Michaelis-Menten kinetics

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Michaelis-Menten kinetics
V0 varies with S
Vmax approached asymptotically
V0 is moles of product formed per sec. when
P is low (close to zero time)
E S?ES?E P
Michaelis-Menten Model
V0 Vmax xS/(S Km)
Michaelis-Menten Equation
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Determining initial velocity (when P is low)
Ignore the back reaction
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Steady-state pre-steady-state conditions
At pre-steady-state, P is low (close to
zero time), hence, V0 for initial reaction
velocity
At equilibrium, no net change of S P or of
ES E
At pre-steady state, we can ignore the back
reactions
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Michaelis-Menten kinetics (summary)
Enzyme kinetics (Michaelis-Menten Graph) At
fixed concentration of enzyme, V0 is almost
linearly proportional to S when S is small,
but is nearly independent of S when S is large
k2
Proposed Model E S ? ES ? E P
ES complex is a necessary intermediate
Objective find an expression that relates rate
of catalysis to the concentrations of S E, and
the rates of individual steps
Start with V0 k2ES, and derive, V0 Vmax
xS/(S Km) This equation accounts for graph
data. At low S (S lt Km), V0 (Vmax/Km)S At
high S (S gt Km), V0 Vmax When S Km, V0
Vmax/2. Thus, Km substrate concentration
at which the reaction rate (V0) is half max.
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Range of Km values
Km provides approximation of S in vivo for many
enzymes
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Lineweaver-Burk plot (double-reciprocal)
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Allosteric enzyme kinetics
Sigmoidal dependence of V0 on S, not
Michaelis-Menten
Enzymes have multiple subunits and multiple
active sites Substrate binding may be cooperative
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Enzyme inhibition
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A competitive inhibitor
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Methotrexate
A competitive inhibitor of dihydrofolate
reductase - role in purine pyrimidine
biosynthesis
Used to treat cancer
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Tetrahydrofolate
Substrate for dihydrofolate reductase
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Kinetics of competitive inhibitor
Increase S to overcome inhibition Vmax
attainable, Km is increased
Ki dissociation constant for inhibitor
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Competitive inhibitor
Vmax unaltered, Km increased
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Kinetics of non-competitive inhibitor
Increasing S cannot overcome inhibition Less E
available, Vmax is lower, Km remains the same for
available E
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Noncompetitive inhibitor
Km unaltered, Vmax decreased
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Enzyme inhibition by DIPF
Group - specific reagents react with R groups of
amino acids
diisopropylphosphofluoridate
DIPF (nerve gas) reacts with Ser in
acetylcholinesterase
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Enzyme inhibition by iodoacetamide
A group - specific inhibitor
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Affinity inhibitor covalent modification
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Reactive analog
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Affinity inhibitor, bromoacetol phosphate
Active site modified
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Vitamins water-soluble
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Vitamins fat-soluble
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Structure of some water-soluble vitamins
Ascorbic acid is a reducing agent (an antioxidant)
B series are components of coenzymes, Must be
modified before they can serve their functions
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B5,transfers acyl group
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B2, oxidation - reduction
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C, reducing agent (antioxidant)
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B3, oxidation-reduction
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B6, group transfer to or from aas
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Prolyl hydroxylase ascorbate
4 - hydroxyproline required in collagen
(connective tissue in vertebrates) Scurvy from
ascorbate deficiency
On amino side of glycine
Enzyme has tightly bound Fe2 ion, which reacts
with O2 to form oxidized iron complex, which
inactivates enzyme, Ascorbate rescues enzyme by
reducing the ferric ion
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Forms of ascorbic acid
Ionized
Reduced
Oxidized
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Structure of some fat-soluble vitamins
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K1, blood coagulation
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A, vision, growth, reproduction
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E, antioxidant
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D, regulates calcium phosphate