Killing bacteria by
inhibiting their enzymes.
BIOCHEMISTRY LAB
CHE554
Enzyme Kinetics
Motivation: Enzymes mediate almost all
the chemistry in cells, and thus in life. They
are the best catalysts known and have
applications in every field as tools for
synthesis, remediation, chemical recycling
and intervention targets.
While human actions or accidents produce
injuries, death is very often dealt by bacteria.
Up to 90% of the native peoples of America
died of European and African diseases even
before colonists vied for the land.
Approach: a chromogenic reaction
catalyzed by β-galactosidase is used to
visualize the effects of substrate
concentration and inhibitors of different
types on enzyme-catalyzed reaction
velocity.
Experiment #7, pages 95-104,
123-130.
http://textbookofbacteriology.net/penicillinWWII.jpg
http://en.wikipedia.org/wiki/
Population_history_of_indigenous_peoples_of_the_Americas
2
Transpeptidase’s
essential role
Penicillium notatum’s
defense
Bacteria resist cell lysis by virtue of their cell
walls. The cell wall is constructed of
peptidoglycan produced by enzymes.
Transpeptidase forms and remodels the
peptide crosslinks between layers of
peptidoglycan.
!
!
http://pharmaxchange.info/press/2011/04/mechanism-of-
3action-of-penicillin/
P. notatum exports a secondary
metabolite we call penicillin, which
disrupts cell wall synthesis and leads to
bacterial death. Penicillin was our first
‘wonder drug’ and has saved many lives.
However evolution is a live and well,
bacteria have evolved.
4http://fullspectrumbiology.blogspot.com/2012/05/penicillin-and-importance-ofmedicines.html
Augmentin:
An enzyme inhibitor and an
inhibitor of the enzyme that
degrades it.
Penicillin inhibits one enzyme
Amoxicillin inhibits
transpeptidase.
but is degraded by another
Clavulanic acid
inactivates many β
lactamases. It is the
additional ingredient in
‘augmentin’.
β lactamases can hydrolyze the
reactive lactam ring of penicillin and
related antibiotics.
5
http://en.wikipedia.org/wiki/Beta-lactamase
As enzymes gain use in consumer products,
remediation strategies, synthesis and more,
we need to be able to characterize their
activity and factors that interfere with it.
6
http://en.wikipedia.org/wiki/Augmentin
Background
(Enzyme Kinetics)
New antibiotics for ‘new’
bacteria
!
Enzymes influence the rate at which
equilibrium is obtained, but not the
equilibrium position of the reaction.
!
Kinetics, in this context, is the study of
reaction product formation as a function of
time. The rate of product formation is a
measure of the reaction velocity.
S
→
P
d([P])
d([S])
v=
=−
dt
dt
Targeting virulence: a new paradigm for antimicrobial therapy
Anne E Clatworthy, Emily Pierson & Deborah T Hung
Nature Chemical Biology 3, 541 - 548 (2007) Published online: 20 August 2007
doi:10.1038/nchembio.2007.24
7
http://www.nature.com/nchembio/journal/v3/n9/fig_tab/nchembio.
2007.24_F1.html
v = reaction velocity
Biology needs reactions that
are not ‘naturally’ fast, because
it needs stable compounds.
9
Wolfenden and Snider (2001) Acc. Chem. Res. 34:938-945.
Enzymes accelerate
reactions by up to x 1021
10 Wolfenden & Snider (2001) Acc. Chem. Res. 34(12): 938-945
Reaction equilibrium vs.
velocity.
Concentration
Rate-limiting step and
transition state energy.
!
[S]0
Keq =
The reaction is accelerated by lowering the
free energy of transition state activation.
[P]eq
[S]eq
‡
kvel = kBT e-ΔG /RT
h
[S]eq
[P]eq
Keq = e-ΔG°/RT
time
[P]0
d[P]/dt = v
v0 =
!
11
k3[ET] [S]0
KM + [S]0
We measure the initial reaction
velocity, when [P] ≈ 0 and [S] ≈ [S]0.
ΔF° =
ΔG° = -RT ln Keq
Background
(Michaelis-Menton)
Observed Initial Rate of
Reaction
!
–
–
–
measure and plot initial velocity (vo) as a function of
substrate concentration ([S]0). Initial velocity is used
to eliminate effects of product buildup (slowing down
reaction).
At some point adding more substrate does not
further increase the reaction rate. A plateau is
observed corresponding to saturation of the
enzyme.
For single substrate, Vmax occurs when all of substrate
is in ES state.
