Enzyme Kinetics
Michaelis-Menton Kinetics
Unlike most chemical reactions, in which rate is proportional to concentration, enzymes have a maximum rate (
saturation
)
E + S
Þ
ES
Þ
E + P; k
1
is rate constant of first reaction, k
-1
of the reverse reaction; k
2
is the forward second reaction
Must make four assumptions:
(1) [S] >> [E]
– there is much more substrate than enzyme
(2) initial velocity = 0
(3) [P] = 0
, so rate of E + P
Þ
ES is irrelevant
(4) d[ES]/dt = 0
– so always same amount of ES (enzyme-substrate complex)
Abbreviated Derivation
to compute the rate, it is necessary to discover the rate of formation and the rate of degradation of ES.
rate of formation depends on forward reaction E
f
+ S
Þ
ES (only free enzyme, E
f
, matters)
v
f
= k
1
[E
f
][S]
rate of degradation depends on forward reaction ES
Þ
E + P and reverse reaction ES
Þ
E + S
v
d
= k
2
[ES] + k
-1
[ES]
Since [ES] does not change, ES is destroyed as quickly as it is formed, so
v
f
= v
d
k
1
[E
f
][S] = k
2
[ES] + k
-1
[ES]
Velocity of reaction depends on rate of formation of P from ES:
v = k
2
[ES] = ( k
2
[E
T
] [S] ) / ( K
m
+ [S] )
K
m
here is defined as (k
-1
+ k
2
) / k
1
; it has units of moles, and is an affinity constant (smaller K
m
= tighter binding)
Since
V
max
= k
2
[E
T
]
, this can be written:
if [S] = K
m
, V = V
max
/ 2
Lineweaver-Burke
A Lineweaver-Burke plot is a method to plot Michaelis-Menton kinetics as a straight line for easy analysis:
The
x-intercept
will be –1/K
m
; the
y-intercept
will be 1/V
max
; and the
slope
will be K
m
/V
max
Function of Enzymes
Enzymes lower the free energy of the transition state of a reaction, but do not alter the equilibrium constant.
Often different enzymes will have very different K
m
’s for the same reaction.
Generally, K
m
will be close to the physiological substrate concentration for that enzyme
one exception is ATPases, which are always saturated since [ATP] is 10-50 times greater than K
m
Effect of changing concentration of substrate ( [S] )
increase [S], increase rate of product formation
decrease [S], decrease rate of product formation
thus, E is sensitive to availability of [S]
exception: ATP
Þ
increase [S], will not affect rate
