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Enzyme kinetics involved theory and application. Inhibition mechanism, catalysis.
Typology: Assignments
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Fri 19 Jan 2009
Images from: D. L. Nelson, Lehninger Principles of Biochemistry, IV Edition, W. H. Freeman ed. A. Cornish-Bowden Fundamentals of Enzyme Kinetics, Portland Press, 2004 A. Cornish-Bowden Enzyme Kinetics, IRL Press, 1988
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Summary:
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Basics
reactions and how the rates are affected by changes in experimental
conditions
increasing concentrations of substrates the rate increases and
approaches a limit where there is no dependence of rate on
concentration (see slide with limiting rate V max)
experiment with enzyme kinetics in a “modern” way, controlling the pH
of the solution etc.
molecular entity: e.g. E is an enzyme molecule and italics lowercase for
the concentration: e.g. e 0 is the enzyme concentration at time zero
(initial concentration). Also square brackets can be used for
concentration, e.g. [E] = enzyme concentration.
For additional material: Fundamentals of Enzyme Kinetics, Athel Cornish-Bowden, 2004 or
Enzyme Kinetics, Athel Cornish-Bowden and C. W. Wharton, IRL Press, 1988
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A simple view: E+A = EA as an equilibrium
reaction is the binding of the substrate
(A) to the enzyme (E) to form and
enzyme-substrate complex (EA) which
then reacts to give the product P and
free enzyme E
enzyme concentration is e 0 , and the
complex concentration is x. The
substrate (A) concentration should too be
(a 0 - x) , but since the substrate
concentration is usually very high:
equilibrium with equilibrium constant K s
EA to E+P and hence the dominant rate
for all the reaction is the rate v = k 0 x or,
considering the form 3.
0
0
s
a a 0 ( a 0 x )
(K )
or 3.
( )
[EA]
[E][A]
s
0 0
s
a
e a
x
x
e x a
(K )
k
s
0 0
a
e a
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The steady-state assumption
excess of substrate there is an initial period,
lasting just a few microseconds, the pre-
steady state , during which the EA complex
concentration builds up
in which [ES] remains approximately constant
over time (Briggs and Haldane, 1925)
For additional material: Fundamentals of Enzyme Kinetics, Athel Cornish-Bowden, 2004 or
Enzyme Kinetics, Athel Cornish-Bowden and C. W. Wharton, IRL Press, 1988
8
A more general view: E+A EA as reversible
reversible with a forward (k 1 ) and a
backward (k (^) - 1 ) constant
concentration of intermediate (dx/dt)
is the difference between the rate at
which it is produced from E + A and
the sum of the rates at which it is
converted back into free E and A and
forward into free E and P
dx/dt should be positive at the instant
of mixing of E with A (because at the
beginning there is no EA and then it builds
up) but then the removal rate of EA
would rapidly increase, until it
balances the rate of production. This
is the steady-state
(e x) a x p
k EA
k
k
0
0
1
k e x a k x k x
x
1 ( 0 ) - 1 - 2
dt
d
( ) - - 0
dt
d
x
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with first-order dependences on both enzyme and substrate,
or second-order kinetics overall.
importantly, the specificity constant , as it is specific for each
enzyme type.
becomes:
The Michaelis-Menten equation:
effects of substrate concentration on a reaction maximum velocity
Images from: David L. Nelson, Lehninger Principles of Biochemistry, IV Edition, W. H. Freeman ed.
e a
k
0
m
0
)
K
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Lineweaver-Burk equation
is a rewriting of the Michaelis-Menten
equation that is often used for the (not
very accurate) determination of kinetic
parameters from the plot.
substrate and inhibited enzymatic
reactions (see next slides)
http://bcs.whfreeman.com/lehninger/ clicking on
Chapter 6: Enzymes “Living graphs” menu
a
Km
V V
1
v
1
Double reciprocal plot:
Biochemistry, IV Edition, W. H. Freeman ed. Images from: David L. Nelson, Lehninger Principles of
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from one substrate to another.
There are multiple possibilities to be considered:
the enzyme, followed by a second transfer from the enzyme to the acceptor
(second substrate)? [ Ping-Pong mechanism]
the active site of the enzyme? [ Ternary complex]
[ Random-order ]
[ Compulsory-order ]
enzyme? Yes.
Types of enzyme mechanism for
reactions of two substrates
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Two substrates mechanism: Ping-Pong
Images from: David L. Nelson, Lehninger Principles of Biochemistry, IV Edition, W. H. Freeman ed.
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Uncompetitive Inhibition (not very
common)
http://bcs.whfreeman.com/lehninger/ clicking on Chapter
6: Enzymes “Living graphs” menu
Images from: David L. Nelson, Lehninger Principles of Biochemistry, IV Edition, W. H. Freeman ed.
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