Enzyme Kinetics II
April 1st, 2005
For this lecture, too, I am greatly indebted to
Dr. Gabriel Fenteany, Department of Chemistry,
University of Illinois at Chicago, for many of the
kcat, KM, and kcat/Km: Catalytic Efficiency
For [S] < Km
v ≈ Vmax[S]/Km = kcat[E]t[S]/Km
Why is the kcat/Km ratio a key measure of catalytic efficiency?
The answer lies with the free energy of the enzyme:transition state complex. The free
energy of this state has to be low enough to enable the enzyme to bind the substrate
at physiological concentrations, but high enough not to unduly restrict k2(kcat).
Note: with certain industrial processes involving
highly soluble substrates (e.g., fructose production
by xylose isomerase) where the reaction can be run
at substrate concentrations much above the Km of
the natural enzyme, you can readily improve the
productivity of the enzymatic reaction by mutating
the enzyme to increase both Km and kcat in tandem
(keeping kcat/Km approximately constant).
Protein engineering to change the cofactor specificity of 2,5-DKG reductase
Banta et al (2002)
Enzyme-Catalyzed Bisubstrate Reactions:
S1 + S2
P1 + P2
A-X + B A + B-X (in transferase reactions)
• Sequential binding of S1 and S2 before catalysis:
– Random substrate binding - Either S1 or S2 can bind
first, then the other binds.
– Ordered substrate binding - S1 must bind before S2.
• Ping Pong reaction - first S1 P1, P1 released before S2
binds, then S2 P2.
Ping Pong reaction
The Pre-Steady State in Chymotrypsin-Catalyzed
Hydrolysis of p-Nitrophenyl Acetate*
ES EP2 E + P2
v = kcat[E]t[S]/(KM + [S])
Steady-state velocity, where
kcat = k2k3/(k2 + k3)
KM = KSk3/(k2 + k3)
KS = k-1/k1
For chymotrypsin: k2 >> k3
Release of P1 is faster than EP2
breaking down to E + P2
*Note: such substrates are called “burst titrants” because they turn over
rapidly to release chromophore only once. By back-extrapolation, they can be
used to quantitate the amount of active enzyme in a reaction solution.
pH-Dependence of Enzyme Activity
Types of Enzyme Inhibition
• Reversible inhibition
(inhibitors that can reversibly bind and dissociate
from enzyme, activity of enzyme recovers when
inhibitor diluted out, usually non-covalent interaction)
– Mixed (noncompetitive)
• Irreversible inhibition
(inactivators that irreversibly associate with enzyme,
activity of enzyme does not recover with dilution,
usually covalent interaction)
Lineweaver-Burk plots illustrating different modes of inhibition
Typically, I is a substrate analog.
Effects of Competitive Inhibitor on
KI (inhibitor dissociation
constant) = koff/kon
KappM = KM(1 + [I]/KI) > KM
Vappmax = Vmax
A Substrate and Its Competitive Inhibitor
Some HIV Protease Inhibitors
Mixed (Noncompetitive) Inhibition
Effects of Mixed (Noncompetitive) Inhibitor
on Enzyme Kinetics
These inhibitors affect kcat only.
KappM = KM
Vappmax = Vmax/(1 + [I]/KI) < Vmax
Effects of Uncompetitive Inhibitor on
•Not the same as noncompetitive (mixed)
•In uncompetitive inhibition, inhibitor only
binds ES and not E alone.
KappM = KM/(1 + [I]/KI) < KM
Vappmax = Vmax/(1 + [I]/KI) < Vmax
ln(residual enzyme activity) vs. time
Slope = -kobs
If [I]>>[E], conditions are pseudo-first
order and slope is -kobs (pseudo-first
order inactivation rate constant)
kinact (second-order inactivation
constant) = k1k2/k-1 = kobs/[I]
Irreversible Inhibition by Adduct Formation
Irreversible Inhibition of Chymotrypsin by TPCK
Q: What can you learn by “defanging” an enzyme by mutating
out its catalytic residues?
Reaction mechanism of a serine protease
(in this case, subtilisin)
Note the three residues of the “catalytic triad”: Ser221, His64, & Asp32.
Take home lesson: even with no catalytic residues, the enzyme still
accelerates the reaction better than 1000-fold the rate of the
uncatalyzed reaction. Way to bind that transition state!