LAB 3
Enzyme Kinetics
• Studying galactosidase activity
at varying substrate
concentrations in the
presence and absence
of an inhibitor
• Michaelis-Menten
enzyme kinetics
• Lineweaver Burk plot
Michaelis-Menten Enzyme
Kinetics
Steady-state Model:
Formation of ES = Disappearance of ES
k1[E][S] = k2[ES] + kcat[ES]
Define a new constant, Km (Michaelis constant):
Km = (k2 + kcat)/k1
Km reflects the affinity of the enzyme for the
substrate:
• low Km = high affinity
• Km = [S] that produces V= 1/2Vmax
The Michaelis-Menten
Equation
V=
Vmax[S]
Km + [S]
1/2Vmax
Hyperbolic function
Simplifying M & M analysis
using a Lineweaver-Burk Plot
• A double-reciprocal representation of V vs. [S]
data: plot 1/V vs. 1/[S]
• Take the inverse of both sides of the M-M
equation to get the L-B equation, which
specifies a line.
M-M
V=
Inverse M-M
Vmax[S]
Km + [S]
1/V = (Km + [S]) / Vmax[S]
Rearrange…
L-B
1/V = 1/Vmax + Km/ Vmax (1/[S])
Determining
Kinetic Parameters
from an L-B Plot
1/V = 1/Vmax + Km/ Vmax (1/[S])
Last week’s experiments
vs. today’s
• Last week studied enzyme at
saturating substrate
concentrations, meaning there
was so much substrate that the
enzyme worked at Vmax all the
time so we could determine
specific activity.
• Today, varying concentration of
substrate to find out what
happens when substrate is
limiting. How strong of an
affinity does the enzyme have for
this substrate? Can determine the
Michaelis constant, Km.
TO DO TODAY
• Vary substrate (ONPG) conc.
over an 80-fold range to
determine Km, the substrate
conc. that gives V = 1/2 V max
• Repeat above using a constant
amount of an inhibitor (IPTG) to
determine Km in the presence of
the inhibitor.
• Determine whether the inhibition
is competitive or noncompetitive by comparing Km &
Vmax -/+ IPTG on MichaelisMenten & Lineweaver-Burk
plots.
Competitive Inhibition
No product formed
• Inhibitor has a chemical structure similar to that
of the substrate and competes for binding to the
active site (can only bind free E).
• Inhibition can be overcome by excess substrate.
• Inhibitor increases Km but leaves Vmax
unchanged.
Noncompetitive Inhibition
Diminished
product
formation
• Inhibitor’s chemical structure may be totally
different from that of the substrate.
• Inhibitor binds a site on the enzyme that is distinct
from the active site.
• EI complex can bind substrate, but cannot
transform it into product as efficiently as the
uninhibited enzyme because of alterations in the
shape/chemistry of the active site.
• Inhibition cannot be overcome by excess
substrate.
• Inhibitor decreases Vmax but leaves Km
unchanged.
Michaelis-Menten
Kinetics with Inhibition
Lineweaver-Burk Plots
with Inhibitors
Ki
• The dissociation constant for an inhibitor
• Whereas Km reflects the affinity of an
enzyme for its substrate, Ki reflects its
affinity for binding to an inhibitor.
• Method of calculating Ki depends on the
type of inhibition.
For competitive inhibition:
Km +I = Km -I ( 1 + [I]/Ki)
For noncompetitive inhibition:
Vmax +I = Vmax -I / ( 1 + [I]/Ki)
Two more types of
inhibition
1. Mixed inhibition
• Inhibitor can bind both E and ES, but with
different affinities (different Kis).
• Both Vmax and Km may change; if inhibitor
binds E with higher affinity than ES, Vmax
decreases and Km increases.
2. Uncompetitive inhibition (quite rare)
• Inhibitor binds only ES (not free E).
• Both Vmax and Km decrease by same factor.
Substrates & an inhibitor
of -galactosidase
What kind of inhibitor
is IPTG likely to be?
TO DO TODAY
• Assay the dilution of PF of beta-gal from
last week that gave Abs of approx. 0.5
– (Remember it has been diluted 2/3 with
glycerol)
• DO NOT ADD ENZYME TO REAGENT
BLANKS (TUBES #10 & 11)
• DO NOT add the enzyme until timing starts
• Time carefully, mix well
• Do the assay twice, once without inhibitor
and again with inhibitor (IPTG)
• Make Michaelis-Menten and Lineweaver Burk plots using Excel following directions
in appendix after Lab 3 in lab manual
• Make sure you understand homework
calculations—15 points
Homework Calculations
15 points
• Protein conc. (mg/ml) for PF using lab 2
result (adjusted for addition of glycerol)
• ONPG & IPTG conc. in nmol/ml
– Volume used = 2.4 ml
– Stock ONPG (mol. wt 301.3) = 4 mg/ml
– Stock IPTG (mol. wt 238.3) = 0.6 mg/ml
• Velocity (Spec. Activity)
– Units = nmol/min/mg protein
– Volume used = 3.4 ml
• Michaelis-Menten plot (ONPG is
substrate)
– without IPTG
– with IPTG
• Lineweaver-Burk plot
– without IPTG
– with IPTG
• Ki, disassociation constant of Inhibitor