Lecture 10
Enzymatic catalysis
Antoine van Oijen
BCMP201 Spring 2008
Today’s lecture
- Enzymes work by lowering ΔG‡
- Role of substrate binding
- Role of catalytic groups
- Enzyme kinetics: Michaelis-Menten
- Inhibition mechanisms
(Unless noted, figures from Lehninger; Principle of Biochemistry)
1
Enzymes speed up chemistry
Nonenzymatic
rate constant
(knon in s-1)
Enzymatic
rate constant
(kcat in s-1)
Acceleration
rate constant
(kcat/knon)
http://xray.bmc.uu.se/Courses/Tables/Tables.html
From once every 100 million years (when the dinosaurs roamed the earth…)
to 40 times a second!
Enzymes lower activation energy ΔG‡
E+S
ES
EP
E+P
Enzymes do not change ΔG0, but lower ΔG‡
(remember, there’s a difference between energetics and kinetics)
2
Enzymes lower activation energy ΔG‡
Rate depends exponentially on activation energy!
For decrease in ΔG‡ of 1 RT (≈ 2.4 kJ/mol):
k = Ae(" #G
m
/ RT)
m
kcat / kuncat =
!
Ae("#Gcat / RT)
Ae
m
("#Guncat / RT)
m
=e
m
["(#G cat "#Guncat ) / RT]
= e1 $ 2.7
Reaction becomes 2.7 times faster
!
For:
5 RT, reaction rate increases
10 RT,
15 RT,
25 RT,
> 100 x
> 20,000 x
> 3 million x
> 10 billion x
Transition states, intermediates, and rate-limiting steps
transition state
intermediates
Rate-limiting step is the transition with the highest ΔG‡
3
Catalytic strategies
1) Noncovalent interactions between substrate and enzyme
2) Covalent interactions / chemical reactions between enzyme’s
residues and substrate
Binding provides major source of free energy
‘lock and key’ binding would be disadvantageous:
Transition state needs to be stabilized, not substrate
4
Transition state analogs
Transition-state analogs will bind tightly and inhibit catalysis
Ester hydrolysis
Carbonate hydrolysis
How does binding help catalysis?
Main energetic barriers contributing to ΔG‡:
-
Distortion
Entropy
Alignment w/ catalytic residues
5
Effect of entropy reduction on reaction rates
Rate increase
1
105 M
108 M
Role of catalytic groups
1) General acid-base catalysis
2) Covalent catalysis
3) Metal ion catalysis
More on reaction mechanisms: Michael Wolfe next week
6
Enzyme kinetics: Michaelis-Menten equation
Leonor Michaelis and Maud Menten (1913):
Rate of catalysis by an enzyme is proportional to substrate
concentration at low levels and becomes independent at high levels:
E+S
k1
k2
ES
k-1
reaction
substrate binding
V0 =
E+P
[S]
Vmax
KM + [S]
!
Enzyme kinetics: Michaelis-Menten equation
E+S
k1
k-1
k2
ES
V0 =
E+P
[S]
KM + [S]
Fraction enzyme
bound to ligand:
Analogous
! to ligand binding, but
k +k
k
KM = 2 "1 instead of "1
k1
k1
!
Vmax
Vmax=k2[E]Total=kcat[E]Total
[E]Total=[E]+[ES]
kcat=turnover rate
!
7
Catalytic efficiency
When [S] !
<< KM :
V0 =
[S]
[S]
Vmax =
kcat [E]Total
KM + [S]
KM + [S]
V0 =
kcat
[S][E]Total
KM
2nd order rate equation with units M-1s-1
!
Catalytic efficiency =
kcat
KM
(theoretical upper limit ~ 109 M-1s-1)
!
Some enzymes are diffusion-limited
8
Lineweaver-Burke representation
V0 =
!
