Enzyme Kinetics
Voet Biochemistry:
Chapter 14, Pages 472 - 493
Voet Fundamentals:
Chapter 11, Pages 328 - 330
Chapter 12, Pages 363 - 374
Lecture 7
Biochemistry 2000
Slide 1
Introduction
Kinetics - study of the rates at which chemical reactions occurs
(quantitative measurement of enzyme properties)
Purpose of enzyme kinetics:
(1)
Understand reaction mechanism (sequence of steps resulting in
catalysis)
(2)
Determine maximum catalytic rate and binding affinities for substrates
and inhibitors (drugs!)
(3)
Identify the catalytic mechanism (in combination with structural
information)
(4)
Understand enzymatic role within an overall metabolic pathway
(5)
Develop enzyme assays (research, protein purification, clinical tests)
Lecture 7
Biochemistry 2000
Slide 2
Transition State
Bimolecular elementary reaction:
Ha – Hb + Hc
Ha + Hb – Hc
Hc must approach Ha-Hb sufficiently closely
to form a bond with Hb as Ha-Hb bond
breaks
transition state: unstable chemical structure
that represents a free energy maxima on a
reaction coordinate diagram
Reaction coordinate:
minimum free energy pathway of a reaction
∆G‡, free energy of activation:
free energy of transition state – reactants
The greater ∆G‡, the slower the reaction!
Lecture 7
Biochemistry 2000
Slide 3
Catalysts (Enzymes)
Catalysts enhance reaction rates by
lowering the activation energy, ∆G‡
∆∆G
∆∆ ‡: difference in activation energy
between catalyzed & uncatalyzed reaction
/RT
∆∆
rate enhancement = e- ∆∆G‡
10 fold rate enhancement: ∆∆G
∆∆ ‡ = 5.7 kJ/mol
106 fold enhancements: ∆∆G
∆∆ ‡ = 34.2 kJ/mol
DG
Catalysts do not change ∆G of the reaction,
reaction
i.e. do not change the equilibrium
Catalysts enhance the rates of both forward
and backwards reactions equally
Remember: ∆G < 0 = favorable reaction
Lecture 7
Biochemistry 2000
Slide 4
Reaction Mechanism
Overall reaction
A
Reactant
P
Product
Elementary reactions
A
I1
Reactant
Intermediate 1
I2
Intermediate 2
P
Product
Reaction mechanism comprises a description
of all elementary reactions involved in an overall reaction.
Other examples for reaction mechanisms:
A+B
A+B
P+Q
I
(e.g. peptide bond formation)
P+Q
A
P+Q
unimolecular reaction: 1 reactant
A+B
P
bimolecular reaction: 2 reactants
Lecture 7
Biochemistry 2000
Slide 5
Rate determining step
Reaction diagram for multistep reaction
Lecture 7
Biochemistry 2000
∆G‡ (Activation energy) for each
elementary reaction
Highest ∆G‡ corresponds to
slowest step in overall reaction
Slowest step is the ratedetermining step
Slide 6
Reaction Rates
measures appearance of product over time:
time
or disappearance of reactant over time
i.e. the velocity, v, of a reaction
v = d[P] / dt
- d[A] / dt
At constant temperature, reaction rate is
proportional to reactant concentrations:
A
P
v = k [A]
1. order
A+B
P
v = k [A] [B]
2. order
2A + B
P
v = k [A]2 [B]
3. order
General Single Product Reaction
aA + bB + ... + zZ
Rate equation
Rate = k [A]a [B]b ... [Z]z
1st order
in general:
aA + bB + cC + …. zZ
P
v = k [A]a [B]b [C]c …. [Z]z
k : rate constant (independent of reactant concentrations)
• reaction order: sum of (a + b + ... + z)
2nd order
• Units of rate constant, k: differ for reactions
with different orders! (units cancel to have M/s for v)
Lecture 7
Biochemistry 2000
P
Slide 7
Enzyme Reactions
Overall reaction:
Enzyme-catalyzed
catalyzed (E)
Substrate (S)
Product (P)
E
S
Elementary reactions: (enzyme is unchanged!)
k1
E+S
k2
ES
k3
EP
k-1
Reaction Rate:
E+P
k-3
-
v = d[P]/dt
Imaging very high substrate concentrations relative to [E]:
all enzyme is converted to ES, the enzyme substrate complex.
Thus:
Lecture 7
v = d[P]/dt = k2 [ES]
Biochemistry 2000
E
P
Slide 8
Measuring enzyme kinetics
1. Measure product formation over time
Use [S] >> [E]
2. Determine initial rate, v0
(before substrate is getting limiting)
Initial rate (v0)
Lecture 7
3. Repeat experiment at
increasing [S]
4. Plot initial rate, v0, versus [S]
Reaction
becomes
faster with
more [S]
(faster
binding to
enzyme)
Biochemistry 2000
Rate saturates,
limited by ES complex
Slide 9
Michaelis Menten Equation
vmax [S]
v0 =
KM + [S]
basic equation of enzymology
describes dependence of rate on [S]
Only valid for [S] >> [E],
called assumption of steady state,
i.e. [ES] about constant during reaction
Lecture 7
Biochemistry 2000
Slide 10
Michaelis Menten Equation
vmax [S]
v0 =
KM + [S]
Vmax: maximal velocity (all E is ES)
KM: Michaelis constant
- substrate concentration at half vmax
KM = (k-1 + k2)/ k1 = breakdown of ES / formation of ES
- rough measure of substrate affinity if k2 << k-1
Lecture 7
Biochemistry 2000
Slide 11
Catalytic efficiency
Vmax proportional to [E]
Catalytic constant (turnover number): kcat = vmax / [E]total
Catalytic efficiency: kcat / KM
Describes rate constant at low substrate concentrations: vo= (kcat/KM)[E][S]
Is limited by diffusion of substrate to enzyme (109 M-1 s-1)
Lecture 7
Biochemistry 2000
Slide 12
Analysis of Kinetic Data
Vmax and KM can only be estimated by eye from
Michealis-Menten plot
Alternative: Lineweaver-Burk plot (double
reciprocal)
Rearrange Michaelis-Menten
Menten equation:
1/v0 = (KM/vmax) 1/[S] + 1/vmax
Plot 1/v0 versus 1/[S]:
Slope: KM/vmax
y intercept: 1/vmax
x intercept: -1/KM
Lecture 7
Biochemistry 2000
Slide 13