥[S]
𝑆 +𝐾 𝑚
………………………………………14.

• v=
𝑆 +𝐾 𝑚
………………………………………14.
• Equation 14 accounts for hyperbolic relation between v and S and is
known as Michaelis-Menten Equation

Line weaver –Burk Equation
• v=
𝑆 +𝐾 𝑚
………………………………………14.
• Taking reciprocal of Michaelis Menten equation
•
1
𝑉
=
𝑆 +𝐾 𝑚
……………………………………….15
• 0R
•
1
𝑉
=
𝐾 𝑚
𝑉 𝑚
∗
1
(𝑆)
+
1
𝑉 𝑚
……………………………………16
• This is Lineweaver Burk Equation of the form
• Y=mx+b

Lineweaver –Burk Plot
 If
1
𝑉
and
1
(𝑆)
are considered as
variables and graph is plotted
against these two variables, a
straight line is observed ,the
slope of this line corresponds to
𝐾 𝑚
𝑉 𝑚
.
 𝑉𝑚 can be calculated from
intercepts, 𝐾 𝑚 can also be
calculated
𝟏
𝑽 𝒎
𝟏
𝑽
𝟏
𝑺

Michaelis menten

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