This document discusses enzyme kinetics for one-substrate reactions. It introduces the Michaelis-Menten equation and describes two common assumptions used to derive it: the rapid equilibrium assumption and the steady-state assumption. The Michaelis-Menten equation relates the reaction rate V to substrate concentration [S], maximum reaction rate Vmax, and Michaelis constant Km. Graphical methods like Lineweaver-Burk, Eadie-Hofstee, and Hanes plots are introduced to determine Km and Vmax values from experimental kinetic data.

1. Enzyme Kinetics A. J. Alhassa 1
5.0 Kinetic of one
substrate reaction
Lecture five

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Enzyme Kinetics
One substrate reactions includes:
Hydrolases (if H2O is considered to be in large excess),
Isomerases
most lyases.
 kinetics knowledge of enzymes has a central role in explaining the mystery of
life due to enzyme involvements in every life processes.
 Enzyme kinetics is aiming at knowing:
(i) the mechanism by which the enzyme operate.
(ii) the Km value which tells among others, the intracellular concentration of the
substrate.
(iii) how the enzyme – catalyzed reaction is regulated in-vivo.
Thereby the enzyme became characterized.
One – substrate (enzyme – catalyzed) reaction could be represented as
E+ S ES E + P
K2
K-2
K-1
K1

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Enzyme Kinetics
The equation describing the kinetics of above reaction is derived by making one
of the following assumptions:
I. Rapid equilibrium assumption
The principal assumption here is that the enzyme reacts rapidly to form ES complex
and that the equilibrium is only slightly disturbed by break down of ES to product.
E + S ES E + P ……………………………I
At equilibrium, K1 = K-1 for K-1 >>> K2
The equilibrium constant K = then = ….II
K
The fractional saturation (F) = ………….III
K1
[E] [S]
[ES]
[ES]
[E] [S]
[ES]
[ES]
[E] +
K2
K-2
K-1

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Enzyme Kinetics
Substitutes II in III for [ES] F =
[E] [S]
K K [E] + [E] [S]
K
*
F = [S]
[S]
K +
Let total enzyme concentration be [E]o then [ES] = F [E]o
[ES] =
[E]о [S]
K [S]
+
The rate of product formation, V = K2 [ES]
V =
K2 [E]o [S]
K + [S]

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Enzyme Kinetics
 The maximum velocity (Vmax) will be observed when all enzymes are in the form of
ES, hence reaction rate depends on total enzyme concentration.
Therefore Vmax = K2 [E]o
K + [S]
V =
Vmax [S]
 The drawback for this assumption is that for most enzymes, K2 > K-1 for the kinetics
of these enzymes other assumption has to be made.

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Enzyme Kinetics
(II) The steady – state assumption
the assumption in this case is that the concentration of ES remains constant
i.e. it is in a steady state or the rate of its formation equals the rate of its
breakdown.
K2
K1
E + S ES E + P
The rate of formation of ES = K1 [E] [S]
The rate of breakdown of ES = K-1 [ES] + K2 [ES]
K1 [E] [S] = K-1 [ES] + K2 [ES]
Dividing both sides by K1

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Enzyme Kinetics
[E] [S] = K-1 [ES] + K2 [ES]
let Km = K-1 + K2
[E] [S] = Km [ES]
[ES] = [E] [S]
Km
[ES]
F =
[E] + [ES]
K1
K1

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Enzyme Kinetics
[E] [S]
Km
=
[E] + [E] [S]
Km
F = [E] [S] Km
Km * Km [E] + [E] [S]
F = [S]
Km + [S]

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Enzyme Kinetics
Since [ES] = F [E]o
Then [ES] = [E]o [S]
Km + [S]
Rate of product formation V = K2 [ES]
V = K2 [E]o [S]
Km + [S]
But Vmax = K2 [E]o
V = Vmax [S]
Km + [S]

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Enzyme Kinetics
 If [S] is small compared with Km, then V = Vmax [S]/Km i.e. the reaction is first order
in [S].
 When [S] is large compared with Km then V = Vmax i.e. the reaction is zero
order in [S].
 At intermediate values of [S], the reaction is of a fractional order in [S].
When V = ½ Vmax, [S] = Km.

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Enzyme Kinetics
Methods of plotting kinetics data
 For easy evaluating values of Km and Vmax from experimental data,
Michaelis – Menten equation most be rearranged. This is done in number of ways
which allowed for graphical representation.
Vmax [S]
V =
Km + [S]
1. Lineweaver – Burk equation:
Taking inverse both sides:
1 Km + [S]
=
V Vmax [S]

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Enzyme Kinetics
1 Km 1
= (1/ [S]) +
V Vmax Vmax
Plotting 1/V against 1/ Vmax, slope = Km/ Vmax and intercept on 1/V axis is 1/ Vmax.

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Enzyme Kinetics
Vmax [S]
V =
Km + [S]
2. Eadie – Hofstee equation:
VKm + V [S] = Vmax [S]
Multiply both sides by Km + [S]
Divide both sides by Km[S]
V/[S] + V/Km = Vmax/Km
V/[S] = - V/Km + Vmax/Km
By plotting V/[S] against V, slope = -1/km and intercept of V – axis = Vmax

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Enzyme Kinetics

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Enzyme Kinetics
Vmax [S]
V =
Km + [S]
3. Hanes equation
Km
1/V = + 1/ Vmax Lineweaver – Burk equation.
Vmax[S]
Km
[S]/V = + [S]/ Vmax
Vmax
Multiply both sides by [S]
By plotting [S]/V against [S],
Slope = 1/Vmax and intercept of [S] axis = - 1/Km

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Enzyme Kinetics