–
–
–
Figure II-8
–
–
–
The Michaelis-Menton equation describes
the relationship between initial velocity (vo)
and initial substrate concentration ([S]0 ).
KM (the Michaelis constant) is equal to the
substrate concentration that yields vo equal to
Vmax/2 .
This constant is used as a general measure
of the stability of the enzyme substrate
interaction.
KM has the form of dissociation constant.
The analogy is best when k3 << k2.
Officially; KM = (k2 + k3) / (k1)
(More generally KM = (k-1 + k2) / (k1) )
Vmax is the velocity achieved when all
enzyme is saturated with substrate.
Lineweaver-Burke
!
Inhibition
The double-reciprocal plot (Lineweaver-Burke
plot).
– Easily calculate KM and Vmax by simply
rearranging Michaelis-Menton equation
– plot 1/[S] versus 1/vo
–
!
!
Still need to measure initial velocity (vo) as a
function of substrate concentration (S).
To combat disease we inhibit
enzymes.
Which kind of inhibition will be
most effective (what type of
inhibitor would you like to
design)?
• Competitive.
• Non-competitive.
• Uncompetitive.
16
Competitive
inhibition
S
E
I
ES
E+P
KI
EI
vo = Vmax[S]/(KM + [S])
becomes vo = Vmax[S]/(K’M + [S]),
K’M = KM(1+[I]/KI)
Vmax is not changed.
S and I compete for E.
Any ES formed reacts at the same
rate as in the absence of inhibitor.
From CHE550
Competitive inhibitors.
!
Competitive inhibitor binds to the free enzyme in
place of the substrate. More substrate is needed to
get the same rate, and maximum rate doesn’t change.
!
One can see and measure inhibition by plotting 1/[S]
versus 1/vo as a function of inhibitor concentration.
Noncompetitive inhibition
S
E
I
KIe
EI
ES
I
PURE noncompetitive:
KIe = KIs
E+P
KIs
E
I
ESI
KIe
EI
S
ES
I
KIs
ESI
KIe = KIs
vo = Vmax[S]/(KM + [S])
becomes vo = V’max[S]/(K’M + [S]),
V’max= Vmax/(1+[I]/Kie)
K’M = KM(1+[I]/KIs)/(1+[I]/Kie)
E+P
Inhibitor binding does not affect the
E ↔ ES equilibrium
vo = Vmax[S]/(KM + [S])
becomes vo = V’max [S]/(K’M + [S]),
K’M = KM
V’max = Vmax/ (1+[I]/KIs)
From CHE550
From CHE550
Noncompetitive Inhibitors.
!
Noncompetitive inhibitor binds to free enzyme or
enzyme-substrate complex. Notice how the curves
differ from that for a competitive inhibitor.
Uncompetitive
inhibition
E
S
ES
I
Pure non-competitive,
Mixed non-competitive
E+P
K’I
IES
I binding affects both the equilibrium
among E states and Vmax.
vo = Vmax[S]/(KM + [S])
becomes vo = V’max [S]/(K’M + [S]),
K’M = KM/(1+[I]/K’I)
Figure II-11
V’max = Vmax/ (1+[I]/K’I)
From CHE550
β-galactosidase
Uncompetitive Inhibitors
!
Lactose → glucose +
galactose.
Uncompetitive inhibitor binds only to the enzymesubstrate complex.
Homotetramer.
Product of the lacZ gene.
The protein can be
expressed in two parts.
lacZα and lacZΩ.
Catalytic activity requires
both.
24
Two Experiments
The Experiment (1)
!
We will employ the enzyme β-galactosidase,
which allows lactose metabolism in the bacterium
Escherichia coli.
!
We will use o-nitrophenyl-β,D-galactopyranoside
(ONPG) instead of lactose because it is
hydrolyzed into a color-containing solution (so we
can monitor the reaction).
!
Day 1: Determine the enzyme concentrations
that produce linear kinetics. This concentration
will be used for Day 2 experiments
!
–
Steps 1-7, Determine Enzyme Activity
–
–
–
We will study its kinetics in the absence and
presence of inhibitors. This will be done using
time-dependent spectroscopy.
•
–
Day 2 Kinetic parameters KM, Vmax and KI:
Steps 1-5, Determine KM and Vmax
–
–
Make the several dilutions of enzyme before
beginning to use the spectrophotometer.
Steps 8-10, data analysis
Calculate the extinction coefficient of ONP.
