1. 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

2. Enzymes speed up chemistry
Nonenzymatic Enzymatic Acceleration
rate constant rate constant rate constant
(knon in s-1) (kcat in s-1) (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

3. Enzymes lower activation energy ΔG‡
Rate depends exponentially on activation energy!
For decrease in ΔG‡ of 1 RT (≈ 2.4 kJ/mol):
m
k = Ae(" #G / RT)
m
Ae("#Gcat / RT)
m m
["(#G cat "#Guncat ) / RT]
kcat / kuncat = m
=e = e1 $ 2.7
("#Guncat / RT)
Ae
!
Reaction becomes 2.7 times faster
!
For: 5 RT, reaction rate increases > 100 x
10 RT, > 20,000 x
15 RT, > 3 million x
25 RT, > 10 billion x
Transition states, intermediates, and rate-limiting steps
transition state
intermediates
Rate-limiting step is the transition with the highest ΔG‡
3

4. 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

5. 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

6. 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

7. 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:
k1 k2
E+S ES E+P
k-1
reaction
substrate binding
[S]
V0 = Vmax
KM + [S]
!
Enzyme kinetics: Michaelis-Menten equation
k1 k2
E+S ES E+P
k-1
[S]
V0 = Vmax
KM + [S]
Fraction enzyme
bound to ligand: Vmax=k2[E]Total=kcat[E]Total
Analogous to ligand binding, but
! [E]Total=[E]+[ES]
k +k k
KM = 2 "1 instead of "1
k1 k1 kcat=turnover rate
! !
7

8. Catalytic efficiency
[S] [S]
V0 = Vmax = kcat [E]Total
KM + [S] KM + [S]
When [S] ! KM :
<< kcat
V0 = [S][E]Total
KM
2nd order rate equation with units M-1s-1
!
kcat
Catalytic efficiency = (theoretical upper limit ~ 109 M-1s-1)
KM
!
Some enzymes are diffusion-limited
8

9. Lineweaver-Burke representation
[S]
V0 = 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

10. 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

11. 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

12. Competitive inhibition
[S]
V0 = Vmax
"KM + [S]
[I] [E][I]
Where " = 1+ and KI =
KI [EI]
!
! !
Competitive inhibitor changes KM (α•KM is ‘apparent’ KM)
Noncompetitive inhibition
[S]
V0 = Vmax
KM + # "[S]
[I] [ES][I]
Where # " = 1+ and KI" =
KI" [ESI]
!
! V !
At high [I], v = max (enzyme ‘dilution’)
#"
!
12

13. Kinetics test for determining inhibition mechanisms
1 KM + [S] KM 1 1
Lineweaver-Burke: = = +
V0 Vmax [S] Vmax [S] Vmax
slope y-intercept
!
1 KM + [S] "KM 1 1
Competitive: = = +
V0 Vmax [S] Vmax [S] Vmax
slope
!
1 KM + [S] KM 1 #"
Noncompetitive: = = +
V0 Vmax [S] Vmax [S] Vmax
y-intercept
!
Kinetics test for determining inhibition mechanisms
1 KM + [S] "KM 1 1 1 KM + [S] KM 1 #"
= = + = = +
V0 Vmax [S] Vmax [S] Vmax V0 Vmax [S] Vmax [S] Vmax
slope y-intercept
! !
1 " 1% 1 " 1%
$ ' $ '
[S] # M & [S] # M &
! !
Competitive Noncompetitive
13

14. 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

15. 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

16. Concentration-dependence of waiting time
Waiting time <τ> = 1/k
Higher [S], shorter <τ>
Michaelis-Menten from the single enzyme’s perspective
Bulk-phase Single-molecule
Lineweaver-Burke Lineweaver-Burke
V0 [S] 1 [S]
= kcat = kcat
[E]T KM + [S] " KM + [S]
[E]T KM + [S] KM 1 1 KM + [S] KM 1 1
= = + " = = +
V0 kcat [S] kcat [S] kcat kcat [S] kcat [S] kcat
! !
( [E]T=[E]+[ES],
! ! Same KM , same kcat
Vmax=k cat[E]T )
16

17. 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
k1 kcat
E+S ES E+P
k-1 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

18. 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

19. Take-home lessons
- Enzymes speed up chemistry by lowering ΔG‡
- Michaelis-Menten kinetics
- Competitive and noncompetitive inhibition
19