2014‐09‐22
Lab training – Enzyme Kinetics & Photometry
Qing Cheng
Qing.Cheng@ki.se
Biochemistry Division, MBB, KI
Lab lecture

Introduction on enzyme and kinetics
 Order of a reaction, first order kinetics
 Michaelis-Menten kinetics
 KM, Vmax and kcat
 Lineweaver-Burk plot
 Enzyme inhibition, competitive and non-competitive inhibition

Spectrophotometer and Beer-Lambert Law

Lab procedure
 Lab execution
 Lab report

Safety in the lab
Lab lecture - Enzyme Kinetics and Photometry
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Introduction – Enzyme

Enzyme-catalyzed reactions are affected by
 Enzyme concentration
 Substrate concentration
Transition state, S‡
 Temperature
 pH
 Inhibitors
 Activators
Free energy 
Enzymes are biological catalysts characterized by
 Catalytic efficiency
Enzyme
 Specificity
Substrate
 Regulated activity
Product
ΔG‡ (without enzyme)
ΔG‡ (with enzyme)
Substrate
ΔG for the reaction
Product
Reaction progress
Lab lecture - Enzyme Kinetics and Photometry
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Introduction – Kinetics

Kinetics is the study of chemical reaction rate (v, stands for velocity)

Enzyme kinetics is the study of enzyme catalyzed reaction

Determination of kinetics parameter  measurement of enzyme activity

First order kinetics  v
k∙ S

Zero order kinetics  v
k∙ S
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Introduction – Order of reactoin
First order reaction
 Reaction rate is proportional to the substrate’s concentration. This is
true when the substrate concentration is low during the reaction, and
the substrate is the determine factor for the reaction rate.

Zero order reaction
 The reaction rate is independent of the substrate concentration. This is
true when the substrate concentration is much higher than the enzyme
concentration during the reaction, and the enzyme is the determine
factor for the reaction rate.
S
k
Reaction rate, v

P
∙
Zero order reaction
k
First order reaction
Substrate concentration [S]
Lab lecture - Enzyme Kinetics and Photometry
20140922
Michaelis-Menten kinetics
To understand how enzyme functions, we need a kinetic description of their
activity.
The reaction rate rises linearly as substrate concentration increases (first
order reaction) and then begins to level off and approach a maximum at
higher substrate concentration (zero order reaction)
For many enzymes, the reaction rate V0 is defined as the number of moles
of product formed per unit time when [P] is low, that is at times close to
zero (hence, V0)



Zero order reaction
Reaction rate, v
Reaction rate, v
V0
[S4]
V0
[S3]
V0
[S2]
V0 [S ]
1
First order reaction
Substrate concentration [S]
Lab lecture - Enzyme Kinetics and Photometry
Time
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Michaelis-Menten kinetics

Consider an enzyme that catalyzes the S to P by the following pathway:
⇌ 
V0 is measured when [P] is low, therefore k4 becomes negligible.
⇌ 
⇌ ⇀  V0 = k2[ES]
 Rate of ES formation =k1[E][S]
 Rate of ES breakdown = (k2+k3)[ES]
Steady state: When [ES] is formed and broken down at the same speed
Lab lecture - Enzyme Kinetics and Photometry
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Michaelis-Menten kinetics

Simplify the previous equation by define a new constant, KM, called
Michaelis constant
 KM has the units of concentration
 KM is independent of either [E] or [S]
⇌ ⇀ Solving [ES]
(because at maximum rate, [ES]=[Etot])
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Michaelis-Menten kinetics
Reaction rate
The lower the KM value
The more efficient the enzyme
Substrate concentration [S]

At very low substrate concentration (
≪
→
):
 The reaction rate is directly proportional to the substrate concentration

≫
→
):
At very high substrate concentration (
 The reaction rate is maximal, independent of substrate concentration.