Steps 6-9, data analysis
Steps 1-4, Inhibitor Effects on Activity
–
Steps 8-10, data analysis (do one inhibitor only)
! The following page lists the people who should use
MGP and those who should use MTG.
Chromogenic substrates
Section 2
Section 1
Inhibitor to use
Name
Locker Group Inhibitor
Danielle Edwards
L41C
An Lien Ho
L35C
Joanna Ng
L35C
Niranjana Warrier
L44C
Kaeto Vin-Nnajiofor
L34C
Morgan Sizemore
L34C
Corey Lee
L31C
Matthew Wolfe
L31C
Derrick Lewis
L28C
Travis Johnson
L38C
Jessime Kirk
L38C
Carl Archemetre
L44C
Falak Patel
L35C
Robert Reed
L41C
Dylan Woolum
L35C
Kalen Wright
L41C
© A.-F. Miller 2013
B
A
B
B
A
B
A
B
A
A
B
A
B
B
A
A
MTG
MGP
MGP
MTG
MTG
MGP
MGP
MTG
MTG
MGP
MGP
MTG
MTG
MGP
MGP
MTG
27
Changes From the Book
!
!
!
We will follow the experimental protocol exactly
for Days 1 and 2 except
–
Skip steps 11-14 on Day 1 (determination of
enzyme concentration)
–
use either MGP, or MTG on Day 2 (see prev.
pg. for who should do which).
–
omit steps 11-13 on Day 2.
We will not be doing Days 3 and 4.
Technical tweaks
– Do not vortex enzyme-containing solutions.
Invert or swish in and out of a pipettor.
– Start a timer as you add enzyme. Record the
time at which you make your first absorbance
reading if it is not exactly at 30 sec. Do the
same for any time point that is not at the target
time.
– Work with a buddy who can adjust your
pipettor for the next addition while you work
with the spectrophotometer.
– For step 10, first plot activity vs. enzyme
amount present, and use only points that fall in
a linear regime, when calculating your stock
solution activity.
icates
final
ne the
action
me by
ck sosphate
lution
ion of
ion in
e A420
e 2, it
o comset of
me over
8. Prepare a plot of A420 versus time for the data
obtained from the reactions in tubes 2 to 6. Plot
the data from all five reactions on a single graph
for comparison.
9. Draw a “best-fit” curve through each set of data
points. For each curve, determine over what
time frame the reaction kinetics appear linear
(where " A420 /"time yields a straight line). Calculate the slope of the linear portion of each
For curve.
step 10 you will see:
10. Use the following equation to determine the !galactosidase activity (micromoles of ONPG
hydrolyzed per minute/per milliliter of enzyme) in each reaction:
Hint for managing the
analysis.
("A420/"time)(1.25/"A420max)
Activity $ %%%%
Vp
The purpose of this equation is to convert ΔA420 to
‘concentration of product formed’.
i.e. we need an extinction coefficient!
We will use the imperfect solution of assuming that the
timecourse you allowed to go to completion converted
ALL substrate to product. Therefore the final (max) [P]
= initial [S] = 0.25 mM (show how I got this).
ε = ΔA420, max / 0.25 mM.
C(t) = ΔA420(t)/(ΔA420 / 0.25 mM)
You made 5 ml of solution. Thus the number of moles
of P you formed is
5x10-3 L x ΔA420(t)* 0.25 x 10-3 mole L-1 /ΔA420,max
29P = 1.25 x10-6 moles x
ΔA420(t) /ΔA420,max
Data Analysis
Run your long time course with a buddy,
each of you can put a tube in the same
spectrophotometer and you can each
take turns reading absorbances
Data Analysis
Example Data from Day 1
A420
Prepare a table in advance so that
during the experiment you will be filling
in boxes with absorbances (also allow
a column for time of observation).
Write your results down in real time.
Enzyme Activity at One
Concentration
A420
Look for linearity over 2-4 minutes
Linear regime for enzyme
activity
For point 10, instead of averaging,
use the slope of the linear range to
calculate activity on a per-volume
basis (volume of stock solution).
!
f
eo
Experimental
Considerations
Pay careful attention to which steps have
experiments and which have data analysis.
You can do the data analysis later.
!
Make sure your data is saved, for example
to the hard drive of one of the computers, in
case your memory stick goes bad.
!
lop
s
to ime
d
te vs. t
a
l
re 20
A4
Delete all old files from the spec. to free up
more ‘experiments’ for use.
!
It will be easy to confuse substances, so
please be careful.
!
related to 1/dilution
33
Safety Considerations
!
Observe all normal laboratory safety
practices.