[S]
Vmax
KM + [S]
1 KM + [S] KM 1
1
=
=
+
V0 Vmax [S] Vmax [S]
Vmax
slope
!
y-intercept
(y=ax + b gives straight line;
a=KM/Vmax. b=1/Vmax)
Steady-state versus pre-steady state kinetics
Steady state: [ES] is constant
To gain information on initial steps to form E•S,
pre-steady state techniques are needed
9
Pre-steady state techniques
Stopped-flow / quenched-flow spectrophotometry
Mix solutions at ~ 1 ms timescale and measure binding/activity
Inhibition mechanisms
Competitive inhibition
Noncompetitive inhibition
10
Competitive inhibition
Alcohol dehydrogenase
Ethanol used as competitive inhibitor with methanol/ethylene glycol poisoning
Noncompetitive inhibition
HIV Reverse Transcriptase
Nevirapine binds between
polymerase and nuclease
domains
(Kohlstaedt et al., Science (1992); 256, 1783)
11
Competitive inhibition
V0 =
Where
" = 1+
[S]
Vmax
"KM + [S]
[I]
KI
and KI =
[E][I]
[EI]
!
!
!
Competitive inhibitor changes KM (α•KM is ‘apparent’ KM)
Noncompetitive inhibition
V0 =
Where
# " = 1+
[S]
Vmax
KM + # "[S]
[I]
KI"
and KI" =
[ES][I]
[ESI]
!
!
V !
At high [I], v = max
#"
(enzyme ‘dilution’)
!
12
Kinetics test for determining inhibition mechanisms
Lineweaver-Burke:
1 KM + [S] KM 1
1
=
=
+
V0
Vmax [S]
Vmax [S]
Vmax
slope
y-intercept
!
1 KM + [S] "KM 1
1
=
=
+
V0
Vmax [S]
Vmax [S]
Vmax
Competitive:
slope
!
Noncompetitive:
1 KM + [S] KM 1
#"
=
=
+
V0
Vmax [S]
Vmax [S]
Vmax
y-intercept
!
Kinetics test for determining inhibition mechanisms
1 KM + [S] "KM 1
1
=
=
+
V0
Vmax [S]
Vmax [S]
Vmax
1 KM + [S] KM 1
#"
=
=
+
V0
Vmax [S] Vmax [S]
Vmax
slope
y-intercept
!
!
1 " 1%
$ '
[S] # M &
1 " 1%
$ '
[S] # M &
!
Competitive
!
Noncompetitive
13
Irreversible inhibition
- Reactive substrate:
Covalent binding to or destruction of essential residue (e.g., chymotrypsin +DIPF)
- Suicide substrates:
Substrate is converted into reactive species
Sequential versus ping-pong
14
Enzyme classification
http://www.chem.qmul.ac.uk/iubmb/enzyme/
Example:
EC 1.1.1.27
Lactate dehydrogenase
Single-molecule enzymology of β-Galactosidase
Xie et al., Nature Chem.Biol. 2 (2006) 87
15
Concentration-dependence of waiting time
Waiting time <τ> = 1/k
Higher [S], shorter <τ>
Michaelis-Menten from the single enzyme’s perspective
!
!
Bulk-phase
Lineweaver-Burke
Single-molecule
Lineweaver-Burke
V0
[S]
=
kcat
[E]T KM + [S]
1
[S]
=
kcat
K
"
M + [S]
[E]T KM + [S] KM 1
1
=
=
+
V0
kcat [S]
kcat [S]
kcat
" =
( [E]T=[E]+[ES],
Vmax=k cat[E]T )
!
!
KM + [S] KM 1
1
=
+
kcat [S]
kcat [S]
kcat
Same KM , same kcat
16
Ergodic theorem
A measurement of some property of an ensemble
at a given time should be equivalent to the long-time
average of the same property on any one member
Waiting time distributions
E+S
k1
k-1
ES
kcat
E+P
Low concentration:
Single-exponential decay
At low [S], k1 is rate-limiting;
at high [S], kcat is rate-limiting
High concentration:
multi-exponential decay: multiple kcat’s !!!
17
Enzymes are highly dynamic entities
Enzymes do not have a constant kcat , but fluctuate over time
Why is this happening?
Rugged Energy Landscape:
Distribution of conformations  different enzymatic activities (kA, kB, kC)
for different conformers A, B, C
Distribution of barrier heights  different transition rates (r AB, rAB, rAB)
between different conformers A, B, C
18
Take-home lessons
- Enzymes speed up chemistry by lowering ΔG‡
- Michaelis-Menten kinetics
- Competitive and noncompetitive inhibition
19