→
):
When KM is equal to the substrate concentration (
 KM is equal to the substrate concentration at which the reaction rate is half
its maxim value
Lab lecture - Enzyme Kinetics and Photometry
20140922
Lineweaver-Burk plot

Vmax is difficult to estimate because the initial reaction rate approaching Vmax asymptotically with
increasing substrate concentration. In addition, the high concentration of substrate often inhibits
reaction rate. To solve this problem, Lineweaver and Burk (1934) had inverted the MichaelisMenten equation, which is referred as Lineweaver-Burk plot (or Double reciprocal plot):
∙
y = ax + b

In this equation, 1/V and 1/[S] are
variables, while KM/Vmax and 1/Vmax are
constants. This can be plotted as a
linear equation (y = ax + b).
Specifically, 1/v is y, 1/[S] is x, KM/Vmax
is a (slope) and 1/Vmax is b (yintercept). We can accurately calculate
KM and Vmax value from a LineweaverBurk plot.
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Nonlinear regression

Indeed, KM and Vmax values can be calculated
directly from the Michaelis-Menten equation
through nonlinear regression.

http://www.colby.edu/chemistry/PChem/scripts/lsfitpl.html
(in short: http://bit.ly/1re1XU4)

Input the data pairs (V and [S])

Choose fit function: ax/(b+x)

Leave Parameter guesses as it is.

Choose Convergence Mode: Damped or Strongly damped

Click Fit or Fit & Plot (Java needed for plotting)
y = ax/(b+x)
Lab lecture - Enzyme Kinetics and Photometry
20140922
Nonlinear regression

Indeed, KM and Vmax values can be calculated
directly from the Michaelis-Menten equation
through nonlinear regression.

http://www.colby.edu/chemistry/PChem/scripts/lsfitpl.html
(in short: http://bit.ly/1re1XU4)

Input the data pairs (V and [S])

Choose fit function: ax/(b+x)

Leave Parameter guesses as it is.

Choose Convergence Mode: Damped or Strongly damped

Click Fit or Fit & Plot (Java needed for plotting)
y = ax/(b+x)
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Inhibition of enzyme activity

Competitive inhibition

Noncompetitive inhibition
Substrate
Competitive inhibitor
Enzyme
Noncompetitive inhibitor
Enzyme
Enzyme
Lab lecture - Enzyme Kinetics and Photometry
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Inhibition of enzyme activity

Competitive inhibition
E + S
+
I
ki
ES
Competitive inhibitor
E + P
Enzyme
I
S
EI
Competitive inhibitor
No inhibitor
No inhibitor
+ Competitive inhibitor
Vmax is not affected KM is increased
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Inhibition of enzyme activity

Noncompetitive inhibition
E + I
ki
EI
S I
S
ES
Noncompetitive inhibitor
E + P
Enzyme
EIS ×
Noncompetitive inhibitor
No inhibitor
No inhibitor
+ Noncompetitive inhibitor
Vmax is decreased
KM is not affected
Lab lecture - Enzyme Kinetics and Photometry
20140922
Inhibition of enzyme activity
Competitive inhibitor
No inhibitor
Vmax is not affected KM is increased
Lab lecture - Enzyme Kinetics and Photometry
Noncompetitive inhibitor
No inhibitor
Vmax is decreased
KM is not affected
Mix inhibition
No inhibitor
Vmax is decreased
KM is increased
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Photometry - Spectrophotometer

How to measure the chemical reactions rate
 Different molecules have different
absorption
 Some molecules (e.g. proteins) have
several absorbance peaks during the
wave scan
 Spectrophotometer
Light source Filter Sample Detector Readout
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Photometry - Beer-Lambert law

Beer-Lambert law is a mathematical means of expressing how light is absorbed by
matter. The law states that the amount of light emerging from a sample is
diminished by three physical phenomena:
 The concentration of absorbing sample in its pathway (C, in unit of molarity, M)
 The distance the light travels through the sample (ℓ, in units of centimeters, cm)
 The probability that the light of that particular wavelength will be absorbed by
the material, also known as molar absorption (or extinction) coefficient (ε), in
units that are reciprocals of molarity and distance in centimeters, M-1cm-1)
T: 0 - 1
A: ∞ - 0
Due to technical limitation, the best reading
range of spectrophotometer is normally
from 0.1 – 1, thus:
o
o
Lab lecture - Enzyme Kinetics and Photometry
If A is too high, dilute the sample
If A is too low, concentrate the sample
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Lab training

