Quiz #3
• Define Enzyme Classes
• Systematic naming
– Given a reaction (including names)
– Use subclass designation if appropriate
• Catalytic mechanisms
– Define
– How does a given amino acid participate?
• Discuss protonation state and reaction.
Enzyme Kinetics
The study of the rates at which
enzyme-catalyzed reactions occur.
Value of Enzyme Kinetics
• Quantitation of Enzyme Activity
– Purification
• Competing Substrates and Inhibitors
– Suggest physiological functions
– Suggest regulatory mechanisms
• Response to Different Conditions
– Reaction mechanism
Kinetic Data
plus
Structure and Mechanism
• Clues to an enzyme’s biological
function
• Ways to modify an enzyme for
therapeutic purposes
Enzyme-Catalyzed Reactions
are
Reversible
(Accelerate Attainment of Equilibrium)
Elementary Reactions
A ——> P
Reaction Intermediates
A ——> I1 ——> I2 ——> P
Two-Step Reactions
(Rate Determining Step)
A
k1
I
k2
P
Chemical Kinetics
• Can reveal the number of reacting
species
• Can reveal the rate of their
interactions
• Are described by Rate Equations
Rate Equations
• Reaction Order or Molecularity:
number of molecules participating in a
reaction
• Velocity (V): molar per second (M•s–1)
• Rate Constant (k): proportional to
frequency of interaction between
reactants
Rate Equations
(General Form)
aA + bB ——> P
V = k[A]a[B]b
k = rate constant
Order of Reaction = a + b
Reaction Order
(Reaction Molecularity)
• First-order or unimolecular
• Second-order or bimolecular
• Third-order very rare
• 4th-order are unknown
Rates of Reactions
First-Order Reactions
A
P
d[A]
d[P]
v = –
=
= k[A]
dt
dt
k = 1st order rate constant (s–1)
Time Course of Reaction
Equilibrium
A or P
A ——> P
PB
A or B
t1/2 (half-life)
AA
Time
Kinetics of Reactions
First-Order Reaction
Substrate
[S]
kF
kB
Product
[P]
("Reactant")
V = kF[S] – kB[P]
kF[S] = kB[P] at equilibrium
Initial Velocity (VO)
Substrate
[S]
kF
kB
Product
[P]
("Reactant")
V = kF[S] – kB[P]
V = kF[S] – kB[P]
Initial Velocity (Vo)
([P] = 0)
kF[S] = kB[P] at equilibrium
Vo = kF[S]
Uncatalyzed Reaction
•
Vo
slope = kF
[S]
Vo = kF [S]
Enzyme Catalysis
Vm ax
VO not proportional
to [S]
Vo
Vo proportional to [S]
[S]
Hyperbolic Relationship
Michaelis-Menten Formulation
Enzyme Kinetics
Experiment:
(1) Mix enzyme + substrate
(2) Record rate of product formation as a function of time (the velocity of
reaction)
(3) Plot initial velocity versus substrate concentration.
(4) Change substrate concentration and repeat
Postulated Pathway of
Enzyme Catalysis:
Formation of Enzyme-Substrate Complex
E + S
k1
k-1
Binding
E—S
k2
Catalysis
E + P
Assumptions:
Initial Velocities
Catalysis is rate limiting
E + S
k1
k-1
Binding
E—S
k2
Catalysis
E + P
(rate limiting)
Vo = k2[ES]
Assumptions
• Binding equilibrium (k–1>>k2)
E + S
k1
k-1
Binding
E—S
k2
E + P
Catalysis
• Steady state (d[ES]dt = 0)
Assumptions
• Binding equilibrium (k–1>>k2)
E + S
k1
k-1
Binding
E—S
k2
E + P
Catalysis
• Steady state (d[ES]dt = 0)
Additionally
• [s]>>>>>>>>>[E-S]
– [S] doesn’t change during initial velocity
• [ET] = [EF] + [E-S]
Progress Curves (M-M Enzyme)
Steady-State
Very short
Michaelis-Menten Equation
VO= Vmax[S]
Km + [S]
Assumes All Enzyme Molecules are
Catalytically Active
Michaelis
Constant
Km = k-1 + k2
k1
KM is the substrate concentration at which the
reaction velocity is half-maximal
High affinity = low Km; Low Affinity = high Km
Michaelis-Menton Enzyme Kinetics
Catalytic Constant
(Turnover Number)
Kcat =
Vmax
[E]T
# of substrate converted to product
=
Unit of time
# of enzyme
Vmax = kcat X # of enzymes
# can be any units (molecules, moles, μmoles)
But all must be the same units
Catalytic Efficiency
• kcat/KM
– Limited by diffusion (108 to 109 M-1s-1)
Lineweaver-Burk Formulation
1
Vo
=
KM
1
Vmax
[S]
+
1
Vmax
Lineweaver-Burk Plot
Eadie-Hofstee Formulation
Vo = –KM
Vo
[S]
+ Vmax
Eadie-Hofstee Plot
Vo
Vmax
Slope = –Km
Vmax
Km
Vo
S
A certain enzyme catalyzes the
conversion of 100 μmoles of A to B in one
second, when the concentration of A is 20
mM. It catalyzes the conversion of 350
μmoles of A to B in one second when the
concentration of A is either 500 mM or
550 mM.
-Calculate Km
-Draw the Michaelis-menton curve and
Lineweaver-Burk plot for this enzyme
-Can you calculate turnover #?