Enzyme: Alkaline Phosphatase (ALP)
 Remove phosphate groups from many types of molecules.
 Function as a dimer, and take effect under alkaline conditions
 Made in liver, bone, and other tissues.
 It can be measured in a routine blood test. Abnormally high serum
levels of ALP may indicate bone, liver disease, etc.
Lab lecture - Enzyme Kinetics and Photometry
20140922
Lab training – Outline

Determine the following parameters of alkaline phosphatase
using p-nitro-phenyl-phosphate (NPP) as substrate
 Optimal pH
 KM
 Vmax
 Inhibition
p-Nitro-Phenyl-Phosphate
(NPP)
Lab lecture - Enzyme Kinetics and Photometry
p-Nitrophenol
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Lab training – Maximal absorbance

Determine the maximal absorbance (λmax) for p-nitrophenol
 Set wavelength scan in the range of 350 – 500 nm

Calculating molar absorption coefficient (ε) using Beer-Lambert law
∙
∙ ∙
Lab lecture - Enzyme Kinetics and Photometry
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Lab training – Incubation time

The effect of incubation time on the amount of product formed
 Incubation at 40⁰C water bath
 Incubation time (9 different time from 0.5-20 min)
 Measure absorbance within 15 min at the end of the reaction
 Plot: amount of product formed (y-axis) against time (x-axis)
dH2O
NFF
Buffer with pH 9.5
Testing tubes (× 9)
Add enzyme
Lab lecture - Enzyme Kinetics and Photometry
Blank tubes (× 9)
Add dH2O
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Lab training – Optimal pH

The effect of pH on the reaction rate (v)
 Incubation at 40⁰C water bath
 Incubation time: 10 min
 Measure absorbance within 15 min at the end of the reaction
 Plot: amount of product formed (y-axis) against time (x-axis)
dH2O
NFF
Buffer with differnt pH
Testing tubes (× 9)
Add enzyme
Blank tubes (× 9)
Add dH2O
Lab lecture - Enzyme Kinetics and Photometry
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Lab training – KM, Vmax, Inhibition

Determine the KM and Vmax value for alkaline phosphatase, and the
inhibition type of the inhibitor provided
 Incubation at 40⁰C water bath
 Incubation time: 10 min
 Measure absorbance within 15 min at the end of the reaction
 Michaelis-Menten plot: Reaction rate (y-axis) against [S] (a-axis)
 Lineweaver-Burk plot: 1/V (y-axis) against 1/[S] (a-axis)
 Determine KM, Vmax, and inhibition type
Each series contains 6 tubes with different substrate concentration [S]
a.
b.
c.
d.
a b c
Lab lecture - Enzyme Kinetics and Photometry
With enzyme only
With enzyme and 1st inhibitor (0.5 mM phosphate solution)
With enzyme and 2nd inhibitor (1 mM phosphate solution)
Blank (with neither enzyme nor the inhibitor)
d
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Lab training – Case study (ADH)

KM determination for alcohol dehydrogenase
 Determine KM, Vmax, of alcohol dehydrogenase using either
methanol or ethanol as substrate from the values in the lab
compendium.
 Determine inhibition type of ethanol on ADH when using
methanol as substrate.
 Calculate the blood alcohol content (BAC) in the patient
undergone ethanol treatment.
Lab lecture - Enzyme Kinetics and Photometry
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Lab note and reports

Write lab notes carefully, which should be approved and countersigned
by your teaching assistant.

A written lab report is needed
 Brief introduction and aim
 Brief description of the execution of the lab work
 Results including all the raw data, calculations including the
equation, and all the plots.
 Don’t forget to specify units in calculations and plots
 Brief conclusions and discussion
 Answer all the questions in the compendium.
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Lab safty







Lab coat, goggles, gloves
No eating or drinking in the lab
Mouth pipetting is prohibited
Prevent accidents
 Be well prepared
 Work calmly
When you leave the lab
 Wash hands
 Remove lab coat
Use your judgment
Ask teaching assistant
Lab lecture - Enzyme Kinetics and Photometry
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Question?
Lab lecture - Enzyme Kinetics and Photometry
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